BWCC Foundation Grant Helps Math Teachers Apply a New Formula
The Business Monthly, The Business Newspaper of Howard and Anne Arundel Counties and BWI Business District
http://www.bizmonthly.com/7_2007_focus/f_4.shtml
By George Berkheimer
A $5,000 grant from the Baltimore Washington Corridor Chamber (BWCC) Foundation will not only guarantee the continuation of an annual conference for math teachers, but will also help organizers extend the event's reach.
The BWCC Foundation has hosted the Baltimore/Washington Math Symposium for the past 13 years in collaboration with the Chamber, the National Security Agency (NSA) and the Howard County Public School System (HCPSS). The event has consistently drawn upwards of 140 middle and high school math teachers from as far away as Hagerstown for a full day of dialogue and instruction focused on the latest methods and technologies for teaching mathematics.
This year, with the Foundation's help, the symposium will be reconstituted as a career-enhancing Maryland Council of Teachers of Mathematics (MCTM) Annual Conference.
"This is perfect timing because we've wanted to start delivering some innovative things beyond the conference," said Jon Wray, president-elect of the MCTM. Wray's tenure will begin on Oct. 19, the date of this year's MCTM Annual Conference, which will be held at Reservoir High School in Fulton.
"We will also begin offering this innovative professional development opportunity to teachers, not only in secondary education positions, but to teachers from pre-kindergarten through [12th grade]," Wray said.
Seeking Equation
The grant came at a time when funding of the symposium was in danger of drying up.
"In the past we've worked with the NSA, the Howard County and Anne Arundel County public school systems and Wayne Wilhelm of Wilhelm Commercial Builders, among others," Wray explained. "Unfortunately, there have been some cuts in funding by the NSA, and we didn't think we'd be able to continue ... [unless we] could partner with the state."
One of the biggest ongoing problems for educators in Maryland, according to Wray, began about five years ago with cuts in the state-administered federal Eisenhower Grant program, which helped Maryland's schools defray some of the costs for teachers' career development.
"Registration fees [for the MCTM Annual Conference] are minimal and an annual [MCTM] membership costs only $20, but it's becoming more difficult to fund faculty and send teachers to conferences like this even when the cost is this low," Wray explained.
The BWCC Foundation grant will help address some of these problems.
"There are lots of other changes taking place at the moment," noted BWCC President and CEO Walt Townshend, who observed that statewide budget cuts have not only made it difficult for teachers to attend conferences, but have also cut into schools' abilities to afford substitute teachers while the regular teachers are absent.
Resolving Irrational Factors
"We're in the midst of seeing if we can align ourselves with the MCTM and find other ways to support them, either financially or by finding ways ... to try to control the time that teachers spend out of the classroom [pursuing career development opportunities]," Townshend said.
This year, for instance, the MCTM Annual Conference has been scheduled on a Maryland State Teachers Association (MSTA) professional's day, when teachers aren't normally in class with students.
"Secondary and high school mathematics teachers will be free to attend," Wray explained. Elementary school teachers who teach a range of subjects, however, will likely have to choose whether they want to attend the math conference or another development option in another curriculum.
Nevertheless, they might still have a chance to benefit from the conference. According to Wray, the Council intends to begin videotaping the conference presentations starting this year and hopes to stream them via the MCTM web site to extend access to all of the teachers who belong to the organization.
Proving New Methods
Steve Leinwand, the principal research scientist at the American Institute of Research, will be the keynote speaker at this year's MCTM Annual Conference. According to Wray, the keynote speaker's stipend will be provided through the BWCC Foundation's original grant.
"Another area the grant will help with is our effort to get people to stay for the entire program," he continued. "The BWCC has offered to buy box lunches for the participants. I think this will go a long way; in the past, participants have had to leave for lunch and many of them decided not to come back [for the symposium's afternoon sessions]."
Additional support from corporate sponsors will pay off with an opportunity to get their name out in front of the participants.
"This is unique," Wray said. "We've had exhibitor support in the past, but this has been mostly educational or commercial companies; we've never before had corporate support outside the field of education."
Meanwhile, the MCTM hopes to raise another $4,500 to $5,000 on its own this year to get the math conference off to a solid start under the new circumstances.
"We're going to start small this year and see how it works out," he said. "We're committed to maintaining this relationship [with the BWCC Foundation] and seeing it grow in the future."
Wednesday, July 18, 2007
Thursday, June 21, 2007
Seattle's Textbook Debate
From the Seattle Post-Intelligencer, Wednesday, May 30, 2007. See
http://seattlepi.nwsource.com/local/317916_math31.html?source=mypi
Schools streamline how math is taught
Same textbooks, same lessons, at the same time
By Jessica Blanchard
When Seattle elementary-schoolers open their math textbooks this fall, they'll all be on the same page -- literally.
In an attempt to boost stagnant test scores, elementary teachers will start using the same math textbooks and materials and covering lessons at the same time as their colleagues at other Seattle elementary schools, the School Board decided Wednesday.
"It's clear to me that the math adoption is long overdue, and Seattle desperately needs a consistent and balanced approach," board member Brita Butler-Wall said.
Lessons will now be taught using the conceptual "Everyday Math" books, which help students discover algorithms on their own and explore multiple ways to solve problems, and the more traditional "Singapore Math" books, which help hone students' basic computation skills through repetition and problem solving. Teachers will follow the district's guidelines for the order the lessons would be taught.
The move is the latest step toward the district's goal of streamlining and standardizing the math curriculum. The district has two formally adopted math programs, but over the years, teachers have had the flexibility to create their own math lessons, culling bits from various other math programs they liked.
That piecemeal approach has worked well for some schools, but not all. And the inconsistency has made it difficult for students transferring from one school to another.
Starting this fall, the math program the board adopted will be usedat nearly all the district's elementary schools, except the few that can show significant progress using another math program. They willbe allowed waivers to continue using their current curriculum.
The board's decision was not without controversy.
There has been considerable debate nationwide in recent years over how best to teach math. Parents and teachers seem to fall into one of two camps -- those who favor more a conceptual, hands-on approach, and those who advocate for a traditional skills-based program.
The combination of "Everyday Math" and "Singapore Math" was intended to be a compromise, to offer a program that has elements of both approaches.
Several of the teachers, principals and parents who spoke at the public-comment session before the board's vote voiced support for the proposed adoption, including Sharon Rodgers, president of the Seattle Council PTSA.
"The kids have waited for long enough for some kind of consistency in math," she said. But most speakers urged board members to reject the standardized curriculum.
Parent M.J. McDermott asked the board to hold off on making a decision until the state's math standards are revised next year.
"If Seattle Public Schools adopts 'Everyday Math,' we will be right back here in a couple years, looking to find a new solution," she said. "It will be money wasted."
------------------
P-I reporter Jessica Blanchard can be reached at 206-448-8322 or jessicablanchard@seattlepi.com
http://seattlepi.nwsource.com/local/317916_math31.html?source=mypi
Schools streamline how math is taught
Same textbooks, same lessons, at the same time
By Jessica Blanchard
When Seattle elementary-schoolers open their math textbooks this fall, they'll all be on the same page -- literally.
In an attempt to boost stagnant test scores, elementary teachers will start using the same math textbooks and materials and covering lessons at the same time as their colleagues at other Seattle elementary schools, the School Board decided Wednesday.
"It's clear to me that the math adoption is long overdue, and Seattle desperately needs a consistent and balanced approach," board member Brita Butler-Wall said.
Lessons will now be taught using the conceptual "Everyday Math" books, which help students discover algorithms on their own and explore multiple ways to solve problems, and the more traditional "Singapore Math" books, which help hone students' basic computation skills through repetition and problem solving. Teachers will follow the district's guidelines for the order the lessons would be taught.
The move is the latest step toward the district's goal of streamlining and standardizing the math curriculum. The district has two formally adopted math programs, but over the years, teachers have had the flexibility to create their own math lessons, culling bits from various other math programs they liked.
That piecemeal approach has worked well for some schools, but not all. And the inconsistency has made it difficult for students transferring from one school to another.
Starting this fall, the math program the board adopted will be usedat nearly all the district's elementary schools, except the few that can show significant progress using another math program. They willbe allowed waivers to continue using their current curriculum.
The board's decision was not without controversy.
There has been considerable debate nationwide in recent years over how best to teach math. Parents and teachers seem to fall into one of two camps -- those who favor more a conceptual, hands-on approach, and those who advocate for a traditional skills-based program.
The combination of "Everyday Math" and "Singapore Math" was intended to be a compromise, to offer a program that has elements of both approaches.
Several of the teachers, principals and parents who spoke at the public-comment session before the board's vote voiced support for the proposed adoption, including Sharon Rodgers, president of the Seattle Council PTSA.
"The kids have waited for long enough for some kind of consistency in math," she said. But most speakers urged board members to reject the standardized curriculum.
Parent M.J. McDermott asked the board to hold off on making a decision until the state's math standards are revised next year.
"If Seattle Public Schools adopts 'Everyday Math,' we will be right back here in a couple years, looking to find a new solution," she said. "It will be money wasted."
------------------
P-I reporter Jessica Blanchard can be reached at 206-448-8322 or jessicablanchard@seattlepi.com
Wednesday, June 13, 2007
The Need for National Curriculum Standards
From the New York Times, Friday, June 8, 2007. See http://www.nytimes.com/2007/06/08/education/08scores.html?_r=1&th&emc=th&oref=slogin
States Found to Vary Widely on Education
By Tamar Lewin
Academic standards vary so drastically from state to state that a fourth grader judged proficient in reading in Mississippi or Tennessee would fall far short of that mark in Massachusetts and South Carolina, the United States Department of Education said yesterday in a report that, for the first time, measured the extent of the differences.
The wide variation raises questions about whether the federal No Child Left Behind law, President Bush's signature education initiative, which is up for renewal this year, has allowed a patchwork of educational inequities around the country, with no common yardstick to determine whether schoolchildren are learning enough.
The law requires that all students be brought to proficiency by 2014 in reading and math and creates sanctions for failure. But in a bow to states' rights it lets each state set its own standards and choose its own tests.
The report provides ammunition for critics who say that one national standard is needed. "Parents and communities in too many states are being told not to worry, all is well, when their students are far behind," said Michael J. Petrilli, a vice president of the Thomas B. Fordham Foundation who served in the Education Department during Mr. Bush's first term.
Education Secretary Margaret Spellings said in a statement, "This report offers sobering news that serious work remains to ensure that our schools are teaching students to the highest possible standards." Still, in a conference call with reporters, she said it was up to the states, not the federal government, to raise standards.
The report for the first time creates a common yardstick to measure the results on state tests against the National Assessment of Educational Progress, considered the gold standard of testing.
The report examines the minimum score a student would have to get on each state's reading and math tests to be deemed proficient - or at grade level - and then determines what the equivalent score for that level of competency would be on the national test. Results on the national test are not used to judge schools under No Child Left Behind.
The national test divides students' scores into three achievement levels, basic, proficient and advanced. Grover J. Whitehurst, director of the Institute of Education Sciences at the Education Department, said the achievement level that many states called proficient was closer to what the national test rated as just basic. And the report shows that not a single state sets its reading proficiency levels as high as the national test.
Although results were not available for all states, the Education Department report based on tests given in the 2004-5 school year illustrated starkly the variations in standards.
For example, an eighth grader in Missouri would need the equivalent of a 311 on the national math test to be judged proficient. That is actually more rigorous than the national test. In Tennessee, however, a student can meet the state's proficiency standard with a 230, a score well below even the basic level on the national exam.
And while a Massachusetts fourth grader would need the equivalent of a 234, or just below the proficiency mark on the national test, to be judged as proficient by the state, a Mississippi fourth grader can meet the state's standard with a state score that corresponds to a 161 on the national test.
Such score differences represent a gap of several grade levels. New York ranked 9th in grade 4 reading, in terms of the rigor of its standards. Its proficiency standards corresponded to 207 on the national test. It ranked third in grade 8 reading. But it was toward the bottom, 29th among 33 states in grade 4 math. And it was 13th in grade 8 math.
New York has since approved new math standards. "The results in reading are positive for New York relative to other states, but math is mixed," State Education Commissioner Richard Mills said. "The comparison reminds us of the need over time to keep raising standards and providing extra help to students."
The report found that eighth graders in North Carolina had to show the least skill to be considered proficient readers while those in Wyoming had to show the most skill. Tennessee set the lowest bar on grade 4 math while Massachusetts set the highest one.
The differences between state proficiency standards were sometimes more than double the national gap between minority and white students' reading levels, which averages about 30 points on the national test, Mr. Whitehurst said.
Many education experts criticize No Child Left Behind, saying it gives states an incentive to set low standards to avoid sanctions on schools that do not increase the percentage of students demonstrating proficiency each year. Those experts argue that uniform national standards are needed.
But Congress is unlikely to go that far. Ms. Spellings said, "It's way too early to conclude we need to adopt national standards" and added that it is also too early to conclude that state standards are too low.
On Tuesday, a survey of state scores in reading and math, released by the Center on Education Policy, an independent Washington group, found that since the passage of No Child Left Behind in 2002, student achievement had increased and the racial achievement gap narrowed in many states.
Ms. Spellings said the results showed the law has "struck a chord of success." Her department's report, though, raises doubts about just how much progress has been made.
Mr. Petrilli said, "Even if students are making progress on state tests, if tests are incredibly easy, that doesn't mean much."
States Found to Vary Widely on Education
By Tamar Lewin
Academic standards vary so drastically from state to state that a fourth grader judged proficient in reading in Mississippi or Tennessee would fall far short of that mark in Massachusetts and South Carolina, the United States Department of Education said yesterday in a report that, for the first time, measured the extent of the differences.
The wide variation raises questions about whether the federal No Child Left Behind law, President Bush's signature education initiative, which is up for renewal this year, has allowed a patchwork of educational inequities around the country, with no common yardstick to determine whether schoolchildren are learning enough.
The law requires that all students be brought to proficiency by 2014 in reading and math and creates sanctions for failure. But in a bow to states' rights it lets each state set its own standards and choose its own tests.
The report provides ammunition for critics who say that one national standard is needed. "Parents and communities in too many states are being told not to worry, all is well, when their students are far behind," said Michael J. Petrilli, a vice president of the Thomas B. Fordham Foundation who served in the Education Department during Mr. Bush's first term.
Education Secretary Margaret Spellings said in a statement, "This report offers sobering news that serious work remains to ensure that our schools are teaching students to the highest possible standards." Still, in a conference call with reporters, she said it was up to the states, not the federal government, to raise standards.
The report for the first time creates a common yardstick to measure the results on state tests against the National Assessment of Educational Progress, considered the gold standard of testing.
The report examines the minimum score a student would have to get on each state's reading and math tests to be deemed proficient - or at grade level - and then determines what the equivalent score for that level of competency would be on the national test. Results on the national test are not used to judge schools under No Child Left Behind.
The national test divides students' scores into three achievement levels, basic, proficient and advanced. Grover J. Whitehurst, director of the Institute of Education Sciences at the Education Department, said the achievement level that many states called proficient was closer to what the national test rated as just basic. And the report shows that not a single state sets its reading proficiency levels as high as the national test.
Although results were not available for all states, the Education Department report based on tests given in the 2004-5 school year illustrated starkly the variations in standards.
For example, an eighth grader in Missouri would need the equivalent of a 311 on the national math test to be judged proficient. That is actually more rigorous than the national test. In Tennessee, however, a student can meet the state's proficiency standard with a 230, a score well below even the basic level on the national exam.
And while a Massachusetts fourth grader would need the equivalent of a 234, or just below the proficiency mark on the national test, to be judged as proficient by the state, a Mississippi fourth grader can meet the state's standard with a state score that corresponds to a 161 on the national test.
Such score differences represent a gap of several grade levels. New York ranked 9th in grade 4 reading, in terms of the rigor of its standards. Its proficiency standards corresponded to 207 on the national test. It ranked third in grade 8 reading. But it was toward the bottom, 29th among 33 states in grade 4 math. And it was 13th in grade 8 math.
New York has since approved new math standards. "The results in reading are positive for New York relative to other states, but math is mixed," State Education Commissioner Richard Mills said. "The comparison reminds us of the need over time to keep raising standards and providing extra help to students."
The report found that eighth graders in North Carolina had to show the least skill to be considered proficient readers while those in Wyoming had to show the most skill. Tennessee set the lowest bar on grade 4 math while Massachusetts set the highest one.
