Volume 106(2), February2006

Angela T. Barlow, University of West Georgia

Janie M. Cates, Douglas County School System

This study investigated the impact of incorporating problem posing in elementary classrooms on the beliefs held by elementary teachers about mathematics and mathematics teaching. Teachers participated in a year-long staff development project aimed at facilitating the incorporation of problem posing into their classrooms. Beliefs were examined via pre- and postsurvey. Results indicated a positive impact on their beliefs about mathematics and mathematics instruction. Data from open-ended written responses verified the impact of problem posing on the teachers and their classrooms. Based on these findings, it is recommended that problem posing be incorporated into all professional learning and undergraduate education programs.

Charles B. Hutchison, University of North Carolina at Charlotte

U.S. schools have experienced a perennial shortage of teachers. Recently, many school districts have been inviting foreign veteran teachers to help mitigate such teacher shortages. This study describes the initial cross-cultural issues four international science teachers encountered when they immigrated to teach in U.S. high schools. In-depth, semistructured interviews of four science teachers (from Ghana, Britain, and Germany) produced the main source of data. The international teachers faced a variety of support system problems, which were not directly classroom related, but nevertheless had an impact on their instructional effectiveness. They also faced teaching-related issues, including differences in school organization and structure, assessment and philosophical beliefs, communication, textbooks, teaching methods, and teacher-student relations. They all expressed a need to become active learners in order to function effectively in their new teaching contexts. The implications are discussed based on the findings.

Sandra Crespo, Michigan State University

Cynthia Nicol, University of British Columbia

Preservice elementary school teachers’ fragmented understanding of mathematics is widely documented in the research literature. Their understanding of division by 0 is no exception. This article reports on two teacher education tasks and experiences designed to challenge and extend preservice teachers’ understanding of division by 0. These tasks asked preservice teachers to investigate division by 0 in the context of responding to students’ erroneous mathematical ideas and were respectively structured so that the question was investigated through discussion with peers and through independent investigation. Results revealed that preservice teachers gained new mathematical (what the answer is and why it is so) and pedagogical (how they might explain it to students) insights through both experiences. However, the quality of these insights were related to the participants’ disposition to justify their thinking and (or) to investigate mathematics they did not understand. The study’s results highlight the value of using teacher learning tasks that situate mathematical inquiry in teaching practice but also highlight the challenge for teacher educators to design experiences that help preservice teachers see the importance of, and develop the tools and inclination for, mathematical inquiry that is needed for teaching mathematics with understanding.

Ji-Eun Lee, Oakland University

This classroom scholarship report is based on the teaching experience using Davydov’s mathematics curriculum, which was developed in the former Soviet Union. While “from arithmetic to algebra” is the normally accepted instructional sequence in school mathematics, Davydov’s curriculum is laid out “from algebra to arithmetic,” focusing on algebraic thinking from the very beginning of the elementary grades. The purpose of this report is not to provide a definitive conclusion about which curriculum or sequence is better nor to address which instructional strategy is right in all circumstances. Rather, it is to explore how primary grade students develop their own conceptual understanding while confronting difficulties met within a specific context. This report provides actual classroom episodes from working with a group of first graders and describes dynamic interactions between the teacher and children while they discuss the use of algebraic expressions and understand the meaning behind them.