【摘要】：分數(shù)的運算在學(xué)生整個初中階段的數(shù)學(xué)學(xué)習(xí)中占有重要地位。分數(shù)運算是一種基本知識和基本技能,屬于初中代數(shù)的核心內(nèi)容。許多運算律需要記憶和熟練運用,學(xué)生能否熟練分數(shù)運算,將對初中階段起到關(guān)鍵作用。預(yù)初年級數(shù)學(xué)學(xué)困生由于數(shù)學(xué)學(xué)習(xí)能力的缺損而導(dǎo)致在學(xué)習(xí)上明顯落后于同年級的普通學(xué)生,在分數(shù)的運算上面屢屢犯錯,計算水平還不能達到教學(xué)要求,在成績上與普通生相比有很大差距,將會導(dǎo)致在未來的學(xué)習(xí)中帶來困難,影響學(xué)生學(xué)習(xí)信心。在此背景下,本文研究以下問題:一、學(xué)困生在分數(shù)運算過程中的解題思路是怎樣的;二、導(dǎo)致學(xué)困生經(jīng)常性出現(xiàn)分數(shù)運算錯誤的原因是什么;三、怎樣對學(xué)困生進行分數(shù)運算的補救。為研究以上問題,本文采用了以下方法:研究一采用測試法和分析法,分析了預(yù)初年級數(shù)學(xué)學(xué)困生的分數(shù)的化簡、分數(shù)的加、減、乘、除和四則混合運算的解題步驟。將33名學(xué)困生和35名普通生成績作為對比,歸納了學(xué)困生在分數(shù)運算解題過程中的典型錯誤;采用問卷調(diào)查法和訪談法,對全體預(yù)初年級學(xué)生做了調(diào)查問卷,訪問了三名學(xué)困生和三名教師,得出學(xué)困生學(xué)習(xí)分數(shù)運算的現(xiàn)狀和導(dǎo)致學(xué)困生運算錯誤的因素。研究二嘗試結(jié)合Montague所提出的認知-元認知解題策略教學(xué)應(yīng)用到分數(shù)運算中,對三名學(xué)困生進行補救教學(xué)的教學(xué)研究。研究發(fā)現(xiàn):一、學(xué)困生有一套自己的乘法運算方法;在分數(shù)除法運算中,將除法轉(zhuǎn)化為乘法后,學(xué)困生習(xí)慣性地將錯誤的乘法運算步驟遷移到除法運算中去;學(xué)困生更傾向于將分數(shù)化成小數(shù)來解題,沒有主動運用運算律使得解題簡便。二、異分母分數(shù)的加減法中,學(xué)困生難以辨別不同分母之間的關(guān)系;對因數(shù)、倍數(shù)、公因數(shù)、公倍數(shù)、最大公因數(shù)和最小公倍數(shù)的概念的不理解和分數(shù)化簡的困難是運算錯誤的主要因素;筆算、口算障礙,較差的學(xué)習(xí)習(xí)慣和不良的學(xué)習(xí)方法也是影響學(xué)生分數(shù)運算的重要因素。三、在補救教學(xué)中融入認知-元認知策略,教導(dǎo)學(xué)生使用自我教導(dǎo)、自我提問、自我監(jiān)控的方式能顯著提高了三名學(xué)困生的分數(shù)運算的成績,但是沒有產(chǎn)生延時效果。
[Abstract]:The calculation of scores plays an important role in the mathematics study of the whole junior middle school. Fractional operation is a kind of basic knowledge and skills, which belongs to the core content of junior high school algebra. Many arithmetic laws need to be memorized and used skillfully. Whether students are proficient in fractional operation will play a key role in junior middle school. Because of the defect of mathematics learning ability, the students with mathematics learning difficulties in the early grade obviously lagged behind the ordinary students of the same grade in learning, and made repeated mistakes in the calculation of scores, and the level of calculation could not meet the teaching requirements. Compared with ordinary students, there is a big gap in performance, which will lead to difficulties in future learning and affect students' confidence in learning. In this context, this paper studies the following problems: first, how to solve the problem in the process of score calculation for students with learning difficulties; second, what is the cause of the students with learning difficulties frequently causing the score calculation errors; third, How to remedy the score calculation of students with learning difficulties. In order to study the above problems, the following methods are adopted in this paper: in the first research, by using the test method and the analysis method, the paper analyzes the steps of solving the problem of the score simplification, the addition, the subtraction, the multiplication, the division and the four mixed operations of the pre-grade mathematics students with learning difficulties. In this paper, 33 students with learning difficulties and 35 ordinary students are compared, and the typical mistakes in the process of solving problems by score calculation are summarized. Three students with learning difficulties and three teachers were interviewed to find out the present situation of learning scores and the factors leading to the errors in the calculation of students with learning difficulties. The second study attempts to apply the cognitive-metacognitive problem-solving strategy teaching proposed by Montague to the score calculation to study the remedial teaching of three students with learning disabilities. The results show that: first, the students with learning difficulties have a set of their own multiplication operation method, in the fractional division operation, division into multiplication, students with learning difficulties habitually transfer the wrong steps of multiplication to division operation; Students with learning difficulties tend to solve problems in fractional numbers, and do not take the initiative to use arithmetic laws to make solving problems simple. Second, in the addition and subtraction of different denominator scores, it is difficult for students with learning difficulties to distinguish the relationship between different denominators. The incomprehension of the concepts of the maximum common factor and the minimum common multiple and the difficulty of fractional simplification are the main factors of the calculation error, and the difficulty of writing and calculating, the poor learning habit and the bad learning method are also the important factors that affect the students' score calculation. Thirdly, incorporating cognitive metacognitive strategies into remedial teaching, teaching students to use self-teaching, self-questioning and self-monitoring can significantly improve the scores of the three students with learning disabilities, but it has no delay effect.
【學(xué)位授予單位】：上海師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：G633.6

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