[math-fun] NYTimes: Panel Proposes Streamlining Math
[Correction: The subject article appeared in the New York Times, not the Los Angeles Times.] FYI -- My translation: "Students who complete Algebra II are more than twice as likely to graduate from college as those completing only Algebra I". "By the end of Grade 3, students should be proficient with the ambition and distraction of whole numbers." "By the end of Grade 5, students should be proficient with uglification and derision of whole numbers." "By the end of Grade 7, students should be 7/3's better at fractions than at the end of Grade 3, and 17% better at percentages than at the end of Grade 6." "15-year-olds in the United States ranked 25th among their peers in 30 developed nations in math literacy and problem solving, which keeps them out of high-paying jobs like engineering and programming, and relegates them to low-paying jobs like lawyers, politicians and CEO's." "The use of a calculator frees up working memory for more complex aspects of problem solving." "Almost half the eighth graders tested could not solve a word problem that required dividing factions among the delegates and the superdelegates." ------ March 13, 2008 Panel Proposes Streamlining Math By TAMAR LEWIN American students math achievement is Âat a mediocre level compared with that of their peers worldwide, according to a new report by a federal panel. The panel said that math curriculums from preschool to eighth grade should be streamlined to focus on key skills  the handling of whole numbers and fractions, and certain aspects of geometry and measurement  to prepare students to learn algebra. ÂThe sharp falloff in mathematics achievement in the U.S. begins as students reach late middle school, where, for more and more students, algebra course work begins, said the report of the National Mathematics Advisory Panel, appointed two years ago by President Bush. ÂStudents who complete Algebra II are more than twice as likely to graduate from college, compared to students with less mathematical preparation. The report, to be released Thursday, spells out specific goals for students. For example, it says that by the end of the third grade, students should be proficient in adding and subtracting whole numbers; two years later, they should be proficient in multiplying and dividing them. By the end of sixth grade, it says, students should have mastered the multiplication and division of fractions and decimals. The report tries to put to rest the long and heated debate over math teaching methods. Parents and teachers in school districts across the country have fought passionately over the relative merits of traditional, or teacher-directed, instruction, in which students are told how to solve problems and then are drilled on them, as opposed to reform or child-centered instruction, which emphasizes student exploration and conceptual understanding. The panel said both methods have a role. ÂThere is no basis in research for favoring teacher-based or student-centered instruction, said Dr. Larry R. Faulkner, the chairman of the panel, at a briefing for reporters on Wednesday. ÂPeople may retain their strongly held philosophical inclinations, but the research does not show that either is better than the other. Districts that have made ÂÂall-encompassing decisions to go one way or the other, he said, should rethink those decisions, and intertwine different methods of instruction to help students develop a broad understanding of math. ÂTo prepare students for algebra, the curriculum must simultaneously develop conceptual understanding, computational fluency and problem-solving skills, the report said. ÂDebates regarding the relative importance of these aspects of mathematical knowledge are misguided. These capabilities are mutually supportive, . The president convened the panel to advise on how to improve math education for the nationÂs children. Its members include math and psychology professors from leading universities, a middle-school math teacher and the president of the National Council of Teachers of Mathematics. Closely tracking an influential 2006 report by the National Council of Teachers of Mathematics, the panel said that the math curriculum should include fewer topics, and then spend enough time on each of them to make it is learned in depth and need not be revisited in later grades. This is how top-performing nations approach the curriculum. After a similar advisory panel on reading made its recommendations in 2000, the federal government used the report as a guide for awarding $5 billion in federal grants to promote reading proficiency. The new report does not call for a national math curriculum, or for new federal investment in math instruction. It does call for more research on successful math teaching, and recommends that the Secretary of Education convene an annual forum of leaders of the national associations concerned with math to develop an agenda for improving math instruction. The report cites a number of troubling international comparisons, including a 2007 assessment finding that 15-year-olds in the United States ranked 25th among their peers in 30 developed nations in math literacy and problem solving. The report says that Americans fell short, especially, in handling fractions. It pointed to the National Assessment of Educational Progress, standardized-test results that are known as the nationÂs report card, which found that almost