The differences between state proficiency standards were sometimes more than double the national gap between minority and white students' reading levels, which averages about 30 points on the national test, Mr. Whitehurst said.
Many education experts criticize No Child Left Behind, saying it gives states an incentive to set low standards to avoid sanctions on schools that do not increase the percentage of students demonstrating proficiency each year. Those experts argue that uniform national standards are needed.
But Congress is unlikely to go that far. Ms. Spellings said, "It's way too early to conclude we need to adopt national standards" and added that it is also too early to conclude that state standards are too low.
On Tuesday, a survey of state scores in reading and math, released by the Center on Education Policy, an independent Washington group, found that since the passage of No Child Left Behind in 2002, student achievement had increased and the racial achievement gap narrowed in many states.
Ms. Spellings said the results showed the law has "struck a chord of success." Her department's report, though, raises doubts about just how much progress has been made.
Mr. Petrilli said, "Even if students are making progress on state tests, if tests are incredibly easy, that doesn't mean much."
Wednesday, April 11, 2007
MARYLAND JOINS IN NATIONAL ALGEBRA II EFFORT
| NINE STATES INVOLVED IN PROJECT TO DESIGN NEW COLLEGE PLACEMENT TEST |
| BALTIMORE, MD (April 10, 2007) |
| Maryland has joined with eight other states in a program to develop a new national assessment for Algebra II. It is envisioned that many colleges and universities will use the assessment for placement decisions in freshman math courses. The test is being produced by the American Diploma Project (ADP) Secondary Math Partnership, under the auspices of Achieve, a nonprofit education policy organization. Joining Maryland in the effort are Arkansas, Indiana, Kentucky, Massachusetts, New Jersey, Ohio, Pennsylvania, and Rhode Island. The test will be a voluntary assessment of the content typically covered in a high school Algebra II course and the math content generally considered by colleges and universities for placement decisions. It will not be tied to high school graduation in Maryland. "College and university leaders tell us that Algebra II is a stepping stone to college success," said State Superintendent of Schools Nancy S. Grasmick. "By mastering Algebra II, students are prepared to enter credit-bearing college mathematics courses and by being clearer on those expectations for both teachers and students, we will help improve the success students will have at the postsecondary level." Algebra II skills are assessed by many postsecondary schools throughout the nation. However, some of the tests used by colleges do not match up with high school Algebra II standards in many states, putting students at a disadvantage. Maryland's involvement in the development of the new assessment will help assure that the test is aligned with the state's Algebra II content standards, and could reduce the amount of mathematics remediation necessary on college campuses. The ADP Secondary Math Partnership will develop the voluntary assessment over the next year and will make it available to states in May 2008. The test could be ready for Maryland implementation in 2009. |
Friday, April 6, 2007
Little benefit found from classroom software
http://www.baltimoresun.com/news/education/bal-md.software06apr06,0,2588364.story?coll=bal-education-k12
From the Baltimore Sun
By Liz Bowie
sun reporter
April 6, 2007
Educational software - which is used in most school districts across Maryland - appears to have no effect in improving student achievement although it can cost as much as $100 per child, a federally funded study has concluded.
The results of the study, which was released this week by the U.S. Department of Education, is likely to prompt school districts, including Baltimore's, to look more closely at whether to purchase the software or invest in other strategies.
The educational software industry is disputing the study's findings, saying they could have been skewed by poor training of teachers and other factors.
Educational software is used throughout Maryland, often for use by students who are struggling academically.
"I think in most school systems there is some reading and math software," said Jayne Moore, director of instructional technology at the state Department of Education. Systems are not buying it for use in every classroom, she said, but are using it strategically.
The industry, which has grown rapidly, has been harmed by instances of corruption.
Former Prince George's County Superintendent Andre J. Hornsby was fired and indicted after the school system purchased software from LeapFrog School House, a company represented by his girlfriend.
Hornsby is charged with receiving kickbacks for steering contracts to the company.
Baltimore, which uses some educational software, is considering buying some of the kind used in the study for ninth-grade algebra students who are having problems, said Linda Chinnia, the chief academic officer.
Baltimore County would not say whether it is using educational software.
Howard County uses math software for thousands of students, including those trying to pass algebra and those trying to learn math facts in elementary school. The county has been trying out in elementary and middle schools a program called FASTTMath, which helps assess what students don't know and drills them.
About 2,200 students use the program in conjunction with teaching strategies that help students understand the concepts behind the drills.
"I think we have always been very careful about the software we select. Our approach is not to replace a teacher," said Jon Wray, who heads math instruction in the county.
Howard high schools are also using the software in classrooms for those struggling with algebra and data analysis. Wray said every high school has at least one class that uses the software and that some have as many as six. The startup cost for each classroom is about $117,000, he said, including the salaries for two teachers.
Moore said algebra software has helped students in Carroll County. But she and local educators said the software works only when used as part of a curriculum.
"I didn't find the study particularly surprising. If we have poor instruction taking place, software isn't going to change achievement," said Prince George's Superintendent John E. Deasy.
His county uses software across the curriculum, although it has not bought any recently, he said. Deasy said he has no illusion that it the software is a "magic bullet."
The study was conducted during the 2003-2004 school year in 132 schools with more than 9,000 students. Teachers who participated were divided between control classrooms and those using a particular software program.
The study found no statistically significant difference between the students in the control group and those in the classrooms with the software.
The federal study, conducted for the Institute of Education Sciences, "doesn't say stop buying this. It says think hard and try to get more evidence," said Phoebe Cottingham, a commissioner at the institute.
From the Baltimore Sun
By Liz Bowie
sun reporter
April 6, 2007
Educational software - which is used in most school districts across Maryland - appears to have no effect in improving student achievement although it can cost as much as $100 per child, a federally funded study has concluded.
The results of the study, which was released this week by the U.S. Department of Education, is likely to prompt school districts, including Baltimore's, to look more closely at whether to purchase the software or invest in other strategies.
The educational software industry is disputing the study's findings, saying they could have been skewed by poor training of teachers and other factors.
Educational software is used throughout Maryland, often for use by students who are struggling academically.
"I think in most school systems there is some reading and math software," said Jayne Moore, director of instructional technology at the state Department of Education. Systems are not buying it for use in every classroom, she said, but are using it strategically.
The industry, which has grown rapidly, has been harmed by instances of corruption.
Former Prince George's County Superintendent Andre J. Hornsby was fired and indicted after the school system purchased software from LeapFrog School House, a company represented by his girlfriend.
Hornsby is charged with receiving kickbacks for steering contracts to the company.
Baltimore, which uses some educational software, is considering buying some of the kind used in the study for ninth-grade algebra students who are having problems, said Linda Chinnia, the chief academic officer.
Baltimore County would not say whether it is using educational software.
Howard County uses math software for thousands of students, including those trying to pass algebra and those trying to learn math facts in elementary school. The county has been trying out in elementary and middle schools a program called FASTTMath, which helps assess what students don't know and drills them.
About 2,200 students use the program in conjunction with teaching strategies that help students understand the concepts behind the drills.
"I think we have always been very careful about the software we select. Our approach is not to replace a teacher," said Jon Wray, who heads math instruction in the county.
Howard high schools are also using the software in classrooms for those struggling with algebra and data analysis. Wray said every high school has at least one class that uses the software and that some have as many as six. The startup cost for each classroom is about $117,000, he said, including the salaries for two teachers.
Moore said algebra software has helped students in Carroll County. But she and local educators said the software works only when used as part of a curriculum.
"I didn't find the study particularly surprising. If we have poor instruction taking place, software isn't going to change achievement," said Prince George's Superintendent John E. Deasy.
His county uses software across the curriculum, although it has not bought any recently, he said. Deasy said he has no illusion that it the software is a "magic bullet."
The study was conducted during the 2003-2004 school year in 132 schools with more than 9,000 students. Teachers who participated were divided between control classrooms and those using a particular software program.
The study found no statistically significant difference between the students in the control group and those in the classrooms with the software.
The federal study, conducted for the Institute of Education Sciences, "doesn't say stop buying this. It says think hard and try to get more evidence," said Phoebe Cottingham, a commissioner at the institute.
Tuesday, March 13, 2007
What are the Curriculum Focal Points? And Why Should We Care? - Part 3
************************
From FOCUS [The Newsletter of the Mathematical Association of American], February 2007, Volume 27, Number 2, p. 31. See http://www.maa.org/pubs/focus.html
----------------------------------------
This is the THIRD (and last) of three articles that appeared in the current issue of FOCUS dealing with NCTM's Curriculum Focal Points.
************************
What are the Curriculum Focal Points? And Why Should We Care?
By Barbara Reynolds
What are the Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics: A Quest for Coherence (National Council of Teachers of Mathematics [NCTM] 2006)? Why should they matter to me? Why should they matter to the mathematics community?
In 2000 the NCTM released the Principles and Standards for School Mathematics, a comprehensive document that built on a bold vision that had been set by An Agenda for Action (NCTM 1980) and expanded in a set of Curriculum and Evaluation Standards for School Mathematics (NCTM 1989). The Principles and Standards sets a challenging comprehensive program, outlining goals that are both broad and deep. Now just six years later, the NCTM has presented us with Curriculum Focal Points. Does this new document represent a change in direction, a strengthening of the guidelines laid out in the Principles and Standards, or (as some might fear) a watering down of the content of the school mathematics curriculum?
When it first came out, I studied the Principles and Standards rather thoroughly, and was excited by its comprehensive vision. If students coming into college and university mathematics courses were educated according to the goals outlined in the Principles and Standards, if they came into college mathematics courses with the depth and breadth of understanding proposed in the Principles and Standards, wouldn't our job as teachers of undergraduate mathematics be so much easier!
My fear as I began to read the Curriculum Focal Points was that I would find a simplified list of competencies, grade-level mastery objectives, and testable outcomes - after all, this is the world of No Child Left Behind (NCLB) - that might represent minimal goals for each grade level of the school mathematics curriculum. My fear was that the Curriculum Focal Points would set minimal goals that would undermine the bold vision set by the Principles and Standards. Would the NCTM sell out to NCLB?
Instead what I see in the Curriculum Focal Points is a balanced set of guidelines that shows one way of developing a prekindergarten through grade 8 mathematics curriculum, guidelines that give focus to one or another area of the objectives set by the Principles and Standards at each grade level, while illustrating ways of making connections to the overall fabric of mathematics throughout the entire prekindergarten through grade 8 mathematics experience of school children. The Curriculum Focal Points are not presented as a curriculum in and of themselves, nor are they presented as a set of lesson plans. Rather they are presented as guidelines for developing an integrated Prekindergarten through Grade 8 mathematics curriculum. These Curriculum Focal Points illustrate one way of making explicit connections both to topics that the child studied in the preceding years, and to content that will be coming in subsequent years. Curriculum developers and textbook writers could use these Curriculum Focal Points as an organizing outline - focal points, actually - to develop mathematics programs that will be integrated and connected across grade levels. Classroom teachers would then be in a position to present mathematics at each grade level that implements the broad vision set by the Principles and Standards, and builds coherently from year to year. The Curriculum Focal Points make it more likely that classroom teachers will have well-designed materials that follow the bold vision set by the Principles and Standards, and that allow them to develop problem solving, reasoning, and critical thinking skills in their students without sacrificing computational skill development.
I began this reflection by asking why these Curriculum Focal Points should matter to me? Why should they matter to those of us who teach undergraduate mathematics? After all, students coming into our undergraduate mathematics classrooms are four or more years beyond Grade 8. What impact might these Curriculum Focal Points have on my own teaching of undergraduate mathematics?
The Curriculum Focal Points could impact my own teaching in two ways: First of all, if more schools adopt school mathematics materials that implement the vision of the Principles and Standards, classroom teachers will need to have a deep and broad understanding of mathematics. Classroom teachers will need an understanding of mathematics that goes well beyond computational fluency and that encompasses deeper mathematical reasoning and problem-solving skills. So we need to think about how to better prepare pre-service teachers, and we need to think about on-going professional development of in-service teachers. Secondly, if the calculus reform movement of the 1980s taught us anything, we must be aware that as school curriculum implements the bold vision expressed in the Principles and Standards - something that will be facilitated by the guidelines set out by the Curriculum Focal Points - we can expect that in four to six years we will be seeing more students whose school mathematics programs implemented this bold vision coming into our own undergraduate mathematics classes. Will we be ready for such students?
---------------------------------
Barbara Reynolds, SDS, is professor of Mathematics and Computer Science at Cardinal Stritch University in Milwaukee, WI. She has a passion for teaching for understanding.
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THIS IS THE THIRD AND LAST POSTING ABOUT THE Curriculum Focal Points.
From FOCUS [The Newsletter of the Mathematical Association of American], February 2007, Volume 27, Number 2, p. 31. See http://www.maa.org/pubs/focus.html
----------------------------------------
This is the THIRD (and last) of three articles that appeared in the current issue of FOCUS dealing with NCTM's Curriculum Focal Points.
************************
What are the Curriculum Focal Points? And Why Should We Care?
By Barbara Reynolds
What are the Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics: A Quest for Coherence (National Council of Teachers of Mathematics [NCTM] 2006)? Why should they matter to me? Why should they matter to the mathematics community?
In 2000 the NCTM released the Principles and Standards for School Mathematics, a comprehensive document that built on a bold vision that had been set by An Agenda for Action (NCTM 1980) and expanded in a set of Curriculum and Evaluation Standards for School Mathematics (NCTM 1989). The Principles and Standards sets a challenging comprehensive program, outlining goals that are both broad and deep. Now just six years later, the NCTM has presented us with Curriculum Focal Points. Does this new document represent a change in direction, a strengthening of the guidelines laid out in the Principles and Standards, or (as some might fear) a watering down of the content of the school mathematics curriculum?
When it first came out, I studied the Principles and Standards rather thoroughly, and was excited by its comprehensive vision. If students coming into college and university mathematics courses were educated according to the goals outlined in the Principles and Standards, if they came into college mathematics courses with the depth and breadth of understanding proposed in the Principles and Standards, wouldn't our job as teachers of undergraduate mathematics be so much easier!
My fear as I began to read the Curriculum Focal Points was that I would find a simplified list of competencies, grade-level mastery objectives, and testable outcomes - after all, this is the world of No Child Left Behind (NCLB) - that might represent minimal goals for each grade level of the school mathematics curriculum. My fear was that the Curriculum Focal Points would set minimal goals that would undermine the bold vision set by the Principles and Standards. Would the NCTM sell out to NCLB?
Instead what I see in the Curriculum Focal Points is a balanced set of guidelines that shows one way of developing a prekindergarten through grade 8 mathematics curriculum, guidelines that give focus to one or another area of the objectives set by the Principles and Standards at each grade level, while illustrating ways of making connections to the overall fabric of mathematics throughout the entire prekindergarten through grade 8 mathematics experience of school children. The Curriculum Focal Points are not presented as a curriculum in and of themselves, nor are they presented as a set of lesson plans. Rather they are presented as guidelines for developing an integrated Prekindergarten through Grade 8 mathematics curriculum. These Curriculum Focal Points illustrate one way of making explicit connections both to topics that the child studied in the preceding years, and to content that will be coming in subsequent years. Curriculum developers and textbook writers could use these Curriculum Focal Points as an organizing outline - focal points, actually - to develop mathematics programs that will be integrated and connected across grade levels. Classroom teachers would then be in a position to present mathematics at each grade level that implements the broad vision set by the Principles and Standards, and builds coherently from year to year. The Curriculum Focal Points make it more likely that classroom teachers will have well-designed materials that follow the bold vision set by the Principles and Standards, and that allow them to develop problem solving, reasoning, and critical thinking skills in their students without sacrificing computational skill development.
I began this reflection by asking why these Curriculum Focal Points should matter to me? Why should they matter to those of us who teach undergraduate mathematics? After all, students coming into our undergraduate mathematics classrooms are four or more years beyond Grade 8. What impact might these Curriculum Focal Points have on my own teaching of undergraduate mathematics?
The Curriculum Focal Points could impact my own teaching in two ways: First of all, if more schools adopt school mathematics materials that implement the vision of the Principles and Standards, classroom teachers will need to have a deep and broad understanding of mathematics. Classroom teachers will need an understanding of mathematics that goes well beyond computational fluency and that encompasses deeper mathematical reasoning and problem-solving skills. So we need to think about how to better prepare pre-service teachers, and we need to think about on-going professional development of in-service teachers. Secondly, if the calculus reform movement of the 1980s taught us anything, we must be aware that as school curriculum implements the bold vision expressed in the Principles and Standards - something that will be facilitated by the guidelines set out by the Curriculum Focal Points - we can expect that in four to six years we will be seeing more students whose school mathematics programs implemented this bold vision coming into our own undergraduate mathematics classes. Will we be ready for such students?
