Students are exposed to a variety of mathematical tricks that ostensibly make it easier for them to solve problems. But tricks also undermine their understanding that mathematics is supposed to make sense; they rob students of opportunities to explore and struggle with ideas; and they obscure mathematical structure.
This study replicated an earlier study that explored the beliefs of a sample of K-8 pre-service teachers (PSTs). Results of this study position PSTs' beliefs along a traditional-reform continuum. The positioning from the current study is compared to that of the former study, to determine the level of progress made toward the National Council of Teachers of Mathematics' commitment to high-quality instruction. To position beliefs, PSTs completed a Likert survey, including open-ended questions, three times throughout their teacher preparation program (TPP): before taking any of their mathematics education courses, after taking both required mathematics education courses, and after student teaching. On the last survey iteration, PSTs completed additional Likert items and open-ended questions regarding their teaching practices. Analysis centered on the relationship between each iteration of the new survey, comparisons to results from the initial study, and the alignment between beliefs and teaching practices. Overarching results convey that even with the passage of eleven years, the positioning of beliefs and teaching practices remained relatively static. Beliefs related to the power of student ideas, mathematical processes, productive disposition, and productive struggle were categorized as being reform oriented. The perception that mathematics is mostly computation and that the expository teaching is the most effective way to teach mathematics were categorized as being strongly traditional. Beliefs that were categorized more centrally related to collaboration and the emphasis on answers. Suggestions are provided for teacher educators to continue their work toward reforming beliefs about mathematics and how to teach mathematics.
This qualitative study explored how Grade 4 students and the researcher co-created language to express statistical concepts in a multilingual Indian classroom during a weeklong instructional sequence. The analysis draws on a situated socio-cultural perspective on language in mathematics. Students' language progressed from simple claims to more refined and sophisticated expressions, enabling them to discuss central tendencies and distributions while acknowledging uncertainty. Co-created phrases such as & amacr;sap & amacr;s resh & amacr; (the nearby line) not only supported communication but also deepened reasoning. The article also discusses what role scaffolding played in refining these informal resources.
