| Summary: | 碩士 === 國立臺中教育大學 === 數學教育學系在職進修教學碩士學位班 === 100 === The concept of addition and subtraction is always regarded as the foundation of other mathematical concepts. Moreover, the application of addition and subtraction is one of the main topics of low-grade mathematics curriculum. Grade 1-9 curriculum guidelines emphasize on the ability of utilization. Thus, more life-related questions are included in elementary school mathematical curriculum.
The amount of 377 students of the first grade in the elementary school had been studied in this research which included five types of addition and subtraction word problems and edited as test tools by me that including combination, separation, sequence, quantity and displacement. Besides, the analysis of PS-P chart and the PCAISM methods were utilized to illustrate the concept chart of personalization hierarchy, investigate the characteristics of personalization hierarchy with various learning types and different solution ways of students in this tests which utilizing addition and subtraction word problems as test tools. Finally, the research results had been shown as below.
1. Solving addition and subtraction word problems by the concept of combination is the most proficient, and solving addition and subtraction word problems by the concept of displacement is less proficient.
2. It is appropriate to solve addition and subtraction word problems of combination and separation by column formula. On the other hand, it is suitable to solve addition and subtraction word problems of sequence and quantity without any limitation of formula.
3.Without limiting students’ methods of using formula to answer questions, there will be less C students.
4. PCAISM reveals that using different methods to answer questions will vary the conceptual hierarchy chart.
The results and findings of this research can provide the first-graders to utilize different methods to solve addition and subtraction problems and can also be the suggestion of future related research. Moreover, the research can be the reference for editing teaching materials and teachers’ reference of cognitive diagnosis and remedial instruction.
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