桃園市某國中七年級學生一元一次方程式錯誤類型與補救教學

The error patterns and remedial teaching of linear equation for seventh-grade students of some junior high school in Taoyuan city

謝宜庭(Yi-ting Hsieh)

指導教授 ： 李武炎

淡江大學/理學院/中等學校教師在職進修數學教學碩士學位班/碩士(2015年)

https://doi.org/10.6846/TKU.2015.00781

摘要

本研究主要目的是在探討七年級學生在學習一元一次方程式的概念時，常犯的錯誤類型與錯誤原因，並施以適當的補救教學藉以觀察學生錯誤類型改善的情形。
本研究是以研究者所任教的桃園市某國民中學三個七年級班學生為研究對象，共計71名有效樣本。主要是參考103學年度上學期康軒版本數學備課用書與相關文獻為依據，自編兩份「一元一次方程式」學習測驗卷，分前、後測兩階段施測，前測施測後，進行為期一週的補救教學，再施行後測。依據前後測施測結果進行統計分析，並利用晤談方式了解學生解題過程與想法，以此研究探討七年級學生在「一元一次方程式」概念的學習狀況與補救教學之成效。
本研究之主要發現如下：
一、七年級學生對於一元一次方程式概念的主要錯誤類型有：1、概念不清的錯誤。2、運算的錯誤。3、符號使用的錯誤。4、應用不相關規則的錯誤。5、粗心遺漏的錯誤。6、誤譯語文詞句的錯誤。7、隨意回答的錯誤。
二、補救教學後的學習成效：1、正負數的四則運算較熟練。2、分配律及去括號的規則順序不易混淆。3、正確使用等量公理，且移項的變號法則錯誤率大幅減少。4、解方程式與化簡代數式的概念更加清楚。5、較能掌握題意並依題意中的條件列出正確的一元一次方程式。

關鍵字

錯誤類型 ； 補救教學 ； 一元一次方程式

並列摘要

The main purpose of this study is to explore seventh-grade students often committed the error type and cause of the error in learning linear equation concepts, and to impose appropriate remedies teaching in order to observe the situation of students the error type of improvement.
The study is based on some junior high school in Taoyuan City, researchers taught three seventh-grade students for the study, a total of 70 valid samples. Mainly on the reference 103 school year semester Kang Xuan version of the math lesson books and literature is based, self-two, "linear equations," Assign before and after the two-stage test Surveying, Surveying after the pre-test, conducted a one-week remedial teaching, after another test purposes. Surveying the results before and after the test based on statistical analysis, and the use of interviews ways to understand students' problem-solving process and ideas, in order to study was to investigate the effectiveness of the learning situation, "linear equations" concept and remedial teaching for seventh-graders.
The main findings of this study are as follows:
Ⅰ. the main error types of linearequation concept for seven-grader students are: 1.the concept of clear mistakes. 2.operation errors. 3.error codes used. 4.the error does not apply the relevant rules. 5.careless omission errors. 6.mistranslation language phrases error. 7.answer random errors.
Ⅱ. the effectiveness of remedial teaching: 1.plus or minus a few of the four operations more skilled. 2.distributive law and the rules of order to the brackets will not be confused. 3.the proper use of the same amount of axioms and rules of shift change numbers significantly reduce the error rate items. 4.the solution equation and simplify algebraic concepts clearer. 5.more able to grasp the meaning of the title and meaning of the questions listed in accordance with the conditions of the correct one dollar equation.
For this study, summarized the error types to impose appropriate remedies teaching, will enhance the students' learning. Hope through this research can provide junior mathematics teachers to teach reference linear equation concept and preparation of assessment test volumes in future.

並列關鍵字

error patterns ； linear equation ； remedial teaching

參考文獻

14、林清山、張景媛 ( 1994 )。國中生代數應用題教學策略效果之評估。國立台灣師範大學教育心理與輔導系教育心理學報，27期，36-63頁。

23、張景媛 ( 1994 )。數學文字題錯誤概念分析及學生建構數學概念的研究。國立台灣師範大學教育心理與輔導系教育心理學報，第27期，175-200頁。

29、教育部 ( 2008 )。國民中小學九年一貫課程綱要數學學習領域。台北：教育部。

4、王釋緯 ( 2012 )。七年級學生學習一元一次方程式之錯誤類型分析-以一所都會型學校為例。國立台灣師範大學數學系在職進修碩士班碩士論文。

中文部分：