從隨機概念發展模型理論初探小六學童樣本空間直觀轉變

Applying Model of Stochastic Conceptual Development to the Transformation of one 6th-grader's Intuitions of Sample Space

本研究旨在探討一位小六學童在數學文字題的引導下，其樣本空間直觀演變的歷程。本研究主要採用詮釋性研究法，收集的資料包括課室觀察錄影、學生學習日誌、研究者札記及與學生的深度訪談內容，並使用隨機概念發展模型(Shaughnessy， 1992)做為分析兒童樣本空間直觀的主要工具，研究發現如下：(一)蘊含樣本空間情境的數學文字題解題能引動學童直觀轉變；(二)個案學童的直觀轉變歷程具有「進階」與「再折返」的特徵；(三)個案學童的二階直觀為兩模型並存的狀態。本研究提出運用直觀來幫助學生產生有意義的學習、將「明顯排列問題情境」做為先備教材及基於生活情境、類比、遊戲以發展樣本空間教學活動等建議。

The purpose of this study was to investigate the evolution process of probabilistic intuition of a six-grader under the guidance of word problems. The interpretive research method was adopted to collect and analyze data from classroom observations， students’ notes， and in-depth interviews. Besides， the model of stochastic conceptual development (Shaughnessy， 1992) was used as main tool to analyze probabilistic intuition. The study got major findings as follows：(1)the mathematical word problems resulted in the intuitions transformation of case student; (2) the evolution process of case student’s probabilistic intuition had the characteristics of going forward and back”; (3) case student’s secondary probabilistic intuition is the state of co-exist. The article also provides some implications about (1) using students’ intuitions is helpful for the construction of meaningful learning; (2)using conspicuous permutation problems as prior materials， and (3)developing teaching activities based on daily life， analogy and games.