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
Wednesday, January 31, 2007
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)
Curriculum Focal Points in Maryland
Article from the Baltimore Sun
Can less equal more?
Proposal to teach math students fewer concepts in greater depth has divided Md. educators
By Liz Bowie
Sun Reporter
January 2, 2007
Teacher Jennifer Dial Santoro asked her eighth-grade geometry class to throw the formula out the window and instead try to reason out the area of shapes drawn on a large grid.
Didma Valenzuela, a girl in the front with her head down, struggled with a parallelogram. Then the class was given a shape that looked like an Egyptian sphinx. Didma figured that she could fill up the space inside the shape with triangles and rectangles and use them to find the area.
"Yes!" she said, slapping Santoro's hand. "And I did it all by myself."
The class in Anne Arundel County's Marley Middle School represents to Santoro the best kind of teaching: students learning to understand the abstract thinking behind math rules and formulas. Too much of the time, Santoro believes, math teachers are flying over material, never giving students a deep grasp of the subject.
It is a complaint that has echoed across the nation. But what is taught in math classrooms in Maryland could be on the verge of changing. In the next several months, math educators here will decide whether they want to slim down the curriculum, focusing on a deeper understanding of a few basic tenets and excluding some of the extraneous material that teachers such as Santoro feel is hindering instruction.
Maryland's soul-searching, and that of more than a dozen states across the country, is the result of a report by a well-regarded group of math educators, the National Council of Teachers of Math. The council released a grade-by-grade list of three essential concepts - just three per year - that each student should learn in kindergarten through eighth grade.
Council President Francis "Skip" Fennell said the organization wanted to address the long-held criticism that America's math curriculum is a mile wide and an inch deep. He hopes that states will change their standards to be more in line with the council's Focal Points report.
"The report is driving those kind of discussions. Already we have spoken to about 12 to 15 states that are doing that," Fennell said.
The discussion is part of a decade-long debate over whether the country has gone too far from the basics toward reform math, a more creative approach that came to be known as "fuzzy" math by detractors. Those who believe in the basics are celebrating, saying they hope the new report will force a 180-degree turn in math instruction.
Most educators agree on the need to improve math education in the United States. Not only has the country lagged behind Asian countries in the number of science and math graduates, more college students are needing remediation. According to state statistics, 30 percent of students in the state's public colleges and universities need math remediation. While most of those students are at community colleges, 17 percent are at the state's four-year institutions.
And most students never catch up. "A child who doesn't learn certain math content in elementary school has little chance of becoming a doctor, engineer or scientist," said W. Stephen Wilson, a Johns Hopkins University math professor.
Fennell said the question that must be asked is "What must every kid do and do well?" Often math teachers are not trained mathematicians, he said, and they enter a classroom each August faced with a laundry list of dozens of standards the state says they must teach.
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.
Another criticism leveled against the Maryland standards is that teachers quickly cover the same concepts many years in a row using more complex equations and bigger numbers each year. Instead, Joy Donlin, coordinator of secondary mathematics in Anne Arundel County, said she would like students to learn one concept, such as fractions, well at one grade level.
"If we did it well, then we wouldn't need to do it again," she said. She said students wouldn't forget those skills because they continue to be used as the student goes up the ladder, through algebra and geometry.
The State Department of Education is now meeting with math supervisors in each jurisdiction around the state to get a consensus on whether they should follow the Focal Points. If changes are suggested, they would not take effect for at least 18 months, said Donna Watts, coordinator for the department's Office of Mathematics.
In the 1960s, students didn't have to understand why a formula worked. It was enough to memorize the facts and do the problems. Then in 1989, a report by the math council helped swing the country toward an approach that encouraged teachers to have students discover the theory behind the formulas. They called the new approach reform math.
But some teachers and school systems took the new ideas to an extreme, according to Fennell and others. They downplayed the importance of learning addition and multiplication facts, allowed elementary students to use calculators and didn't do enough drills. "In some systems, they aren't learning basic facts. They aren't allowed to memorize times tables," said Alice Rau, a math teacher at Carroll County's Francis Scott Key High School.
The critics have had support from a conservative Washington think tank, the Thomas B. Fordham Foundation, that has commissioned reports on the issue and has been a vocal advocate for change.