---------------------------------
Barbara Reynolds, SDS, is professor of Mathematics and Computer Science at Cardinal Stritch University in Milwaukee, WI. She has a passion for teaching for understanding.
----------------------------------
THIS IS THE THIRD AND LAST POSTING ABOUT THE Curriculum Focal Points.
Focus on Focal Points - Part 2
************************
From FOCUS [The Newsletter of the Mathematical Association of America], February 2007, Volume 27, Number 2, pp. 29-31. See http://www.maa.org/pubs/focus.html
----------------------------------------
This is the SECOND of three articles that appeared in the current issue of FOCUS dealing with NCTM's Curriculum Focal Points. The third article will follow shortly.
************************
Focus on Focal Points
A Commentary on Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics, NCTM, Reston, VA, 2006.
By Anthony Ralston
Background
In 1989 and 2000 NCTM (The National Council of Teachers of Mathematics) published two reports, Curriculum and Evaluation Standards for School Mathematics (hereafter the Standards)[1] and Principles and Standards for School Mathematics (hereafter PSSM) [2] on standards for school mathematics. The first of these, at least, was very important in influencing school mathematics curricula but both - although the second less so - have been rubbished by some mathematicians, mostly research mathematicians, many of whom act - and write - as if NCTM were The Great Satan of mathematics education.
But now with the publication under review here there is (almost) universal praise from the most zealous of the traditional (as opposed to reform) Math Warriors (hereafter TMWs) even though the NCTM makes clear that Curriculum Focal Points (hereafter CFP) builds on and is closely tied to PSSM. Phrases such as "an end to the math wars" or "it's about time" for this "role reversal" now roll off the lips of prominent TMWs. How can this be? If the NCTM was as hopeless as it had been portrayed and if CFP only builds on previously denigrated NCTM publications, how can there now be such praise for its latest work? Read on!
Rules of Engagement
If you wish to produce a document on a controversial subject that will be praised or, at least, not damned by any side, the first rule is: Keep it short. If you do, there will be much less text to shoot at. The Standards at 258 pages and PSSM at 402 pages were full of detail that could be castigated by those so inclined.
Avoiding the trap of the Standards and PSSM, the authors of CFP have obeyed this rule admirably. Not counting the boilerplate at the front, CFP is 41 pages short. Of these, 20 pages are an Appendix that relates the Focal Points to PSSM. Nicely color-coded for ease of use, this Appendix may, indeed, be valuable to curriculum developers but it is just what it claims to be: An appendix. The Appendix is followed by one page of references. Ten of the remaining pages are introductory material explaining the motivation of CFP and explaining what Focal Points are, how they should be used, and how they relate generally to PSSM. These do contain the most telling indication that NCTM's approach has not changed:
"[CFP] assumes that the mathematical processes described in Principles and Standards will be implemented in instruction that requires students to discuss and validate their mathematical thinking; create and analyze a variety of representations that illuminate the connections within the mathematics; and apply the mathematics that they are learning in solving problems, judging claims, and making decisions."
The guts of CFP, however, are contained in 10 other pages, one each for the ten grades from Prekindergarten to Grade 8, each of which contains the focal points for that grade.
A second rule is this: Wherever possible, be ambiguous. Then just about everyone can interpret what you have written as supporting his or her perspective. CFP abounds with language subject to whatever interpretation the reader might wish to put on it.
Take, for example, "fluency" (as in "fluency with multidigit addition and subtraction") which appears 25 times whereas "proficiency" appears only once in the entire document and that in the introductory pages. Fluency is the kind of word that can be interpreted as mastery by those who want a back-to-basics approach to mathematics but as meaning only that students can deal with numbers flexibly and efficiently by those who wish to avoid the "drill and kill" instruction of the past. Is this just a quibble? I think not. CFP says in three places that "students should develop fluency with efficient procedures, including the standard algorithm". Clear enough, isn't it? When studying division, this surely impliess that the student should learn the standard algorithm for long division.
Well, not quite. One reader of CFP submitted the following question to the NCTM website for Questions and Answers on CFP (http://www.nctm.org/focalpoints/qa.asp): "Does the Standard Algorithm have to be mastered by all students?" In the answer posted on the website, the response suggests that students should use "efficient procedures, including the standard algorithm - meaning including [italic in original], not exclusively, access to the standard algorithm".
All clear now? And later, "we recognize that use of the standard algorithms may be an issue with some. The key here is the understanding of the algorithm, any algorithm, however it is defined".
Sweet are the uses of ambiguity.
Throughout CFP the language has been very carefully chosen so as not to upset any of the most vocal traditionalists, mostly research mathematicians, who were so critical of the Standards and PSSM. The result is a document so spineless that traditionalists have praised it and reformers will only be mildly dismayed. (Full disclosure: I have been a peripheral warrior in the Math Wars but hardly a neutral one. I am totally unsympathetic to the traditionalists whom, I believe, have utterly failed to grasp how mathematics education needs to adapt to a world where calculators and computers are ubiquitous. But neither am I a fan of the so-called reform curricula that are generally much too timid in proposing changes in school mathematics.)
The C-word
Well, there I've done it by using just the word the TMWs feel so strongly about, namely "calculators". It is particularly noteworthy that the word "calculators(s)" appears nowhere - I repeat, nowhere - in CFP . How can this be at a time when whether or how much students use calculators in elementary school arithmetic is one of the most, perhaps the most controversial issue in elementary school mathematics education? The authors of CFP would, I think, answer this question by pointing to the section in CFP on "How Should Curriculum Focal Points Be Used" where they say "Its [CFP's] presentations of the focal points include neither suggestions for tools to use in teaching nor recommendations for professional development in content or pedagogy."
Thus, we won't discuss calculators because we aren't giving any "suggestions for tools". On the other hand there are five references to those other tools, "pencil-and-paper". The fact is that one just cannot speak or write persuasively about the elementary school mathematics curriculum in the 21st century without dealing with the issue of whether or, if so, when calculators should be used in teaching that curriculum.
CFP does, at least, pay lip service to the benefits of mental calculation which is mentioned four times. Three of these are in the context of estimating sums, differences, products or quotients or calculating them mentally "depending on the context and the numbers involved", making it clear that little more than knowledge of the addition and multiplication tables is expected here. (Am I wrong? Perhaps but, if so, this is another example of purposeful ambiguity.) The fourth instance advocates the building of "facility with mental computation" to do "addition and subtraction in special cases such as 2,500 + 6,000 and 9,000 - 5,000". While I applaud any mention of mental arithmetic, CFP essentially trivializes what students may accomplish in this domain.
The absence of even the word "calculator" is the most important reason why CFP has been so widely praised by NCTM's heretofore opponents. But the refusal even to discuss the crucial issue of calculators just panders to the anti-calculator brigade; it means that anyone using CFP for curriculum development has no guidance whatever on how much or how little use of calculators to build into a curriculum.
Fuzzy Math
The paeans of joy in the American press (e.g., the Wall Street Journal [3], the New York Times [4], the New York Sun [5], the Washington Times [6], the Jewish World Review [7], and probably elsewhere also) all praised the retreat of NCTM from the "fuzzy math" of the Standards and PSSM. What is "fuzzy math"? It is, as I have written elsewhere [8], "a fuzzy concept meaning whatever the critics of new [i.e., reform] curricula want it to mean at a given time". Sometimes it refers to those [mythical] people who wish to favor inexact rather than exact answers. At other times it refers to anyone who favors "constructivist math" [5] (whatever that may be).
In fact, the canard that NCTM ever favored fuzzy math, however you might define it, has never been true; it is, indeed, a lie which is repeated endlessly without any evidence whatsoever in the hope that if you repeat a lie often enough, people will believe it. I know of no one in NCTM or the math education community generally who has ever espoused teaching children that exact answers are not important and always to be desired, when they can be obtained with reasonable effort. Nor does any math educator doubt that instant recall of the addition and multiplication tables is necessary for anyone studying arithmetic.
At least, CFP, like the Standards and PSSM before it, does stress the value of being able to estimate, not as a way to avoid calculating exact answers but rather when an estimate is all that is required or to enable checking the reasonableness of answers on a calculator. Indeed, any good contemporary elementary school mathematics curriculum must emphasize the value of being able to estimate answers.
The Math Wars
Various comments about CFP ([3], [9]) have expressed the belief or hope that its publication would bring an end to the Math Wars that for years now have roiled the US math education scene. On one side have been the TMWs, the most vocal of whom are research mathematicians but also including parents, business groups and some teachers. On the other side are the RMWs (reform math warriors) whose leaders are mainly math educators but with significant support from parents and teachers.
Viewed by itself, it is easy to see why CFP appears to signal an end the Math Wars. It has so little content and that which it has is expressed in such anodyne or ambiguous form that no one is likely to get very agitated about anything it says. Thus, it is possible for TMWs to use CFP to declare victory in the Math Wars while RMWs will view such a claim as ridiculous.
Indeed, viewed as the authors of CFP state they intended, namely as an extension of the Standards and PSSM, CFP resolves none of the issues in the Math Wars. Moreover, despite the response of TMWs to CFP and the prior publication of the Common Ground report [10], none of the really significant issues in the Math Wars have been resolved nor can they be in any foreseeable future.
Briefly stated, at the elementary school level, these issues revolve around the question of whether arithmetic should focus on attaining proficiency with the classical pencil-and-paper algorithms for the four arithmetic functions or whether the elementary school curriculum should embrace the wide use of calculators in teaching arithmetic to achieve sound understanding of arithmetic itself as well as to prepare students as well as possible for the further study of mathematics. There are similar issues with respect to middle school and secondary school mathematics but most of the heat in the Math Wars has been focused on the elementary school curriculum.
These issues are nowhere near being resolved. While we should all applaud any attempt to achieve a debate more civilized than at some times in the past, publications like the Common Ground report and now CFP merely fudge the important issues. But resolution of the arguments in the Math Wars, not fudging, is crucial to the future of American - but not just American - school mathematics. My own view is that the main controversies in the Math Wars will not be definitively settled for many years until, at least, the main protagonists have long since left the field of battle. In the meantime, it is important that those who feel strongly about the reform mathematics agenda fight for their beliefs with undiminished intensity and without propitiation of their antagonists.
The Real Issue
Sadly, however, despite my strong belief in the need to reform American school mathematics, neither the success nor failure of this reform will have much effect on American mathematics education for the foreseeable future. The real tragedy of mathematics education in American schools is the declining number of first-class mathematics teachers (and the growing number of uncredentialled teachers) in secondary schools and the growing number of mathematics-averse teachers in elementary schools. Nothing in the No Child Left Behind Act (NCLB) will reverse this trend. Indeed, the opposite is much more likely with NCLB already beginning to prove that act most destructive of good education ever passed by the United States Congress.
This is not the place to discuss why teaching, particularly mathematics teaching, is failing to attract the best and the brightest that we need in American schools (but see [11]). Nor is it the place to discuss the disaster that the testing regimen in NCLB is wreaking on American schools. But until the teaching profession does start to attract large numbers of the best and the brightest, a publication like CFP, whatever you think of it, cannot possibly contribute much to improve the state of American school mathematics education.
References
1. National Council of Teachers of Mathematics, Curriculum and Evaluation Standards for School Mathematics, NCTM, Reston, VA, 1989.
2. National Council of Teachers of Mathematics, Principles and Standards for School Mathematics, NCTM, Reston, VA, 2000.
3. John Hechinger, New Report Urges Return to Basics in Teaching Math, Wall Street Journal, 12 September 2006.
4. Teaching Math, Singapore Style, Editorial, The New York Times, 18 September 2006.
5. Andrew Wolf, Turnaround in the Math Wars, The New York Sun, 15 September 2006.
6. Phyllis Schafly, Parents Right, Experts Wrong, Washington Times, 27 September 2006.
7. Debra J. Saunders, Fuzzy Memory on Fuzzy Math, The Jewish World Review (http://jewishworldreview.com/0906/saunders091406.php3), 14 September 2006.
8. Anthony Ralston, Research Mathematicians and Mathematics Education: A Critique, Notices of the American Mathematical Society, Vol. 51, 2004, p408.
9. R. James Milgram as quoted in Education Week, 12 September 2006.
10. Ball, D. L., Ferrini-Mundy, J., Milgram, R. J., Schmid, W., Schaar, R., Reaching for Common Ground in K-12 Mathematics Education, http://www.maa.org/common-ground, also in Notices of the AMS, Vol. 52, pp1055-1058. (See also: A. Ralston, K-12 Mathematics Education: How Much Common Ground Is There?, FOCUS, January, 2006, pp14-15.)
11. Anthony Ralston, The Real Scandal in American School Mathematics, Education Week, 27 April 2005 (also: http://www.doc.ic.ac.uk/~ar9/TeacherQual.html)
From FOCUS [The Newsletter of the Mathematical Association of America], February 2007, Volume 27, Number 2, pp. 29-31. See http://www.maa.org/pubs/focus.html
----------------------------------------
This is the SECOND of three articles that appeared in the current issue of FOCUS dealing with NCTM's Curriculum Focal Points. The third article will follow shortly.
************************
Focus on Focal Points
A Commentary on Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics, NCTM, Reston, VA, 2006.
By Anthony Ralston
Background
In 1989 and 2000 NCTM (The National Council of Teachers of Mathematics) published two reports, Curriculum and Evaluation Standards for School Mathematics (hereafter the Standards)[1] and Principles and Standards for School Mathematics (hereafter PSSM) [2] on standards for school mathematics. The first of these, at least, was very important in influencing school mathematics curricula but both - although the second less so - have been rubbished by some mathematicians, mostly research mathematicians, many of whom act - and write - as if NCTM were The Great Satan of mathematics education.
But now with the publication under review here there is (almost) universal praise from the most zealous of the traditional (as opposed to reform) Math Warriors (hereafter TMWs) even though the NCTM makes clear that Curriculum Focal Points (hereafter CFP) builds on and is closely tied to PSSM. Phrases such as "an end to the math wars" or "it's about time" for this "role reversal" now roll off the lips of prominent TMWs. How can this be? If the NCTM was as hopeless as it had been portrayed and if CFP only builds on previously denigrated NCTM publications, how can there now be such praise for its latest work? Read on!
Rules of Engagement
If you wish to produce a document on a controversial subject that will be praised or, at least, not damned by any side, the first rule is: Keep it short. If you do, there will be much less text to shoot at. The Standards at 258 pages and PSSM at 402 pages were full of detail that could be castigated by those so inclined.
Avoiding the trap of the Standards and PSSM, the authors of CFP have obeyed this rule admirably. Not counting the boilerplate at the front, CFP is 41 pages short. Of these, 20 pages are an Appendix that relates the Focal Points to PSSM. Nicely color-coded for ease of use, this Appendix may, indeed, be valuable to curriculum developers but it is just what it claims to be: An appendix. The Appendix is followed by one page of references. Ten of the remaining pages are introductory material explaining the motivation of CFP and explaining what Focal Points are, how they should be used, and how they relate generally to PSSM. These do contain the most telling indication that NCTM's approach has not changed:
"[CFP] assumes that the mathematical processes described in Principles and Standards will be implemented in instruction that requires students to discuss and validate their mathematical thinking; create and analyze a variety of representations that illuminate the connections within the mathematics; and apply the mathematics that they are learning in solving problems, judging claims, and making decisions."
The guts of CFP, however, are contained in 10 other pages, one each for the ten grades from Prekindergarten to Grade 8, each of which contains the focal points for that grade.
A second rule is this: Wherever possible, be ambiguous. Then just about everyone can interpret what you have written as supporting his or her perspective. CFP abounds with language subject to whatever interpretation the reader might wish to put on it.
Take, for example, "fluency" (as in "fluency with multidigit addition and subtraction") which appears 25 times whereas "proficiency" appears only once in the entire document and that in the introductory pages. Fluency is the kind of word that can be interpreted as mastery by those who want a back-to-basics approach to mathematics but as meaning only that students can deal with numbers flexibly and efficiently by those who wish to avoid the "drill and kill" instruction of the past. Is this just a quibble? I think not. CFP says in three places that "students should develop fluency with efficient procedures, including the standard algorithm". Clear enough, isn't it? When studying division, this surely impliess that the student should learn the standard algorithm for long division.
