數學臆測教學中教師擔任協調者角色之教學行為

Teaching Behaviors of Teachers: The Role of Moderator in Teaching Mathematical Conjecture

本研究是以個案研究法探討教師在臆測教學以協調者角色介入的教學行為。本研究採立意取樣， 以一位資深的數學臆測教學六年級教師為個案教師。蒐集的資料包含因倍數單元六節教學錄影 和學生學習單，資料分析架構是以活動的擁有權、想法的擁有權，來形成四個象限的教師角色， 並加入第三維度代表臆測教學五個階段。本篇探討的角色以協調者為主，協調者是教師具有活 動的擁有權，而學生具有想法的擁有權。研究結果發現：在臆測教學中，個案教師以協調者介 入主要是在效化階段，其次是證實階段和提出猜想階段。教學行為主要是辨認、比較與整合。 臆測教學不同階段採用不同的教學行為介入，在提出猜想階段，以協調者角色介入的目的是在 徵求學生比較自己的猜想和其他猜想的異同；在效化階段，是在徵求學生表達自己的立場；在 證實階段，是為了徵求學生辨認各種猜想之間的包含關係。本研究也發現即使相同的教學行為 在教學不同階段的介入也會不同，比較在提出猜想階段，是為了觀察更豐富的數學關係。比較 在效化階段，是為了區別不同猜想之間的前提條件是否相同，比較在證實階段是為了幫助學生 釐清各種猜想證明的先後順序。整合在效化階段，是為了幫助學生從多個類似的猜想中選出或 整合出一個最完整、最具代表的猜想。

The purpose of the study was to explore teacher behavior when playing the role of moderator in teaching conjecture in mathematics. A teacher was selected as a case study. The case was a sixth-grade teacher experienced in teaching conjecture. Collected data included six lessons of factors and multiple units. The analytical framework is based on the ownership of activities and ideas to form the role of teachers in the four quadrants, and the third dimension is added to represent the five stages of conjecture teaching. The role discussed in this article focuses on quadrant II－Moderator, which is characterized with the teacher having ownership of the activity and the student having ownership of thought. The results indicated that the role of the moderator frequently occurred in the validation stage, followed by the justification stage and formulation stage. Teaching behaviors consisted of recognizing, comparing, and integrating. In the formulation stage, the moderator asked students to compare their own conjectures with those of others. In the validation stage, the moderator asked students to express their position. In the justification stage, the moderator called for an inclusive relationship among the generalized conjectures. Students were required to compare in the formulation stage as the case teacher asked them to look at additional mathematical relationships, whilst they were required to compare in the validation stage to clarify the similarities and differences of the premises among the conjectures. In the justification stage, the case teacher asked students to compare in order to sequence the conjectures to be justified. In the validation stage, students were asked to integrate or select the most complete and representative conjectures.