Just as reading teachers were arguing the pros and cons of whether phonics or whole language should be taught, a simultaneous debate has raged over traditional and reform math. The reform programs critics dislike the most are TERC and Everyday Math.
Today, many school districts in Maryland use some version of reform math, and many teachers and administrators say they believe in the approach as long as it is balanced. Baltimore County, for instance, recently purchased two new textbooks for elementary grades, one that uses the traditional approach and a second called Investigations by TERC that will supplement that style with reform math, said Patricia Baltzley, director of the county's math office.
"It is the best of both worlds," Baltzley said. Like Donlin in Anne Arundel, she says she believes students must memorize facts and learn formulas. Reform math is compatible with the changes the council is calling for, they say.
But others disagree. John Haven, whose children attended Montgomery County public schools, believes far too much time in classrooms is spent on nonessential math work. He made an unscientific study of math teaching in Montgomery and concluded that, by his standards, 20 to 40 percent of what is taught is a waste of time. "It is a huge impact on math instruction. It is like having popcorn parties every Tuesday and Friday," he said.
He believes using the math council's Focal Points will mean abandoning reform math, a change he would welcome. But Fennell says the council is only clarifying previous stands.
While the debate might seem academic, it will not be if Maryland changes its math standards. Maryland's standards are voluntary, but teachers in all counties pay close attention to them because they form the basis for what is tested on the Maryland State Assessments.
The new Focal Points are also likely to cause a major shift in the content in textbooks. "There are 750-page math textbooks," Fennell said. Faced with hundreds of state standards around the country, he said, publishers decided to try to cover everything that might be taught.
He and others would like to see textbooks get down to the essentials. Wilson said the sixth-grade math textbook for Singapore is 36 pages long, and Singapore scores highest on math exams worldwide.
"You have to have a car to carry around a textbook in the United States," he said.
Can less equal more?
Proposal to teach math students fewer concepts in greater depth has divided Md. educators
By Liz Bowie
Sun Reporter
January 2, 2007
Teacher Jennifer Dial Santoro asked her eighth-grade geometry class to throw the formula out the window and instead try to reason out the area of shapes drawn on a large grid.
Didma Valenzuela, a girl in the front with her head down, struggled with a parallelogram. Then the class was given a shape that looked like an Egyptian sphinx. Didma figured that she could fill up the space inside the shape with triangles and rectangles and use them to find the area.
"Yes!" she said, slapping Santoro's hand. "And I did it all by myself."
The class in Anne Arundel County's Marley Middle School represents to Santoro the best kind of teaching: students learning to understand the abstract thinking behind math rules and formulas. Too much of the time, Santoro believes, math teachers are flying over material, never giving students a deep grasp of the subject.
It is a complaint that has echoed across the nation. But what is taught in math classrooms in Maryland could be on the verge of changing. In the next several months, math educators here will decide whether they want to slim down the curriculum, focusing on a deeper understanding of a few basic tenets and excluding some of the extraneous material that teachers such as Santoro feel is hindering instruction.
Maryland's soul-searching, and that of more than a dozen states across the country, is the result of a report by a well-regarded group of math educators, the National Council of Teachers of Math. The council released a grade-by-grade list of three essential concepts - just three per year - that each student should learn in kindergarten through eighth grade.
Council President Francis "Skip" Fennell said the organization wanted to address the long-held criticism that America's math curriculum is a mile wide and an inch deep. He hopes that states will change their standards to be more in line with the council's Focal Points report.
"The report is driving those kind of discussions. Already we have spoken to about 12 to 15 states that are doing that," Fennell said.
The discussion is part of a decade-long debate over whether the country has gone too far from the basics toward reform math, a more creative approach that came to be known as "fuzzy" math by detractors. Those who believe in the basics are celebrating, saying they hope the new report will force a 180-degree turn in math instruction.
Most educators agree on the need to improve math education in the United States. Not only has the country lagged behind Asian countries in the number of science and math graduates, more college students are needing remediation. According to state statistics, 30 percent of students in the state's public colleges and universities need math remediation. While most of those students are at community colleges, 17 percent are at the state's four-year institutions.
And most students never catch up. "A child who doesn't learn certain math content in elementary school has little chance of becoming a doctor, engineer or scientist," said W. Stephen Wilson, a Johns Hopkins University math professor.