Well, not quite. One reader of CFP submitted the following question to the NCTM website for Questions and Answers on CFP (http://www.nctm.org/focalpoints/qa.asp): "Does the Standard Algorithm have to be mastered by all students?" In the answer posted on the website, the response suggests that students should use "efficient procedures, including the standard algorithm - meaning including [italic in original], not exclusively, access to the standard algorithm".
All clear now? And later, "we recognize that use of the standard algorithms may be an issue with some. The key here is the understanding of the algorithm, any algorithm, however it is defined".
Sweet are the uses of ambiguity.
Throughout CFP the language has been very carefully chosen so as not to upset any of the most vocal traditionalists, mostly research mathematicians, who were so critical of the Standards and PSSM. The result is a document so spineless that traditionalists have praised it and reformers will only be mildly dismayed. (Full disclosure: I have been a peripheral warrior in the Math Wars but hardly a neutral one. I am totally unsympathetic to the traditionalists whom, I believe, have utterly failed to grasp how mathematics education needs to adapt to a world where calculators and computers are ubiquitous. But neither am I a fan of the so-called reform curricula that are generally much too timid in proposing changes in school mathematics.)
The C-word
Well, there I've done it by using just the word the TMWs feel so strongly about, namely "calculators". It is particularly noteworthy that the word "calculators(s)" appears nowhere - I repeat, nowhere - in CFP . How can this be at a time when whether or how much students use calculators in elementary school arithmetic is one of the most, perhaps the most controversial issue in elementary school mathematics education? The authors of CFP would, I think, answer this question by pointing to the section in CFP on "How Should Curriculum Focal Points Be Used" where they say "Its [CFP's] presentations of the focal points include neither suggestions for tools to use in teaching nor recommendations for professional development in content or pedagogy."
Thus, we won't discuss calculators because we aren't giving any "suggestions for tools". On the other hand there are five references to those other tools, "pencil-and-paper". The fact is that one just cannot speak or write persuasively about the elementary school mathematics curriculum in the 21st century without dealing with the issue of whether or, if so, when calculators should be used in teaching that curriculum.
CFP does, at least, pay lip service to the benefits of mental calculation which is mentioned four times. Three of these are in the context of estimating sums, differences, products or quotients or calculating them mentally "depending on the context and the numbers involved", making it clear that little more than knowledge of the addition and multiplication tables is expected here. (Am I wrong? Perhaps but, if so, this is another example of purposeful ambiguity.) The fourth instance advocates the building of "facility with mental computation" to do "addition and subtraction in special cases such as 2,500 + 6,000 and 9,000 - 5,000". While I applaud any mention of mental arithmetic, CFP essentially trivializes what students may accomplish in this domain.
The absence of even the word "calculator" is the most important reason why CFP has been so widely praised by NCTM's heretofore opponents. But the refusal even to discuss the crucial issue of calculators just panders to the anti-calculator brigade; it means that anyone using CFP for curriculum development has no guidance whatever on how much or how little use of calculators to build into a curriculum.
Fuzzy Math
The paeans of joy in the American press (e.g., the Wall Street Journal [3], the New York Times [4], the New York Sun [5], the Washington Times [6], the Jewish World Review [7], and probably elsewhere also) all praised the retreat of NCTM from the "fuzzy math" of the Standards and PSSM. What is "fuzzy math"? It is, as I have written elsewhere [8], "a fuzzy concept meaning whatever the critics of new [i.e., reform] curricula want it to mean at a given time". Sometimes it refers to those [mythical] people who wish to favor inexact rather than exact answers. At other times it refers to anyone who favors "constructivist math" [5] (whatever that may be).
In fact, the canard that NCTM ever favored fuzzy math, however you might define it, has never been true; it is, indeed, a lie which is repeated endlessly without any evidence whatsoever in the hope that if you repeat a lie often enough, people will believe it. I know of no one in NCTM or the math education community generally who has ever espoused teaching children that exact answers are not important and always to be desired, when they can be obtained with reasonable effort. Nor does any math educator doubt that instant recall of the addition and multiplication tables is necessary for anyone studying arithmetic.
At least, CFP, like the Standards and PSSM before it, does stress the value of being able to estimate, not as a way to avoid calculating exact answers but rather when an estimate is all that is required or to enable checking the reasonableness of answers on a calculator. Indeed, any good contemporary elementary school mathematics curriculum must emphasize the value of being able to estimate answers.
The Math Wars
Various comments about CFP ([3], [9]) have expressed the belief or hope that its publication would bring an end to the Math Wars that for years now have roiled the US math education scene. On one side have been the TMWs, the most vocal of whom are research mathematicians but also including parents, business groups and some teachers. On the other side are the RMWs (reform math warriors) whose leaders are mainly math educators but with significant support from parents and teachers.
Viewed by itself, it is easy to see why CFP appears to signal an end the Math Wars. It has so little content and that which it has is expressed in such anodyne or ambiguous form that no one is likely to get very agitated about anything it says. Thus, it is possible for TMWs to use CFP to declare victory in the Math Wars while RMWs will view such a claim as ridiculous.
Indeed, viewed as the authors of CFP state they intended, namely as an extension of the Standards and PSSM, CFP resolves none of the issues in the Math Wars. Moreover, despite the response of TMWs to CFP and the prior publication of the Common Ground report [10], none of the really significant issues in the Math Wars have been resolved nor can they be in any foreseeable future.
Briefly stated, at the elementary school level, these issues revolve around the question of whether arithmetic should focus on attaining proficiency with the classical pencil-and-paper algorithms for the four arithmetic functions or whether the elementary school curriculum should embrace the wide use of calculators in teaching arithmetic to achieve sound understanding of arithmetic itself as well as to prepare students as well as possible for the further study of mathematics. There are similar issues with respect to middle school and secondary school mathematics but most of the heat in the Math Wars has been focused on the elementary school curriculum.
These issues are nowhere near being resolved. While we should all applaud any attempt to achieve a debate more civilized than at some times in the past, publications like the Common Ground report and now CFP merely fudge the important issues. But resolution of the arguments in the Math Wars, not fudging, is crucial to the future of American - but not just American - school mathematics. My own view is that the main controversies in the Math Wars will not be definitively settled for many years until, at least, the main protagonists have long since left the field of battle. In the meantime, it is important that those who feel strongly about the reform mathematics agenda fight for their beliefs with undiminished intensity and without propitiation of their antagonists.
The Real Issue
Sadly, however, despite my strong belief in the need to reform American school mathematics, neither the success nor failure of this reform will have much effect on American mathematics education for the foreseeable future. The real tragedy of mathematics education in American schools is the declining number of first-class mathematics teachers (and the growing number of uncredentialled teachers) in secondary schools and the growing number of mathematics-averse teachers in elementary schools. Nothing in the No Child Left Behind Act (NCLB) will reverse this trend. Indeed, the opposite is much more likely with NCLB already beginning to prove that act most destructive of good education ever passed by the United States Congress.
This is not the place to discuss why teaching, particularly mathematics teaching, is failing to attract the best and the brightest that we need in American schools (but see [11]). Nor is it the place to discuss the disaster that the testing regimen in NCLB is wreaking on American schools. But until the teaching profession does start to attract large numbers of the best and the brightest, a publication like CFP, whatever you think of it, cannot possibly contribute much to improve the state of American school mathematics education.
References
1. National Council of Teachers of Mathematics, Curriculum and Evaluation Standards for School Mathematics, NCTM, Reston, VA, 1989.
2. National Council of Teachers of Mathematics, Principles and Standards for School Mathematics, NCTM, Reston, VA, 2000.
3. John Hechinger, New Report Urges Return to Basics in Teaching Math, Wall Street Journal, 12 September 2006.
4. Teaching Math, Singapore Style, Editorial, The New York Times, 18 September 2006.
5. Andrew Wolf, Turnaround in the Math Wars, The New York Sun, 15 September 2006.
6. Phyllis Schafly, Parents Right, Experts Wrong, Washington Times, 27 September 2006.
7. Debra J. Saunders, Fuzzy Memory on Fuzzy Math, The Jewish World Review (http://jewishworldreview.com/0906/saunders091406.php3), 14 September 2006.
8. Anthony Ralston, Research Mathematicians and Mathematics Education: A Critique, Notices of the American Mathematical Society, Vol. 51, 2004, p408.
9. R. James Milgram as quoted in Education Week, 12 September 2006.
10. Ball, D. L., Ferrini-Mundy, J., Milgram, R. J., Schmid, W., Schaar, R., Reaching for Common Ground in K-12 Mathematics Education, http://www.maa.org/common-ground, also in Notices of the AMS, Vol. 52, pp1055-1058. (See also: A. Ralston, K-12 Mathematics Education: How Much Common Ground Is There?, FOCUS, January, 2006, pp14-15.)
11. Anthony Ralston, The Real Scandal in American School Mathematics, Education Week, 27 April 2005 (also: http://www.doc.ic.ac.uk/~ar9/TeacherQual.html)
In FOCUS: Curriculum Focal Points - Part 1
************************
From FOCUS [The Newsletter of the Mathematical Association of America], February 2007, Volume 27, Number 2, pp. 27-28. See http://www.maa.org/pubs/focus.html . The articles are posted with the approval of the Editor of FOCUS.
----------------------------------------
This is the FIRST of three articles that appeared in the current issue of FOCUS dealing with NCTM's Curriculum Focal Points. The other two articles will follow shortly.
************************
In FOCUS: Curriculum Focal Points
As noted in our November issue, the National Council of Teachers of Mathematics (NCTM) recently released a document entitled Curriculum Focal Points. The document is available online at http://www.nctm.org/focalpoints/downloads.asp, where one can also find a lot more information and discussion, including questions and answers on the document. NCTM says the document extends the Council's leadership of more than twenty-five years by describing an approach to curriculum development that focuses on areas of emphasis within each grade from prekindergarten through grade 8. Curriculum Focal Points, widely reported in the news media, was hailed by some as a retreat from NCTM's previous positions. This misreading is addressed in each of the three articles that follow. We hope that they will shed some light on the goals and content of Curriculum Focal Points. The articles below are the opinions of the authors and do not reflect a position or stance of the MAA.
NCTM's Curriculum Focal Points
By Francis (Skip) Fennell
The publication by the National Council of Teachers of Mathematics (NCTM) of Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics: A Quest for Coherence marks the Council's next step in implementing the vision set forth in the Principles and Standards for School Mathematics (NCTM, 2000), with a particular emphasis on curricular expectations.
The genesis of the Curriculum Focal Points, released on September 12, 2006, was a conference at the Park City Mathematics Institute in 2004 organized by NCTM with the Association of State Supervisors of Mathematics (ASSM). It brought together mathematicians, supervisors of mathematics, and mathematics educators with the intent to examine the K-12 mathematics standards of each of the states and how they were influenced by Principles and Standards for School Mathematics. The expectation was that the consistency of the findings would guide a discussion that could begin to lead to a meeting of the minds about the important mathematics that should be taught at various grades. Instead, the outcome was the discovery that there was little consistency between standards and expectations or of what content fell in what grade, and perhaps most troubling was the consequent realization that this lack of consistency was inevitably detrimental to the teaching and learning of K-12 mathematics nationwide.
An analysis of the conference findings resulted in the publication entitled "Standards and Curriculum: A View from the Nation," (NCTM, 2005). This joint report by NCTM and ASSM provides insights into where we appear to be headed in our expectations for students' mathematics learning. The report is an initial attempt to examine across states the impact of Principles and Standards for School Mathematics on curriculum reform, discern how state educational agencies approached the task of developing state standards, and bring to light areas of commonality and difference. The findings from this endeavor laid a foundation for discussions about the future direction of local, state, and national mathematics curricula. From this were born the idea and concept of what became the Curriculum Focal Points.
Extensive, thoughtful, and at times intensely debated discussions among a group of nine writers generated the concept and early drafts of the curriculum focal points. The written draft of the writers, who represented expertise in mathematics and mathematics education as well as classroom experience from prekindergarten through grade 8, was reviewed and commented upon by some 70 reviewers, including mathematicians, mathematics educators, and policy makers. After extensive further revisions, the publication was presented to the NCTM Board of Directors, which on April 24, 2006 approved it for publication.
Curriculum focal points are important mathematical topics for each grade level. They are the related ideas, concepts, skills, and procedures that form the foundation for understanding, lasting learning, and success in higher level mathematics, beginning with algebra. NCTM views the Curriculum Focal Points as a framework for developing mathematics curriculum at the state and school district level. The focal points are intended to frame discussions that will eventually inform the decisions of textbook publishers and assessment developers, as well.
The Curriculum Focal Points address curriculum, or what is taught, rather than instruction, or how it is taught. By design, there is no mention of instructional strategies, instructional materials, technological tools (e.g. the calculator), or manipulative materials. This was the intent of the writers of the focal points-to provide a publication that would foster discussion, dialogue, and decision-making relative to the important mathematics for prekindergarten through grade 8. The ultimate goal would be for these suggestions, the focal points, to lead to the development of mathematics curriculum goals that are more cohesive from grade to grade and from school to school. Through its Connections, the new publication also shows additional ways in which the focal points connect to Principles and Standards.
The Curriculum Focal Points provides an example, a critical foundation, for the next generation of curricula and related assessments. Curriculum developers can place Curriculum Focal Points and a local or state curriculum side by side when refining their current curricula. Curriculum developers can determine how much time to devote to the focal points as the mathematical core for a particular grade level, and then build other mathematics topics around these important areas of focus.
Media Coverage
The Curriculum Focal Points release was widely reported in the news media and generated considerable discussion within the mathematics and education communities. Some inaccurate coverage raised questions among many who were asking "Is what the Wall Street Journal and New York Times reported true? Is NCTM really going back to basics?"
In a letter sent to the Wall Street Journal and published on September 26, I wrote, "Contrary to the impression left in your article, learning the basics is certainly not 'new marching orders' from the NCTM, which has always considered the basic computation facts and related work with operations to be important. Nor is the new focal-points approach to curriculum development a 'remarkable reversal' for NCTM. As stated in NCTM's 1989 and 2000 standards, conceptual understanding and problem solving are absolutely fundamental to learning mathematics. The council has never promoted estimation 'rather than precise answers.' Estimation is a critical component to the overall understanding and use of numbers."
A letter to the editor of the New York Times published on September 24, stated, "What some refer to as basic skills (for example, multiplication facts, and fluency with the addition, subtraction, multiplication and division of whole numbers) have always been a fundamental core of elementary school mathematics. Always. But we want more. We want children to understand the mathematics they are learning and we want them to be able to solve problems, which is, in the long run, why we do mathematics."
The Curriculum Focal Points are in no way a reversal of the Council's long-standing position on teaching students to learn critical foundational topics (e.g. multiplication) with conceptual understanding, and they are not a retreat from Principles and Standards for School Mathematics. Rather, the Curriculum Focal Points are the next step in implementing the Standards. The appendix in Curriculum Focal Points directly links the focal points to virtually all the expectations in Principles and Standards.
One of the questions asked most frequently is about the standard algorithm and whether the Curriculum Focal Points expressly states that all students must learn the standard algorithm. The grade 2 focal point suggests efficient procedures, including the standard algorithm-including, not exclusively, access to the standard algorithm. Students should use what they can do efficiently and accurately. Most important, they should not use any algorithm until it is understood.
Similarly, for grade 4 the quick recall of multiplication facts and fluency with efficient procedures, including the standard algorithm, is a focus. Again, and importantly, fluency emerges through deep understanding of the multiplication process-how multiplication is represented and how properties, particularly the distributive property, are used when multiplying. Students become fluent through their understanding of how and why procedures work - with a focus on place value and properties of operations.
The Purpose
Today's mathematics curricula tend to be dominated by long lists of very specific goals, standards, objectives, or learning expectations. By contrast, Curriculum Focal Points describes significant mathematical concepts and skills for each grade level. They are a way to organize and connect critical mathematics topics from grade to grade. Organizing a curriculum around the focal points can provide students with a more coherent ever expanding body of mathematical knowledge.
Mathematics leaders should use the Curriculum Focal Points to launch discussions about the next generation of curriculum standards, textbooks, and tests. Such dialogue, discussion, and debate is critical and can lead to the development of new models for curriculum, instruction, materials, and assessments. Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics represents an important, initial step in advancing collaborative discussions about what mathematics students should know and be able to do.
From FOCUS [The Newsletter of the Mathematical Association of America], February 2007, Volume 27, Number 2, pp. 27-28. See http://www.maa.org/pubs/focus.html . The articles are posted with the approval of the Editor of FOCUS.
