| Summary: | 碩士 === 國立臺北教育大學 === 數學暨資訊教育學系(含數學教育碩士班) === 105 === This study aims to explore the problem-solving performance of the constructed response items on pre-algebra knowledge by conducting exploratory research, that rely mainly on paper-pencil test and data analysis, supplemented by semi-structured interviews. The subjects of this present study are 308 students, two classes from first to sixth grades of an elementary school in New Taipei City where the researcher works. After the paper-pencil test of all the subjects, their problem-solving performance was categorized into low, medium and high score groups. Two students from each group were interviewed and the results are listed as follows.
When it comes to “operational rules,” students’ performance on constructed response items of commutative law are superior than the ones of associative law. Students’ confusion on mathematic symbols makes it difficult for them to apply distributive law. The result shows that most of the students have a clear concept of the four fundamental operations of arithmetic and the older, the better. As regards “quantitative relation”, students have done well on constructed response items of transitive law. Third graders perform better on reciprocal relation than second graders and second graders are better than first graders. The students are more capable of recognizing numeral patterns and the patterns of geometric shape-changing are harder for them. Students have excellent performance on the constructed response items of operational symbol in reference to “problem representation” while the first graders’ concept of an equal mark is still at the stage of calculation result. Fill-in the blank questions in division are more difficult for the students. The performance of higher graders on equation listing and problem solving are both lower the average, and this shows that only part of the students have the ability of comprehending and solving questions.
Constructed response items reflex elementary school students’ problem-solving approaches and their problem-solving performance is influenced by the tasks given in class. It is shown in the data of interview that when teachers are able to utilize more diverse and higher-level math tasks, it benefits students’ comprehension and application of pre-algebra knowledge.
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