In this study I examine the structures of 2 teachers' beliefs about what makes mathematics intrinsically motivating and provide instances of the representations of their beliefs at 2 times: before the introduction of middle school mathematics curricula organized around the tenets of Realistic Mathematics Education and after 1 year of implementing a pilot program. Personalconstructs analyses are paired with observations of teachers' classrooms and their beliefs and perceptions as reported in semistructured interviews. Results indicate that the teachers became more attuned to the conceptual complexity and challenge of mathematics activities and placed less emphasis on task ease over their year of involvement in the pilot program. Results are discussed in relation to “job-embedded learning,” a form of staff development that fosters teachers' development of meaning with regard to reforms, and how such learning enables shifts in teacher beliefs and practice.
James A. Middleton
This article examines the relationship between teachers' and students' personal constructs with regard to intrinsic motivation in the mathematics classroom. The research focused on (a) the ways in which teachers attempted to build student motivation into their lessons and (b) the belief systems of teachers as compared to those of their students. In a repertory grid task, students and teachers were asked to distinguish what they believed makes mathematics motivating.
James A. Middleton and Marja van den Heuvel-Panhuizen
The middle grades offer unique challenges to the mathematics teacher, especially in this time of transition from traditional to reformed curricula and methods. The range and conceptual quality of mathematical knowledge that students have as they enter grades 5 and 6 vary greatly. Many students have been accelerated through textbooks, resulting in a high degree of proficiency at arithmetic computation but sometimes with little conceptual understanding of the underlying mathematics. Many other students will enter the middle grades with only rudimentary understanding of addition and subtraction. This disparity of skills and understanding creates a difficult dilemma for middle school teachers. Should they review the arithmetic that students have already experienced, or should they forge ahead to a higher level of more difficult mathematics? This decision need not be perceived as a dichotomy. Methods exist for exploring higher-order mathematical topics conceptually that allow understanding by students of varying knowledge levels whatever their base knowledge may be.
James A. Middleton and Photini A. Spanias
in this review we examine recent research in the area of motivation in mathematics education and discuss findings from research perspectives in this domain. We note consistencies across research perspectives that suggest a set of generalizable conclusions about the contextual factors, cognitive processes, and benefits of interventions that affect students' and teachers' motivational attitudes. Criticisms are leveled concerning the lack of theoretical guidance driving the conduct and interpretation of the majority of studies in the field. Few researchers have attempted to extend current theories of motivation in ways that are consistent with the current research on learning and classroom discourse. In particular, researchers interested in studying motivation in the content domain of school mathematics need to examine the relationship that exists between mathematics as a socially constructed field and students' desire to achieve.
James A. Middleton, Marja van den Heuvel-Panhuizen, and Julia A. Shew
Middle Grades Students Should be able to understand, represent, and use numbers in a variety of equivalent forms, including fractions, decimals, and percents. They should develop number sense for fractions and other representations of rational number. Students should also be able to represent such relationships in graphical form (NCTM 1989).
Amanda K. Riske, Catherine E. Cullicott, Amanda Mohammad Mirzaei, Amanda Jansen, and James Middleton
We introduce the Into Math Graph tool, which students use to graph how “into" mathematics they are over time. Using this tool can help teachers foster conversations with students and design experiences that focus on engagement from the student’s perspective.
NCTM Research Committee
Eric Gutstein, James T. Fey, M. Kathleen Heid, Iris DeLoach-Johnson, James A. Middleton, Matthew Larson, Barbara Dougherty, and Harry Tunis
The NCTM's Research Committee has prepared this article as a means to raise the awareness about equity and issues surrounding equity from a research perspective as well as to support the NCTM's commitment to the Equity Principle. The committee discusses the concept of equity from three perspectives: as a subject of research, as a “critical lens” with which to examine research, and as a cross-disciplinary theme. Equity issues offer a unique opportunity to unite research and practice within mathematics education and across other disciplines.
NCTM Research Committee
M. Kathleen Heid, Matthew Larson, James T. Fey, Marilyn E. Strutchens, James A. Middleton, Eric Gutstein, Karen King, and Harry Tunis
This article discusses the challenge of improving the interrelationships between research and practice in mathematics education, and it outlines actions being taking to respond to that challenge. The need for improvement is bidirectional. The practice of classroom mathematics teaching needs to be better informed by an understanding of the implications of existing bodies of research, and researchers need to learn more from the insights and knowledge of practitioners. Building on its series of initiatives designed to use research to guide mathematics teaching and learning, NCTM has made a new commitment to a flexible, nimble, and sustainable initiative that will strengthen the bidirectional link between research and practice. This initiative includes the development of Research Analyses, Briefs, and Clips (ABCs), research syntheses designed through collaboration of teacher leaders and researchers to inform instructional leaders and policymakers about research perspectives on critical issues of practice.
James A. Middleton, Barbara Dougherty, M. Kathleen Heid, Beatriz D'Ambrosio, Robert Reys, Iris de Loach-Johnson, Eric (Rico) Gutstein, and Marilyn Hala
This article by the NCTM's Research Committee presents a call for an Agenda for Research Action in Mathematics Education. The committee reviews central crosscutting issues for mathematics education research that address concerns from the political and practitioner communities regarding the coherence and utility of mathematics education research. Issues of values and feasibility are highlighted, and a broader definition of theoretical and empirical scholarship is promoted. The committee proposes that the mathematics education research community take up the mantle of authority for defining rigor and evidence in much the same way as NCTM did when facing similar criticism in earlier crises (e.g., the Agenda for Action and the Standards).