A central part of the charge to the Research Advisory Committee (RAC) from the Board of Directors of the National Council of Teachers of Mathematics (NCTM) is to “act as a catalyst within the mathematics education research community to support and to focus attention on important or under-discussed issues.” In this report we respond to this charge by raising issues related to the role and potential effect of research in a school culture that has become so complex that systematic study of problems seems almost impossible. Before launching into this discussion, we provide an update on research activities of special significance.
Wim Van Dooren, Dirk De Bock, Dirk Janssens, and Lieven Verschaffel
The overreliance on linear methods in students' reasoning and problem solving has been documented and discussed by several scholars in the field. So far, however, there have been no attempts to assemble the evidence and to analyze it in a systematic way. This article provides an overview and a conceptual analysis of students' tendency to use linear methods beyond their applicability range. We start from an analysis of the linearity concept and its properties and representations. The main part consists of a summary and discussion of unwarranted applications of each of these properties and representations in various mathematical content domains in order to unravel similarities and differences. After that, we speculate on the factors that seem to be at the roots of the occurrence and persistence of the overreliance on linearity. Finally, we discuss educational implications and suggest perspectives for further research.
David W. Stinson
This article shows how equity research in mathematics education can be decentered by reporting the “voices” of mathematically successful African American male students as they recount their experiences with school mathematics, illustrating, in essence, how they negotiated the White male math myth. Using post-structural theory, the concepts discourse, person/identity, and power/agency are reinscribed or redefined. The article also shows that using a post-structural reinscription of these concepts, a more complex analysis of the multiplicitous and fragmented robust mathematics identities of African American male students is possible—an analysis that refutes simple explanations of effort. The article concludes, not with “answers,” but with questions to facilitate dialogue among those who are interested in the mathematics achievement and persistence of African American male students—and equity and justice in the mathematics classroom for all students.
Andreas L. Stylianides
Many researchers and curriculum frameworks recommend that the concept of proof and the corresponding activity of proving become part of students' mathematical experiences throughout the grades. Yet it is still unclear what “proof” means in school mathematics, especially in the elementary grades, and what role teachers have in cultivating proof and proving among their students. In this article, I propose a conceptualization of the meaning of proof in school mathematics and use classroom episodes from third grade to elaborate elements of this conceptualization and to illustrate its applicability even in the early elementary grades. Furthermore, I use the conceptualization to develop a tool to analyze the classroom episodes and to examine aspects of the teachers' role in managing their students' proving activity. This analysis supports the development of a framework about instructional practices for cultivating proof and proving in school mathematics.
Susan N. Friel, Frances R. Curcio, and George W. Bright
Our purpose is to bring together perspectives concerning the processing and use of statistical graphs to identify critical factors that appear to influence graph comprehension and to suggest instructional implications. After providing a synthesis of information about the nature and structure of graphs, we define graph comprehension. We consider 4 critical factors that appear to affect graph comprehension: the purposes for using graphs, task characteristics, discipline characteristics, and reader characteristics. A construct called graph sense is defined. A sequence for ordering the introduction of graphs is proposed. We conclude with a discussion of issues involved in making sense of quantitative information using graphs and ways instruction may be modified to promote such sense making.
Laura K. Eads
Arithmetic is growing in importance at all school levels. This was quite apparent at the April 1954 meeting of the National Council of Teachers of Mathematics in Cincinnati. The theme of the meeting was “Mathematics on the March” but arithmetic was given serious consideration by speakers and panelists representing schools, colleges, and industry.
Edited by Howard F. Fehr
In 1958, the structure of the Danish school system was changed, and in connection with this the curricula for each subject at all school levels were revised. This provided an opportunity to create a mathematics curriculum which reflects the trends reported in recent international discussions on the problem of modernization of mathematics teaching. This newly created curriculum is now being used in grades 8 to 11, and next year will go into operation in grade 12, the last secondary school year.
When the recent National Assessment of Educational Progress (NAEP) showed that “only about 40 percent of the 17-year-olds appear to have mastered basic fraction computation” (Carpenter et al. 1981). it underscored a problem that is very familiar to teachers of mathematics at all school levels: learning fractions and teaching fractions are two very difficult tasks. Another NAEP conclusion may also be familiar to teachers, but it merits their constant attention: when computational skills with fractions have been mastered by age 13, students have little understanding of them. Once they have forgotten procedures for computing fractions, few teenagers can reconstruct them