基本數學運算能力高低者的乘法運算策略選擇與大腦認知負荷之研究 (III)

Abstract

過去數學解題歷程的研究顯示運算能力在解題歷程的重要性。缺乏基礎的運算能力，將無法達到對數學概念真正的理解，因此培養良好的運算能力方能成就良好的數學能力。如果在教育階段能培養良好的基本運算能力，將有助於複雜的數學解題能力以及相關的知識理解。過去關於運算能力的大腦研究多著重在簡單算術上，較複雜的算術活動並沒有太多探索。本研究試圖探究基本運算能力高低者在執行較複雜的乘法運算時的大腦認知活動負荷情形，以期能將結果解釋基本運算能力與數學成就的關係。研究中共有五個實驗，實驗一探討在不同策略的運算方式以及不同作業難度時，是否大腦活化區域與活化程度有所不同，我們假設不同策略的運算方式會導致不同的認知負荷；實驗二的目的則是運用不同的工作記憶作業做為第二項作業，以進一步釐清不同運算策略的工作記憶認知處理成分；實驗三比較高、中、低三種表現的三組受試者在不同表徵形式下不同運算方式的表現情況；實驗四檢測運算能力高低的兩群受試者，在不同運算方式上的大腦活化情況；實驗五探討運算能力高、低組的受試者在面對不同題型時的策略選擇與運算能力差異。預計在計畫第一、二年中，分別執行實驗一、二與實驗三、四，計畫第三年執行第五個實驗，並綜合分析上述實驗的結果。

It has been shown that computational ability is important in solving mathematical problems. Without basic computation efficiency, the comprehension of mathematical concept will be impaired. Therefore, good computational ability is a base for mathematical learning and performance. In most of previous brain studies on mathematics, only simple concepts or problems were investigated. In the present studies, we would like to examine the cognitive loading and brain activity when subjects with different computational ability work on complex multiplicative problems in order to understand the relationship between computational ability and mathematical performance. Five experiments are proposed. In experiment 1, different computational strategies and level of difficulty on multiplicative problems are manipulated. The behavioral and fMRI data are collected. It is hypothesized that cognitive loadings are different with different computational strategies. In experiment 2, different working memory tasks will be used as a second task while subjects solve multiplicative problems in order to further understand the involvement of different working memory components. In experiment 3, how subjects with different mathematical performance perform on exact and approximate computation with different representation of multiplicative problems are examined. In experiment 4, the brain activation of subjects with different mathematical performance on exact and approximate computation will be examined. In experiment 5, the strategy selection and brain activation of subjects with different mathematical performance in face of complex multiplicative problems are examined. Experiment 1 and 2 will be executed in the first year. Experiment 3 and 4 will be executed on the second year. In the third year, the fifth experiment will be executed and the data will be analyzed in a comprehensive way.