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This is the FIRST of three articles that appeared in the current issue of FOCUS dealing with NCTM's Curriculum Focal Points. The other two articles will follow shortly.
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In FOCUS: Curriculum Focal Points
As noted in our November issue, the National Council of Teachers of Mathematics (NCTM) recently released a document entitled Curriculum Focal Points. The document is available online at http://www.nctm.org/focalpoints/downloads.asp, where one can also find a lot more information and discussion, including questions and answers on the document. NCTM says the document extends the Council's leadership of more than twenty-five years by describing an approach to curriculum development that focuses on areas of emphasis within each grade from prekindergarten through grade 8. Curriculum Focal Points, widely reported in the news media, was hailed by some as a retreat from NCTM's previous positions. This misreading is addressed in each of the three articles that follow. We hope that they will shed some light on the goals and content of Curriculum Focal Points. The articles below are the opinions of the authors and do not reflect a position or stance of the MAA.
NCTM's Curriculum Focal Points
By Francis (Skip) Fennell
The publication by the National Council of Teachers of Mathematics (NCTM) of Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics: A Quest for Coherence marks the Council's next step in implementing the vision set forth in the Principles and Standards for School Mathematics (NCTM, 2000), with a particular emphasis on curricular expectations.
The genesis of the Curriculum Focal Points, released on September 12, 2006, was a conference at the Park City Mathematics Institute in 2004 organized by NCTM with the Association of State Supervisors of Mathematics (ASSM). It brought together mathematicians, supervisors of mathematics, and mathematics educators with the intent to examine the K-12 mathematics standards of each of the states and how they were influenced by Principles and Standards for School Mathematics. The expectation was that the consistency of the findings would guide a discussion that could begin to lead to a meeting of the minds about the important mathematics that should be taught at various grades. Instead, the outcome was the discovery that there was little consistency between standards and expectations or of what content fell in what grade, and perhaps most troubling was the consequent realization that this lack of consistency was inevitably detrimental to the teaching and learning of K-12 mathematics nationwide.
An analysis of the conference findings resulted in the publication entitled "Standards and Curriculum: A View from the Nation," (NCTM, 2005). This joint report by NCTM and ASSM provides insights into where we appear to be headed in our expectations for students' mathematics learning. The report is an initial attempt to examine across states the impact of Principles and Standards for School Mathematics on curriculum reform, discern how state educational agencies approached the task of developing state standards, and bring to light areas of commonality and difference. The findings from this endeavor laid a foundation for discussions about the future direction of local, state, and national mathematics curricula. From this were born the idea and concept of what became the Curriculum Focal Points.
Extensive, thoughtful, and at times intensely debated discussions among a group of nine writers generated the concept and early drafts of the curriculum focal points. The written draft of the writers, who represented expertise in mathematics and mathematics education as well as classroom experience from prekindergarten through grade 8, was reviewed and commented upon by some 70 reviewers, including mathematicians, mathematics educators, and policy makers. After extensive further revisions, the publication was presented to the NCTM Board of Directors, which on April 24, 2006 approved it for publication.
Curriculum focal points are important mathematical topics for each grade level. They are the related ideas, concepts, skills, and procedures that form the foundation for understanding, lasting learning, and success in higher level mathematics, beginning with algebra. NCTM views the Curriculum Focal Points as a framework for developing mathematics curriculum at the state and school district level. The focal points are intended to frame discussions that will eventually inform the decisions of textbook publishers and assessment developers, as well.
The Curriculum Focal Points address curriculum, or what is taught, rather than instruction, or how it is taught. By design, there is no mention of instructional strategies, instructional materials, technological tools (e.g. the calculator), or manipulative materials. This was the intent of the writers of the focal points-to provide a publication that would foster discussion, dialogue, and decision-making relative to the important mathematics for prekindergarten through grade 8. The ultimate goal would be for these suggestions, the focal points, to lead to the development of mathematics curriculum goals that are more cohesive from grade to grade and from school to school. Through its Connections, the new publication also shows additional ways in which the focal points connect to Principles and Standards.
The Curriculum Focal Points provides an example, a critical foundation, for the next generation of curricula and related assessments. Curriculum developers can place Curriculum Focal Points and a local or state curriculum side by side when refining their current curricula. Curriculum developers can determine how much time to devote to the focal points as the mathematical core for a particular grade level, and then build other mathematics topics around these important areas of focus.
Media Coverage
The Curriculum Focal Points release was widely reported in the news media and generated considerable discussion within the mathematics and education communities. Some inaccurate coverage raised questions among many who were asking "Is what the Wall Street Journal and New York Times reported true? Is NCTM really going back to basics?"
In a letter sent to the Wall Street Journal and published on September 26, I wrote, "Contrary to the impression left in your article, learning the basics is certainly not 'new marching orders' from the NCTM, which has always considered the basic computation facts and related work with operations to be important. Nor is the new focal-points approach to curriculum development a 'remarkable reversal' for NCTM. As stated in NCTM's 1989 and 2000 standards, conceptual understanding and problem solving are absolutely fundamental to learning mathematics. The council has never promoted estimation 'rather than precise answers.' Estimation is a critical component to the overall understanding and use of numbers."
A letter to the editor of the New York Times published on September 24, stated, "What some refer to as basic skills (for example, multiplication facts, and fluency with the addition, subtraction, multiplication and division of whole numbers) have always been a fundamental core of elementary school mathematics. Always. But we want more. We want children to understand the mathematics they are learning and we want them to be able to solve problems, which is, in the long run, why we do mathematics."
The Curriculum Focal Points are in no way a reversal of the Council's long-standing position on teaching students to learn critical foundational topics (e.g. multiplication) with conceptual understanding, and they are not a retreat from Principles and Standards for School Mathematics. Rather, the Curriculum Focal Points are the next step in implementing the Standards. The appendix in Curriculum Focal Points directly links the focal points to virtually all the expectations in Principles and Standards.
One of the questions asked most frequently is about the standard algorithm and whether the Curriculum Focal Points expressly states that all students must learn the standard algorithm. The grade 2 focal point suggests efficient procedures, including the standard algorithm-including, not exclusively, access to the standard algorithm. Students should use what they can do efficiently and accurately. Most important, they should not use any algorithm until it is understood.
Similarly, for grade 4 the quick recall of multiplication facts and fluency with efficient procedures, including the standard algorithm, is a focus. Again, and importantly, fluency emerges through deep understanding of the multiplication process-how multiplication is represented and how properties, particularly the distributive property, are used when multiplying. Students become fluent through their understanding of how and why procedures work - with a focus on place value and properties of operations.
The Purpose
Today's mathematics curricula tend to be dominated by long lists of very specific goals, standards, objectives, or learning expectations. By contrast, Curriculum Focal Points describes significant mathematical concepts and skills for each grade level. They are a way to organize and connect critical mathematics topics from grade to grade. Organizing a curriculum around the focal points can provide students with a more coherent ever expanding body of mathematical knowledge.
Mathematics leaders should use the Curriculum Focal Points to launch discussions about the next generation of curriculum standards, textbooks, and tests. Such dialogue, discussion, and debate is critical and can lead to the development of new models for curriculum, instruction, materials, and assessments. Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics represents an important, initial step in advancing collaborative discussions about what mathematics students should know and be able to do.
Wednesday, February 7, 2007
Advanced Placement Testing Report Released
Md., Va. Earn High Marks on AP Exams
By Jay Mathews
Washington Post Staff WriterWednesday, February 8, 2006; A08
Last year, a record 23 percent of American seniors graduated from high school having taken at least one Advanced Placement exam, the College Board said yesterday in a report dramatizing the rising influence of AP on teaching, college admission and state education policy.
In its annual AP report released yesterday, the College Board rated each state's success in preparing students for AP exams in 35 subjects, with Maryland and Virginia scoring near the top. The report hailed advances by minorities in taking the three-hour exams and analyzed the strength of the AP science and calculus courses that President Bush said in his State of the Union address should get a new dose of federal teacher training funds.
Nationally, 14.1 percent of all graduating seniors last year scored at least 3 out of 5 points, the level at which most colleges give course credit, on at least one AP exam, compared with 10.2 percent of seniors in 2000, the report said. The top five states in that category in 2005 were New York with 22.8 percent; Maryland, 21 percent; Utah, 20.5 percent; California, 19.7 percent; and Virginia, 19.3 percent.
In addition, the number of minorities taking AP courses has soared, according to the College Board. The number of African Americans taking the courses has gone from 19,797 in 1995 to 62,179 in 2005. For Hispanics, the increase in that period was from 32,195 to 134,811, with great gains in Hispanic AP participation in Florida, Maryland, the District, California and Texas.
Among those taking the 2005 AP tests, whites and Asians each had passing rates of 63.3 percent. The passing rate for Hispanics was 46.5 percent and for African Americans, 27.8 percent.
Bob Schaeffer, director of public education for FairTest, a testing watchdog organization, said his group is not as critical of AP as it is of the SAT, which it says is used too much by colleges to decide which students to admit. The AP "is a gateway test, not a gatekeeping test," Schaeffer said, and it's one that he thought helped both him and his son when they were in high school.
But, he added, there is a danger that the College Board will oversell the AP as a cure for American high schools' ills. "The College Board has really seized the opportunity to promote this," he said.
Unlike the College Board's other major test, the SAT, which has a strong rival in the ACT college entrance exam, the AP is by far the largest supplier of exams that can earn college credit for U.S. high school students.
Trevor Packer, executive director of the AP program, said that, on the contrary, his data show that AP is still underused, to the detriment of many students who would benefit from a more challenging program.
The rapid growth of the AP test -- with the number of students taking the test doubling since 1995 -- has been praised by some educators as a way to invigorate low-performing high schools and criticized by others for putting too much pressure on students and forcing schools to teach subjects the AP way. Students in some Washington area schools complain about four hours of daily homework because of so many AP classes, but a University of California at Los Angeles study shows most high school students do less than an hour a day.
Packer said that about 150,000 high school students have access to AP calculus courses, but a College Board analysis of PSAT scores shows that five times as many have the capacity to do well in those courses if they were offered at their schools. The analysis showed that 100,000 students had access to AP biology, but eight times as many could do well in that course.
College and high school experts wrote the AP exams given last May to students from 11,498 public and 3,075 private schools. Usually half the exam time is devoted to multiple-choice questions scored by machines and the other half to essay or free-response questions scored by AP teachers and college professors meeting in summer grading sessions. The much smaller International Baccalaureate program gives five-hour exams that are usually all free-response questions.
The exams are designed to mimic college introductory course final exams. Some students do well enough on AP tests to start college as sophomores.
Some area high schools were recognized yesterday for having the nation's highest percentage of seniors receiving scores of 3 and above on AP exams. The Thomas Jefferson High School for Science and Technology in Fairfax County was best among large schools in calculus BC, chemistry, French language, French literature, U.S. government and politics and U.S. history. Walter Johnson High School in Montgomery County was best in world history among large schools. Two D.C. private schools were also at the top -- National Cathedral among small schools in French literature, and Sidwell Friends among medium schools in English literature and composition.
Maryland Superintendent of Schools Nancy S. Grasmick attributed the state's AP success to its emphasis on raising minority achievement and participation. Acting Virginia Superintendent of Public Instruction Patricia Wright said her state opened doors to AP courses and other learning opportunities "once reserved for students in elite schools and programs."
By Jay Mathews
Washington Post Staff WriterWednesday, February 8, 2006; A08
Last year, a record 23 percent of American seniors graduated from high school having taken at least one Advanced Placement exam, the College Board said yesterday in a report dramatizing the rising influence of AP on teaching, college admission and state education policy.
In its annual AP report released yesterday, the College Board rated each state's success in preparing students for AP exams in 35 subjects, with Maryland and Virginia scoring near the top. The report hailed advances by minorities in taking the three-hour exams and analyzed the strength of the AP science and calculus courses that President Bush said in his State of the Union address should get a new dose of federal teacher training funds.
Nationally, 14.1 percent of all graduating seniors last year scored at least 3 out of 5 points, the level at which most colleges give course credit, on at least one AP exam, compared with 10.2 percent of seniors in 2000, the report said. The top five states in that category in 2005 were New York with 22.8 percent; Maryland, 21 percent; Utah, 20.5 percent; California, 19.7 percent; and Virginia, 19.3 percent.
In addition, the number of minorities taking AP courses has soared, according to the College Board. The number of African Americans taking the courses has gone from 19,797 in 1995 to 62,179 in 2005. For Hispanics, the increase in that period was from 32,195 to 134,811, with great gains in Hispanic AP participation in Florida, Maryland, the District, California and Texas.
Among those taking the 2005 AP tests, whites and Asians each had passing rates of 63.3 percent. The passing rate for Hispanics was 46.5 percent and for African Americans, 27.8 percent.
Bob Schaeffer, director of public education for FairTest, a testing watchdog organization, said his group is not as critical of AP as it is of the SAT, which it says is used too much by colleges to decide which students to admit. The AP "is a gateway test, not a gatekeeping test," Schaeffer said, and it's one that he thought helped both him and his son when they were in high school.
But, he added, there is a danger that the College Board will oversell the AP as a cure for American high schools' ills. "The College Board has really seized the opportunity to promote this," he said.
Unlike the College Board's other major test, the SAT, which has a strong rival in the ACT college entrance exam, the AP is by far the largest supplier of exams that can earn college credit for U.S. high school students.
Trevor Packer, executive director of the AP program, said that, on the contrary, his data show that AP is still underused, to the detriment of many students who would benefit from a more challenging program.
The rapid growth of the AP test -- with the number of students taking the test doubling since 1995 -- has been praised by some educators as a way to invigorate low-performing high schools and criticized by others for putting too much pressure on students and forcing schools to teach subjects the AP way. Students in some Washington area schools complain about four hours of daily homework because of so many AP classes, but a University of California at Los Angeles study shows most high school students do less than an hour a day.
Packer said that about 150,000 high school students have access to AP calculus courses, but a College Board analysis of PSAT scores shows that five times as many have the capacity to do well in those courses if they were offered at their schools. The analysis showed that 100,000 students had access to AP biology, but eight times as many could do well in that course.
College and high school experts wrote the AP exams given last May to students from 11,498 public and 3,075 private schools. Usually half the exam time is devoted to multiple-choice questions scored by machines and the other half to essay or free-response questions scored by AP teachers and college professors meeting in summer grading sessions. The much smaller International Baccalaureate program gives five-hour exams that are usually all free-response questions.
The exams are designed to mimic college introductory course final exams. Some students do well enough on AP tests to start college as sophomores.
Some area high schools were recognized yesterday for having the nation's highest percentage of seniors receiving scores of 3 and above on AP exams. The Thomas Jefferson High School for Science and Technology in Fairfax County was best among large schools in calculus BC, chemistry, French language, French literature, U.S. government and politics and U.S. history. Walter Johnson High School in Montgomery County was best in world history among large schools. Two D.C. private schools were also at the top -- National Cathedral among small schools in French literature, and Sidwell Friends among medium schools in English literature and composition.
Maryland Superintendent of Schools Nancy S. Grasmick attributed the state's AP success to its emphasis on raising minority achievement and participation. Acting Virginia Superintendent of Public Instruction Patricia Wright said her state opened doors to AP courses and other learning opportunities "once reserved for students in elite schools and programs."
Wednesday, January 31, 2007
Letter to the National Math Panel's Teacher Task Group
January 30, 2007
To the National Mathematics Advisory Panel's Teacher Task Group:
After reading the Teachers and the Professional Education of Teachers Task Group report from your January 10-11 meeting, we felt the need to write you. We applaud that you are looking at the relationship between teachers mathematics knowledge and student achievement and that you are looking at models for "mathematics specialists" at the elementary (K-5) level.
A number of state and national reports focused on improving student learning in mathematics and strengthening teachers' understanding of mathematical concepts and instructional pedagogy, have begun to call for the placement of mathematics specialists in public schools. These reports (Adding It Up: Helping Children Learn Mathematics, 2001; Keys to Math Success: A Report from the Maryland Mathematics Commission, 2001; National Council of Teachers of Mathematics Principles and Standards of School Mathematics, 2000; National Mathematics Advisory Panel: A Report from the National Center for Learning Disabilities, 2006; The Mathematical Education of Teachers, 2001) have converged around a common idea.