half the eighth graders tested could not solve a word problem that required dividing fractions. After hearing testimony and comments from hundreds of organizations and individuals, and sifting through 16,000 research publications, the panelists shaped their report around recent research on how children learn. For example, the panel found that it is important for students to master their basic math facts by heart. ÂFor all content areas, practice allows students to achieve automaticity of basic skills  the fast, accurate, and effortless processing of content information  which frees up working memory for more complex aspects of problem solving, the report said. Dr. Faulkner, a former president of the University of Texas at Austin, said the panel Âbuys the notion from cognitive science that kids have to know the facts. ÂIn the language of cognitive science, working memory needs to be predominately dedicated to new material in order to have a learning progression, and previously addressed material needs to be in long-term memory, he said. The report also cites recent findings that students who depend on their native intelligence learn less than those who believe that success depends on how hard they work. Dr. Faulkner said the current Âtalent-driven approach to math, that either you can do it or you canÂt, like playing the violin needed to be changed. ÂExperimental studies have demonstrated that changing childrenÂs beliefs from a focus on ability to a focus on effort increases their engagement in mathematics learning, which in turn improves mathematics outcomes, the report says ÂWhen children believe that their efforts to learn make them Âsmarter, they show greater persistence in mathematics learning. The report makes a plea for shorter and more accurate math textbooks. Given the shortage of elementary teachers with a solid grounding in math, the report recommends further research on the use of math specialists to teach several different elementary grades, as is done in many top-performing nations. The report also recommends a revamping of the math content on the national assessment test, to focus on the same skills that the report emphasizes. Here are the panelÂs recommended benchmarks for elementary school math education: Benchmarks in Math Education Fluency With Whole Numbers 1 By the end of Grade 3, students should be proficient with the addition and subtraction of whole numbers. 2 By the end of Grade 5, students should be proficient with multiplication and division of whole numbers. Fluency With Fractions 1 By the end of Grade 4, students should be able to identify and represent fractions and decimals, and compare them on a number line or with other common representations of fractions and decimals. 2 By the end of Grade 5, students should be proficient with comparing fractions and decimals and common percents, and with the addition and subtraction of fractions and decimals. 3 By the end of Grade 6, students should be proficient with multiplication and division of fractions and decimals. 4 By the end of Grade 6, students should be proficient with all operations involving positive and negative integers. 5 By the end of Grade 7, students should be proficient with all operations involving positive and negative fractions. 6 By the end of Grade 7, students should be able to solve problems involving percent, ratio, and rate and extend this work to proportionality. Geometry and Measurement 1 By the end of Grade 5, students should be able to solve problems involving perimeter andarea of triangles and all quadrilaterals having at least one pair of parallel sides (i.e.,trapezoids). 2 By the end of Grade 6, students should be able to analyze the properties of two-dimensional shapes and solve problems involving perimeter and area, and analyze the properties of three dimensional shapes and solve problems involving surface area and volume. 3 By the end of Grade 7, students should be familiar with the relationship between similar triangles and the concept of the slope of a line. Source: National Mathematics Advisory Panel, 2008.
Interesting, especially as I just came across this paper, written in 2002: http://www.maa.org/devlin/LockhartsLament.pdf (sorry If you've seen it before) It pretty much sums up (or rather argues thoroughly) my views on the matter. Henry Baker wrote:
[Correction: The subject article appeared in the New York Times, not the Los Angeles Times.]
FYI -- My translation: "Students who complete Algebra II are more than twice as likely to graduate from college as those completing only Algebra I".
"By the end of Grade 3, students should be proficient with the ambition and distraction of whole numbers."
"By the end of Grade 5, students should be proficient with uglification and derision of whole numbers."
"By the end of Grade 7, students should be 7/3's better at fractions than at the end of Grade 3, and 17% better at percentages than at the end of Grade 6."
"15-year-olds in the United States ranked 25th among their peers in 30 developed nations in math literacy and problem solving, which keeps them out of high-paying jobs like engineering and programming, and relegates them to low-paying jobs like lawyers, politicians and CEO's."
"The use of a calculator frees up working memory for more complex aspects of problem solving."
"Almost half the eighth graders tested could not solve a word problem that required dividing factions among the delegates and the superdelegates."
