215:, a report on the topics considered central for mathematics in pre-kindergarten through eighth grade. Its inclusion of standard algorithms led editorials in newspapers like the Chicago Sun Times to state that the "NCTM council has admitted, more or less, that it goofed," and that the new report cited "inconsistency in the grade placement of mathematics topics as well as in how they are defined and what students are expected to learn." NCTM responded by insisting that it considers "Focal Points" a step in the implementation of the Standards, not a reversal of its position on teaching students to learn foundational topics with conceptual understanding. Francis Fennell, president of the NCTM, stated that there had been no change of direction or policy in the new report and said that he resented talk of “math wars”. The Focal Points were one of the documents consulted to create the new national
231:. The National Math Panel examined and summarized the scientific evidence related to the teaching and learning of mathematics, concluding in their 2008 report, "All-encompassing recommendations that instruction should be entirely 'student centered' or 'teacher directed' are not supported by research. If such recommendations exist, they should be rescinded. If they are being considered, they should be avoided. High-quality research does not support the exclusive use of either approach." The Panel effectively called for an end to the Math Wars, concluding that research showed "conceptual understanding, computational and procedural fluency, and problem-solving skills are equally important and mutually reinforce each other. Debates regarding the relative importance of each of these components of mathematics are misguided."
69:(fixed, step-by-step procedures for solving math problems) versus a more inquiry-based approach in which students are exposed to real-world problems that help them develop fluency in number sense, reasoning, and problem-solving skills. In this latter approach, conceptual understanding is a primary goal and algorithmic fluency is expected to follow secondarily. Some parents and other stakeholders blame educators saying that failures occur not because the method is at fault, but because these educational methods require a great deal of expertise and have not always been implemented well in actual classrooms.
118:
proficiency in a standard method are asked to invent another method of arriving at the answer. Some parents have accused reform math advocates of deliberately slowing down students with greater ability in order to "paper-over" the inequalities of the
American school system. Some teachers supplement such textbooks in order to teach standard methods more quickly. Some curricula do not teach long division. Critics believe the NCTM revised its standards to explicitly call for continuing instruction of standard methods, largely because of the negative response to some of these curricula (see
122:). College professors and employers have sometimes claimed that students that have been taught using reform curricula do not possess basic mathematical skills. One study found that, although first-grade students in 1999 with an average or above-average aptitude for math did equally well with either teacher-directed or student-centered instruction, first-grade students with mathematical difficulties did better with teacher-directed instruction.
110:. Commentators have argued that there is philosophical support for the notion that "algorithmic fluency" requires the very types of cognitive activity whose promotion reform advocates often claim is their approaches' unique virtue. However, such arguments assume that reformers do not want to teach the standard algorithms, which is a common misunderstanding of the reform position.
177:
procedural skill level in both types of curricula as measured by traditional standardized tests. More research is needed, but the current state of research seems to show that reform textbooks work as well as or better than traditional textbooks in helping students achieve computational competence while promoting greater conceptual understanding than traditional approaches.
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which are unfamiliar to many adults, and books which lack explanations of methods or solved examples make it difficult to help with homework. Compared to worksheets that can be completed in minutes, constructivist activities can be more time-consuming. (Reform educators respond that more time is lost
105:
Critics of reform point out that traditional methods are still universally and exclusively used in industry and academia. Reform educators respond that such methods are still the ultimate goal of reform mathematics, and that students need to learn flexible thinking in order to face problems they may
117:
and others that concluded that direct teaching of traditional algorithms is counterproductive to conceptual understanding of math. Critics have protested some of the consequences of this research. Traditional memorization methods are replaced with constructivist activities. Students who demonstrate
85:
maintain that students must first develop computational skills before they can understand concepts of mathematics. These skills should be memorized and practiced, using time-tested traditional methods until they become automatic. Time is better spent practicing skills rather than in investigations
176:
Reform educators have responded by pointing out that research tends to show that students achieve greater conceptual understanding from standards-based curricula than traditional curricula and that these gains do not come at the expense of basic skills. In fact students tend to achieve the same
149:, criticized for failing "to convey critical mathematical concepts and ideas that should and can be within reach for high school students", downplaying "algebraic structure and skills" and "inability to build geometry up from foundations in a mathematically sound and coherent way".
