肢體障礙國中生之數學認知——一個建構教學的行動研究

Mathematical cognition of physically-handicapped secondary school students—An action research with constructive teaching experiments.

王琇慧(Hsiu-Yue Wang) ； 邱守榕(Sou-Yung Chiu)

《科學教育》 12期 (2002/08) Pp. 1-20

https://doi.org/10.6767/JSE.200208.0001

摘要

本研究一面以數學活動為主進行教學實驗，肢體障礙國中生的數學認知行為，一面在數學教學改進的行動中自我評析，數學科教學能力的成長。本研究方法包含了行動研究和質性研究兩者的主要要素，規劃且設計教學實驗，開發且使用數學活動工作單。研究發現如下：
一、肢體障礙國中生的學習意願不低於一般學生，其數學認知發展與一般學生亦無大差異，其中腦性麻痹生較受到生理障礙的牽制，這些現象有：（一）手部功能不佳造成：1.書寫與計算的時間比別人久，2.仰賴心算行為，以「心算」代替筆算，3.畫幾何圖形的困難；（二）手部功能非常不好又伴隨語言障礙的學生，他們的語文能力不佳，影響數學問題的閱讀；（三）不但手部功能不好且有視力障礙的學生，因手眼無法協調，影響畫圖能力，會畫出單位長不一的直角坐標系統；（四）因腦部受傷造成其他生理上的缺陷，影響數學學習。
二、教師數學教學能力唯有在求解實際教學問題的需要之上才能成長。由於研究者在教學互動中，有意識地使用訊息加工處理法來分析學生的數學認知行為，得以瞭解學生的需求與困難，隨而調整教學。經由行動研究，重新認識學習者自行建構數學知識的可行條件與教師督導的必要性，隨而設計與編製解題導向的數學活動工作單，在課堂中適時以合作學習策略搭設鷹架，引導學生提問、佈題討論、互助的教學能力皆有成長。

關鍵字

肢體障礙 ； 數學認知 ； 鷹架 ； 建構教學 ； 合作學習 ； 行動研究 ； 訊息加工處理

並列摘要

It is to explore the mathematical cognition of physically-handicapped secondary school students with teaching experiments based on mathematics activities situated in the real classroom. As action-researcher, the author reflects on the effectiveness of her experimental teaching, as well as on her own growth of pedagogical mathematical knowledge through the whole course of the study.
Both elements of action research and qualitative inquiry methodologies are employed. Work-sheets for the mathematical activities, including tasks of solving simultaneous equations by substitution method, Gaussian elimination method, graphing the equation in the coordinate plane, etc, are designed as tools to explore the scaffolding of learning algebra with multiple representations, used in the lessons, and collected as raw-data to identify student& difficulties, errors, and achievements.. All the mathematics lessons are vedeotapped, reviewed, partly transcribed, to analyse both the cognitve and the affective aspects in the instructional processes with information processing approach.
The major findings are:
1.The willingness to learn mathematics among the physically-handcapped students is the same as that of the normal students. Only the students with cerebral palsy, badly troubled with hand-writing deficiency, encounter serious difficulty in handling. The phenomenon is as follows:
(1) Poor hand function causes: (i) much more time to write and calculate; (ii) dependent on mental computation or coast estimation; mental computation instead of written computation; (iii) graphing difficulty.
(2)Those who have very poor hand function coupled with language disability are difficult to read mathematical problem.
(3) Those who have very poor hand function coupled with visual disability have poor eye-hand coordination. It influences the students to paint and they will draw an uneven unit in the Cartesian Plane.
(4) The other physiological disorder.
Cerebral palsy with the other physiological disorder could influence the mathematical learning. Students with cerebral palsy are limited by other physiological factors, so they learn slowly. But they have their own ways to learn the skill and get the mathematical knowledge gradually by overcoming their handicaps.
2.The only way to foster pedagogical mathematics knowledge is to visualize and make sense of problems in mathematics instruction and their solving by problem-oriented teaching experiments. Having used information processing approach, teacher enquires consciously what’s the students’ learning difficulty researchers becomes aware of known misconception toward constructivist teaching, and re-evaluated the practicableness of the learner's constructing knowledge by herself and the necessity of teacher's monitoring.

並列關鍵字

Physically handicapped ； mathematical cognition ； scaffolding ； constructive teaching ； cooperative learning ； action research ； information processing approach ； pedagogical mathematics knowledge