for Reviewing Research on
Before selecting studies
reviewed on this web site or making decisions based on these studies,
please read the following background information about research on mathematics
is a critical skill in the information age. We must improve achievement
to maintain our economic leadership. … Math achievement is improving
slightly, but much more work must be done to ensure that our children
receive a sound background in mathematics. … [We must] ensure schools
use scientifically based methods with long-term records of success to
teach math” (U. S. Department of Education). http://www.ed.gov/nclb/methods/math/math.html
Three recent and relevant published research reviews are listed below. Click on the box in the main diagram above for more information.
1. Adding It Up: Helping Children Learn Mathematics, from the National Research Council, edited by Kilpatrick, Swafford, and Findell. The main recommendation is that all students should be mathematically proficient, and that mathematical proficiency has five strands: (i) conceptual understanding, (ii) procedural fluency, (iii) strategic competence, (iv) adaptive reasoning, and (v) productive disposition.
2. A Research Companion to Principles and Standards for School Mathematics, from NCTM, edited by Kilpatrick, Martin, and Schifter. The research base for NCTM’s Principles and Standards is summarized in this book.
3. Improving Achievement in Mathematics, from the International Academy of Education, by Grouws and Cebulla. Research on improving achievement in mathematics is reviewed and summarized. Research-based strategies identified include: opportunity to learn, focus on meaning, learning new concepts while solving problems, opportunities for both invention and practice, openness to student solution methods and student interaction, small-group learning, whole-class discussion, number sense, concrete materials, and students’ use of calculators. Back to top
Some relevant information from the NAEP and SAT tests are listed below. Click on the box in the main diagram above for more information.
1. National Assessment of Educational Progress (NAEP). An analysis of trends in NAEP results across the nation show that average computation scores were higher in 1999 than in 1973 for all ages measured, namely, 9-, 13-, and 17-year-olds.
2. SAT® Math Scores for 2005 Highest on Record. Back to top
Some results from the Third International Mathematics and Science Study (TIMSS, now called Trends in International Mathematics and Science Study) are listed below. Click on links in the box for more information.
1. TIMSS-1995. US 12th graders performed very poorly in the TIMSS international comparison. One clear difference between the US and all other countries is that the US is the only country to offer a non-integrated curriculum of algebra I, geometry, and algebra II. All other countries in the world have an integrated high school mathematics curriculum.
2. TIMSS-1999 8th Grade Video Study. The US preformed below average on the international test. Methods of mathematics instruction in 8th grade were examined in the US and 6 countries that outperformed the US. Some differences include (i) US lessons tend to reduce the complexity of problems, (ii) US lessons contain more review and the least new content, (iii) US lessons are least likely to emphasize connections.
3. TIMSS-R 1999. The TIMSS test was repeated in 1999 with certain countries and also several states and consortia of schools in the US. One US group with high performance was the Michigan Invitational Group, a consortium of middle schools in Michigan from urban, rural, and suburban settings that used NCTM-Standards-Based curricula with strong professional development. Back to top
4. TIMSS 2003. The TIMSS test was repeated in 2003. See box for a link to information.
Some results from cognitive science are listed here. Click on the box in the main diagram above for more information. Some findings from cognitive science are that (i) the mind much prefers that new ideas be framed in concrete rather than abstract terms, (ii) there are significant differences among rote knowledge, inflexible knowledge, and deep structure knowledge, and (iii) deep structure knowledge can be facilitated by solving more problems in multiple contexts and focusing on meaning. Back to top
Some mathematics program ratings are summarized below. Click on the box in the main diagram above for more information.
1. The American Association for the Advancement of Science (AAAS) rated algebra textbooks in two categories – With Potential and Little Potential. Texts in the With Potential category were: Concepts in Algebra, Core-Plus Mathematics, Focus on Algebra, Interactive Mathematics Program, MATH Connections, Mathematics Modeling Our World, and UCSMP Algebra.
2. The US Department of Education reviewed mathematics programs in 1999 and rated five programs Exemplary: Cognitive Tutor Algebra, College Preparatory Mathematics, Connected Mathematics, Core-Plus Mathematics, and the Interactive Mathematics Program. Back to top
Two national mathematics education research review panels are listed below. Click on the box in the main diagram above for more information.
1. What Works Clearinghouse. This panel has been established by the US Department of Education to review research and identify scientifically research based programs and strategies in mathematics. As of December 2003, no results are yet available.
2. The Mathematical Sciences Education Board (MSEB) has established a panel to review the evaluation data on the effectiveness of NSF-supported and commercially generated mathematics curriculum materials. As of December 2003, this panel has prepared a non-public first draft of a report which is under review. Back to top
Within the context of research
in mathematics education, the Iowa Mathematics Content Network project
has undertaken to review some of the research on mathematics instructional
strategies and programs. The Iowa Department of Education has set up a
panel consisting of nine Iowa mathematics educators to review this research.
This is an ongoing project, and the research reviews presented on this
web site at any given time should not be considered comprehensive or complete.
They should also be interpreted in the context of the information in the
main diagram shown above as well as in the context of the particular educational
settings in which they might be applied.
Some of the key themes identified so far in studies having a research design rated 3 or above are: