國中數學教學活動之知識表徵－個案研究

Knowledge Representation of Mathematics Activity in Junior High school-case Study

黃珂琳(Ke-Lin Huang) ； 邱守榕(Sou-Yung Chiu)

《科學教育》 14期 (2005/01) Pp. 37-60

https://doi.org/10.6767/JSE.200501.0037

摘要

本研究在以數學活動為主的教學實驗中，探詢教師在課堂中提供給學生的數學知識，以及活動程序，對其中之要素加以識別，析出教學表徵。
本研究採個案研究法，研究對象為一位中部地區資深老師及其30名國一生，以其在數學課中使用合作學習教學法，所進行的數學活動的「教」與「學」為個案。課室觀察中，現場錄影、錄音、做田野筆記及課後晤談等方式採集原始資料，連續觀察十九週，共十四個單元，選取其中十一個小課題：七巧板、線對稱多邊形、等量公理、代數式的運算、誤差、角平分線、三角形兩邊中點連線定理、摺兩條平行直線、利用三角板畫圓的直徑和圓與六邊形、三角形的外角和、柱體體積，作為訊息加工處理的模式分析內容，採用識別數學活動要素在「教」「學」過程中的作用，自肯定布魯納的三階知識表徵的功能識別出教師的教學表徵以及十一個教學課題中教學表徵之共通性。研究發現：（一）在輸入方面，老師的課堂中呈現的數學活動要素共有觀察、閱讀、聆聽講解、觀看示範等等；在CPU方面，共有回憶、聯想、猜測、判斷等數學活動的要素；在輸出方面，數學活動要素共有實物操作、模仿、記錄、討論、測量、抄寫筆記或板書、發表、回應、朗誦、比較、分類等等。（二）以布魯納的三種表徵形式：動作表徵、影像表徵、符號表徵，楊老師的課堂中不斷在這三種形式中進行轉換及對應，讓學生在這些轉換及對應中看到該數學概念的特性。
在十一個單元當中，楊老師的教學表徵有以下幾點共通性：使用多元表徵呈現數學知識、利用適當的比喻釐清學生的概念、以實際操作加深學生的印象、適時提問有利於學生進行高層次思考、舉例說明數學概念並舉反例使學生瞭解正反例之間的差異、善用幾何作圖工具協助學生建立正確的數學知識、藉機複習學生以前學過的數學知識以溫故知新、發現教材內容不足或前後難以銜接之時，自行增補教學內容。

關鍵字

數學活動 ； 訊息加工處理 ； 教學表徵

並列摘要

The purposes of this study were to explore teachers' teaching students about the mathematical fundamentals and representation from the teaching experiment in mathematics activities.
This case is an individual study. The participants of this study were 30 7-grade students and a senior teacher named Yang teaches in the central of Taiwan. Yang uses of collaborative learning in mathematics teaching which consists of mathematics activities including 11 units (tang ram, linear symmetric, polygon, equal axiom, operations of algebraic equations, error, the line bisected angle, theorem of connection between middle points of 2 sides in a triangle, making 2 parallel lines, use the triangular pad to draw the diameters of cycles and cycles and hexagons, the sum of exterior angles of a triangle, the volume of a pillar) we chose to data analyze. Besides, researcher bases on the theory of information processing to discriminate the elements of the mathematics activity and Burner's theory to distinguish the instructional representations of teacher's teaching and the intercommunity between the instructional representations of the 11 units.
The results were summarized as follows:
Ⅰ. Use the information processing theory to discriminate the elements of the mathematics activities in class. In input, there are observation, reading, speech listening, watching the model, etc in Yang's classes. In CPU, there are memory, association, guessing, judgment, etc. In output, there are object manipulation, imitation, record, discussion, measuring, writing in notebook or writing on board, presentation, reply, speaking, comparison and classification, etc.
Ⅱ. By Burner's theory about three forms of representation: enactive representation, iconic representation and symbolic representation. Yang leads students to understand the mathematical conception in the applications of these three forms.
Ⅲ. In these 11 units, there many intercommunities in Yang's instructional representation: show out the knowing of mathematics by diversity, let students know the general ideals of suitable analogy, to deepen the image of mathematics by process, question in the right time to make higher order thinking, take counter examples and let students know what is different, help students building their correct idea of mathematics by using graphic tools, review what they learned before in anytime, to make up when context deficiently.

並列關鍵字

mathematical activity ； information processing theory ； instructional representations