[[alternative]]A Case Study of the Instructional Representations of A Vocational High School Mathematics Teacher to let His Students like to Learning Mathematics

[[abstract]]The purpose of this study was to investigate the instructional representations of a vocational high school mathematics teacher making his students like to learn mathematics. This case study is based on a vocational high school math teacher and his students from four classes for a period of ten weeks. The purpose was to explore the students’ learning characteristics, the sources and the types of the client teacher’s instructional representation, the client teacher’s characteristics, as well as the students’ perception toward the client teacher. This is a case study. The methodology of Data collection included classroom observation, interviews with the client teacher, the beginning teacher she assisted, and the students, as well as the reflective journals, conclusive feedback and referential documents. The interviews and observations were recorded. Furthermore, there was video taping of each class at the beginning and the end of the research for the purpose of analysis. A questionnaire on students’ responses to the teacher’s representations was used. In the procedure of data analysis, the methodology of triangulation was adopted to establish the validity of the research. The major findings of this research were as follows: I. The learning characteristics of the students in math learning included (1) going home without book bags and reluctance in learning. (2) being in the habit of laziness and indulging in internet on-line games. (3) lacking a high standard of academic results.(4) most students would adjust their learning attitudes because of the teacher’s teaching style. (5) poor learning attitudes in junior high schools. (6) lacking the ability to calculate. (7) concepts about mathematics were incomplete. II. The sources of the client’s instructional representation were derived from (1) the experience from the worst class in junior high school. (2) a competent teacher in senior high school. (3) the experience of being the tutor and part time job in the cram school. (4) the conflict of reality and idea philosophy. (5) teaching experience for several years. (6) self-personality analysis and learning from the good models of relatives. III. A wide variety of instructional representations were used by the teacher, including humorous explanation, analogy, illustration, demonstration, concept association, body language, eliciting, question and answer, discussion, rewards and punishment, advise after class, open book tests, mathematical exercise, hands-on manipulation etc. The major instructional representation of the client teacher in the study was not only (1) to activate students’ motivation during the whole class but also (2) to reverse the teacher-centered mode to a teacher-student interaction in order to exhibit professionalism and creativity. IV. The students’ perception toward the teacher included (1) students regain the confidence and achievement of math learning. (2) Students gradually became interested in math learning because of the teacher’s teaching style. (3) Students liked the teacher-student interactive way of teaching. (4) the instructional representations such as concept association and eliciting not only provide students the confidence to look for the answers but also reconstruct student’ concepts and knowledge of mathematics. (5) Students need the teacher to play the multiple and various roles to lead them to explore the function of mathematics. (6) The teacher’s multiple instructional representations are constant and unanimous. (7) The students benefited from the teacher’s multiple instructional representations. Finally, based upon the findings during the case study, some suggestions were offered for teaching math in vocational high schools and for further research.