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)
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