故事情境輔助國二低成就學生數學學習之個案研究-以等差數列與等差級數為例

A Case Study of Story-based Instruction Supporting Low Achievement Students’ Mathematics Problem-solving on the Arithmetic Sequence and Series Unit

紀笙儀(Sheng-yi Chi)

指導教授 ： 賴婷鈴

淡江大學/教育學院/教育科技學系數位學習在職專班/碩士(2015年)

https://doi.org/10.6846/TKU.2015.00724

摘要

本研究旨在故事情境教材輔助學生等差數列與等差級數數學學習中，以瞭解三名國中二年級數學低成就學生解題行為與學習態度的情形為何，並探討學習過程中的學習困難。
本研究採以個案研究法做為研究方法，研究對象為宜蘭縣某國中三名國二數學低成就學生，個案在運用故事情境之數位教材學習後，透過觀察、文件分析以及訪談等方式進行資料蒐集與分析後，其研究結果發現如下：
一、學生在解題過程中，能觀察到數列與圖形規律性並且瞭解題意；也能檢索到重要訊息，但部分題型未能正確將訊息轉化為數列相關名詞；能組織出問題與訊息的關聯性，但部分題型無法找出可用公式後推算出解題程序；另外能解決一步驟數學問題，但部分學生未能正確解決兩步驟以上數學問題。
二、錯誤類型包含「無法觀察出數列、圖形的規律」、「容易誤解題意」、「無法將觀察到的數列、圖形規律正確轉化為數學語言」、「缺乏將待解問題轉換成數學問題的能力」、「概念不熟或推算錯誤」、「誤用公式或混用錯誤」以及「計算能力不足或粗心」，
三、運用故事情境輔助數學學習，學生能保持高度的學習興趣及解題動機。
四、運用故事情境輔助數學學習，三位數學低成就學生能夠理解數列單元的基礎概念，對基本數學事實之建構有正面幫助。

關鍵字

數學低成就 ； 故事情境 ； 數學解題

並列摘要

This study aims to understand how three second-year junior high school students with low mathematic achievement solve mathematical problems,their learning attitude and the challenges they encounter in the learning process while assisting them with story-based instruction in learning arithmetic sequence and arithmetic series.
　　The research employs case study methodology. Research subjects are three second-year junior high school students in Yi-Lan County. After utilizing story based scenario in digital learning, the data were collected and analyzed through observation of the subjects, document analyses and interviews with the subjects. The research finding are:
1. In the process of solving mathematical problems, students observed the pattern of the sequence of numbers and understood the meaning of word problems. They could also retrieve important infotmation in the word problem, but some type of mathematical problems the students could notinterpret into arithmetic sequence related words correctly. The students could associate mathematical problems and infotmation in word problems, but could not find applicable formula to solve the mathematical problem; the students could solve single step mathematical problem but some of the students could not solve more than two-step mathematical problems correctly.
2. The type of errors occurred included: not being able to observe the pattern in arithmetic sequences and pictures; easily misunderstanding mathematical problems; not being able to interpret observed patterns in arithmetic sequences and pictures into mathematic language correctly; lack in ability to interpret mathematic problems; not being familiar with the concepts; incorrect calculation; misuse of formulas or mixing formulas incorrectly and insufficient ability to calculate or not being attentive enough.
　　With story based scenario to assist mathematics learning, students could stay keen tolearn and be motivated to solve mathematical problems. Using story based scenario to assist mathematicslearning, the three students with low mathematic achievement could understand the basic concept of arithmetic sequence unit. It brings positive effects in constructing basic mathematic facts.

並列關鍵字

Mathematical Low-Achievement ； Story-based Instruction ； Mathematicals Problem-solving

參考文獻

朱家儀、黃秀霜、陳惠萍(2013)。「攜手計畫課後扶助方案」補救教學方法之探究。課程與教學季刊，16(1)，93-114。

施文玲(2007)。以學習理論為基礎的數位化教學策略。生活科技教育月刊，40(2)，32-41。

中文部分

方吉正(2006)。情境認知學習理論與教學應用。載於張新仁(主編)，學習與教學新趨勢(345-402頁)。臺北市：心理。

方信宏(2011)。國小六年級數理資優生在數形規律問題的解題歷程之個案研究(未出版碩士論文)。國立臺北教育大學，臺北市。