Research Supporting NCTM-Standards-Based Mathematics Education Reform

By admin - Last updated: Sunday, October 24, 2022 - Save & Share - Leave a Comment

Prepared by Eric Hart

There is a rigorous and extensive research base for NCTM-Standards-based reform in mathematics education. A brief sample of that research base, related to several major themes of reform, is included here.

1. Teaching Mathematics for Understanding

“There is a long history of research, going back to the 1940s and the work of William Brownell, on the effects of teaching for meaning and understanding in mathematics. Investigations have consistently shown that an emphasis on teaching for meaning has positive effects on student learning, including better initial learning, greater retention, and an increased likelihood that the ideas will be used in new situations. These results have also been found in studies conducted in high-poverty areas.” (Grouws & Cebulla, 2000, p. 13)

“Instructional programs that emphasize conceptual development, with the goal of understanding, can facilitate significant mathematics learning without sacrificing skill proficiency.” (Hiebert, 2003, p. 16)

“Students who memorize facts or procedures without understanding often are not sure when and how to use what they know, and such learning is often quite fragile.” (Bransford, Brown, & Cocking, 1999, cited in NCTM, 2000, p. 20)

“Students who develop conceptual understanding early perform best on procedural knowledge later.” (Grouws & Cebulla, 2000, p. 15)

A Few References:

2. Teaching Mathematics Using Problem-Based Instructional Tasks (Teaching Through Problem Solving)

“What do the findings from research suggest about the feasibility and efficacy of teaching mathematics through problem solving? The research reviewed herein suggests both the feasibility and efficacy of such approaches.” (Stein, Boaler, & Silver, 2003, pp. 255-56)

“Problem solving should be the site in which all of the strands of mathematics proficiency converge.” (Kilpatrick, Swafford, & Findell, 2001, p. 421)
(Strands are: conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, and productive disposition.)

“Students can learn new skills and concepts while they are working out solutions to problems.” (Grouws & Cebulla, 2000, p. 15)

A Few References:

3. Meaningful Distributed Practice of Concepts, Skills, and Problem Solving

“… practice on computational procedures should be designed to build on and extend understanding.” (Kilpatrick, Swafford, & Findell, 2001, p. 423)

“If students are to develop both proficiency and understanding of skills, the most efficient instructional approach is to build understanding into the students’ experience from the beginning.” (Hiebert, 2003, p. 18)

“What’s the most efficient way to allocate practice time? … The straightforward answer that we can draw from research evidence is that distributing study time over several sessions generally leads to better memory of the information than conducting a single study session.” (Willingham, 2002)

“Practice should be used with feedback to support all strands of mathematical proficiency and not just procedural fluency.” (Kilpatrick, Swafford, & Findell, 2001, p. 423)
(Strands are: conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, and productive disposition.)

“If students overpractice procedures before they understand them, it is more difficult to make sense of them later.” (Hiebert, 2003, p. 17)

“If students are initially drilled too much on isolated skills, they have a harder time making sense of them later.” (Grouws & Cebulla, 2000, p. 16)

A Few References:

4. Assessment for Learning

Extensive research reviews have concluded that stronger formative assessment (assessment for learning) produces significant learning gains. (Black & Wiliam, 1998a, 1998b)

A Few References:

5. Traditional and Reform (NCTM-Standards-Based) Approaches

“On tests of conceptual understanding and problem solving, students who learn from reform curricula consistently outperform students who learn from traditional curricula by a wide margin. On tests of basic skills, there are generally no significant differences between students who learn from traditional or reform curricula.” (Schoenfeld, 2002)

“Students in alternative programs implemented with fidelity for reasonable lengths of time have learned more and learned more deeply than in traditional programs.” (Hiebert, 2003, p. 20)

“[There is] considerable evidence that the promises of reform mathematics are real and the fears of the anti-reformers unjustified.” (Swafford, 2003)

“The studies reported in this book provide much needed evidence that the new programs work.” (Kilpatrick, 2003)

“Presuming that traditional approaches have proven to be successful is ignoring the largest database we have.” (Hiebert, 2003, p. 13)

In the traditional approach, “… the teacher demonstrates or leads a discussion on how to solve a sample problem. The aim is to clarify the steps in the procedure so that students will be able to execute the same procedure on their own. [Then] students practice using the procedure by solving problems similar to the sample problem.” (Stigler & Hiebert, 1997, p. 18)

A Few References:

6. General Research Base for Improving Mathematics Teaching and Learning

Published Research Reviews

National Textbook Evaluations and Reviews

Research Review Panels

National and International Tests

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