| Summary: | 碩士 === 中原大學 === 教育研究所 === 94 === The Difference Between Six Grader Algebra Problem Solving Performance and Elementary Teachers' Beliefs About Word Problem Solving
Abstract
The purposes of this research include (a) to understand six grader algebra problem solving performance, (b) to understand elementary teachers' beliefs about student word problem solving performance and about word problem solving instruction, (c) to investigate the difference between student word problem solving performance and elementary teachers' beliefs about word problem solving.
A modified instrument of “The Exam of Basic word problem”is adopted to measure word problem solving performance of six graders. 318 students are selected from 10 grade six classes of two elementary schools in Taoyuan as the samples. On the other hand, “The Questionnaire for Development of Teachers' Beliefs About word Problem Solving” is administered to the elementary teachers who had taught mathematics in a grade six class during the last 3 years. 386 elementary teachers are conveniently selected, and the response rate is 81.86%. We used SPSS to conduct data analysis, and the results of our research as following:
1. The word problem solving performance of six graders
(1) Students perform better under general context than average context.
(2) Under general context, students have better performance on solving word problem with the structure of result-unknown than start-unknown. Under average context, there is no significant difference between performance on solving word problem with the structure of result-unknown and start-unknown.
(3) Under general context, students have better performance on solving word problem with verbal representation than story representation. Under average context, students have better performance on solving word problem with symbolic representation than story representation and verbal representation.
(4) Student problem solving performance is influenced by his or her own informal strategies
2. The effect of teacher background on teacher belief about word problem solving instruction
(1) More male than female teacher embrace “symbol-precedence view”.
(2) More engineering and others background than mathematical background embrace “the structure of word problem instruction beliefs developed in this research”.
(3) More engineering background than mathematical background embrace “word-problem -instruction view” and “symbol-precedence view”.
(4) More others background than mathematical background embrace “word-problem-instruction view” and “algebraic-standing view”.
(5) More “teachers who have been taught more than 60 classes” than “teachers who have been taught 25-59 classes” embrace “the structure of word problem instruction beliefs developed in this research”.
(6) More “teachers who have been taught more than 60 classes” than “teachers who have been taught 25-59 classes” embrace “word-problem-instruction view” and “algebraic-standing view”.
3. The characteristics of elementary teachers' beliefs about word problem arranging and about word problem solving instruction, and the relationship between the two beliefs.
(1) According to the characteristics of elementary teachers’ arrangement of word problem, they can be divided into the following three groups:
a. Word problems with the structure of result-unknown are arranged as first priority.
b. Word problems with symbolic representation, word representation and story representation are arranged in sequence.
c. Word problems with the structure of start-unknown are arranged as first priority.
(2) The teachers with different beliefs about word problem solving instruction have different evaluation of students’ performance on word problem solving.
(3) The teachers with different problem arranging have different beliefs about word problem solving instruction.
According to our research, we made some suggestions about curriculum material and instruction, teacher education, and the future research.
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