Reform mathematics

Reform mathematics is one name for mathematics instruction based on recommendations originally published in 1989 by the National Council of Teachers of Mathematics (NCTM). [http://nctm.org] The document Principles and Standards for School Mathematics attempts to set forth a vision for precollege mathematics education in the United States and Canada. The recommendations were adopted by many education agencies, from local to federal levels through 1990s and 2000s, and continue to serve as the basis for many states' mathematics standards, and for many federally funded textbook projects. The standards called for a de-emphasis on manual arithmetic in favor of students' discovering their own knowledge and conceptual thinking.

Mathematics in this style has been called "standards-based mathematics" [ [http://www.pdkintl.org/kappan/k0111tra.htm "Standards-Based Mathematics Curriculum Materials: A Phrase in Search of a Definition"] By Paul R. Trafton, Barbara J. Reys, and Deanna G. Wasman] or "reform mathematics". [ [http://mathematicallysane.com/analysis/reformvsbasics.asp Reform Mathematics vs. the Basics] ] Less favorable terminology which have appeared in press and web articles include "Where's the math?", [ [http://www.sfgate.com/cgi-bin/article.cgi?file=/chronicle/archive/1999/10/17/ED92574.DTL San Francisco Chronicle: Where's the Math?] ] "anti-math", [ [http://www.mathematicallycorrect.com/klein.htm The State's Invisible Math Standards: "With Zacarias' anti-math policies in force..."] ] "math for dummies", [ [http://www.dehnbase.org/hold/ Math Framework in California NCTM "A State Dummies Down", editorial, The Business Journal (Sacramento), 10 April 1995] ] "no-math mathematics", [ [http://web.archive.org/web/20060112214419/http://www.joannejacobs.com/mtarchives/015317.html joannejacobs.com: Eth-no-math] ] "rainforest algebra", [ [http://www.texaspolicy.com/pdf/1997-11-15-rejectedbooks.pdf] Texas adopts textbook rejected by nation: Adoption of "Rainforest Algebra" appears to contradict this logic] "math for women and minorities", [ [http://www.mathematicallycorrect.com/house.htm] David Klein: "This misguided view of women and minorities..."] and "new new math". [ [http://www.cbsnews.com/stories/2000/05/28/eveningnews/main200272.shtml] New, New Math = Controversy CBS News 5/28/2000]

Principles and Standards

The momentum for reform in mathematics education began in the early 1980s, as educators reacted to the "new math" of the 1960s and 1970s. The work of Piaget and other developmental psychologists was shifting the focus of mathematics educators from mathematics content to how children best learn mathematics. [ John A. Van de Walle, "Elementary and Middle School Mathematics: Teaching Developmentally" Longman, 2001, ISBN 08013-3253-2]

Reform mathematics curricula challenge students to make sense of new mathematical ideas through explorations and projects, often in real contexts. [ John A. Van de Walle, "Elementary and Middle School Mathematics: Teaching Developmentally" Longman, 2001, ISBN 08013-3253-2] Reform texts emphasize written and verbal communication, working in groups, making connections between concepts, and connections between representations. By contrast, "traditional" textbooks emphasize procedural mathematics and provide step-by-step examples with skill exercises.

Traditional mathematics focuses on teaching algorithms that will lead to the correct answer. Because of this focus on application of algorithms, the traditional math student must always use the specific method that is being taught. This kind of algorithmic dependence is de-emphasized in reform mathematics. [http://www.wgquirk.com/chap3.html The NCTM Calls it "Math"] ] Reformers do not oppose correct answers, but prefer to focus students' attention on the process leading to the answer, rather than the answer itself. The presence of occasional minor errors is deemed less important than the overall thought process.

Controversy

While "Principles and Standards for School Mathematics" has been championed by mathematicians, educators and administrators as raising standards for all students, it has been criticized for valuing understanding processes more than correct procedures. Parents opposing reform mathematics have complained about decreased focus on basic computation skills and confusion caused by the increased emphasis on exploration and explanation. [http://www.nytimes.com/2007/06/14/nyregion/14math.html] Integrated math texts have been criticized as covering too many topics in a haphazard sequence, while spending only brief time on topics such as solving linear equations which a traditional algebra class might devote months to deep understanding of a few important single topics.Fact|date=April 2008

The development and large scale adoption of curricula such as Mathland have been criticized for partially or entirely abandoning teaching of standard arithemetic methods such as regrouping or common denominators. By 2008, some states such as Georgia [ [http://www.macon.com/198/story/423847.html New high school math may test teachers, students By Julie Hubbard - [e-mail] Aug 6, 2008] ] were still introducing reforms such as Integrated mathematics. Protests from groups of parents and citizens in math-related careers such as Mathematically Correct have led to many districts and states abandoning such textbooks as obsolete or failures. Some states such as Washington and California [ [http://www.pdkintl.org/kappan/k0111jac.htm Implementing Standards: The California Mathematics Textbook Debacle By Bill Jacob "students there will be drilled on formal skills...expectations for thinking and reasoning will be gone] ] have revised their mathematics standards to partially or largely repudiate the basic beliefs of reform mathematics, and re-emphasize mastery of the standard mathematics facts and methods used by mathematics professionals.

The American Institutes for Research (AIR) reported in 2005 that the NCTM proposals pushed students into "unrealistically advanced mathematics content in the early grades."cite web |url=http://www.air.org/news/documents/Singapore%20Report%20(Bookmark%20Version).pdf |title= What the United States Can Learn From Singapore’s World-Class Mathematics System |accessdate=2008-01-29 |format= |work=]

Some have called for a balance between reform and traditional mathematics teaching styles rather a "war" between either style. [ [http://seattlepi.nwsource.com/local/351655_math18.html February 17, 2008 10:44 p.m. State's proposed new math standards don't add up, critics say By JESSICA BLANCHARD "the district's elementary and middle-school math textbook choices lack a good balance between reform and traditional learning styles"] ]

ee also

* Education in the United States
* Mathematically Correct, which opposes the NCTM standards
* Prof David Klein (California State University Northridge), who opposes the NCTM standards

Notes

External links

* [http://standards.nctm.org/ NCTM standards online] 120-day free access, otherwise the public is required to pay to purchase or view the standards.
** [http://my.nctm.org/standards/document/index.htm Log in for full access to Principles and Standards online]
** [http://my.nctm.org/standards/previous/currevstds/ Original 1989 Curriculum and Evaluation Standards]
** [http://my.nctm.org/standards/previous/profstds/ 1991 Professional Standards]
** [http://my.nctm.org/standards/previous/assstds/ 1995 Assessment Standards]