AbstractsMathematics

Students’ and teachers’ long-term (i.e. three years) experiences in three classes of the traditional direct instruction and constructivist class discussion approach to the mathematics teaching at a Taiwanese junior high school and at an experimental school in Taiwan were discussed in this study. This research utilized qualitative methods. The study adopted content analysis approaches from a qualitative perspective. This was combined with the perspectives of social constructivism and situated learning theories to interpret students’ learning and growth. The research findings of this study revealed differences in the group of students exposed to the constructivists teaching environment. These differences were evident in their mathematical competencies and richer students’ autonomy. However, when compared to the traditional teaching environment there were several challenges such as time use, understanding all classmates’ dialogue, mathematical writing ability in explaining and communicating their thinking and more teacher work. Constructivist class discussion classrooms in this study appeared open, relaxed, lively, friendly, and supportive of each other in building new knowledge. This was apparent in School E where the environment provided more opportunities for students to develop their own mathematical ideas. This environment also produced a more social/collective/adaptive form of mathematical knowledge, with ongoing assessment of information provided by the teachers, to inform instructional practices. The data presented here show that students exposed to the constructivist discussion approach had richer learning experiences which may be viewed as a result of their active participation during instruction. Compared to the their peers in School T, the traditional direct instructional group, School E students had more learning roles - (knowledge explorers, knowledge producers, and knowledge adventurers). Student in School T acted mainly as knowledge receivers; they mostly received and followed the teacher’s instruction and explanations of mathematical concepts, and then applied the received procedures to solve given mathematical problems. The findings of the sequential relationship between teachers’ perceptions of mathematics/learning, teaching practice, and students’ knowledge/perceptions sheds new light on the social relationships between teaching and learning and the situated influences among classroom practices and students’ knowledge/competencies/perceptions. This investigation revealed that the constructivist approach seems to be an excellent medium to provide quality education. It is recommended that educators should re-introduce the use of a constructivist approach to teaching Mathematics because of its potential to enhance the quality of Mathematics education, which in turn augments students’ competency as future Mathematicians.