The effect on teachers of using mathematical investigation tasks as tools for assessment
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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 tasks are not always planned properly.My research demonstrated that teachers attending my professional courses found the mathematical investigation tasks to be useful for assessment purposes, providing them with additional information about their pupils, not obtainable through conventional assessment methods. The additional criteria (I introduced) for evaluating the pupils' work aided in defining these additional areas. I found that while teachers were quite willing to use the mathematical investigation tasks to supplement the conventional tests, they were reluctant to use them as replacements.Exposure to the Assessment Task Bank influenced to a certain degree, the way the teachers in my study assessed their students. The tests of the teachers who were participants in my study now regularly include elements that were previously absent: questions requiring explanations and questions with more than one possible answer.Although the teachers of my study were increasingly using questions that required higher-order thinking, the tendency was to use the tests in a summative manner, rather than formatively. In other words, many teachers found it difficult to use test results for planning their subsequent lessons. While they were able to analyze their students' work and could report in some detail on each student's performance, they failed to understand how this should affect their teaching. Before they were exposed to the tasks they had administered tests merely in order to provide grades, whereas now the teachers were often trying to understand the students' thinking.While long-term change is still elusive, my research has demonstrated that exposure to reform mathematics through the mathematical investigative tasks of the Assessment Task Bank did have some influence on the teachers' view of mathematics, as well as their teaching and assessment practices.
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