------ March 13, 2008
Panel Proposes Streamlining Math
By TAMAR LEWIN
American students’ math achievement is “at a mediocre level” compared with that of their peers worldwide, according to a new report by a federal panel. The panel said that math curriculums from preschool to eighth grade should be streamlined to focus on key skills the handling of whole numbers and fractions, and certain aspects of geometry and measurement to prepare students to learn algebra.
“The sharp falloff in mathematics achievement in the U.S. begins as students reach late middle school, where, for more and more students, algebra course work begins,” said the report of the National Mathematics Advisory Panel, appointed two years ago by President Bush. “Students who complete Algebra II are more than twice as likely to graduate from college, compared to students with less mathematical preparation.”
The report, to be released Thursday, spells out specific goals for students. For example, it says that by the end of the third grade, students should be proficient in adding and subtracting whole numbers; two years later, they should be proficient in multiplying and dividing them. By the end of sixth grade, it says, students should have mastered the multiplication and division of fractions and decimals.
The report tries to put to rest the long and heated debate over math teaching methods. Parents and teachers in school districts across the country have fought passionately over the relative merits of traditional, or teacher-directed, instruction, in which students are told how to solve problems and then are drilled on them, as opposed to reform or child-centered instruction, which emphasizes student exploration and conceptual understanding. The panel said both methods have a role.
“There is no basis in research for favoring teacher-based or student-centered instruction,” said Dr. Larry R. Faulkner, the chairman of the panel, at a briefing for reporters on Wednesday. “People may retain their strongly held philosophical inclinations, but the research does not show that either is better than the other.”
Districts that have made ‘’all-encompassing decisions to go one way or the other,” he said, should rethink those decisions, and intertwine different methods of instruction to help students develop a broad understanding of math.
“To prepare students for algebra, the curriculum must simultaneously develop conceptual understanding, computational fluency and problem-solving skills,” the report said. “Debates regarding the relative importance of these aspects of mathematical knowledge are misguided. These capabilities are mutually supportive, .”
The president convened the panel to advise on how to improve math education for the nation’s children. Its members include math and psychology professors from leading universities, a middle-school math teacher and the president of the National Council of Teachers of Mathematics.
Closely tracking an influential 2006 report by the National Council of Teachers of Mathematics, the panel said that the math curriculum should include fewer topics, and then spend enough time on each of them to make it is learned in depth and need not be revisited in later grades. This is how top-performing nations approach the curriculum.
After a similar advisory panel on reading made its recommendations in 2000, the federal government used the report as a guide for awarding $5 billion in federal grants to promote reading proficiency.
The new report does not call for a national math curriculum, or for new federal investment in math instruction. It does call for more research on successful math teaching, and recommends that the Secretary of Education convene an annual forum of leaders of the national associations concerned with math to develop an agenda for improving math instruction.
The report cites a number of troubling international comparisons, including a 2007 assessment finding that 15-year-olds in the United States ranked 25th among their peers in 30 developed nations in math literacy and problem solving.
The report says that Americans fell short, especially, in handling fractions. It pointed to the National Assessment of Educational Progress, standardized-test results that are known as the nation’s report card, which found that almost half the eighth graders tested could not solve a word problem that required dividing fractions.
After hearing testimony and comments from hundreds of organizations and individuals, and sifting through 16,000 research publications, the panelists shaped their report around recent research on how children learn.
For example, the panel found that it is important for students to master their basic math facts by heart.
“For all content areas, practice allows students to achieve automaticity of basic skills the fast, accurate, and effortless processing of content information which frees up working memory for more complex aspects of problem solving,” the report said.
Dr. Faulkner, a former president of the University of Texas at Austin, said the panel “buys the notion from cognitive science that kids have to know the facts.”
“In the language of cognitive science, working memory needs to be predominately dedicated to new material in order to have a learning progression, and previously addressed material needs to be in long-term memory,” he said.
The report also cites recent findings that students who depend on their native intelligence learn less than those who believe that success depends on how hard they work. Dr. Faulkner said the current “talent-driven approach to math, that either you can do it or you can’t, like playing the violin” needed to be changed.
