本研究目的係探討國小五、六年級不同能力學童的數學解題過程中，受到
哪些因素影響及這些因素在學童解題期間的心理特質與差異。本研究以五
、六年級低、中、高解題能力者各一位為研究對象，個別進行５份試卷的
數學解題實驗。採取「非同步放聲思考」的研究方法，獲取學生解題期間
，短期記憶所處理的訊息。本研究擬訂出數學解題過程的五個解題成分模
型，作為分析的參考架構。 研究結果發現：1.對問題的知覺、了解及表
徵:(1) 高解題能力者傾向從問題的情境或特例中，觀察各部分間的關係
且評估其可用性，才開始作答；而低解題能力者傾向只知覺到單一或少數
的關係。 (2)對同一問題，受試者們經常形成許多種類的詮釋。尤其低解
題能力者較常形成不同於題意的詮釋，甚至加入自己的意義。 (3)只是要
求低解題能力者畫圖來幫助解題，很難如此就獲得助益。2.相關數學知識
或概念的了解: 低解題能力者應用的數學知識傾向是一些類似的問題情境
、關鍵詞或語法知識，且低解題能力者所學到的數學知識經常只是一些口
訣或是表層的了解。3.擬定策略與執行: 幾乎所有有效的解題策略都來自
高解題能力者，計有十三種不同的一般策略。 4.察覺與監控策略的執行:
受試者對於策略執行的察覺可以分出五個層次: 沒有察覺；無關係的察覺
；含糊的察覺；關係性的察覺；反省的察覺。另外對於策略執行的監控，
本研究發現有五種類型的監控，大多數出現在高解題能力者的解題歷程
。5.回顧解答: 受試者很少主動回顧解答。尤其中、低解題能力者經常表
示不喜歡檢查或不知道怎麼檢查。

The purpose of this study is to investigate which factors
affect problem solving processes and psychological traits of
these factors during problem solving. The study selected 6
samples from 5-th & 6-th grade students, and classify
them by low, average, high abilities ,and used non-
synchronic thinking-aloud method to obtain problem
solvers' information in short term memory during problem
solving processes. The study designed a model of five
components of mathematical problem solving processes
that are used analytical framework. According to these
components, the findings of the study have: 1. Perception,
understanding and representation of the problem. (1) High
abilities tend to observing relations of problem context and
evaluating availability of these relations , but low abilities
only tend to perceiving single or few relations. (2) To
the same problem, different problem solver often formulate
different and various meaning. (3) To low abilities, it is
enough to assist him successful problem solving by making a
graph or a diagram. 2. Understanding of math concepts. Low
abiities tend to apply some similar context or keywords of
the problem, and math knowledge of low abilities is
often formula for incantation or surface understanding.
3. Design and perform strategy. Effective problem-solving
strategies are almost from high abilities. 4. Awareness and
control. Awareness can be distinct from five levels:
unawareness; unrelational awareness; unclear
awareness; relational awareness; reflective awareness. 5.
Looking back. Problem solvers of the study have few looking
back. In particular, average or low abilities often reprent
them to dislike check or unknow how to check.
The purpose of this study is to investigate which factors