一位七年級學生的比率構念－從解速率問題表現的觀點

Seventh Grader's Rate Construct-From His Performance on Solving Speed Problems

葉建德(Gen-Der Yeh) ； 劉祥通(Shiang-Tung Liu)

《科學教育月刊》 279期 (2005/06) Pp. 2-20

https://doi.org/10.6216/SEM.200506_(279).0001

摘要

本研究旨在探討一位七年級學生的比率構念。研究方法為個案研究，採用工作單為基準的訪談法蒐集資料，根據受試者在工作單上的解題與寫作表現，進一步訪談學生，以了解學生的解題想法。個案是一位七年級的男生，受訪時就讀於嘉義市某私立中學，在班上的數學成績約在前1/3。工作單問題的設計分成五個部份，分別是單位比率、合成性、比率的可重複性、座標軸變換與座標軸單位變換，共有十個問題，因受限於篇幅，本文只呈現六組「問題、訪談原案與分析」。重要的研究發現如下：(1) 個案能透過計算單位比率以比較速率快慢問題。(2) 座標變換之後，不影響他對等速運動圖形的認知。(3) 個案能察覺座標單位變換影響等速圖形的陡度，並且略具速率為合成比率的概念。

關鍵字

比率 ； 速率 ； 工作單爲基礎的訪談 ； 個案研究

並列摘要

The purpose of this study was to explore a seventh grader's construct of rate. The study was a case study. The task-structured interview technique was conducted in the process of data collection. According to the interviewee's performance of solving problems and writing on the tasks, the researcher made further interview to understand his thinking of solving problems. The subject in the present study was a seventh-grade student in a private school in Chiayi city, and his mathematics achievement was better than the other two third students in his class. The tasks consisted of five components-unit rate, chunked rate, repeatability, coordinate axis transformation and transformation of coordinate axis unit, respectively. There were ten questions in the tasks, but only six groups of them were presented here, due to the limitation of capacity in this study. The major findings of this study were as follows: (1) He could solve speed problem by computing unit rate. (2)His cognition of constant motion graphic was not influenced by the transformation coordinate axis. (3)He could recognize the steepness of constant motion graphic was influenced by the coordinate axis unit transformation, and he almost could understand that speed was a conception of chunked rate.

並列關鍵字

rate ； speed ； structured-task ； case study