Each report calls for a mathematics specialist to be placed in schools as a resource for providing ongoing professional development, teaching, curriculum development, assessment, and parent and community education to improve the teaching, learning, and assessment process. The National Council of Teachers of Mathematics Principles and Standards for School Mathematics (2000) states, "There is an urgent and growing need for mathematics teacher-leaders--specialists positioned between classroom teachers and administrators who can assist with the improvement of mathematics education (375)."
We agree there is a need for mathematics specialists, however we believe there is a clear need for them at all grade levels/bands (K-5, 6-8, and 9-12).
As Maryland mathematics leaders who work with state and local school district K-12 mathematics teachers, we believe that there are close relationships between mathematics content knowledge, the use of effective pedagogy, and increased student achievement. However, in reviewing data from the mathematics portion of the 2005 National Assessment of Educational Progress (NAEP), as well as standardized assessment data from individual U.S. states, a clear trend exists. Standardized test scores drop dramatically when students enter the middle school grades (6-8), and then gradually, but slowly, begin to "recover" as students progress through the high school years. There is a sufficient need for mathematics specialists to receive focused training on state of the art practices in exemplary mathematics instruction, research on student learning, providing professional development that leads to positive change, and strategies for teaching and mentoring others.
When observing K-12 mathematics teachers one can usually separate them into two categories: those who have pedagogical knowledge, but lack mathematical content knowledge; and those who have mathematical content knowledge, but lack pedagogical knowledge. While elementary and middle school teachers generally fall into the first category, many high school teachers fall into the second category.
Elementary and middle school mathematics teachers often enter teaching with a wealth of pedagogical knowledge but only a small amount of mathematical content knowledge. Most pre-service K-8 programs give teachers training on numerous instructional techniques while only touching on mathematics content beyond the elementary and middle grades level. Mathematics specialists in grades K-8 would help elementary and middle school mathematics teachers develop deep understanding of the connections between the mathematical topics that they teach in their grade levels and the future mathematics topics that their students will learn.
High school mathematics teachers enter teaching with a great deal of mathematical content knowledge but with very limited pedagogical knowledge. Most secondary mathematics pre-service programs include only one or two methods of instruction courses for teacher-candidates seeking to teach high school mathematics. Teacher-candidates are coming out of these programs with an excellent understanding of mathematics, the connection between the mathematics they will teach, and future mathematics topics the students will learn. But they lack the knowledge of how to best impart the mathematics knowledge to their students. High school teachers need "mathematics specialists" who can help them attain this pedagogical knowledge. Mathematics specialists for grades 9-12 would not only be able to fill any content gaps teachers may have, they would be able to train high school mathematics teachers on best practices in secondary mathematics instruction, connections to STEM related fields, and assist in building (and retaining) a professional learning community amongst mathematics teachers.
Our school district was Maryland's first to respond to the call for mathematics specialists over 6 years ago when we placed five school-based specialists in our lowest performing elementary schools. To date, there are twelve elementary, six middle, and three high school mathematics specialists in twenty-four of our sixty nine schools. Based on the continued need (and success of these individuals) at each level, we have requested local funding for one more mathematics specialist in a middle school and three more in high schools for next school year.
We agree that "mathematics specialists" are needed to develop and retain a qualified, creative, effective mathematics teaching force. We urge that you use this vital opportunity to consider widening your scope of recommendations to include "mathematics specialists" at all grade levels/bands. We believe that all mathematics teachers need to be experts in mathematics content knowledge and mathematics pedagogy, and that "mathematics specialists" are the most effective way to make this happen.
Thank you for considering these important facts as you finalize your task group's recommendations.
Sincerely,
Kay B. Sammons
Coordinator, Elementary (K-5) Mathematics
Howard County Public Schools
Ellicott City, Maryland
B. Scott Ruehl
Coordinator, Secondary (6-12) Mathematics
Howard County Public Schools
Ellicott City, Maryland
Jonathan A. Wray
President-Elect, Maryland Council of Teachers of Mathematics
Secondary (6-12) Mathematics Instructional Facilitator
Howard County Public Schools
Ellicott City, Maryland
To the National Mathematics Advisory Panel's Teacher Task Group:
After reading the Teachers and the Professional Education of Teachers Task Group report from your January 10-11 meeting, we felt the need to write you. We applaud that you are looking at the relationship between teachers mathematics knowledge and student achievement and that you are looking at models for "mathematics specialists" at the elementary (K-5) level.
A number of state and national reports focused on improving student learning in mathematics and strengthening teachers' understanding of mathematical concepts and instructional pedagogy, have begun to call for the placement of mathematics specialists in public schools. These reports (Adding It Up: Helping Children Learn Mathematics, 2001; Keys to Math Success: A Report from the Maryland Mathematics Commission, 2001; National Council of Teachers of Mathematics Principles and Standards of School Mathematics, 2000; National Mathematics Advisory Panel: A Report from the National Center for Learning Disabilities, 2006; The Mathematical Education of Teachers, 2001) have converged around a common idea.
Each report calls for a mathematics specialist to be placed in schools as a resource for providing ongoing professional development, teaching, curriculum development, assessment, and parent and community education to improve the teaching, learning, and assessment process. The National Council of Teachers of Mathematics Principles and Standards for School Mathematics (2000) states, "There is an urgent and growing need for mathematics teacher-leaders--specialists positioned between classroom teachers and administrators who can assist with the improvement of mathematics education (375)."
We agree there is a need for mathematics specialists, however we believe there is a clear need for them at all grade levels/bands (K-5, 6-8, and 9-12).
As Maryland mathematics leaders who work with state and local school district K-12 mathematics teachers, we believe that there are close relationships between mathematics content knowledge, the use of effective pedagogy, and increased student achievement. However, in reviewing data from the mathematics portion of the 2005 National Assessment of Educational Progress (NAEP), as well as standardized assessment data from individual U.S. states, a clear trend exists. Standardized test scores drop dramatically when students enter the middle school grades (6-8), and then gradually, but slowly, begin to "recover" as students progress through the high school years. There is a sufficient need for mathematics specialists to receive focused training on state of the art practices in exemplary mathematics instruction, research on student learning, providing professional development that leads to positive change, and strategies for teaching and mentoring others.
When observing K-12 mathematics teachers one can usually separate them into two categories: those who have pedagogical knowledge, but lack mathematical content knowledge; and those who have mathematical content knowledge, but lack pedagogical knowledge. While elementary and middle school teachers generally fall into the first category, many high school teachers fall into the second category.
Elementary and middle school mathematics teachers often enter teaching with a wealth of pedagogical knowledge but only a small amount of mathematical content knowledge. Most pre-service K-8 programs give teachers training on numerous instructional techniques while only touching on mathematics content beyond the elementary and middle grades level. Mathematics specialists in grades K-8 would help elementary and middle school mathematics teachers develop deep understanding of the connections between the mathematical topics that they teach in their grade levels and the future mathematics topics that their students will learn.
High school mathematics teachers enter teaching with a great deal of mathematical content knowledge but with very limited pedagogical knowledge. Most secondary mathematics pre-service programs include only one or two methods of instruction courses for teacher-candidates seeking to teach high school mathematics. Teacher-candidates are coming out of these programs with an excellent understanding of mathematics, the connection between the mathematics they will teach, and future mathematics topics the students will learn. But they lack the knowledge of how to best impart the mathematics knowledge to their students. High school teachers need "mathematics specialists" who can help them attain this pedagogical knowledge. Mathematics specialists for grades 9-12 would not only be able to fill any content gaps teachers may have, they would be able to train high school mathematics teachers on best practices in secondary mathematics instruction, connections to STEM related fields, and assist in building (and retaining) a professional learning community amongst mathematics teachers.
Our school district was Maryland's first to respond to the call for mathematics specialists over 6 years ago when we placed five school-based specialists in our lowest performing elementary schools. To date, there are twelve elementary, six middle, and three high school mathematics specialists in twenty-four of our sixty nine schools. Based on the continued need (and success of these individuals) at each level, we have requested local funding for one more mathematics specialist in a middle school and three more in high schools for next school year.
We agree that "mathematics specialists" are needed to develop and retain a qualified, creative, effective mathematics teaching force. We urge that you use this vital opportunity to consider widening your scope of recommendations to include "mathematics specialists" at all grade levels/bands. We believe that all mathematics teachers need to be experts in mathematics content knowledge and mathematics pedagogy, and that "mathematics specialists" are the most effective way to make this happen.
Thank you for considering these important facts as you finalize your task group's recommendations.
Sincerely,
Kay B. Sammons
Coordinator, Elementary (K-5) Mathematics
Howard County Public Schools
Ellicott City, Maryland
B. Scott Ruehl
Coordinator, Secondary (6-12) Mathematics
Howard County Public Schools
Ellicott City, Maryland
Jonathan A. Wray
President-Elect, Maryland Council of Teachers of Mathematics
Secondary (6-12) Mathematics Instructional Facilitator
Howard County Public Schools
Ellicott City, Maryland
Tuesday, January 23, 2007
News (or No News) from the National Mathematics Advisory Panel
From Education Week, January 17, 2007, Volume 26, Number 19, p. 8. See http://www.edweek.org/ew/articles/2007/01/17/19math.h26.html
Math Panel Issues Its First Report, But Holds Off on Policy Proposals
By Sean Cavanagh
A national advisory panel studying mathematics instruction has completed an interim report on its work for the White House, though members of the group have not yet offered specific recommendations for improving teaching and learning in that subject.
The Bush administration, which appointed the 17 voting members of the National Mathematics Advisory Panel a year ago, originally had hoped the group's preliminary report would give some specific advice, possibly to help guide the distribution of federal math grants.
But the panel's chairman, former University of Texas President Larry R. Faulkner, said members did not want to issue detailed recommendations before their research is complete. The 16-page interim report instead briefly describes the panel's progress so far, its organization into subcommittees studying different topics, and the rules it is following in its research.
"We are in the midst of a serious review of the evidence," Mr. Faulkner said in an interview from New Orleans, the site of the panel's fifth public meeting. "We're not really in a [sufficiently advanced] state to communicate findings."
Francis M. "Skip" Fennell, a panelist who is the president of the National Council of Teachers of Mathematics, said the group had collected detailed information through four separate committees studying different math topics. That work, however, is still ongoing, he said.
"We now have at least some substantial thinking about where this is moving," he said. "All of the groups need more time to write and flesh things out."
The interim report sets ground rules for how the panel will issue findings, saying that "every assertion or statement of fact in its final report [will] either be labeled as a definition or opinion, or backed up by a citation." The group will also try to convey how strong or weak the pool of research is in every area of math instruction, it says.
President Bush announced the formation of the panel last February, charging it with providing recommendations on how schools and teachers could prepare students for algebra and higher-level math, and identify proven strategies for accomplishing that goal. The panel was asked to produce a preliminary report by Jan. 31 of this year, and a final document by Feb. 28, 2008. Mr. Faulkner said a complete set of recommendations would be issued in that final report.
Modeled on Reading
Mr. Bush formed the math panel amid a flurry of proposals made last year by his administration and federal lawmakers on math and science education. While most of those proposals stalled in Congress, the panel pressed ahead with its work, holding meetings across the country to review research, debate approaches to math instruction, and hear testimony from experts and the general public. Only last week, however, new legislation was unveiled with the goal of shoring up students' mastery of math and science through voluntary national standards.
Bush administration officials modeled the math group after the National Reading Panel, which was convened during the Clinton presidency to identify effective classroom strategies in that subject. The reading panel's report provided a basis for the Bush administration's policies in awarding grants through its $1 billion-a-year Reading First program that has been mired in controversy.
The impact of the math panel's activity, however, is less certain. Administration officials said last year they hoped the panel's work-even its interim report-could shape the distribution of grants under the president's proposed "Math Now" initiative, a $250 million grant program to support instruction in elementary and middle schools. So far, Congress has neither appropriated funds for nor authorized the creation of Math Now.
How Much Impact?
Mr. Faulkner acknowledged that the goals for the interim report have changed, because of both the uncertainty about Math Now and the panelists' realization of how much work they have left to do. He believes administration officials were aware of the group's progress, noting that Raymond J. Simon, the deputy U.S. secretary of education, serves on the panel as a nonvoting member.
During their meetings, several panelists have pointed out that several federally commissioned studies on how to improve math education have been conducted over the past 20 years-reports that were well received but ultimately had little bearing on school policy. They said they wanted their work to have a broader reach.
Math experts have engaged in bitter debates over the years about how best to teach math. That divide is often defined as pitting advocates of teaching basic skills against those who argue that students should be exposed to more conceptual learning.
Many in the math field were encouraged by the publication of "Curriculum Focal Points," a document released by the influential National Council of Teachers of Mathematics in September. ("Math Organization Attempts to Bring Focus to Subject," Sept. 20, 2006: http://www.edweek.org/ew/articles/2006/09/20/04nctm.h26.html)
The 41-page guidelines offer a more concise, streamlined set of topics than teachers have had previously, and observers say the guidance will help educators sort through often-contradictory priorities presented in textbooks and academic standards.
Mr. Faulkner said while the panel "was not prepared to endorse a curriculum," there was a sense among the group's members that the NCTM was "on good footing" in having published the document.
Math Panel Issues Its First Report, But Holds Off on Policy Proposals
By Sean Cavanagh
A national advisory panel studying mathematics instruction has completed an interim report on its work for the White House, though members of the group have not yet offered specific recommendations for improving teaching and learning in that subject.
The Bush administration, which appointed the 17 voting members of the National Mathematics Advisory Panel a year ago, originally had hoped the group's preliminary report would give some specific advice, possibly to help guide the distribution of federal math grants.
But the panel's chairman, former University of Texas President Larry R. Faulkner, said members did not want to issue detailed recommendations before their research is complete. The 16-page interim report instead briefly describes the panel's progress so far, its organization into subcommittees studying different topics, and the rules it is following in its research.
"We are in the midst of a serious review of the evidence," Mr. Faulkner said in an interview from New Orleans, the site of the panel's fifth public meeting. "We're not really in a [sufficiently advanced] state to communicate findings."
Francis M. "Skip" Fennell, a panelist who is the president of the National Council of Teachers of Mathematics, said the group had collected detailed information through four separate committees studying different math topics. That work, however, is still ongoing, he said.
"We now have at least some substantial thinking about where this is moving," he said. "All of the groups need more time to write and flesh things out."
The interim report sets ground rules for how the panel will issue findings, saying that "every assertion or statement of fact in its final report [will] either be labeled as a definition or opinion, or backed up by a citation." The group will also try to convey how strong or weak the pool of research is in every area of math instruction, it says.
President Bush announced the formation of the panel last February, charging it with providing recommendations on how schools and teachers could prepare students for algebra and higher-level math, and identify proven strategies for accomplishing that goal. The panel was asked to produce a preliminary report by Jan. 31 of this year, and a final document by Feb. 28, 2008. Mr. Faulkner said a complete set of recommendations would be issued in that final report.
Modeled on Reading
Mr. Bush formed the math panel amid a flurry of proposals made last year by his administration and federal lawmakers on math and science education. While most of those proposals stalled in Congress, the panel pressed ahead with its work, holding meetings across the country to review research, debate approaches to math instruction, and hear testimony from experts and the general public. Only last week, however, new legislation was unveiled with the goal of shoring up students' mastery of math and science through voluntary national standards.
Bush administration officials modeled the math group after the National Reading Panel, which was convened during the Clinton presidency to identify effective classroom strategies in that subject. The reading panel's report provided a basis for the Bush administration's policies in awarding grants through its $1 billion-a-year Reading First program that has been mired in controversy.
The impact of the math panel's activity, however, is less certain. Administration officials said last year they hoped the panel's work-even its interim report-could shape the distribution of grants under the president's proposed "Math Now" initiative, a $250 million grant program to support instruction in elementary and middle schools. So far, Congress has neither appropriated funds for nor authorized the creation of Math Now.
How Much Impact?
Mr. Faulkner acknowledged that the goals for the interim report have changed, because of both the uncertainty about Math Now and the panelists' realization of how much work they have left to do. He believes administration officials were aware of the group's progress, noting that Raymond J. Simon, the deputy U.S. secretary of education, serves on the panel as a nonvoting member.
During their meetings, several panelists have pointed out that several federally commissioned studies on how to improve math education have been conducted over the past 20 years-reports that were well received but ultimately had little bearing on school policy. They said they wanted their work to have a broader reach.
Math experts have engaged in bitter debates over the years about how best to teach math. That divide is often defined as pitting advocates of teaching basic skills against those who argue that students should be exposed to more conceptual learning.
