透過數學教學案例提昇教師比與比值教學的專業知識

摘要本研究目的是探討透過數學教學案例提昇教師比與比值教學的專業知識。研究者於校外成立數學案例討論團體，透過五位國小教師參與前測、四次案例討論、後測……等方法蒐集相關資料。討論的案例內容包含「比和比值的概念」、「相等的比」及「比語意情境類型及困難度」有關教師比與比值的數學知識、學習者數學認知知識以及數學教學知識。本研究發現透過數學教學案例的討論，能提昇教師比與比值教學的專業知識，包括：(一)數學知識方面：透過案例討論教師們概念能獲得釐清並建立相關數學概念，使教師們的數學概念更趨完善，而且更能掌握教材；(二)在學習者數學認知知識方面：藉由案例的研讀及討論，教師們更能察覺學生的迷思概念及解題策略；(三)在教學知識方面：教師們在教學順序的安排上更趨完整及精準。而研究結果也顯示，透過數學教學案例的討論，教師們教學專業知識的成長為多元且有其差異性，並促進教師數學教學信念的改變。關鍵字：比、解題策略、迷思概念

關鍵字

比；解題策略；迷思概念

並列摘要

Abstract The purpose of the study was to enhance teachers’ professional knowledge of teaching ratio through teaching cases in mathematics. The researcher organized a team to discuss various cases in mathematics teaching and collected relevant data by pretests, verbatim of cases and posttests… and so on. The contents of the cases include “the concepts of ratio”, “equivalent proportions” and “types and their difficulties to teach ratio in various scenarios and to express precise concepts semantically”. The discussion concluded the knowledges of areas and teaching skills, and how the learners responded to the ways of teaching. The research found that teachers could enhance their professional knowledges of ratio through teaching cases in mathematics. The research contained three main sections: (1) Specialized knowledges of mathematics: Teachers clarified mathematic concepts and established relevant mathematical languages. They could have better command of using the materials and their ideas of teaching mathematics could be more perfect. (2) Organized knowledges of mathematics for student: teachers could be awared of the learners’ misconceptions and problem solving strategy. (3) Knowledge of teaching mathematics: teachers could arrange the steps in teaching certain concepts and abtain better results. The study also showed that teachers upgrated multiple professional teaching knowledges and skills through these discussions, and established their special abilities to change to better beliefs in teaching. Keywords：ratio, problem solving strategy, misconceptions