A Prospective Teacher’s Conception of Teaching Initial Fraction while Designing Plan as well as Interpreting Textbook

• Main Authors: Shu-Ru Tsai, 蔡淑茹
• Other Authors: Shu-I Chang
• Format: Others
• Language: zh-TW
• Published: 2016
• Online Access: http://ndltd.ncl.edu.tw/handle/vqde7y

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) === 104 === A Prospective Teacher’s Conception of Teaching Initial Fraction while Designing Plan as well as Interpreting Textbook ABSTRACT The purpose of this study is using the problem posing in the textbook-based design to explore a prospective teacher’s teaching concept of initial fraction. Data used in this study is collected by viedo recording and sound recording of semi-structural interviews. Below are some findings of this study in “control of teaching materials” and “facilitating students’ learning”: I. Control of Teaching Materials As for the questions pertaining to the concept of equal division, preliminary understanding of fractions, and first-stage equivalent fractions, Beibei mainly adopts graphic representation, pure text description, and abstract situations like fraction symbols as teaching methods. Therefore, such kinds of questions don’t correspond with the actual operations required in textbooks and the teaching objective of concrete situations. This question setting mode follows the main question setting concept but cancels the graphic representation and the overall unitage. Therefore, it disaffiliates itself from the concrete situations. In consequence, this kind of abstract question setting mode fails to enhance the teaching effect. The design of after-class exercises is similar to the question setting mode in class or even more difficult. Therefore, it also fails to enhance the learning effect of the main questions. However, as for the questions selected in the exercises, priority consideration should be given to the questions not involved in textbook content and the design of question setting to inspect the schoolchild’s confusion about the concept and deepen their understanding concept of fractions. The questions on the concept of equal division and comparison of common denominator fractions are relatively complete. Therefore, the teaching and study should focus on the content with which the learner gets easily confused. II. Facilitating Students’learning Beibei gives enough consideration to the students’ life experiences and arouses their existing knowledge before setting the questions about the concept of equal division, preliminary understanding of fractions, and first-stage equivalent fractions. The question setting content gives enough consideration to the students’ cognitive comprehension condition. Pure text description and pure fraction symbols are adopted as the representation mode highlighting the content which the students find hard to understand. Before presenting problem solving exercises on the concept of equal division, preliminary understanding of fraction, comparison and addition and subtraction operations of common denominator fractions, conversion of improper fractions to mixed fractions and vice versa, and the concept of unitage, the following methods are adopted to help students understand the meaning of the question: direct explanation and questioning, assisting after listening to their explanation of the question meaning, and providing real life examples in relation to the question. When students meet difficulties in solving problems, pre-service teachers may help students solve the problems by asking schoolchild to do actual operation (paper folding), assisting the identification of fraction terms via living language and teaching tools, reviewing existing knowledge, and using icons. In addition, the teachers should be aware that the schoolchild may make mistakes for intuitive judgment of equal division, ignorant of unitage, influence of fundamental mode of integers, and algorithm. Therefore, pre-service teachers should help the schoolchild to form the correct problem solving method through repeated actual operations, relating it with real life examples, unitage reversion, and graphic representation. Keywords: initial concept of fractions, Mathematics teaching concept, prospective teacher