| Summary: | 碩士 === 國立中興大學 === 應用數學系所 === 105 === This research aims to study the problem solving process of trigonometric function word problems among vocational high school freshmen with different mathematics achievements. Thinking aloud method and interview were used as the data collection instruments to investigate their math problem solving process, math problem solving strategy and factors influencing successfulness of problem solving.
The major findings of this study are summarized as follows:
1. Problem solving process: Subjects’ problem solving processes are roughly separated into 5 steps: reading questions, analyzing the questions, making plans to solve the questions, carrying out the plans, verification and checking.
2. Problem solving strategies: subjects used several strategies including recalling mathematical experiences, logical reasoning, applying algebra, reviewing process, making charts, simplifying questions…etc.
3. Factors influencing successfulness of problem solving
(1) Problem solving knowledge domain
a. Semantic knowledge: Able to understand the questions, grasp the keynote of the questions and analyze the meaning of the questions.
b. Schemata knowledge: Able to extract useful information from the context of the questions.
c. Strategic knowledge: Able to apply various applicable knowledge to plan and monitor problem solving process.
d. Procedural knowledge: Able to apply features, theorems and formulas of trigonometric functions to calculate and solve correctly.
(2) Metacognition domain: Including self-awareness, self-prediction and self-evaluation.
(3) Affective attitude domain: Subjects’ confidence and patience had influence on problem solving.
Finally, according to the research findings, suggestions for mathematics teaching and future research are provided, hoping to serve as a reference for future instructors and researchers.
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