Fennell said the question that must be asked is "What must every kid do and do well?" Often math teachers are not trained mathematicians, he said, and they enter a classroom each August faced with a laundry list of dozens of standards the state says they must teach.
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.
Another criticism leveled against the Maryland standards is that teachers quickly cover the same concepts many years in a row using more complex equations and bigger numbers each year. Instead, Joy Donlin, coordinator of secondary mathematics in Anne Arundel County, said she would like students to learn one concept, such as fractions, well at one grade level.
"If we did it well, then we wouldn't need to do it again," she said. She said students wouldn't forget those skills because they continue to be used as the student goes up the ladder, through algebra and geometry.
The State Department of Education is now meeting with math supervisors in each jurisdiction around the state to get a consensus on whether they should follow the Focal Points. If changes are suggested, they would not take effect for at least 18 months, said Donna Watts, coordinator for the department's Office of Mathematics.
In the 1960s, students didn't have to understand why a formula worked. It was enough to memorize the facts and do the problems. Then in 1989, a report by the math council helped swing the country toward an approach that encouraged teachers to have students discover the theory behind the formulas. They called the new approach reform math.
But some teachers and school systems took the new ideas to an extreme, according to Fennell and others. They downplayed the importance of learning addition and multiplication facts, allowed elementary students to use calculators and didn't do enough drills. "In some systems, they aren't learning basic facts. They aren't allowed to memorize times tables," said Alice Rau, a math teacher at Carroll County's Francis Scott Key High School.
The critics have had support from a conservative Washington think tank, the Thomas B. Fordham Foundation, that has commissioned reports on the issue and has been a vocal advocate for change.
Just as reading teachers were arguing the pros and cons of whether phonics or whole language should be taught, a simultaneous debate has raged over traditional and reform math. The reform programs critics dislike the most are TERC and Everyday Math.
Today, many school districts in Maryland use some version of reform math, and many teachers and administrators say they believe in the approach as long as it is balanced. Baltimore County, for instance, recently purchased two new textbooks for elementary grades, one that uses the traditional approach and a second called Investigations by TERC that will supplement that style with reform math, said Patricia Baltzley, director of the county's math office.
"It is the best of both worlds," Baltzley said. Like Donlin in Anne Arundel, she says she believes students must memorize facts and learn formulas. Reform math is compatible with the changes the council is calling for, they say.
But others disagree. John Haven, whose children attended Montgomery County public schools, believes far too much time in classrooms is spent on nonessential math work. He made an unscientific study of math teaching in Montgomery and concluded that, by his standards, 20 to 40 percent of what is taught is a waste of time. "It is a huge impact on math instruction. It is like having popcorn parties every Tuesday and Friday," he said.
He believes using the math council's Focal Points will mean abandoning reform math, a change he would welcome. But Fennell says the council is only clarifying previous stands.
While the debate might seem academic, it will not be if Maryland changes its math standards. Maryland's standards are voluntary, but teachers in all counties pay close attention to them because they form the basis for what is tested on the Maryland State Assessments.
The new Focal Points are also likely to cause a major shift in the content in textbooks. "There are 750-page math textbooks," Fennell said. Faced with hundreds of state standards around the country, he said, publishers decided to try to cover everything that might be taught.
He and others would like to see textbooks get down to the essentials. Wilson said the sixth-grade math textbook for Singapore is 36 pages long, and Singapore scores highest on math exams worldwide.
"You have to have a car to carry around a textbook in the United States," he said.
NCTM's Curriculum Focal Points
A great deal of national attention has been paid to The National Council of Teachers of Mathematics' (NCTM's) Curriculum Focal Points for Grades PreK-8: A Quest for Coherence.
NCTM (2006) states, "Curriculum focal points are important mathematical topics for each grade level, pre-K-8. These areas of instructional emphasis can serve as organizing structures for curriculum design and instruction at and across grade levels."
To read more about the CFPs or download a copy, click here.
NCTM (2006) states, "Curriculum focal points are important mathematical topics for each grade level, pre-K-8. These areas of instructional emphasis can serve as organizing structures for curriculum design and instruction at and across grade levels."
To read more about the CFPs or download a copy, click here.
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