234:
The Panel's final report met with significant criticism within the mathematics education community for, among other issues, the selection criteria used to determine "high-quality" research, their comparison of extreme forms of teaching, and the amount of focus placed on algebra.
72:
A backlash, which advocates call "poorly understood reform efforts" and critics call "a complete abandonment of instruction in basic mathematics," resulted in "math wars" between reform and traditional methods of mathematics education.
193:, which was seen as more balanced than the original 1989 Standards. This led to some calming, but not an end to the dispute. Two recent reports have led to considerably more cooling of the Math Wars. In 2006, NCTM released its
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not know a method for. Critics maintain that it is unreasonable to expect students to "discover" the standard methods through investigation, and that flexible thinking can only be developed after mastering
97:. Student innovation is acceptable, even welcome, as long as it is mathematically valid. Calculator use can be appropriate after number sense has developed and basic skills have been mastered.
102:
in reteaching poorly understood algorithms.) Emphasis on reading and writing also increases the language load for immigrant students and parents who may be unfamiliar with
English.
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inventing alternatives, or justifying more than one correct answer or method. In this view, estimating answers is insufficient and, in fact, is considered to be dependent on strong
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Morgan, Paul; Farkas, George; Maczuga, Steve (20 June 2014), "Which
Instructional Practices Most Help First-Grade Students With and Without Mathematics Difficulties?",
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While the discussion about math skills has persisted for many decades, the term "math wars" was coined by commentators such as John A. Van de Walle and
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Critics of reform textbooks say that they present concepts in a haphazard way. Critics of the reform textbooks and curricula support methods such as
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Supporters of traditional mathematics teaching oppose excessive dependence on innovations such as calculators or new technology, such as the
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35:(NCTM) and subsequent development and widespread adoption of a new generation of mathematics curricula inspired by these standards.
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When
Politics Took the Place of Inquiry: A Response to the National Mathematics Advisory Panel’s Review of Instructional Practices
871:
98:
661:
912:
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90:. Learning abstract concepts of mathematics is perceived to depend on a solid base of knowledge of the tools of the subject.
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On April 18, 2006, President Bush created the
National Mathematics Advisory Panel, which was modeled after the influential
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Examples of reform curricula introduced in response to the 1989 NCTM standards and the reasons for initial criticism:
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197:, which was seen by many as a compromise position. In 2008, the National Mathematics Advisory Panel, created by
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One aspect of the debate is over how explicitly children must be taught skills based on formulas or
155:, criticized for not explicitly teaching children standard algorithms, formulas or solved examples
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Hiebert, James (2003). "What research says about the NCTM Standards". In
Kilpatrick, J. (ed.).
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677:"National Mathematics Advisory Panel: Strengthening Math Education Through Research"
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Standards-Based School
Mathematics Curricula: What Are They? What Do Students Learn?
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Foundations of
Success: The Final Report of the National Mathematics Advisory Panel
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276:
337:
Reform
Mathematics vs. The Basics: Understanding the Conflict and Dealing with It
247: – Educational plan meant to reduce perceived racism and sexism in education
27:, textbooks and curricula that were triggered by the publication in 1989 of the
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143:, criticized for not containing explicit instruction of the standard algorithms
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571:"Which Curriculum Is Most Effective in Producing Gains in Students' Learning?"
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philosophy and curricula, which differ significantly in approach and content.
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Debate over modern mathematics education, textbooks and curricula in the U.S.
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Chicago Sun Times "Fuzzy teaching ideas never added up" September 13, 2006
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169:, which emphasizes direct instruction of basic mathematical concepts, and
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161:, criticized for putting emphasis on non-traditional arithmetic methods.
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A Research
Companion to Principles and Standards for School Mathematics
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Preliminary Report, National Mathematics Advisory Panel, January 2007
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California Department of Education § 2021 mathematics framework
219:, which have been adopted by most of the United States since 2010.
