AbstractsMathematics

This study set out to determine the relationship between assessment practices and teaching methods. I wanted to investigate whether making mathematical investigation assessment tasks available to elementary-school mathematics teachers would have a positive effect on their teaching. Research tells us that standardized tests influence instruction. My research explored whether a national Assessment Task Bank of mathematical investigative tasks could influence teachers.With these aims in mind, the following research questions were formulated:1. Will the teachers' use of mathematical investigation tasks for assessment purposes influence their view of mathematics?2. Will the teachers' use of mathematical investigation tasks for assessment purposes influence the way they teach, and if so, in what ways?3. Will the teachers' use of mathematical investigation tasks for assessment purposes influence the way they assess their students, and if so, in what ways?My research was divided into two parts: 1) a national study involving teachers-leaders throughout the country; and 2) an intensive study in a small Israeli community, called Sharon. The first part examined how the national courses on assessment that I conducted affected the participating teacher-leaders in terms of their concept of mathematics, their teaching methods and their assessment practices. The second part examined the same issues with regard to the mathematics coordinators in the Sharon community. In each case, I have detailed my experiences so that the reader can gain a view of all facets of the study.The research methodology adopted was based on a constructivist paradigm, sometimes referred to as a "naturalistic inquiry", utilizing ethnographic principles wherein the data collection and analysis procedures were eclectic. In the course of the five years of my research, I used many strategies of data collection - ++ for example, unstructured participant-observations, interviews, questionnaires and content analysis of artifacts (tests and tasks written by teachers).The ideas of reform mathematics (as defined in Ch 2 of this thesis) are based on a broadened vision of mathematics with emphasis on higher-order thinking. My research indicated that the use of mathematical investigation tasks helped the teachers in my study reach the awareness that mathematics, even on the elementary school level, involves generalizations, justifications and even creativity.Prior to my research, and because of my position, I was aware that Israeli teachers were concerned primarily with teaching routine procedures and that their work sheets for the most part involved single-answer exercises. My research indicated that the use of mathematical investigation tasks indeed influenced the way teachers teach. Verbalization-having the students explain "Why"-has become integral to the teaching practices of the participants in my study. Nowadays, the Israeli teachers I worked with use "authentic tasks" in their classrooms: real-life situations that involve some mathematics. Unfortunately, these…