| 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) === 103 === The purpose of this study is using a textbook-based design to explore a prospective teacher’s fraction division teaching knowledge. The data is collected through a semi-structure interview with video and sound recording, providing a description for the prospective teacher participant’s professional knowledge regarding fraction division teaching from two aspects: Mathematical Content Knowledge and Mathematical Pedagogical Content Knowledge.
I. Mathematical Content Knowledge
In faction division teaching, here’s Hui-hui’s knowledge about students: she believes that in all sorts of fraction division problems, students are able to solve the problems by reducing fractions to the similar denominator, and carefully describe the differences between other solutions depending on context; she ascribes students’ mistakes to being influenced by fractional addition and multiplication, erroneous usage of invert-and-multiply algorithm, not comprehending the meaning of the questions, and confusion of units; she is capable of explaining students’ thinking of different solutions in the same topic.
II. Mathematical Pedagogical Content Knowledge
In faction division teaching, here’s Hui-hui’s knowledge about curriculum and teaching: she discerns the activity’s objective from the questions in the textbook and proses the pedagogical key points, and considers the arrangement of questions in the textbook intentionally and arranged from easy to difficult, therefore all of the problems listed in the textbook should be instructed and the order of these problems should not be changed; she believes that based on the remaining time of the class, teachers should be focused on utilizing the teaching objectives to pose computational problems or word problems to evaluate the students; she considers most of the representations in the textbook correspond to the questions listed in it, a few unlabeled parts can be achieved through classroom discussions; facing student misconceptions in different situations, she would restate the concepts by providing illustrations or encourage students to discover errors through guided dialogues.
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