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623:
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353:"A quarter century of US 'math wars' and political partisanship"
205:
National Council of Teachers of Mathematics 2006 recommendations
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573:. National Council of Teachers of Mathematics. Archived from
614:. Martin, W.; Schifter, D. Reston, VA: NCTM. pp. 5–23.
29:
Curriculum and Evaluation Standards for School Mathematics
339:, John A. Van de Walle Virginia Commonwealth University
249:
Pages displaying short descriptions of redirect targets
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The largest supporter of reform in the US has been the
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Principles and Standards for School Mathematics (PSSM)
291: – Approach to teaching mathematics in the 1960s
299:
Pages displaying wikidata descriptions as a fallback
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799:
522:"A Review of Four High-School Mathematics Programs"
187:National Council of Teachers of Mathematics (NCTM)
436:"What to Do about Canada's Declining Math Scores"
540:"Washington State high school math text review"
173:, which emphasizes frequent cumulative review.
595:Senk, Sharon L.; Thompson, Denisse R. (2003).
201:, called for a halt to all extreme positions.
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60:National Council of Teachers of Mathematics
33:National Council of Teachers of Mathematics
877:Investigations in Numbers, Data, and Space
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478:Educational Evaluation and Policy Analysis
368:"Current Reforms in Mathematics Education"
141:Investigations in Numbers, Data, and Space
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341:; "Debate has degenerated to 'math wars'"
261: – Liberation-focused math education
410:"Strategies for Constructivist Teaching"
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113:Some curricula incorporate research by
908:Education reform in the United States
681:United States Department of Education
297: – inquiry-based learning method
7:
273: – British mathematics educator
464:"The Faulty Logic of The Math Wars"
223:National Mathematics Advisory Panel
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557:"Public statement on math reform"
440:Education Policy; commentary #427
872:Interactive Mathematics Program
599:. Mahwah, NJ: Lawrence Erlbaum.
355:. California State University.
283:Mathematics for social justice
279: – Educational researcher
267: – American mathematician
1:
852:Core-Plus Mathematics Project
285: – Approach to education
259:Critical mathematics pedagogy
147:Core-Plus Mathematics Project
918:Mathematics education reform
663:Letter to the New York Times
81:Those who disagree with the
792:Standards-based mathematics
538:Wilson, W. Stephen (2009).
386:"Logo Programming Language"
265:David Klein (mathematician)
209:In 2006, the NCTM released
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649:February 10, 2012, at the
559:. University of Minnesota.
923:Standards-based education
434:Stokke, Anna (May 2015).
520:Harel, Guershon (2009).
490:10.3102/0162373714536608
366:Thomas, Edwards (2018).
83:inquiry-based philosophy
23:are debates over modern
801:Traditional mathematics
631:Curriculum Focal Points
245:Anti-racist mathematics
212:Curriculum Focal Points
195:Curriculum Focal Points
44:traditional mathematics
42:. The debates focus on
867:Integrated mathematics
809:Mathematically Correct
741:"America's maths wars"
229:National Reading Panel
99:Constructivist methods
19:In the United States,
913:Mathematics education
847:Connected Mathematics
710:. March 2008. p. 45."
217:Common Core Standards
153:Connected Mathematics
25:mathematics education
857:Everyday Mathematics
444:C. D. Howe Institute
414:Bright Hub Education
928:Ideological rivalry
748:. 6 November 2021.
137:(no longer offered)
108:foundational skills
88:foundational skills
54:Advocates of reform
839:Reform mathematics
181:Later developments
48:reform mathematics
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665:, Francis Fennell
372:Indiana Education
295:Three-part lesson
77:Critics of reform
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794:controversy
691:28 December
40:David Klein
902:Categories
824:Saxon math
581:2009-08-15
420:2018-05-18
395:2018-05-18
305:References
171:Saxon math
67:algorithms
754:0013-0613
724:Jo Boaler
271:Jo Boaler
21:math wars
882:Mathland
819:NYC HOLD
647:Archived
508:26180268
289:New Math
239:See also
135:Mathland
499:4500292
449:11 June
46:versus
31:by the
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633:, NCTM
506:
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543:(PDF)
525:(PDF)
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504:PMID
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494:PMC
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