RESEARCH IN MATHEMATICS EDUCATION: WHAT IT CAN AND CANNOT DO

Think of the many things that can be investigated in mathematics education; it is easy to be overwhelmed. Four key ingredients can be identified:

• The students trying to learn mathematics—their maturity, their intellectual ability, their past experiences and performances in mathematics, their preferred learning styles, their attitude toward mathematics, and their social adjustment.

• The teachers trying to teach mathematics—their own understanding of mathematics, their beliefs relative to both mathematics itself and how it is learned, their preferred styles of instruction and interaction with students, their views on the role of assessment, their professionalism, and their effectiveness as a teacher of mathematics.

• The content of mathematics and its organization into a curriculum—its difficulty level, its scope and position in possible sequences, its required prerequisite knowledge, and its separation into skills, concepts, and contextual applications.

• The pedagogical models for presenting and experiencing this mathematical content—the use of optimal instructional techniques, the design of instructional materials, the use of multimedia and computing technologies, the use of manipulatives, the use of classroom grouping schemes, the influences of learning psychology, teacher requirements, the role of parents and significant others, and the integration of alternative assessment techniques.

All of these ingredients, and their interactions, need to be investigated by careful research. Again, it is easy to be overwhelmed (Begle and Gibb, 1980). Our position is that educational research cannot take into account all of these variables. The result we must live with is acceptance that educational research cannot answer definitively all of the questions we might ask about mathematics education. At best, we can expect research in mathematics education to be helpful in these ways:

• It can inform us (e.g., about new pedagogical or assessment techniques).

• It can educate us (e.g., about the pros/cons of using different grouping models).

• It can answer questions (e.g., about the potential impact of professional development models for teachers).

• It can prompt new questions (e.g., about the impact of using the Internet to make real-world connections).

• It can create reflection and discussion (e.g., about the beliefs that students and teachers hold toward mathematics).

• It can challenge what we currently do as educators (e.g., about our programs for accommodating students with differing ability levels or learning styles).

• It can clarify educational situations (e.g., about how assessment can inform instruction).

• It can help make educational decisions and educational policy (e.g., about student access to calculators or performance benchmarks).

Yet, research in mathematics education can also be counterproductive or fall short of what we would expect in these ways:

• It can confuse situations (e.g., about which math curriculum is the best).

• It can focus on everything but your situation (e.g., about your classroom, your specific students, and their learning of mathematics).

• It can be hidden by its own publication style (e.g., its scholarly vocabulary and overwhelming statistics).

• It can be flawed (e.g., about the interpretation of the research data).

• It can be boring and obtuse (e.g., its technical jargon, its overuse of statistics and graphs, and its pompous style).

Above all, despite the wishes of many teachers and administrators, educational research cannot PROVE anything! At best, educational research provides information that the community of educators can use, misuse, or refuse. It is a well-established notion that research results tend not to be used by educators and at times are purposely ignored. For example, Reys and Yeager (1974) determined that while 97.5 percent of the elementary teachers frequently read general education journals, 87.5 percent of these same teachers seldom or never read the research flavored articles. When asked why, 80 percent of the teachers replied with “lack of time” or “lack of direct classroom implications.” In contrast and on a more positive side, Short and Szabo (1974) found that mathematics teachers at the secondary level were much more knowledgeable about and favorable toward educational research than their colleagues in English and social science.

The situation needs to change, as research results must be reflected on and integrated as an important part of the mathematics education plan and process . The entire education community—mathematics teachers, administrators, parents, must take and share in the responsibility for this reflection process and integration of research results, whether it occurs at the individual learner level, the classroom level, the district level, the university level, or the state level. This article is written to serve as a catalyst for promoting reflection, discussion, and problem solving within this education community, helping this same community continue to shift from the “yesterday” mind to the “tomorrow” mind in its approach to mathematics education.