James A. Middleton

Motivation for achievement in mathematics: Findings, generalizations, and criticisms of the research

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.

Assessing Artistic and Problem-Solving Performance in Minority and Nonminority Students Using a Nontraditional Multidimensional Approach

The persistent underrepresentation of ethnic minority students in gifted programs requires change. Because identification tools used for entry into gifted programs often are held responsible for minority underrepresentation, this study investigated several nontraditional assessments for their efficacy in identifying both minority and nonminority students. A sample of 433 sixth-grade students responded to a drawing task and to two problem-solving assessments. Peer and teacher nominations also were used in the identification process. Findings indicated that the assessments identified a proportionate number of minority and nonminority students with potential in art or problem solving. The study holds promise for a multidimensional approach and for specific nontraditional assessments as means of effectively identifying both minority and nonminority student talents in art and problem solving. The study also suggests directions for further research.

Using a Functional Approach to Change Preservice Teachers' Understanding of Mathematics Software

Abstract This study examined the structure of two preservice teachers’ understandings of educational software in mathematics using repertory grid techniques. Specifically, the study focused on how teacher educators can enable preservice teachers to discern the features of mathematics software, and develop pedagogical goals that reflect the affordances and constraints of available tools. Results showed a deepening of knowledge and a differentiation of knowledge following experiences of exploration, evaluation, and comparison of different types of software. Results imply that directing preservice teachers’ attention to utilizing the functional characteristics of software for developing plans and for the design of instruction may be fruitful for more effective integration of software in their future teaching. However, participants’ preexisting content knowledge and their pedagogical worldview tempered this effect.

Promoting Critical-Thinking Dispositions by Using Problem Solving in Middle School Mathematics

Abstract This review of research generates principles for the design of instructional programs that foster critical-thinking dispositions. The dispositional aspect of critical thinking may be considered part of attitudinal memory, readily activated if sufficiently strong. We describe evidence suggesting that ill-structured problem-solving can provide middle schoolers with motivating activities that strengthen critical-thinking dispositions, thus fostering sensitivity to occasions for thinking critically and the inclination for engaging in such practices. The Jasper Series and Decision Making are reviewed as cases of programs for middle level mathematics learning that afford opportunities for ill-structured problem-solving activities that incorporate five important attitudestrengthening elements. Fazio (1995) identified these elements as direct experience, sensory experience, emotional reaction, freely chosen behavior, and attitude rehearsal. We describe how the design of the two mathematics programs incorporates attitude-strengthening elements that can potentially foster critical-thinking dispositions. Based on this review, we present a set of design principles to promote those dispositions.

An Agenda for Research Action in Mathematics Education: Beginning the Discussion

This article by the NCTMs 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 AgendaforAction and the Standards).

Developing Elementary Teachers’ Knowledge about Functions and Rate of Change through Modeling

The purpose of this article is to describe the development of elementary school teachers’ mathematical knowledge for teaching as they participated in a Modeling Instruction environment that placed heavy emphasis on improving their subject-matter knowledge as a basis for affecting the development of their pedagogical content knowledge. We investigate the development of the teachers’ content knowledge and pedagogical content knowledge by considering the results of our iterative revisions with supporting documentation of the insights we made as we refined the course to explore teachers’ knowledge. We conclude that Modeling Instruction helped the teachers conceive of mathematics as a tool to explain scientific phenomena and provided the teachers with opportunities to reflect upon the process of learning mathematics, which were both foundational to the development of their subject matter knowledge and their pedagogical content knowledge.

How Engineering Standards Are Interpreted and Translated for Middle School.

In this exploratory study we examined the alignment of Next Generation Science Standards (NGSS) middle school engineering design standards with lesson ideas from middle school teachers, science education faculty, and engineering faculty (4–6 members per group). Respondents were prompted to provide plain language interpretations of two middle school Engineering Design performance expectations and to provide examples of how the performance expectations could be applied in middle school classrooms. Participants indicated the challenges and benefits of implementing these performance expectations and indicated personal experiences that helped them to interpret the performance expectations. Quality of lessons differed depending on the performance expectation being addressed. Generally, respondents were better able to generate ideas that addressed the paradigm of students ‘‘analyz[ing] data from tests to determine similarities and differences among several design solutions’’ than having students ‘‘define the criteria and constraints of a design problem.’’ A notable finding was the scarcity of quality engineering lesson ideas. The greatest proportion of lessons were categorized as Vague and/or Overly Broad. It appears that NGSS engineering design standards can too easily be decoded in an excessively expansive manner, thus resulting in indefinite ideas that are difficult to translate into classroom practice.

The Role of Large-Scale Studies in Mathematics Education

The goal for this monograph has been to present the state of the art in large-scale studies in mathematics education. Although the chapters collected here are not intended to be a comprehensive compendium of such research, this selection of work does serve both to represent large-scale studies in the field of mathematics education and to raise awareness of the issues that arise in conducting such studies. As can be seen from the studies included in this volume, the term “large-scale study” can cover a wide variety of research endeavors. Indeed, as we indicated in the introductory chapter, the IES and NSF Common Guidelines (U.S. Department of Education & National Science Foundation, 2013) recognize many different types of research, and large-scale studies can fall into more than one of these categories. The different types of research have correspondingly different purposes which require different sample sizes and methods of analysis. Moreover, the findings from different types of research have different degrees of generalizability. Despite these many differences, there are common features that large-scale studies share. For example, large-scale studies require large sample sizes, although exactly how large “large” depends on the design of the study. In contrast to small-scale studies, large-scale studies usually employ complex statistical analysis and have the potential to produce more readily generalizable results than small-scale studies.

Why Mathematics Education Needs Large-Scale Research

Over the years our community has benefitted greatly from the application of survey methods to the discernment of patterns in student mathematics performance, attitudes, and to some degree, policies and practices. In particular, such research has helped us discover differential patterns in socioeconomic, gender, and ethnic groups and point out that, as a system, mathematics curriculum and instruction has hardly been equitable to all students. From the National Center on Education Statistics (in the US), large scale studies such as High School and Beyond, the Longitudinal Study of American Youth, and the National Assessment of Educational Progress came important calls to focus attention on improving instruction for marginalized populations and to increase emphasis on more complex problem solving than had typically been the norm (Dossey & Wu, 2013).

A path analysis of the relationship among critical motivational variables and achievement in reform-oriented mathematics curriculum

Abstract This study investigated the relationship among critical motivational variables and mathematics achievement as middle grades students engaged in a reform-oriented curriculum, Mathematics in Context. We tested 327 students in fifth, sixth, and seventh grade before and after two years of implementation. We performed a path analysis with subscales representing latent motivational variables and with achievement on the Iowa Test of Basic Skills as the outcome variable. The variables stimulation and control interacted to produce task interest, which, in turn, contributed to achievement gains. Effort was a byproduct of the stimulation afforded by the mathematical tasks. Attributions of success and failure were outcomes of interest. Utility mediated the effort on tasks and the attributions the tasks engendered. Results show that, with curriculum designed to emphasize utility and interest, students forged a high degree of motivation. Also, their achievement increased dramatically, in part, as a function of this increase in motivation.