For all practical purposes, mathematical reform in Latin America began with the First Inter-American Conference on Mathematical Education, held in Bogota, Colombia, December 4 to 9, 1961.
Edited by Howard F. Fehr
Harold P. Fawcett
Inspired teaching at all levels, from the kindergarten through the graduate school, is a necessary condition for reform in mathematics education.
Drawing on several decades of research findings, the National Council of Teachers of Mathematics (NCTM) produced, between 1989 and 1995, three volumes of Standards in which members of the mathematics education community formulated new visions of mathematics learning, teaching, and assessment. These new visions comprise an ambitious agenda for the mathematics classroom—one that includes, but surpasses, mastery of facts and procedures, the mainstay of extant practice—designed to engage students in the exploration of mathematical ideas and their interrelationships. Students would now be invited to articulate their ideas, and teachers to identify and mobilize those elements in children's thinking upon which stronger conceptions can be built. Paralleling this ambitious departure in teaching practice, new means of assessment were proposed to capture progress toward these far-reaching goals.
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.
Robert Reys, Barbara Reys, Richard Lapan, Gregory Holiday and Deanna Wasman
This study compared the mathematics achievement of eighth graders in the first three school districts in Missouri to adopt NSF-funded Standards-based middle grades mathematics curriculum materials (MATH Thematics or Connected Mathematics Project) with students who had similar prior mathematics achievement and family income levels from other districts. Achievement was measured using the mathematics portion of the Missouri Assessment Program (MAP) administered to all 8th graders in the state annually beginning in the spring of 1997. Significant differences in achievement were identified between students using Standards-based curriculum materials for at least 2 years and students from comparison districts using other curriculum materials. All of the significant differences reflected higher achievement of students using Standards-based materials. Students in each of the three districts using Standards-based materials scored higher in two content areas (data analysis and algebra), and these differences were significant.
Kimberly Hufferd-Ackles, Karen C. Fuson and Miriam Gamora Sherin
The transformation to reform mathematics teaching is a daunting task. It is often unclear to teachers what such a classroom would really look like, let alone how to get there. This article addresses this question: How does a teacher, along with her students, go about establishing the sort of classroom community that can enact reform mathematics practices? An intensive year-long case study of one teacher was undertaken in an urban elementary classroom with Latino children. Data analysis generated developmental trajectories for teacher and student learning that describe the building of a math-talk learning community—a community in which individuals assist one another's learning of mathematics by engaging in meaningful mathematical discourse. The developmental trajectories in the Math-Talk Learning Community framework are (a) questioning, (b) explaining mathematical thinking, (c) sources of mathematical ideas, and (d) responsibility for learning.
Edited by Howard F. Fehr
Editor's note.—Professor Byran Thwaites of Southampton, along with Professor Cyril Hope of Worchester, is among the prime movers of reform in mathematical education in England. This paper gives not only a general review of the reform movement but also an overall philosophy of English education in language that is clear and altogether charming.—Howard F. Fehr.
In this report I offer an exploration of the insights that may be provided by a situated perspective on learning. Through an extension of my previous analysis of students learning mathematics in 2 schools (Boaler, 1998), I consider the ways in which a focus on the classroom community and the behaviors and practices implicit within such communities may increase one's understanding of students' mathematical knowledge production and use. The implications of such a focus for classroom pedagogy and assessment as well as for research in mathematics education are considered.
Julie E. Riordan and Pendred E. Noyce
Since the passage of the Education Reform Act in 1993, Massachusetts has developed curriculum frameworks and a new statewide testing system. As school districts align curriculum and teaching practices with the frameworks, standards-based mathematics programs are beginning to replace more traditional curricula. This paper presents a quasi-experimental study using matched comparison groups to investigate the impact of one elementary and one middle school standards-based mathematics program in Massachusetts on student achievement. The study compares statewide standardized test scores of fourth-grade students using Everyday Mathematics and eighth-grade students using Connected Mathematics to test scores of demographically similar students using a mix of traditional curricula. Results indicate that students in schools using either of these standards-based programs as their primary mathematics curriculum performed significantly better on the 1999 statewide mathematics test than did students in traditional programs attending matched comparison schools. With minor exceptions, differences in favor of the standards-based programs remained consistent across mathematical strands, question types, and student sub-populations.
Daniel F. McGaffrey, Laura S. Hamilton, Brian M. Stecher, Stephen P. Klein, Delia Bugliari and Abby Robyn
A number of recent efforts to improve mathematics instruction have focused on professional development activities designed to promote instruction that is consistent with professional standards such as those published by the National Council of Teachers of Mathematics. This paper describes the results of a study investigating the degree to which teachers' use of instructional practices aligned with these reforms is related to improved student achievement, after controlling for student background characteristics and prior achievement. In particular we focus on the effects of curriculum on the relationship between instructional practices and student outcomes. We collected data on tenth-grade students during the 1997–98 academic year. Some students were enrolled in integrated math courses designed to be consistent with the reforms, whereas others took the more traditional algebra and geometry sequence. Use of instructional practices was measured through a teacher questionnaire, and student achievement was measured using both the multiple-choice and open-ended components of the Stanford achievement tests. Use of standards-based or reform practices was positively related to achievement on both tests for students in integrated math courses, whereas use of reform practices was unrelated to achievement in the more traditional algebra and geometry courses. These results suggest that changes to instructional practices may need to be coupled with changes in curriculum to realize effects on student achievement.