Research Issues in the Learning and Teaching of Algebra - Vol. 4

Research Issues in the Learning and Teaching of Algebra - Vol. 4

Research Issues in the Learning and Teaching of Algebra - Vol. 4

Research Issues in the Learning and Teaching of Algebra - Vol. 4

Excerpt

We clearly know more today about teaching and learning mathematics than we did twenty years ago, and we are beginning to see the effects of this new knowledge at the classroom level. This is possible in part because of the financial support that has become available to researchers. If theory building and knowledge acquisition are to have a basis broad enough to inform policy and influence educational practice, such support is essential. Although funding levels remain low in comparison to existing needs, there are several research projects either completed or in progress that could not have been undertaken without support.

In particular, we can point to several significant sets of studies based on emerging theoretical frameworks. For example, young children's early number learning and older children's understanding of rational numbers have been the subject of several recent research programs. Most of us who do research would agree that our work is more likely to be profitable when it results from an accumulation of knowledge acquired through projects undertaken within a coherent framework rather than through single, isolated studies. To establish such a framework, researchers must be provided with the opportunity to exchange and refine their ideas and viewpoints. Conferences held in Georgia and Wisconsin during the seventies serve as examples of the role such meetings can play in providing a vehicle for increased communication, synthesis, summary, and cross-disciplinary fertilization among researchers working within a specialized area of mathematical learning.

Over the past few years, the members of the Research Advisory Committee of the National Council of Teachers of Mathematics (NCFM) have observed specializations emerge that could benefit from collaborative efforts. We therefore proposed to the National Science Foundation that funding be provided for the purpose of establishing research agendas in several areas where conceptual and methodological consensus seemed possible. We believed that such a project was needed at this time for two reasons: first, to direct research efforts toward important questions, and second, to encourage the development of support mechanisms essential to collaborative chains of inquiry. Four such specialized areas were selected for this project: the teaching and assessing of problem solving, the teaching and learning of algebra, effective mathematics teaching, and the learning of number concepts by children in the middle grades.

The plan for the project included a working group conference in each of the four areas, with monographs of conference proceedings to be published by the National Council of Teachers of Mathematics. An overview monograph, written by advisory board members, was also planned. The advisory board consisted of F. Joe Crosswhite, James G. Greeno, Jeremy Kilpatrick, Douglas B. McLeod, Thomas A. Romberg, George Springer, James W. Stigler, and Jane O. Swafford, while I served as project director. For each . . .

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