Many in the math field were encouraged by the publication of "Curriculum Focal Points," a document released by the influential National Council of Teachers of Mathematics in September. ("Math Organization Attempts to Bring Focus to Subject," Sept. 20, 2006: http://www.edweek.org/ew/articles/2006/09/20/04nctm.h26.html)
The 41-page guidelines offer a more concise, streamlined set of topics than teachers have had previously, and observers say the guidance will help educators sort through often-contradictory priorities presented in textbooks and academic standards.
Mr. Faulkner said while the panel "was not prepared to endorse a curriculum," there was a sense among the group's members that the NCTM was "on good footing" in having published the document.
Saturday, January 20, 2007
U.S. Education Posting "Continuous improvement"
http://www.washingtonpost.com/wp-dyn/content/article/2007/01/19/AR2007011901360.html
Printed in the Washington Post
5 Myths About U.S. Kids Outclassed by the Rest of the World
Printed in the Washington Post
5 Myths About U.S. Kids Outclassed by the Rest of the World
By Paul Farhi
Sunday, January 21, 2007; B02
The usual hand-wringing accompanied the Department of Education's release late last year of new statistics on how U.S. students performed on international tests. How will the United States compete in the global economy, went the lament, when our students lag behind the likes of Singapore and Hong Kong in math and science? American fourth-graders ranked 12th in the world on one international math test, and eighth-graders were 14th. Is this further evidence of the failure of the nation's schools?
Not exactly. In fact, a closer look at how our kids perform against the international "competition" suggests that this story line may contain more than a few myths:
1. U.S. students rate poorly compared with those in the rest of the world.
This is true only if you cherry-pick the results. University of Pennsylvania researchers Erling E. Boe and Sujie Shin looked at six major international tests in reading, math, science and civics conducted from 1991 through 2001. Their conclusion: Americans are above average when compared with 22 other industrialized nations. In civics, no nation scored significantly higher than the United States; in reading, only 13 percent did. Even in math and science -- the two subjects considered "vital" to future technological competitiveness -- the United States fell in roughly the middle of the pack. No gold star, but hardly a crisis, either.
More interesting, when compared with students in the world's most industrialized countries, U.S. students were on par with the others in every subject (and outperformed everyone in civics). And every Western country, not just the United States, lagged behind Japan in math and science, suggesting that the "achievement gap" in these subjects is an East-West phenomenon rather than an American one.
2. U.S. students are falling behind.
Actually, American students are mostly improving, or at worst holding their own. As the Trends in International Mathematics and Science Study (TIMSS) shows, America's eighth-graders improved their math and science scores in 1995, 1999 and 2003. Only students in Hong Kong, Latvia and Lithuania -- three relatively tiny and homogenous entities -- improved more than the United States did. Indeed, no nation included in the major international rankings educates as many poor students or as ethnically diverse a population as does the United States. Yet even as the percentage of historically low-achieving students has increased, our test scores have risen. Unfortunately, news accounts focus on the relative position of American students (are we No. 1 or No. 12?) rather than on their absolute performance (did they improve, regardless of what others did?).
3. U.S. students won't be well prepared for the modern workforce.
This myth has been bandied around since at least the turn of the century -- the 19th century -- by business leaders who blame schools for inadequately preparing workers. It's part of the never-ending notion that U.S. schools are in crisis.
Education researcher Gerald W. Bracey cites a March 1957 cover story in Life magazine -- at the height of post-Sputnik paranoia over Soviet scientific prowess -- that contrasts the stern, rigorous education of a Moscow teenager (complicated physics and chemistry courses) with the carefree lifestyle of a Chicago youth (rehearsals for his high school musical). The cover headline: "Crisis in Education." In the 1980s, when Japan seemed to be an unstoppable economic juggernaut, the seminal policy manifesto "A Nation at Risk," written by a blue-ribbon panel at the behest of the Department of Education, warned that deficiencies in high school graduates "come at a time when the demand for highly skilled workers in new fields is accelerating rapidly."
Despite these doomsday cases, the United States survived and, by many measures, bested the competition. Today, with the Soviet Union a memory and Japan facing its own economic and demographic problems, the anxieties have shifted to China and other Asian rivals.
4. Bad schooling has undermined America's competitiveness.
This canard -- perhaps the biggest of them all -- was given a boost by the recent World Economic Forum survey of international economies. Typically this annual survey ranks the U.S. economy as the most competitive in the world, but last year it put the United States in sixth place. However, the drop had nothing to do with test scores or school performance. Rather, the forum cited U.S. trade and budget deficits, a low savings rate, tax cuts and the federal government's increased spending on defense and homeland security.
Another recent survey, by the Council on Competitiveness, a Washington-based business advisory group, found that over the past two decades the U.S. economy grew faster than that of any other advanced nation, and generated a third of the world's economic growth. Yet this performance followed a period in which the authors of "A Nation at Risk" were warning that a "rising tide of [educational] mediocrity . . . threatens our very future as a nation." That was in 1983. Those high-school mediocrities are now turning 40, and presumably have been playing a part in helping the U.S. economy grow "faster than any other advanced economy" over the past two decades.
A dynamic economy is much more than the sum of its test scores. It's part of a culture that rewards innovation and risk-taking, and values unconventional problem-solving. Much of this is nurtured in our schools, even if it can't be quantified on a test.
Recently, Newsweek International's Fareed Zakaria noted Singapore's success on international math and science exams, but asked Education Minister Tharman Shanmugaratnam why Singapore produced so few top-ranked scientists, entrepreneurs, inventors, business executives and academics. "We both have meritocracies," he replied. America's "is a talent meritocracy, ours is an exam meritocracy. There are some parts of the intellect that we are not able to test well -- like creativity, curiosity, a sense of adventure, ambition. Most of all, America has a culture of learning that challenges conventional wisdom, even if it means challenging authority. These are the areas where Singapore must learn from America."
Our current (and past) economic success suggests something that educational alarmists and their sky-is-falling friends in the news media seem reluctant to admit: American schools may have a lot to fix, but they may be doing a few things right, too.
5. How we stack up on international tests matters, if only for national pride.
Yes, we're a nation of strivers and self-improvers; the American drive to be the biggest and the best in everything seems part of our national character. But if being No. 1 in education is our goal, shouldn't we also want to be No. 1 in all the things closely linked to academic achievement, such as quality of childhood health care and reduction of childhood poverty? National pride can be a destructive concept, especially when it views learning as a zero-sum game ("their" gains are "our" losses, and vice versa). Continuous improvement should be our goal, regardless of whether we're No.1 in the test-score Olympics.
Thursday, January 18, 2007
Dr. Fennell's Views on Mathematics Assessment
From NCTM's President's Message http://www.nctm.org/news/president/2006_12president.htm
Originally published in December 2006
Go Ahead, Teach to the Test!
by Dr. Francis "Skip" Fennell, NCTM President
Since NCTM released Curriculum Focal Points, I have learned that columnists can say whatever they want in a headline to lure readers into their article. You have to admit, my headline grabbed you, didn’t it? Well, now that I have your attention, I’ll get serious. Let’s talk about assessment—formative assessment, to be exact. Read more.
Originally published in December 2006
Go Ahead, Teach to the Test!
by Dr. Francis "Skip" Fennell, NCTM President
Since NCTM released Curriculum Focal Points, I have learned that columnists can say whatever they want in a headline to lure readers into their article. You have to admit, my headline grabbed you, didn’t it? Well, now that I have your attention, I’ll get serious. Let’s talk about assessment—formative assessment, to be exact. Read more.
Tuesday, January 16, 2007
Are K-8 Schools Better?
http://www.baltimoresun.com/news/education/bal-te.md.middle16jan16001519,0,7855121.story?coll=bal-home-headlines
From the Baltimore Sun
Study raises doubts on K-8
JHU research finds no academic benefit over middle schools, undercuts city's push
By Liz Bowie
Sun reporter
January 16, 2007
Johns Hopkins University researchers have concluded that expanding elementary schools to sixth, seventh and eighth grades does not help adolescents do better academically - a finding that raises questions about changes in Baltimore and other urban districts.
In a multiyear study of Philadelphia's newest schools for kindergarten through eighth grade, the researchers found no significant difference in achievement between those students and their peers in traditional middle schools of sixth through eighth grades.
Worried about an achievement slump in the middle grades, Baltimore and several other urban systems are returning to the concept of putting adolescents in schools with elementary students.
"District after district is getting misled by thinking our K-8 schools are doing better than our middle schools," said Douglas Mac Iver, a Hopkins education researcher who has studied middle schools for more than a decade.
Shutting down a middle school in a neighborhood with gang violence and open-air drug markets to open a new school will not insulate the students from those influences, he said: "The grade span itself is not some magic bullet."
Baltimore has shifted students from traditional middle schools into K-8 schools, opening 18 of the new schools last fall and shutting one middle school.
The school board plans to expand up to 12 more elementaries to K-8 schools in coming years.
Philadelphia and Baltimore made the move based on test data that showed their existing K-8 students scored better on tests. The Baltimore schools' chief academic officer, Linda Chinnia, said test data from the city's schools was dramatic.
For instance, 54 percent of sixth-graders in the established K-8 schools passed the state reading test, compared with 36 percent in the traditional middle schools. Attendance was better and behavior problems fewer in the K-8 schools, she said.
But Mac Iver and his wife, Martha Mac Iver, said the data on the established K-8 schools could be skewed. At least in Philadelphia, he said, those older schools are in slightly more affluent areas of the city, and they tend to be able to attract and retain better teachers.
Hard to teach
For several decades, educators have debated where to put 11- to 14-year-olds, the most difficult-to-teach age because of the rapid physical and emotional development that occurs during those years.
Historically, when most children left school after eighth grade, schools were organized in one building. Then, in the middle of the 20th century, educators decided to keep sixth-graders in elementary schools and move seventh-, eighth- and ninth-graders into junior high schools.
Change came again in the late 1960s and early 1970s, when school districts began building middle schools for sixth through eighth grades, which today is the most common configuration, according to Alan Summers, director of professional development at the National Middle School Association.
"Currently, there is no research that says what should be the most effective grade configuration," Summers said.
The Mac Ivers' research did not look just at test scores from one grade at a middle school compared with the same grade at a K-8 school, as most school systems do.
The research went deeper, investigating how good a job middle schools did in educating the students over three years. The researchers looked at the growth students achieved in their three middle school years.
The research could help guide administrators deciding how to reform middle schools in their districts.
What it shows, Mac Iver said, is that the quality of the teaching, the curriculum and other factors matter just as much.
Because Baltimore's major push toward having many more K-8 schools is new, there is no statistical information on how the new schools are working.
But the city also is trying to improve the rigor of academics, standardizing the curriculum in all the middle grades and looking at requiring all eighth-graders to take algebra.
Chinnia said the district does not intend to use one model for all middle schools but rather to offer parents and students a variety of options for middle school.
Some parents feel more comfortable having their students in their neighborhood elementary school, she said, while others would prefer to have their children in a large middle school with more course offerings.
Math programs
Mac Iver said his research indicates that students who were taught using several different reform math programs scored higher than their peers who did not use those programs.
"Our research has consistently shown the positive effects of National Science Foundation-supported reform mathematics programs on student achievement," he said, adding that it must include coaching for teachers and other kinds of teacher training.
As inner-city middle schools have grown tougher, parents have often lobbied to have their children stay in the neighborhood, where they believe children will be safer.
Besides Baltimore and Philadelphia, other cities have also begun shrinking the number of middle schools and increasing the K-8 schools. Dayton, Ohio, is in the process of eliminating all of its middle schools; New York has expanded 42 elementary schools to eighth grade and will close 14 of its failing middle schools.
Teachers are key
Summers believes the pitfall in creating K-8 schools is that the school might not be large enough to provide teachers who specialize. For instance, a math teacher in a small school might have to teach Algebra I and other levels of math, or math and science, and therefore might not be as experienced in teaching one subject.
And he said that sometimes the developmental needs of middle-schoolers are lost in K-8 schools.
"The desire to go to K-8 is fine as long as you treat them as early adolescents and not elementary school kids," he said.
From the Baltimore Sun
Study raises doubts on K-8
JHU research finds no academic benefit over middle schools, undercuts city's push
By Liz Bowie
Sun reporter
January 16, 2007
Johns Hopkins University researchers have concluded that expanding elementary schools to sixth, seventh and eighth grades does not help adolescents do better academically - a finding that raises questions about changes in Baltimore and other urban districts.
In a multiyear study of Philadelphia's newest schools for kindergarten through eighth grade, the researchers found no significant difference in achievement between those students and their peers in traditional middle schools of sixth through eighth grades.
Worried about an achievement slump in the middle grades, Baltimore and several other urban systems are returning to the concept of putting adolescents in schools with elementary students.
"District after district is getting misled by thinking our K-8 schools are doing better than our middle schools," said Douglas Mac Iver, a Hopkins education researcher who has studied middle schools for more than a decade.
Shutting down a middle school in a neighborhood with gang violence and open-air drug markets to open a new school will not insulate the students from those influences, he said: "The grade span itself is not some magic bullet."
Baltimore has shifted students from traditional middle schools into K-8 schools, opening 18 of the new schools last fall and shutting one middle school.
The school board plans to expand up to 12 more elementaries to K-8 schools in coming years.
Philadelphia and Baltimore made the move based on test data that showed their existing K-8 students scored better on tests. The Baltimore schools' chief academic officer, Linda Chinnia, said test data from the city's schools was dramatic.
For instance, 54 percent of sixth-graders in the established K-8 schools passed the state reading test, compared with 36 percent in the traditional middle schools. Attendance was better and behavior problems fewer in the K-8 schools, she said.
But Mac Iver and his wife, Martha Mac Iver, said the data on the established K-8 schools could be skewed. At least in Philadelphia, he said, those older schools are in slightly more affluent areas of the city, and they tend to be able to attract and retain better teachers.
Hard to teach
For several decades, educators have debated where to put 11- to 14-year-olds, the most difficult-to-teach age because of the rapid physical and emotional development that occurs during those years.
Historically, when most children left school after eighth grade, schools were organized in one building. Then, in the middle of the 20th century, educators decided to keep sixth-graders in elementary schools and move seventh-, eighth- and ninth-graders into junior high schools.
Change came again in the late 1960s and early 1970s, when school districts began building middle schools for sixth through eighth grades, which today is the most common configuration, according to Alan Summers, director of professional development at the National Middle School Association.
"Currently, there is no research that says what should be the most effective grade configuration," Summers said.
The Mac Ivers' research did not look just at test scores from one grade at a middle school compared with the same grade at a K-8 school, as most school systems do.
The research went deeper, investigating how good a job middle schools did in educating the students over three years. The researchers looked at the growth students achieved in their three middle school years.
The research could help guide administrators deciding how to reform middle schools in their districts.
What it shows, Mac Iver said, is that the quality of the teaching, the curriculum and other factors matter just as much.
Because Baltimore's major push toward having many more K-8 schools is new, there is no statistical information on how the new schools are working.
But the city also is trying to improve the rigor of academics, standardizing the curriculum in all the middle grades and looking at requiring all eighth-graders to take algebra.
Chinnia said the district does not intend to use one model for all middle schools but rather to offer parents and students a variety of options for middle school.
Some parents feel more comfortable having their students in their neighborhood elementary school, she said, while others would prefer to have their children in a large middle school with more course offerings.
Math programs
Mac Iver said his research indicates that students who were taught using several different reform math programs scored higher than their peers who did not use those programs.
"Our research has consistently shown the positive effects of National Science Foundation-supported reform mathematics programs on student achievement," he said, adding that it must include coaching for teachers and other kinds of teacher training.
As inner-city middle schools have grown tougher, parents have often lobbied to have their children stay in the neighborhood, where they believe children will be safer.
Besides Baltimore and Philadelphia, other cities have also begun shrinking the number of middle schools and increasing the K-8 schools. Dayton, Ohio, is in the process of eliminating all of its middle schools; New York has expanded 42 elementary schools to eighth grade and will close 14 of its failing middle schools.
Teachers are key
Summers believes the pitfall in creating K-8 schools is that the school might not be large enough to provide teachers who specialize. For instance, a math teacher in a small school might have to teach Algebra I and other levels of math, or math and science, and therefore might not be as experienced in teaching one subject.
And he said that sometimes the developmental needs of middle-schoolers are lost in K-8 schools.
"The desire to go to K-8 is fine as long as you treat them as early adolescents and not elementary school kids," he said.
