國小六年級數學低成就學生是否伴隨閱讀能力落後在數學文字題解題歷程的表現差異

Differences in Cognitive Processes of Mathematics Low Achievers with and without Low Reading Abilities when Solving Word Problems

研究目的
本研究旨在探討國小六年級「數學低成就伴隨閱讀能力落後」、「數學低成就但閱讀能力一般水準」這兩類學生，與「數學程度及閱讀能力皆為一般水準」的對照組，在數學文字題解題歷程的表現差異，藉以了解前兩組學生產生困難的環節。
研究設計／方法／取徑
本研究將學生分為「數學低成就伴隨閱讀能力落後」、「數學低成就但閱讀能力一般水準」、與「數學程度及閱讀能力皆為一般水準」的對照組，總共三組。以「放聲思考法」和「結構式晤談法」蒐集學生解數學文字題時，其「問題轉譯」、「問題整合」、「解題計劃與監控」、「解題執行」四個解題步驟的表現。
研究發現或結論
研究結果發現「數學低成就伴隨閱讀能力落後」的學生從「問題轉譯」到「解題執行」都有困難。「數學低成就但閱讀能力一般水準」的學生則在「解題計劃」、「解題執行」顯著不足，而其「解題計劃」表現的落後，可能與其數學概念基模不夠完整有關。
研究原創性／價值
過去的數學低成就研究，並沒有將「數學低成就伴隨閱讀能力落後」與「數學低成就但閱讀能力一般水準」兩類學生予以區分，了解他們的困難癥結有何不同。本研究發現這兩類學生在解數學文字題的困難環節是不同的，因此在數學學習困難的診斷上，應將這兩類學生區分，依其困難處的不同，分別設計補救教學。所以本研究結果具教育應用的意義與價值。
教育政策建議或實務意涵
建議在數學補救教學之前，可參考本研究之施測程序，進行數學文字題解題困難之評估與診斷，然後再根據學生的困難癥結設計補救教學內容。

Purpose
This study investigated the differences in the cognitive processes of low achievers in mathematics with and without low reading abilities when solving word problems.
Design/methodology/approach
The think aloud method and structural interviews were adopted. The study participants were 30 low achievers in mathematics with low reading abilities (MLRL), 30 low achievers in mathematics with average reading abilities (ML-only), and 30 students with average mathematics and reading abilities (Normal). All of the participants were sixth graders. Their performance in problem translation, problem integration, solution planning and monitoring, and solution execution for word problems was assessed.
Findings/results
The results indicated that the MLRL group had difficulties in all aspects of solving word problems. The ML-only group encountered difficulties in solution planning and solution execution. The students’poor performance in solution planning might be related to the insufficient schematic knowledge of mathematical concepts.
Originality/value
This study identified that the major difficulties faced by MLRL and ML-only students in word problem solving differed. This is valuable for learning diagnosis and supplemental instruction.
Suggestions/implications
The data collection procedure adopted in this study is recommended for use by teachers for assessment and diagnosis before supplemental instruction.