교과서에 제시된 문장제의 형태와 수학적 오류 분석

Abstract

This study was conducted to examine relations between types of word problems and mathematical errors. It was done by examining errors that arise during the word problem solving process. The word problems used to collect data were found in the first term section of the third grade mathematics textbook under the seventh revised national curriculum. To analyze the types of word problems, the study selected 73 questions realated to the four fundamental arithmetic operations in the first-term of the third grade mathematics textbooks and then analyzed three categories such as sentence length, types of the four fuundamental arithmetic operations, and kinds of materials used in actual life. To gather and interpret errors, the study targeted 55 third graders in Y elementary school in Busan and conducted an evaluation using 10 word problem questions. After the evaluation was conducted, the types of errors were analyzed. The errors were then divided into three types: misunderstanding of the question, calculation errors, and technical errors. In order to examine the relations between types of word problems and mathematical errors, we compared and analyzed the sentence length, types of the four fundamental arithmetic operations, kinds of materials used in actual life and the three most comon error types. Our results are given as follows. First, there is an average of 18.5 words used in each sentence. The word problems used had child friendly vocabulary and content related to real life, such as places, plays, school supplies, plant & animals, traffic & transportation, food, and people. Second, 51.9% of errors in word problem solving process come from misunderstanding the question. The reason discovered are that students don’t grasp the sentence types and make formulas with only simple numbers suggested. This is due to lack of vocabulary, and accordingly the proper teaching is required. Third, according to error analysis of arithmetic operation types, errors from misunderstanding have a correlation. The analysis of errors of types of the four fundamental arithmetic operations shows the largest technical errors are in mixed calculation and division. Analysis on the calculation structures show that addition and subtraction in larger numbers are related to errors in the calculation process. In conclusion, analysis on the types of errors found in word problem solving gives important information about teaching children and further pertinent studies should be conducted in various fields.