師資培育生之小數除法概念及其相關教學知識的現況探究

An Investigation on Preservice Teachers’ Concepts and Pedagogy Knowledge of Decimal Division

本研究旨在探討師資培育生對於小數除法及小數除法教學之相關知識的瞭解，主要目的有三：（一）分析師資培育生的小數除法概念，（二）探討師資培育生對於國小學生在小數除法學習的瞭解情形，（三）調查師資培育生在小數除法的教學知識理解情形。本研究採問卷調查法，以自編問卷試題進行資料蒐集，研究對象為全國五所教育大學462 位四年級師資培育生，主要研究發現有：
一、師資培育生對於餘數為一位小數的問題多能成功解題。在除法直式運算過程中，部分師資培育生不瞭解被除數與除數進行相同的單位量轉換後，商不變，但餘數會隨之改變的現象；甚至認為移動小數點之目的只為方便計算，而不瞭解其數學意義。
二、多數師資培育生較能瞭解學生的小數除法學習發展情形，但仍有少數師資培育生無法明確指出學生解題過程中的錯誤，或不清楚進行小數除法運算時，學生普遍會遇到的困難。
三、多數師資培育生在安排小數教學序列時，忽略相關概念之先後順序及學生的學習發展程序；部分師資培育生採取以口訣或算則方式進行教學。
四、師資培育生在開放式問題的填答意願低，答題情形亦不甚理想；部分師資培育生描述其想法及教法時，出現表達不完整、以簡略字詞敘述，或以程序性知識回答的情況。

This purpose of this research was to investigate the preservice teachers’ understanding regarding decimal division and the related pedagogy knowledge. There were three goals for this research: (1) to explore the preservice teachers’ concept of decimal division; (2) to examine the preservice teachers’ awareness of the current decimal division learning performance in elementary schools; (3) to investigate the preservice teachers’ knowledge on teaching decimal division. The participants were 462 seniors who enrolled in teacher preparation programs from 5 universities of education. Data were collected via self-constructed questionnaires and tests. The main findings were as the follows:
1. Most participants had no problem solving long division problems with 1-digit remainder. However, some participants did not understand the reason why the quotient was the same but the remainder changed accordingly when the dividend and the divisor were converted to a new unit during the long division procedure. Some participants even thought that moving the decimal point during the procedure was for easier calculation.
2. Most of the participants had clear images regarding students’ development of decimal division. However, some participants could not identify students’ mistakes, and/or the difficulties students may encounter while solving decimal division problems.
3. Most participants ignored the learning sequences of decimal division when they were asked to design learning activities. Some participants only taught by mnemonics or algorithm.
4. The answering rate and the passing rate of opening questions were both low. Some participants gave incomplete, abbreviated descriptions, and/or procedural knowledge when they were asked to describe their thinking and/or teaching instructions.