“Experimental studies have demonstrated that changing children’s beliefs from a focus on ability to a focus on effort increases their engagement in mathematics learning, which in turn improves mathematics outcomes,” the report says “When children believe that their efforts to learn make them ‘smarter,’ they show greater persistence in mathematics learning.”
The report makes a plea for shorter and more accurate math textbooks. Given the shortage of elementary teachers with a solid grounding in math, the report recommends further research on the use of math specialists to teach several different elementary grades, as is done in many top-performing nations.
The report also recommends a revamping of the math content on the national assessment test, to focus on the same skills that the report emphasizes.
Here are the panel’s recommended benchmarks for elementary school math education:
Benchmarks in Math Education Fluency With Whole Numbers
1 By the end of Grade 3, students should be proficient with the addition and subtraction of whole numbers.
2 By the end of Grade 5, students should be proficient with multiplication and division of whole numbers.
Fluency With Fractions
1 By the end of Grade 4, students should be able to identify and represent fractions and decimals, and compare them on a number line or with other common representations of fractions and decimals.
2 By the end of Grade 5, students should be proficient with comparing fractions and decimals and common percents, and with the addition and subtraction of fractions and decimals.
3 By the end of Grade 6, students should be proficient with multiplication and division of fractions and decimals.
4 By the end of Grade 6, students should be proficient with all operations involving positive and negative integers.
5 By the end of Grade 7, students should be proficient with all operations involving positive and negative fractions.
6 By the end of Grade 7, students should be able to solve problems involving percent, ratio, and rate and extend this work to proportionality.
Geometry and Measurement
1 By the end of Grade 5, students should be able to solve problems involving perimeter andarea of triangles and all quadrilaterals having at least one pair of parallel sides (i.e.,trapezoids).
2 By the end of Grade 6, students should be able to analyze the properties of two-dimensional shapes and solve problems involving perimeter and area, and analyze the properties of three dimensional shapes and solve problems involving surface area and volume.
3 By the end of Grade 7, students should be familiar with the relationship between similar triangles and the concept of the slope of a line.
Source: National Mathematics Advisory Panel, 2008.
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That's an interesting paper. Thanks for posting it! I agree with the notion that math is fascinating and beautiful and should be discovered as we pursue a goal. I think that works best for many things, in fact. In engineering, I try to always think of the product I'm trying to ship, and pursue the shortest path there, so that I don't get bogged down in abstract best practices that I learned by rote (design a top-down class hierarchy from the start, document everything, keep things checked in and documented, make sure everyone agrees that an approach is optimal...). That's not to say everyone should do that, but I find that always trying to reach the overall goal is tremendously motivating. I disagree with the notion that math is fundamentally like art or philosophy, though, which is not to say that it's any less wonderful. Math seems to me to be more of an erector set than a paint set: it lets you build wonderful machines, rather than expressing gut-wrenching or beautiful emotions. At least, I'm not familiar with any particularly angry, grieving or jubilant theorems. I suppose there are technical artists: tinkerers like Bach (sometimes; he did incredible "artistic" music too) and movie backdrop painters whose work you can't distinguish from a photograph. And you can wax philosophical about how theorems about infinity relate to human existance. But those aren't at the core of their natures. I think maybe the author resorts to philosophy and art because "craft" and "technical genius" aren't as revered. I think that's unfortunate. I find deep satisfaction and a sense of wonder when I see something before me that started in my imagination, even though for me those things are almost always expressions of function rather than humanity. A friend of mine recently criticized ballroom dancing for being too rule-bound compared to social dances, and I took similar exception. I dance social dances like West Coast Swing in a club when I want to be expressive. But I danced the international ballroom dances like Waltz and Quickstep because they took tremendous control and concentration to even make it through the figures, much less make them smooth and connected. Both of those things leave marks on the soul: being moved emotionally at the expression of something you felt so deeply and never realized could be expressed so beautifully, and being moved to wonder at something so complex, precise, elegant or functional that you never realized could be done within the constraints of the system. On Thu, 13 Mar 2008, Emma Cohen wrote:
Interesting, especially as I just came across this paper, written in 2002: http://www.maa.org/devlin/LockhartsLament.pdf (sorry If you've seen it before)
It pretty much sums up (or rather argues thoroughly) my views on the matter.
