| Summary: | 碩士 === 國立臺南大學 === 應用數學系碩士在職專班 === 107 === The purpose of this study was to investigate the solving performance of division for third graders. By generalizing their error patterns and analyzing the possible reasons for making mistakes in order to know students’ difficult part in learning. The result could be reference for teachers. The researcher designed a specific test of “Division” including 19 questions in 12 types. The participants selected to complete the test were 46 third graders from a public elementary school in Rende District, Tainan City. After testing, some of them were interviewed according to their performances and willingness. The statistic tools of SPSS 21.0 were used to analyze the quantitative data linking the details of interview to figure out the error patterns and the possible reasons for their mistakes.
The results were summarized as follows:
1. The error performance of division operation for third graders :
a. There were approximately 30%-40% of the students making mistakes in two-step solving questions.
b. It was remarkable that students were easily confused by the types of “ the quotient should be complemented zero ” questions because of different places of complementing zero.
2. The main error patterns of division for third graders:
a. Errors in estimating quotient.
b. Errors in 9×9 Multiplication Table.
c. Validity in estimating quotient, but defectiveness in calculating process.
d. Errors in calculation of decomposition by tens place and hundreds place.
e. Lack of complementing zero in quotient.
f. Complementing zero in quotient with wrong places.
g. Complementing zero in quotient with correct places, but without calculation of decomposition.
h. Forget to make out remainder.
i. Misunderstanding the word problem and taking an irrelevant number as the divisor.
j. Without any concept of two-step solving skills such as addition or subtraction first , then followed by division.
k. Students were confused by other types of questions, and made quotient plus 1.
l. Other errors including transcribing the wrong number of dividend, using multiplication to solve division questions and calculating incompletely.
3. The main error reasons of division operation for third graders:
a. Misunderstanding the relation between dividend and divisor, and lacking of the necessity of sharing completely in division.
b. In the column form of division, students easily had errors in calculation of multiplication and subtraction.
c. Students’error in estimating quotient resulted from their unfamiliar concepts of place value and decomposition.
d. Students were confused by different types of questions of complementing zero in quotient.
e. Students were incapable of understanding the questions.
f. Students’ incomplete arithmetic skills caused errors.
g. Students misused irrelevant concepts for solution.
h. Students’irrelevant omission caused errors.
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