Current reform efforts, which aim to improve the mathematics abilities of American citizens, call for mathematics instruction that emphasizes sense making, reasoning and argumentation. This study was conducted to understand the outcomes of Collaborative Reasoning, a reform-oriented instructional strategy, in seventh and eighth grade mathematics classrooms. An embedded, quasi-experimental, mixed-methods design was used to investigate: the effects of Collaborative Reasoning on students' mathematics performance, and the ways in which students' reasoning abilities change as a result of participating in Collaborative Reasoning. The quantitative results revealed statistically significant changes in mathematics performance from pre-test to post-test. Post-test analysis showed a statistically significant difference in assessment scores, with the treatment group out-performing their comparison group peers. The qualitative results of the study show that as a result of participating in Collaborative Reasoning sessions, students were choosing reasoning strategies that were more appropriate, were using appropriate reasoning strategies more consistently, and were better able to verbally explain their reasoning. Finally, it was found that as students participate in Collaborative Reasoning their discourse becomes less calculational and more conceptual in nature, and more students become active participants within small group discussions. / Math & Science Education

The core purposes of this study were twofold: (1) to ascertain whether mathematics teachers support reform oriented teaching practices, and (2) to discover whether there is correspondence between what classroom mathematics teachers say they should do when they teach mathematics and what they really do in the classroom. To carry out this investigation, elementary, middle and high school mathematics teachers responded to survey questions about their beliefs and practices and were observed. There are two major research questions that underlie this research and several secondary questions. The primary questions are: 1. Do in-service mathematics teachers support the major principles of reform oriented mathematics instruction? 2. To what extent do in-service mathematics teachers exhibit reform-oriented teaching in their classrooms? Among the secondary research questions are the following: 3. Does professional development support reform oriented teaching practices? 4. Do teachers' beliefs vary with respect to the grade level they teach? 5. Do teachers' beliefs vary with respect to their levels of education? The subjects were mathematics teachers from three grade levels, elementary, middle and high school selected from three school districts in northeastern United States. One hundred seventy-four mathematics teachers participated in the main study. Ten of the teachers who completed the Questionnaire voluntarily participated in in-class observations and post-observation interviews. The Reformed Teaching Observation Protocol (RTOP) was used for the observation. All 10 teachers were interviewed individually immediately either after the in-class observation took place or a day later. The most salient finding of the study was that while teachers express a strong belief in the major tenets of reform oriented mathematics teaching, their actual demonstration of this type of teaching is far less evident. Pearson correlation analysis demonstrated only marginal relationships between teachers' demographic characteristics and their beliefs. A multiple regression analysis found that only 6% of the variance in beliefs is accounted for by the demographic variables. One of the major conclusions of the research is that teachers feel compelled to teach in ways that are discrepant from their beliefs in order to prepare their students for the standardized tests, which are now a critical component of educational accountability. Educational implications, limitations of the study and suggestions for future research are discussed. / Educational Psychology