Henry Baker wrote:
[Correction: The subject article appeared in the New York Times, not the Los Angeles Times.]
FYI -- My translation: "Students who complete Algebra II are more than twice as likely to graduate from college as those completing only Algebra I".
"By the end of Grade 3, students should be proficient with the ambition and distraction of whole numbers."
"By the end of Grade 5, students should be proficient with uglification and derision of whole numbers."
"By the end of Grade 7, students should be 7/3's better at fractions than at the end of Grade 3, and 17% better at percentages than at the end of Grade 6."
"15-year-olds in the United States ranked 25th among their peers in 30 developed nations in math literacy and problem solving, which keeps them out of high-paying jobs like engineering and programming, and relegates them to low-paying jobs like lawyers, politicians and CEO's."
"The use of a calculator frees up working memory for more complex aspects of problem solving."
"Almost half the eighth graders tested could not solve a word problem that required dividing factions among the delegates and the superdelegates."
------ March 13, 2008
Panel Proposes Streamlining Math
By TAMAR LEWIN
American students? math achievement is ?at a mediocre level? compared with that of their peers worldwide, according to a new report by a federal panel. The panel said that math curriculums from preschool to eighth grade should be streamlined to focus on key skills the handling of whole numbers and fractions, and certain aspects of geometry and measurement to prepare students to learn algebra.
?The sharp falloff in mathematics achievement in the U.S. begins as students reach late middle school, where, for more and more students, algebra course work begins,? said the report of the National Mathematics Advisory Panel, appointed two years ago by President Bush. ?Students who complete Algebra II are more than twice as likely to graduate from college, compared to students with less mathematical preparation.?
The report, to be released Thursday, spells out specific goals for students. For example, it says that by the end of the third grade, students should be proficient in adding and subtracting whole numbers; two years later, they should be proficient in multiplying and dividing them. By the end of sixth grade, it says, students should have mastered the multiplication and division of fractions and decimals.
The report tries to put to rest the long and heated debate over math teaching methods. Parents and teachers in school districts across the country have fought passionately over the relative merits of traditional, or teacher-directed, instruction, in which students are told how to solve problems and then are drilled on them, as opposed to reform or child-centered instruction, which emphasizes student exploration and conceptual understanding. The panel said both methods have a role.
?There is no basis in research for favoring teacher-based or student-centered instruction,? said Dr. Larry R. Faulkner, the chairman of the panel, at a briefing for reporters on Wednesday. ?People may retain their strongly held philosophical inclinations, but the research does not show that either is better than the other.?
Districts that have made ??all-encompassing decisions to go one way or the other,? he said, should rethink those decisions, and intertwine different methods of instruction to help students develop a broad understanding of math.
?To prepare students for algebra, the curriculum must simultaneously develop conceptual understanding, computational fluency and problem-solving skills,? the report said. ?Debates regarding the relative importance of these aspects of mathematical knowledge are misguided. These capabilities are mutually supportive, .?
The president convened the panel to advise on how to improve math education for the nation?s children. Its members include math and psychology professors from leading universities, a middle-school math teacher and the president of the National Council of Teachers of Mathematics.
Closely tracking an influential 2006 report by the National Council of Teachers of Mathematics, the panel said that the math curriculum should include fewer topics, and then spend enough time on each of them to make it is learned in depth and need not be revisited in later grades. This is how top-performing nations approach the curriculum.
After a similar advisory panel on reading made its recommendations in 2000, the federal government used the report as a guide for awarding $5 billion in federal grants to promote reading proficiency.
The new report does not call for a national math curriculum, or for new federal investment in math instruction. It does call for more research on successful math teaching, and recommends that the Secretary of Education convene an annual forum of leaders of the national associations concerned with math to develop an agenda for improving math instruction.
The report cites a number of troubling international comparisons, including a 2007 assessment finding that 15-year-olds in the United States ranked 25th among their peers in 30 developed nations in math literacy and problem solving.
The report says that Americans fell short, especially, in handling fractions. It pointed to the National Assessment of Educational Progress, standardized-test results that are known as the nation?s report card, which found that almost half the eighth graders tested could not solve a word problem that required dividing fractions.
After hearing testimony and comments from hundreds of organizations and individuals, and sifting through 16,000 research publications, the panelists shaped their report around recent research on how children learn.
