This paper focuses on the discourse of teachers and instructors in a TEAMS (Teaching Exploratively for All Mathematics Students) professional development (PD) setting and on the discursive mechanisms that afford such learning. We conceptualize learning in this PD as a change in a teacher's pedagogical discourse—from alignment with Delivery Pedagogical Discourse (DPD) to alignment with Explorative Pedagogical Discourse (EPD). This change in pedagogical discourse involves commognitive conflicts between the DPD and EPD. Data for the study include 8 videotaped sessions from a 2-year TEAMS PD for middle school mathematics teachers. Results show that conflict revolved around four themes. The most common was about students' abilities and its relation to instruction. The others were: Who is responsible for constructing mathematics knowledge in class? Limited view of the EPD, and what is considered ordinary instruction? We also identified four levels of conflict, ranging from commognitive conflict that is implicit to the participants, to conflict that is made explicit and reflected upon. Finally, results show movement from implicit conflict towards explication of conflict during the two years of the PD.
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Einat Heyd-Metzuyanim Michal Tabach Talli Nachlieli 《Journal of Mathematics Teacher Education》2016,19(6):547-574
The mathematics education field, including prospective teacher education program, has seen a continuous effort to change teaching practices to be more cognitively demanding, conceptually oriented and student centred. Our goal in this study was to examine how certain underlying assumptions about mathematical learning, as reflected in a skilled instructor’s discourse, align with opportunities to learn. The data included a set of fully transcribed 11 lessons from an introductory algebra course. The method of analysis was built upon the communicational (commognitive) framework and included discerning between the instructor’s mathematizing and identifying talk. This framework was extended to quantify the instructor’s identifying talk over the whole set of lessons. Our findings showed that at the surface level, the instruction in the class seemed to align with “explorative” goals. On a deeper level, however, it was more aligned with “ritual” goals that are concerned with producing narratives about people, not about mathematics. 相似文献
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The paper opens with the theoretical construct of figural concepts. It is argued that geometrical figures are characterized by both conceptual and sensorial properties. A geometrical figure is a mental abstract, ideal entity, the meaning of which is governed by a definition. At the same time, it is an image: it possesses extensiveness (spatiality), shape and magnitude. In geometrical reasoning the two categories of properties should merge absolutely, with the sensorial components providing the dynamics of invention and the conceptual component guaranteeing the logical course of the mathematical process. The paper investigates the effects of interaction between the conceptual and the figural components of a number of geometrical figures under the impact of age and mathematical competence. It has been found that age does not improve the control of the conceptual component on the interpretation of figures (between ages 14 and 17) in contrast to what one could expect. Usually, as an effect of age (grade) the interpretation gets worse. On the other hand, there are striking differences between the three competence levels considered. Strong mathematical students are characterized by their capacity to overcome the apparent contradiction between the figural, direct, impressions and the definitory properties. Their decision is, ultimately, determined according to the formal constraints (axioms and definitions). 相似文献
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