Reform mathematics is an approach to

mathematics education In contemporary education, mathematics education, known in Europe as the didactics or pedagogy of mathematics – is the practice of teaching, learning and carrying out scholarly research into the transfer of mathematical knowledge. Although rese ...

, particularly in North America. It is based on principles explained in 1989 by the

National Council of Teachers of Mathematics Founded in 1920, The National Council of Teachers of Mathematics (NCTM) is a professional organization for schoolteachers of mathematics in the United States. One of its goals is to improve the standards of mathematics in education. NCTM holds an ...

(NCTM). The NCTM document ''Curriculum and Evaluation Standards for School Mathematics'' (''CESSM'') set forth a vision for K–12 (ages 5–18)

in the

United States The United States of America (U.S.A. or USA), commonly known as the United States (U.S. or US) or America, is a country primarily located in North America. It consists of 50 states, a federal district, five major unincorporated territorie ...

and

Canada Canada is a country in North America. Its ten provinces and three territories extend from the Atlantic Ocean to the Pacific Ocean and northward into the Arctic Ocean, covering over , making it the world's second-largest country by tot ...

. The ''CESSM'' recommendations were adopted by many local- and federal-level education agencies during the 1990s. In 2000, the NCTM revised its ''CESSM'' with the publication of ''

Principles and Standards for School Mathematics ''Principles and Standards for School Mathematics'' (''PSSM'') are guidelines produced by the National Council of Teachers of Mathematics (NCTM) in 2000, setting forth recommendations for mathematics educators. They form a national vision for pres ...

'' (''PSSM''). Like those in the first publication, the updated recommendations became the basis for many states' mathematics standards, and the method in textbooks developed by many federally-funded projects. The ''CESSM'' de-emphasised manual arithmetic in favor of students developing their own conceptual thinking and problem solving. The ''PSSM'' presents a more balanced view, but still has the same emphases. Mathematics instruction in this style has been labeled ''standards-based mathematics'' or ''reform mathematics''.

Principles and standards

Mathematics education reform built up momentum in the early 1980s, as educators reacted to the "

new math New Mathematics or New Math was a dramatic but temporary change in the way mathematics was taught in American grade schools, and to a lesser extent in European countries and elsewhere, during the 1950s1970s. Curriculum topics and teaching pract ...

" of the 1960s and 1970s. The work of Piaget and other developmental psychologists had 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, The

summarized the state of current research with the publication of ''Curriculum and Evaluation Standards'' in 1989 and ''

'' in 2000, bringing definition to the reform movement in North America. Reform mathematics curricula challenge students to make sense of new mathematical ideas through explorations and projects, often in real-world contexts. Reform texts emphasize written and verbal communication, working in cooperative groups, and making connections between concepts and between representations. In contrast, "traditional" textbooks emphasize procedural mathematics and provide step-by-step examples with skill-building exercises.

Traditional mathematics Traditional mathematics (sometimes classical math education) was the predominant method of mathematics education in the United States in the early-to-mid 20th century. This contrasts with non-traditional approaches to math education.The NCTM Calls it "Math"
/ref> Instead of leading students to find the exact answers to specific problems, reform educators focus students on the overall process which leads to an answer. Students' occasional errors are deemed less important than their understanding of an overall thought process. Research has shown that children make fewer mistakes with calculations and remember algorithms longer when they understand the concepts underlying the methods they use. In general, children in reform classes perform at least as well as children in traditional classes on tests of calculation skill, and perform considerably better on tests of problem solving.

Controversy

''Principles and Standards for School Mathematics'' was championed by educators, administrators and some mathematicians as raising standards for all students; others criticized it for its prioritizing the understanding of processes over the learning of standard calculation procedures. Parents, educators and some mathematicians opposing reform mathematics complained about students becoming confused and frustrated, claiming that the style of instruction was inefficient and characterized by frequent false starts. Proponents of reform mathematics countered that research showed that correctly-applied reform math curricula taught students basic math skills at least as well as curricula used in traditional programs, and additionally that reform math curricula was a more effective tool for teaching students the underlying concepts. Communities that adopted reform curricula generally their students' math scores increase. However, one study found that first-grade students with a below-average aptitude in math responded better to teacher-directed instruction. During the 1990s, the large-scale adoption of curricula such as

Mathland ''MathLand'' was one of several elementary mathematics curricula that were designed around the 1989 NCTM standards. It was developed and published by Creative Publications and was initially adopted by the U.S. state of California and schools run b ...

was criticized for partially or entirely abandoning teaching of standard arithmetic methods such as practicing regrouping or finding common denominators. Protests from groups such as Mathematically Correct led to many districts and states abandoning such textbooks. Some states—such as California—revised their mathematics standards to partially or largely repudiate the basic tenets of reform mathematics, and to re-emphasize mastery of standard mathematics facts and methods. The American Institutes for Research (AIR) reported in 2005 that the NCTM proposals "risk exposing students to unrealistically advanced mathematics content in the early grades." This is in reference to NCTM's recommendation that algebraic concepts, such as understanding patterns and properties like

commutativity In mathematics, a binary operation is commutative if changing the order of the operands does not change the result. It is a fundamental property of many binary operations, and many mathematical proofs depend on it. Most familiar as the name of ...

(2+3=3+2), should be taught as early as first grade. The 2008 National Mathematics Advisory Panel called for a balance between reform and traditional mathematics teaching styles, rather than a for a "war" to be waged between the proponents of the two styles. In 2006 NCTM published its ''Curriculum Focal Points'', which made clear that standard algorithms, as well as activities aiming at conceptual understanding, were to be included in all elementary school curricula, . A common misconception was that reform educators did not want children to learn the standard methods of arithmetic. As the NCTM ''Focal Points'' made clear, such methods were still the ultimate goal, but reformers believed that conceptual understanding should come first. Reform educators believed that such understanding is best pursued by first llowing children to attempt to solve problems using their own understanding and methods. Eventually, under guidance from the teacher, students eventually arrive at an understanding of standard methods. Even the controversial NCTM ''Standards'' of 1989 did not call for abandoning standard algorithms, but instead recommended a decreased emphasis on complex paper-and-pencil computation drills, and an increased emphasis on mental computation, estimation skills, thinking strategies for mastering basic facts, and conceptual understanding of arithmetic operations. During the peak of the controversy in the 1990s, unfavorable terminology for reform mathematics appeared in press and web articles, including ''Where's the math?'', ''anti-math'', ''math for dummies'', ''

rainforest algebra ''Focus on Algebra'' was the widely cited 812-page-long algebra textbook which contained significant content outside the traditional field of mathematics. The real-life context, intended to make mathematics more relevant, included chili recipes, an ...

'', ''math for women and minorities'', and ''new new math''.
New, New Math = Controversy CBS News 5/28/2000 Most of these critical terms refer to the 1989 ''Standards'' rather than the ''PSSM''. Beginning in 2011, most states adopted the

Common Core Standards The Common Core State Standards Initiative, also known as simply Common Core, is an educational initiative from 2010 that details what K–12 students throughout the United States should know in English language arts and mathematics at the conc ...

, which attempted to incorporate reform ideas, rigor (introducing ideas at a younger age), and a leaner math curriculum.

Notes

External links

NCTM standards online
120-day free access, otherwise the public is required to pay to purchase or view the standards. {{Mathematics education Education reform Mathematics education Mathematics education reform Standards-based education

Principles and standards

Controversy

See also

Notes

External links