For example, the panel found that it is important for students to master their basic math facts by heart.
?For all content areas, practice allows students to achieve automaticity of basic skills the fast, accurate, and effortless processing of content information which frees up working memory for more complex aspects of problem solving,? the report said.
Dr. Faulkner, a former president of the University of Texas at Austin, said the panel ?buys the notion from cognitive science that kids have to know the facts.?
?In the language of cognitive science, working memory needs to be predominately dedicated to new material in order to have a learning progression, and previously addressed material needs to be in long-term memory,? he said.
The report also cites recent findings that students who depend on their native intelligence learn less than those who believe that success depends on how hard they work. Dr. Faulkner said the current ?talent-driven approach to math, that either you can do it or you can?t, like playing the violin? needed to be changed.
?Experimental studies have demonstrated that changing children?s beliefs from a focus on ability to a focus on effort increases their engagement in mathematics learning, which in turn improves mathematics outcomes,? the report says ?When children believe that their efforts to learn make them ?smarter,? they show greater persistence in mathematics learning.?
The report makes a plea for shorter and more accurate math textbooks. Given the shortage of elementary teachers with a solid grounding in math, the report recommends further research on the use of math specialists to teach several different elementary grades, as is done in many top-performing nations.
The report also recommends a revamping of the math content on the national assessment test, to focus on the same skills that the report emphasizes.
Here are the panel?s recommended benchmarks for elementary school math education:
Benchmarks in Math Education Fluency With Whole Numbers
1 By the end of Grade 3, students should be proficient with the addition and subtraction of whole numbers.
2 By the end of Grade 5, students should be proficient with multiplication and division of whole numbers.
Fluency With Fractions
1 By the end of Grade 4, students should be able to identify and represent fractions and decimals, and compare them on a number line or with other common representations of fractions and decimals.
2 By the end of Grade 5, students should be proficient with comparing fractions and decimals and common percents, and with the addition and subtraction of fractions and decimals.
3 By the end of Grade 6, students should be proficient with multiplication and division of fractions and decimals.
4 By the end of Grade 6, students should be proficient with all operations involving positive and negative integers.
5 By the end of Grade 7, students should be proficient with all operations involving positive and negative fractions.
6 By the end of Grade 7, students should be able to solve problems involving percent, ratio, and rate and extend this work to proportionality.
Geometry and Measurement
1 By the end of Grade 5, students should be able to solve problems involving perimeter andarea of triangles and all quadrilaterals having at least one pair of parallel sides (i.e.,trapezoids).
2 By the end of Grade 6, students should be able to analyze the properties of two-dimensional shapes and solve problems involving perimeter and area, and analyze the properties of three dimensional shapes and solve problems involving surface area and volume.
3 By the end of Grade 7, students should be familiar with the relationship between similar triangles and the concept of the slope of a line.
Source: National Mathematics Advisory Panel, 2008.
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... and what about http://www.math.uni-bielefeld.de/~sieben/workshop.pdf ?
On Thu, 13 Mar 2008, Henry Baker wrote:
"By the end of Grade 3, students should be proficient with the ambition and distraction of whole numbers."
"By the end of Grade 5, students should be proficient with uglification and derision of whole numbers."
"By the end of Grade 7, students should be 7/3's better at fractions than at the end of Grade 3, and 17% better at percentages than at the end of Grade 6."
Continuing on, then, At Grade 9, at least 60% of students should score above the mean in sadistics. At Grade 11, students' rate of improvement in deferential calculus should reach an inflection point and continue to approach the global maximum (which can be expected to be reached and continue downward after reaching grad school). At Grade 12, the sum of students passing AP exams in infantile calculus should reach 37% (plus a constant) In the sophomore year of college, a sufficiency of students should have proficiencies in the various dimensions of mathematics that sufficiently many of their proficiency vectors lie within the prerequisite subspaces for mythematically-oriented majors. -- Two added to one -- if that could but be done", It said, "with one's fingers and thumbs!" Recollecting with tears how, in earlier years, It had taken no pains with its sums.
participants (4)
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Emma Cohen -
Henry Baker -
Jason -
sieben＠math.uni-bielefeld.de