數學探究教學的任務與學生的回應：一位大學數學教師教學實踐歷程的觀察

Teaching Tasks and Student Responses in an Inquiry-Based College Mathematics Course: A Case Study

本研究旨在探討大學數學課程實施探究教學歷程中教師關注的任務與學生回應。採個案研究法，以107學年度上學期「數學探索」課程中的師生為對象，透過教學錄影與觀察、師生訪談、學生問卷和解題討論來蒐集資料。質性資料轉錄後進行歸類分析，量化資料以平均數來呈現，以不同資料與人員的比對來進行三角校正。結果發現，教師的數學探究教學在「佈題－解題」的歷程中展開，教師以挑戰性問題來佈題，以提問的方式來引導學生釐清並完成解題。從教師提問的焦點來看，其教學歷程較關注的是提供線索與搭橋、要求學生說明兩個任務，而教師關注的任務引發的學生回應聚焦在搜尋比對和解題。從學生訪談和問卷的結果來看，大都肯定與經歷了探究對數學學習的價值。

This study investigated teaching tasks and student responses in a college-level mathematics course taught through an inquiry-based approach in the fall semester of 2018. The case study method was employed, and data were collected from video footage and observations of classes, interviews with teachers and students, discussions regarding problem solving, and a questionnaire. Qualitative data were classified on the basis of the teacher’s and students’ performance, and quantitative data were gathered from the questionnaire. In addition, triangulation was conducted on the analytical results and data, which were gathered from multiple sources. The results of this study indicated that the teacher’s inquiry-based mathematics instruction followed the process of “problem proposal and solution.” Specifically, the teacher assigned challenging tasks to the students to spark their motivation for inquiry. He then adopted the strategy of posing questions to guide the students through problems that required clarification and solutions. Analyzing the teacher’s questions, we found that the tasks assigned by the teacher were primarily related to “providing hints and bridging” and “asking for explanation.” The students’ learning process focused on the tasks of “searching and comparison” and “problem solving.” According to each of the student’s performance on the questionnaire and interview, most of them stated that the inquiry-based approach enabled them to understand the value of mathematics instruction.