Investigating Standards-Based Mathematics Education: A Study of Middle-Grades Students' Algebraic Thinking

Mary Huntley

Efforts to improve school mathematics over the past decade, prompted by recommendations from the National Council of Teachers of Mathematics, have resulted in the development, commercial publication, and adoption of comprehensive reform mathematics curricula in schools and districts across the U.S. These materials differ in substantive ways from traditional textbooks, and have sparked acrimonious debate among stakeholders in mathematics education. While differences in opinion about what is important for students to learn and how it should be taught are not new, rapid dissemination of criticism (as well as support) of the reform curricula has precipitated an urgent call for research-based evidence of their effectiveness. The purpose of this study is to examine the impact of one reform mathematics curriculum (the Connected Mathematics Project [CMP]) on students’ conceptual understanding and skills in one content area (algebra) using structured clinical interviews. This research will be guided by two questions. 1. On problems representing the big ideas of algebra, and on problems that present stumbling blocks for many students who use traditional algebra curricula, to what extent do CMP students construct effective (accurate, efficient, and flexible) solution strategies? 2. What are the critical features of instruction in CMP classrooms (e.g., nature of instructional tasks, role of the teacher, social culture of the classroom, mathematical tools as learning supports, and equity/accessibility) that may affect students’ learning of algebra? Twelve teachers will participate in this study – four each from urban, suburban, and rural settings. Each will be asked to help select three pairs of students who are likely to be cooperative and represent a range of success in mathematics. An assessment will be developed consisting of problems representing the big ideas of algebra, and problems documented in the literature as being troublesome and impediments to students’ learning. After refining the items through extensive pilot testing, assessments will be administered via one-hour clinical interviews with structured probes to each of the 36 pairs of students late in the school year. Students will have access to written problem statements, scratch paper, and graphing calculators. All interviews will be audiotaped. To verify fidelity of implementation and to investigate critical features of instruction in CMP classrooms that may affect students’ learning of algebra, each of the 12 teachers will be observed three times throughout the school year. A detailed analysis of the interview transcripts and classroom observation data will be performed. Textbooks play a key role in classroom practice and thus are strong determinants of what students have an opportunity to learn. Careful study of reform mathematics curricula is necessary if over a decade of work and large sums of money are to result in lasting, evidence-based usable knowledge that can help schools improve the ways in which children are educated.

About Mary Huntley

My undergraduate degree is in mathematics and computer science, and my masters degree is in applied mathematics. I spent one year as an intern at the Eastman Kodak Research Laboratories modeling the film development process, then spent five years using mathematical models to study various aspects of meteorology. In 1997 I earned my doctorate under the advisement of Jim Fey at the University of Maryland, College Park. My dissertation examined theoretical and practical considerations of integrating mathematics and science in the middle-school curriculum. As a graduate student I had the opportunity to work on three NSF-funded projects: a teacher enhancement project, a teacher preparation project , and a curriculum development project. After earning my doctorate I spent two years working as an independent consultant, then spent two years working as a research associate for WestEd’s National Center for Improving Science Education. During this time I conducted research, evaluation, and curriculum analysis on a variety of projects ranging in size and scope, from small local projects to others, with international collaborators, that have implications for national policy. During the 2001/2002 academic year I served as a rotator at the National Science Foundation, where my primary responsibility involved overseeing projects involving grades Pre-K-12 mathematics instructional materials development. During Fall 2002 I joined the faculty at the University of Delaware as an assistant professor in the Department of Mathematical Sciences. I am particularly interested in investigating the effects of curricula on students’ learning of algebra, and the effects of curricula on teachers’ knowledge of and teaching of algebra.