認知解題策略對國小數學低成就學童文字題解題能力之實驗研究

A Study of Experiment for Low Mathematical Achievement of Elementary School Students in the Instruction of Word Problem Solving

孫扶志(Fu-Chih Sun)

《測驗統計年刊》 4期 (1996/12) Pp. 71-124

https://doi.org/10.6773/JRMS.199612.0071

摘要

本研究係為了協助數學學習有困難的低成就學生能夠有效的學習，以獲得正確的數學概念、原理原則，及熟練的計算技巧與有效的解題策略，因此實驗教學架構設計上依循兩種主要的途徑：一是透過數學解題策略與技巧的教學，來引導學生進行解題活動；二是從評量著手，發展一套能夠敏銳偵察數學解題歷程的評量工具，提供更多有效的訊息，以針對個別學生解題歷程上的缺陷，來進行補救教學。因此，本研究有以下兩項主要研究：一、有鑑於後設認知、動機信念與認知解題策略對數學文字題解題能力之影響，研究者擬設計「綜合解題訓練課程」進行此一統合後設認知、動機信念、認知解題策略的實驗教學研究，探討此一課程是否對於學童之文字題解題能力有所助益。二、運用動態評量的理念，透過標準化程序設計「漸進提示之中介訓練課程」，融合文字題解題教學與評量，以補充標準化情境下，能力測驗訊息的不足，採個別化的方式實施，達到補救教學的實質效益。本研究針對台中縣潭陽國小四年級學生，進行數學低成就學生之篩選，以數學成就實際成績與期望成績達.97個標準差的三十名學生為實驗樣本，依性別隨機分派至三個實驗組，分別施以「綜合解題訓練課程」、「動態評量之漸進提示中介訓練課程」及「一般課內複習課程」之實驗教學處理，以瞭解三項課程在數學文字題解題能力、後設認知、動機信念、數學文字題解題遷移能力方面的影響差異情形。針對各組進行不同實驗處理後，在排除智力、數學成就與各項前測之共變因素影響下，以單因子共變數分析加以考驗，其結論如下：一、「認知綜合解題訓練課程」的教學，對於數學低成就學生，在數學文字題解題表現上，包括遷移試題的學習、保留階段的學習，均有明顯的幫助。二、「動態評量之漸進提示中介訓練課程」的教學，對於數學低成就學生，在數學文字題解題表現上，包括遷移試題的學習、保留階段的學習，亦能有明顯的助益。三、「認知綜合解題訓練課程」及「動態評量之漸進提示中介訓練課程」的教學，對於數學低成就學生，在數學學習之「後設認知」與「動機信念」表現上，並未能有明顯的效果提昇。四、「認知綜合解題訓練課程」之教學，對於數學低成就學生，在數學文字題解題保留階段的表現上，遠較「動態評量之漸進提示中介訓練課程」，更具顯著的學習保留效果。根據上述實驗教學之研究結果，提出下列建議：一、重視認知解題歷程與策略之教學：包括1.解題歷程的教學 2.認知策略之教學 3.解題統整能力之訓練。二、重視後設認知、動機信念與數學文字題解題表現之關係：包括1.後設認知策略之訓練 2.動機信念之增進。三、重視個別化的動態評量與教學介入歷程：包括1.個別化的動態評量 2.師生互動之教學 3.立即有效的診斷與補救。四、數學文字題陳述及評量方式的改進：包括 1.重視解題與實際經驗之關係 2.多元題型的診斷評量。

並列摘要

The main purpose of this study was: (1) to design the synthesize-problem-solving training course that includes metacognition, motivation-belief, and the cognitive problem solving strategies and, further, to help students learn mathematics word problem solving. (2) to design the graduated-prompting-procedure training course that includes instruction of problem solving and assessment and, further, to improve effects of individual remedial instruction. The sample of this study including 30 lower mathematical achievement students, was selected from 6 general classes of one public elementary school in Taichung County. Measurements of this study include (1) the test of word problem solving (2) the scale of metacognition (3) the scale of motivation-belief (4) the transfer-posttest of word problem solving. Above measurements were used to assess students' abilities concerning mathematics and word problem solving. According to the analysis of one-way ANCOVA, the results are as follows: 1.For lower mathematical achievement students, there are significant effects in performance of word problem solving, transfer-posttest and maintenance stage, after the instruction of the synthesize-problem-solving training course. 2.For lower mathematical achievement students, there are significant effects in performance of word problem solving, transfer-posttest and maintenance stage, after the instruction of the graduated-prompting-procedure training course. 3.For lower mathematical achievement students, there are nonsignificant effects in performance of metacognition and motivation-belief after the instructions of either synthesize-problem-solving training course or graduated-prompting-procedure training course. 4.For lower mathematical achievement students, in performance of maintenance stage there are more significant effects after the instructions of synthesize-problem-solving training course than graduated-prompting-procedure training course. According to the results, some suggestions were given.