教師的數學教學知識與其對兒童數學知識認知之探討

An Investigation of Teachers' Pedagogical Content Knowledge and the Knowledge of Children's Cognition in Mathematics

本研究主要為瞭解國小教師之數學知識、數學教學知識及對兒童的數學知識之現況，並分析數學教學相關的三種知識之間的關係。研究結果發現：（一）在數學知識方面，教師對於本研究問卷所包含的數學課程之基本知識，三分之二教師具有中等以上程度的認知表現。（二）在對兒童數學知識的認知方面，教師對兒童數學學習的困難認知有三種：（1）兒童對數學概念的理解困難，不易運算解題；（2）實物操作困難，兒童不容易從操作中獲取具體概念；（3）兒童可以模仿解題，但概念混淆。教師對兒童對數學概念的理解困難，不易運算解題的認知程度最高。（三）在數學教學知識方面，包含三種認知：（1）由教師向兒童說明解釋概念與實物操作；（2）讓兒童分組討論與實物操作；（3）提供解題練習，讓兒童精熟解題方法。教師對由教師向兒童說明解釋概念與實物操作的認知程度最高。（四）教師的數學知識高低，對於兒童數學學習困難的三項認知以及數學教學知識的三項認知，皆未具顯著影響關係。（五）教師的數學教學知識與其對兒童數學知識的認知之間，具有典型相關。教師認知兒童的數學概念理解困難，但是偏重使用解釋說明教學，未來加強教師的數學知識與善用多元教學方式，幫助兒童理解數學概念，值得深入探討。

This study examined elementary school teachers’ mathematics knowledge， pedagogical knowledge and the knowledge of children’s cognition in mathematics. Teachers exhibited middle and upper level of basic mathematics knowledge. Three types of children’s difficulties in mathematical learning were indicated from teachers：（a）The difficulty of understanding concepts and the operation process；（b）The difficulty of practical operation in problem solving；（c）Children may imitate teachers’ solution without understanding the mathematical concepts well. Three types of pedagogical knowledge were indicated from teachers：（a）The oral explanation and demonstration by teachers；（b） Providing children with mathematical exercises to master learning；and （c）The collaborative learning and discuss in mathematical problem solving. The results show the canonical correlation between pedagogical knowledge and the knowledge of children’s cognition in mathematics. Further analysis of teachers’ pedagogical content knowledge as well as revision in teacher education programs designed to integrate content and pedagogy are suggested.