Thursday, January 11, 2007
CSMC State Mathematics Standards Database
The Center for the Study of Mathematics Curriculum (CSMC) has provided links to current online state-level mathematics curriculum frameworks. This represents the current set of state mathematics curricula.
To view this list, click here.
To view this list, click here.
NCLB Up for Renewal
Sounds like both parties of Congress can be blamed for lack of funding....
From the Contra Costa Times [CA], Thursday, January 4, 2007. See
http://www.contracostatimes.com/mld/cctimes/news/politics/16377135.htm
Bush to Seek Renewal of Education Law
By Nancy Zuckerbrod
[Associated Press]
WASHINGTON - President Bush plans to meet with lawmakers next week to boost efforts to renew the No Child Left Behind education law, according to a Democratic congressional aide.
The top Democrats and Republicans on the House and Senate committees that deal with education issues planned to attend the White House meeting Monday, the aide said on the condition of anonymity because the White House had not announced the session.
Monday is also the day the Bush administration is commemorating the fifth anniversary of what is widely considered the most significant federal education law in decades.
Education Secretary Margaret Spellings, in an interview with The Associated Press on Wednesday, said she was optimistic the law would be renewed for five more years. She said it is a natural issue on which Bush and Democrats, who won control of Congress in November, can come together.
"It's on everybody's list of things where we might forge agreement as we have done before," she said.
The law seeks to ensure that all children can read and do math at grade level by 2014, which has placed unprecedented demands on schools. They have been required to step up testing, raise teacher quality and place more attention on the achievements of minority children.
Poor schools that get federal aid but do not make enough progress must provide tutoring, offer public school choice to students or initiate other reforms such as overhauling their staffs.
Spellings said there were a few "bright-line principles" that the administration would not agree to alter under a rewrite of the law. Among them is the requirement that all students are proficient in reading and math by 2014 - a goal many observers call unrealistic.
Spellings said the administration was open to debating how student achievement should be measured. Critics, including the teachers' unions, have said the current law does not give enough credit to schools that make significant strides in student achievement but fall short of reaching an annual target.
"There is too much punishing going on," said Reg Weaver, president of the National Education Association, the largest teachers union in the country. Weaver also called the law "grossly underfunded."
Sen. Edward M. Kennedy, D-Mass., and Rep. George Miller, D-Calif., who are to lead the committees overseeing education, say the administration has provided about $50 billion less than originally called for by Congress.
Republicans say it is common practice for legislation to be funded at less than the full level Congress authorizes.
Spellings declined to preview the amount Bush would seek when he releases his annual budget in February. She did indicate an interest in getting more money to teachers who work in schools that have difficulty attracting people.
Bush sought $500 million from Congress for that purpose last year and got about $100 million.
"Our best teachers, or are most experienced teachers, are in places with our least challenged learners," Spellings said.
Spellings also reaffirmed the administration's view that the law, which focuses on early and middle grades, should be expanded in high schools.
From the Contra Costa Times [CA], Thursday, January 4, 2007. See
http://www.contracostatimes.com/mld/cctimes/news/politics/16377135.htm
Bush to Seek Renewal of Education Law
By Nancy Zuckerbrod
[Associated Press]
WASHINGTON - President Bush plans to meet with lawmakers next week to boost efforts to renew the No Child Left Behind education law, according to a Democratic congressional aide.
The top Democrats and Republicans on the House and Senate committees that deal with education issues planned to attend the White House meeting Monday, the aide said on the condition of anonymity because the White House had not announced the session.
Monday is also the day the Bush administration is commemorating the fifth anniversary of what is widely considered the most significant federal education law in decades.
Education Secretary Margaret Spellings, in an interview with The Associated Press on Wednesday, said she was optimistic the law would be renewed for five more years. She said it is a natural issue on which Bush and Democrats, who won control of Congress in November, can come together.
"It's on everybody's list of things where we might forge agreement as we have done before," she said.
The law seeks to ensure that all children can read and do math at grade level by 2014, which has placed unprecedented demands on schools. They have been required to step up testing, raise teacher quality and place more attention on the achievements of minority children.
Poor schools that get federal aid but do not make enough progress must provide tutoring, offer public school choice to students or initiate other reforms such as overhauling their staffs.
Spellings said there were a few "bright-line principles" that the administration would not agree to alter under a rewrite of the law. Among them is the requirement that all students are proficient in reading and math by 2014 - a goal many observers call unrealistic.
Spellings said the administration was open to debating how student achievement should be measured. Critics, including the teachers' unions, have said the current law does not give enough credit to schools that make significant strides in student achievement but fall short of reaching an annual target.
"There is too much punishing going on," said Reg Weaver, president of the National Education Association, the largest teachers union in the country. Weaver also called the law "grossly underfunded."
Sen. Edward M. Kennedy, D-Mass., and Rep. George Miller, D-Calif., who are to lead the committees overseeing education, say the administration has provided about $50 billion less than originally called for by Congress.
Republicans say it is common practice for legislation to be funded at less than the full level Congress authorizes.
Spellings declined to preview the amount Bush would seek when he releases his annual budget in February. She did indicate an interest in getting more money to teachers who work in schools that have difficulty attracting people.
Bush sought $500 million from Congress for that purpose last year and got about $100 million.
"Our best teachers, or are most experienced teachers, are in places with our least challenged learners," Spellings said.
Spellings also reaffirmed the administration's view that the law, which focuses on early and middle grades, should be expanded in high schools.
Why You Should Learn Algebra
This reading reminds me of some statistics that I have read (Wynn 2005) that support mathematics and science as important "Gatekeepers" for those with a college-bound focus.
From the Los Angeles Times, Friday, January 5, 2007. See http://www.latimes.com/news/printedition/asection/la-oe-eggen5jan05,1,2836776.story
Why You Should Learn Algebra
Those who complain about its impracticality ignore that math teaches the mind how to think.
By David Eggenschwiler
David Eggenschwiler is an English professor emeritus at USC.
EVERY YEAR, as many California high school seniors struggle with basic algebra, which is required for graduation, Times readers complain, "Who needs it? How many students will ever use it?" Well, I use it every day; I'm using it now, even though I haven't worked an algebraic equation since my son was in the seventh grade several years ago.
Mathematics and science are unnatural practices. As physics professor Alan Cromer has brutally and elegantly written, "the human mind wasn't designed to study physics," and of course mathematics is the language of physics. "Design" here does not indicate an intelligent designer, which would suggest a creator with a math phobia. Rather it indicates evolutionary processes by which the human brain and mind have come to be what they are.
During the approximately 2 million years that it took for our Homo forebears to progress from habilis to sapiens, they had little use for mathematical reasoning abilities. Their sapientia seems to have been more suited in a good Darwinian sense to the immediate demands of their survival, such as eating, mating and avoiding premature death. Whether for good or ill, as time may tell, our situations have changed much in the last few thousand years, and so have demands on our poor, lagging minds. I don't mean only the obvious and oft-repeated claim that technical jobs require greater skills. That is clear enough in auto mechanics and computer programming. I mean the need to think abstractly, systematically and rationally in various ways.
Science and mathematics have the most exacting demands for such thinking, but there are many other disciplines that require it. Even the practices of critical reading and writing that I teach are soft but still demanding forms of rationality, and I occasionally fear that the human mind was not designed to study them either.
Fortunately, however, the mind can be altered; the brain can learn to function in different ways. We can even, if pushed hard enough, learn to think in what physicist Lewis Wolpert has called "the unnatural nature of science." Because our minds are not greatly civilized into reason (as political speeches show), we need some hard instruction to learn to do what we do not do naturally, and as the ancient Greeks discovered, mathematics is a fine schoolmaster (or mistress) for that purpose. In most scholastic and academic disciplines, what you learn to think about is not as important as how you learn to think.
I encourage my college honor students to think in odd, even deviant ways, but I couldn't do that if they had not already learned how to think abstractly and systematically. They have taken their algebra and physics and are ready to think still differently, even while becoming creative writers and musicians.
One of the most brilliantly wacky English professors I know once studied engineering. I was going to be a physicist before I was seduced into the pleasant valleys of the social sciences and humanities.
So let us not hear repeatedly that high school algebra is a waste of time because it does not directly train students for the job market. Even in a vocational program, it teaches the mind how to think. In some cases it might even teach students to think about the universe, which is a very nice way to spend one's life.
Let us instead ask the harder question: How can we better prepare students to study algebra? It would surely not be easy, but it is worth doing.
- 83% of all students who take Algebra I and Geometry go to college.
- Only 27% of low-income students who do not take Algebra I and Geometry go to college.
- Low-income students who take Algebra I are 300% more likely to go to college than those who don’t.
- 89% of students who take Chemistry go to college.
From the Los Angeles Times, Friday, January 5, 2007. See http://www.latimes.com/news/printedition/asection/la-oe-eggen5jan05,1,2836776.story
Why You Should Learn Algebra
Those who complain about its impracticality ignore that math teaches the mind how to think.
By David Eggenschwiler
David Eggenschwiler is an English professor emeritus at USC.
EVERY YEAR, as many California high school seniors struggle with basic algebra, which is required for graduation, Times readers complain, "Who needs it? How many students will ever use it?" Well, I use it every day; I'm using it now, even though I haven't worked an algebraic equation since my son was in the seventh grade several years ago.
Mathematics and science are unnatural practices. As physics professor Alan Cromer has brutally and elegantly written, "the human mind wasn't designed to study physics," and of course mathematics is the language of physics. "Design" here does not indicate an intelligent designer, which would suggest a creator with a math phobia. Rather it indicates evolutionary processes by which the human brain and mind have come to be what they are.
During the approximately 2 million years that it took for our Homo forebears to progress from habilis to sapiens, they had little use for mathematical reasoning abilities. Their sapientia seems to have been more suited in a good Darwinian sense to the immediate demands of their survival, such as eating, mating and avoiding premature death. Whether for good or ill, as time may tell, our situations have changed much in the last few thousand years, and so have demands on our poor, lagging minds. I don't mean only the obvious and oft-repeated claim that technical jobs require greater skills. That is clear enough in auto mechanics and computer programming. I mean the need to think abstractly, systematically and rationally in various ways.
Science and mathematics have the most exacting demands for such thinking, but there are many other disciplines that require it. Even the practices of critical reading and writing that I teach are soft but still demanding forms of rationality, and I occasionally fear that the human mind was not designed to study them either.
Fortunately, however, the mind can be altered; the brain can learn to function in different ways. We can even, if pushed hard enough, learn to think in what physicist Lewis Wolpert has called "the unnatural nature of science." Because our minds are not greatly civilized into reason (as political speeches show), we need some hard instruction to learn to do what we do not do naturally, and as the ancient Greeks discovered, mathematics is a fine schoolmaster (or mistress) for that purpose. In most scholastic and academic disciplines, what you learn to think about is not as important as how you learn to think.
I encourage my college honor students to think in odd, even deviant ways, but I couldn't do that if they had not already learned how to think abstractly and systematically. They have taken their algebra and physics and are ready to think still differently, even while becoming creative writers and musicians.
One of the most brilliantly wacky English professors I know once studied engineering. I was going to be a physicist before I was seduced into the pleasant valleys of the social sciences and humanities.
So let us not hear repeatedly that high school algebra is a waste of time because it does not directly train students for the job market. Even in a vocational program, it teaches the mind how to think. In some cases it might even teach students to think about the universe, which is a very nice way to spend one's life.
Let us instead ask the harder question: How can we better prepare students to study algebra? It would surely not be easy, but it is worth doing.
Wednesday, January 10, 2007
A Response to "Can less equal more?"
The following is a letter to the editor written in response to Liz Bowie's Baltimore Sun article, "Can less equal more?"
January 2, 2007
Dear Ms. Bowie,
I want to thank you for your article's attention to NCTM's Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics, a very important document and topic in the field of mathematics education. I should point out, however, that the following statement in your article reveals a basic misunderstanding of the focal points' impact on potential mathematics curriculum revisions at the state and local levels. You write:
Maryland, for instance, has between 50 and 60 objectives for each grade. The math council would narrow that to three. For instance, for fourth grade, the council says students should learn quick recall of multiplication and division facts, have an understanding of decimals and fractions and an understanding of area, including how to find the area of two-dimensional shapes.
The focal points are not synonymous with mere objectives/indicators. In fact, "These curriculum focal points should be considered as major instructional goals and desirable learning expectations, not as a list of objectives for students to master (NCTM, p. 10)."
Unfortunately, your statement incorrectly leads readers to believe that the focal points are merely a subset of objectives, that can be potentially drawn out from the 50-60 or so indicators contained in a given grade level's Maryland Voluntary State Curriculum (VSC). As Maryland has entered the dialogue/analysis stage to investigate how we will best implement the Curriculum Focal Points into the development of Prekindergarten-Grade 8 mathematics curriculum, you can probably imagine the confusion readers will have when they read the statement in your article.
Additionally NCTM states, "The set of curriculum focal points described here represents an attempt to provide curriculum developers with a clear organizational model for establishing a mathematics curriculum from prekindergarten through grade 8 by identifying for each grade level important content that can build connected and integrated mathematical understanding. The curriculum focal points and their accompanying "connections' to related content outline instructional targets for a basic, integrated, grade-by-grade framework for a coherent mathematics curriculum (p. 7)."
These connections, physically located to the right of the actual focal points for each specific grade level, can be found beginning on page 11 and ending on page 20. Take page 16, for example (Curriculum Focal Points and Connections for Grade 4). Reading the full page, you will find that the entire body of ideas presented here (not just the statements written in bold print) make up a coherent set of related topics, concepts, skills, and ideas, that if taught well, would favorably impact the mathematical learning of a fourth grader.
When approached by local journalists, talk show hosts and producers, teachers, administrators, publishers, bloggers, parents, and other interested individual's about NCTM's Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics and its impact on mathematics in Maryland, I encourage all to thoroughly read the 41 page document for further clarity (See: http://www.nctm.org/focalpoints). It is written very plainly and leaves little room for ambiguity.
Sincerely,
Jon Wray
President-Elect, Maryland Council of Teachers of Mathematics (MCTM)
January 2, 2007
Dear Ms. Bowie,
I want to thank you for your article's attention to NCTM's Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics, a very important document and topic in the field of mathematics education. I should point out, however, that the following statement in your article reveals a basic misunderstanding of the focal points' impact on potential mathematics curriculum revisions at the state and local levels. You write:
Maryland, for instance, has between 50 and 60 objectives for each grade. The math council would narrow that to three. For instance, for fourth grade, the council says students should learn quick recall of multiplication and division facts, have an understanding of decimals and fractions and an understanding of area, including how to find the area of two-dimensional shapes.
The focal points are not synonymous with mere objectives/indicators. In fact, "These curriculum focal points should be considered as major instructional goals and desirable learning expectations, not as a list of objectives for students to master (NCTM, p. 10)."
Unfortunately, your statement incorrectly leads readers to believe that the focal points are merely a subset of objectives, that can be potentially drawn out from the 50-60 or so indicators contained in a given grade level's Maryland Voluntary State Curriculum (VSC). As Maryland has entered the dialogue/analysis stage to investigate how we will best implement the Curriculum Focal Points into the development of Prekindergarten-Grade 8 mathematics curriculum, you can probably imagine the confusion readers will have when they read the statement in your article.
Additionally NCTM states, "The set of curriculum focal points described here represents an attempt to provide curriculum developers with a clear organizational model for establishing a mathematics curriculum from prekindergarten through grade 8 by identifying for each grade level important content that can build connected and integrated mathematical understanding. The curriculum focal points and their accompanying "connections' to related content outline instructional targets for a basic, integrated, grade-by-grade framework for a coherent mathematics curriculum (p. 7)."
These connections, physically located to the right of the actual focal points for each specific grade level, can be found beginning on page 11 and ending on page 20. Take page 16, for example (Curriculum Focal Points and Connections for Grade 4). Reading the full page, you will find that the entire body of ideas presented here (not just the statements written in bold print) make up a coherent set of related topics, concepts, skills, and ideas, that if taught well, would favorably impact the mathematical learning of a fourth grader.
When approached by local journalists, talk show hosts and producers, teachers, administrators, publishers, bloggers, parents, and other interested individual's about NCTM's Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics and its impact on mathematics in Maryland, I encourage all to thoroughly read the 41 page document for further clarity (See: http://www.nctm.org/focalpoints). It is written very plainly and leaves little room for ambiguity.
Sincerely,
Jon Wray
President-Elect, Maryland Council of Teachers of Mathematics (MCTM)
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