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Research on Mathematics Information
Created under MathStar NM

Why do teachers need to know about research? There are many reasons teachers need to know about research. Perhaps the most important is that because teachers are very in tune with what children know and how children think, teachers need to be able to set the research agenda and guide practice in the field. The growing movement in collaborative action research supports the notion of teachers as the ones who should be researching their own field.

A second reason teachers need to be familiar with the research is that this knowledge can support the teacher in doing what she knows works for kids. If questioned by administrators or parents, being able to site the research helps the teacher justify methods and practices and encourages others to let the teacher continue with her effective work.

A third reason for knowing the research is that it provides teachers with the vocabulary to describe what they do in terms that reflect a knowledge of the field. Being able to name different practices and ideas helps the teacher to understand and communicate her or his ideas about teaching practices.

An Agenda for the future

RAND Corporation's recommendations for mathematics education research
The following information is summarized from the upcoming, Rand Report: Achievement for All.

The RAND corporation was asked to suggest a research agenda for mathematics education that would be more focused and result in better results in terms of practice and student achievement. They recommend the development of communities of researchers, practitioners, and policy makers engaged in problem-centered research.

The Case for Mathematics
The first issue that has to be tackled is to make a case for mathematics itself. No one considers it to be OK if a child can't read, but many consider an inability to do math to be all right, even normal. We need to make a case for the importance of mathematics - in school, as a gatekeeper that limits life options, and as a necessity for all citizens.

The Research Agenda

Grounded in the need to ensure all students gain mathematical proficiency (see Adding It Up: How Children Learn Math) are the following suggestions for areas of research:

  1. Content:
    Focus on algebra broadly interpreted and in relation to number and geometry. Include opportunities to reason deeply about relationships and variables.
  2. Doing:
    Focus on doing mathematics How does one successfully learn, do and use mathematics? How does a student gain fluency and flexibility in doing math?
  3. Teaching and Learning:
    Focus on teachers and professional development. What kinds of professional development help teachers assist students to achieve mathematically?

What do we know about mathematics learning?

Research suggests that we need to change mathematics education because students are not learning the math they need or are expected to know. Nearly all students learn to add, subtract, multiply, and divide whole numbers, and the majority learn to do very simple arithmetic with fractions, decimals, and percents. However, students' knowledge and skills are apparently learned without much depth of conceptual understanding. This problem becomes evident when we study performance on related items that require students to extend these skills, reason about them, or explain why they work.

We have used the same basic methods to teach mathematics in the United States for nearly a century. In traditional mathematics teaching, the emphasis is on teaching procedures; little attention is given to helping students develop conceptual ideas, or to connecting the procedures they are learning with the concepts that show why they work.

Characteristics of instruction that build deeper understanding of mathematics:

  • Build directly on students' experiences, entry knowledge and skills.
  • Provide opportunities for both invention and practice. Classroom activity which revolves around solving problems that require some creative work by the students and some practice of already learned skills.
  • Focus on the development of multiple methods that reflect student thinking about mathematics. Classroom discourse should focus on thinking reasoning and problem solving as part of developing an understanding of mathematical concepts.
  • Require students to provide explanations. Students should be expected to present solutions to problems, to describe the methods they use, and to explain why they work.
Research shows that:
  • Instructional programs that emphasize conceptual development, with the goal of developing students' understanding, can facilitate significant mathematics learning without sacrificing skill proficiency.
  • Students learn new concepts and skills while they are solving problems.
  • If students over-practice procedures before they understand them, they have more difficulty making sense of them later.
Those programs that share the core instructional features mentioned above, and which have been implemented as intended for reasonable lengths of time, show that students perform as well or better than their traditionally taught peers.

Recommended websites

What barriers are there to mathematics achievement for many students? What strategies have worked in overcoming these barriers?

There are many factors that affect the success of culturally diverse students including the teachers' beliefs, values and attitudes toward diversity, involvement of the community in the lives of their children and their schools, the quality of curricula materials, teaching strategies and culturally responsive opportunities to learn. Students come to school with very different experiences, languages, learning styles, and dispositions for learning. Each child has different prior cultural experiences, interaction styles, and frames of reference, which are central to their learning and thinking processes. Many students have less access to the monetary or cultural capital, language, tools and resources, and relevant learning experiences than mainstream students have.

Effective teachers are able to acknowledge multiple ways of knowing and honor individual and cultural differences in a positive manner so that students can make links between school and home. Classroom behaviors should be examined in terms of discourse patterns, grouping and instructional strategies. Teachers need to examine their own expectations, practices, curricula, and the kinds of opportunities they provide for students to learn.

Recommended websites

  • Teaching and Learning Mathematics in Poor Communities A Report to the Board of Directors of the National Council of Teachers of Mathematics. Submitted by Task Force on Mathematics Teaching and Learning in Poor Communities.
  • Weaving Gender Equity into Math reform This project investigates the specific question of gender equity in math reform, as well as the larger equity issues that these reforms pose for students from various academic, socio-economic, and linguistic backgrounds.

What do we know about technology uses and mathematics learning?

This response is extracted from the article, Does it Compute? The Relationship Between Educational Technology and Student Achievement in Mathematics.
New research using data drawn from the 1996 National Assessment of Educational Progress (NAEP) in mathematics, appears to confirm used properly, technology can lead to gains in academic achievement and positively influence the social environment of the school, reducing teacher and student absenteeism and increasing morale. Yet it is important that the scope of technology in schools be limited to those areas where it provides benefits, and reduced in areas where it does not.

The study suggests that teachers should focus on using computers to apply higher-order skills learned elsewhere in class. Additionally, the study suggests that federal and state policy makers should redouble their efforts to ensure that teachers are properly trained to use computers, and that the quality of the teacher training offered is high and intensive, since this training is such an important component of making technology use successful. Third, the primary focus of all technology initiatives should be on middle schools rather than elementary schools. The effects of technology appear to be much smaller in the fourth than the eighth grade.

Computers are neither cure-alls for the problems facing schools, nor mere fads that have no impact on student learning. Rather, when they are properly used, computers may serve as important tools for improving student proficiency in mathematics, as well as the overall learning environment in the school.

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What do we know about successful professional development for mathematics teachers?

The key to raising the quality of learning, teaching and leadership in our school is a new kind of professional development that supports teachers as learners. We can't expect teachers to prepare today's students for the mathematics required for success in school and the world without engaging teachers in their own learning opportunities. These can not be one-shot workshops but must involve continuous experiences supported by teachers knowledgeable in mathematics content and pedagogy and able to model instruction which is both equitable and integrates modern technologies.

The professional development in mathematics needs to focus on content and the big math ideas. Because many teachers have never had opportunities to make sense of mathematics concepts there needs to be significant time for teachers to develop an understanding of math concepts, reasoning and procedures. The professional development needs to examine instructional models and help develop inquiry-based instruction. Then teachers need to reflect on their efforts in promoting student learning.

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