HKIER

摘要

本研究設計數學乘法任務，將乘法相關數學語言融入課室話語實踐的行動，探討學生對乘法任務的解題表現。研究者首先分析和整理現行教科書乘法單元內容的異同，設計結合生活情境的乘法文字題，採用話語實踐方式教學，蒐集學生資料，包含現場教學的錄影、學生記錄的學習單、教師的教學省思等文件，了解學生在乘法任務解題的表現。研究發現和結論為：（1）教科書內容涵蓋乘法相關類型任務與數學語言，提供學生乘法概念的思維並發展解題策略；（2）學生在乘法任務「先乘再加減」的解題表現多元但列式易錯誤，透過話語實踐能辨識任務特徵；而「先加減再乘」教學後的解題表現流暢且正確率高，能充分理解題意並以完整句子描述想法；（3）透過OGAP乘法級數「先乘再加減」的任務結合話語實踐可協助學生了解「倍」、「剩下」、「不足」、「超過」、「幾倍多多少」或「幾倍少多少」的數學語言和詞彙；而「先加減再乘」的任務可強化學生解題策略的應用和運算能力的流暢度。

關鍵詞：乘法；數學話語；解題

Abstract

This study explored students’ performance in solving multiplication problems by designing mathematics text problem tasks and integrating multiplication-related mathematics discourse into teaching activities. Teachers used discourse to guide students in problem solving. The researcher first analyzed and sorted out the similarities and differences in the contents of multiplication units in the current three editions of textbooks, and then designed multiplication text problems that combined life situations and used discourse to teach. Data collected included on-site teaching videos, students’ worksheets, teachers’ teaching reflections and other documents to understand the performance of students in solving multiplication tasks. The findings were: (a) the contents of textbooks covered multiplication-related types of problems and mathematical discourse activities, providing students with the concept of multiplication and developing their problem-solving strategies; (b) students’ performance of “multiply-then-add-and-subtract” tasks was diverse, easy to make mistakes, but able to identify characteristics of the problem through discourse communication; furthermore, after instructing “add-and-subtract-then-multiply” tasks, students had fluent and accurate performance, and were able to understand the meaning of the problem and express ideas in complete sentences; (c) through the OGAP multiplication series task of “multiply-then-add-and-subtract” combined with discourse practices, students could understand “times,” “remaining,” “insufficient,” “exceeding,” “how many times more” or “how many times less” (mathematical language and vocabulary); the task of “add-and-subtract-then-multiply” strengthened students’ application of problem-solving strategies and fluency in calculation skills.

Keywords: multiplication; mathematical discourse; problem solving