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.
這是三年期計畫的第一年期中報告。此計畫之研究目的在於探究運算能力高低不同者在乘法運算時的策略選擇與大腦認知負荷情形。因此本年度的研究目的在於找出未來fMRI研究中適合的刺激材料，也就是從不同難易度以及不同數字記憶負荷量的題型中，篩選出能達成研究目的的乘法題目。因為人們學習運算需要一些基本能力支援。有大量的文獻在探討這些基本能力是那些。部分研究建議像是工作記憶以及執行功能的一般認知能力；有些研究則認為領域特殊能力也是必要的，像是大數目的概數感、群數（numerosity of a set）以及執行運算時的數字表徵。然而，哪些能力扮演重要的角色仍持續在爭議中。本研究以47位大學生為樣本，探究一般認知能力中的工作記憶能力及領域特殊能力中概數感，與乘法運算之間的關係，並從實驗中了解在不同乘法運算能力中受試者在難度不同與不同數字負荷題型中的策略選擇。研究結果顯示，工作記憶中的記憶更新功能與乘法運算成就有高度相關，概數感則與乘法運算成就不相關。乘法運算能力不同的受試者在不同的乘法題型中之策略選擇不同。而工作記憶能力高者在乘法運算的速度相較於工作記憶能力低者快。
This is the first year report of the 3 year grant project. Our goal of this project is to examine the effect of cognitive loading and its 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. Therefore the purpose of the first year was finding out the appropriate stimuli used for the further fMRI studies and tested some debates about the relationship between the essential capacities and multiplication. People learning arithmetic needs support of some foundational abilities. There was a great deal of literature on these essential capacities. Some studies suggested the general cognitive abilities, such as working memory (WM) and the executive function were very important. Other studies believed some domain-specific capabilities, such as approximating numerosity system (ANS), representing the numerosity of a set, and using number representations in arithmetic operations, were the core functions. However, which components played the important role on learning arithmetic was still in debates. Using a group of 47 young college students as samples, this study examined the relationship among general cognitive abilities (4 kinds of WM tasks； memory updating, MU； operation span, OS； sentence span, SS； spatial short-term memory, SSTM), a domain-specific capability (ANS), and multiplication performances. According to the performance of the participants, we separated them into high/low multiplication accuracy group and high/low MU ability (known as related to the executive function) group. We compared the strategies differences, reaction time, and accuracy of multiplication from the different performance/ability groups. The results revealed that there were high correlations between the multiplication performance and WM abilities, especially between MU and multiplication. There seems to be low correlations between ANS and multiplication achievements, same with ANS and WM abilities. The strategies, speed, and accuracy between high and low performance groups were very different. The speeds of multiplication in high MU participants were faster than lower ones. These results were interesting for future study.