This research was conducted in two junior high schools in Taiwan, a traditional school and an experimental school during 2002 and 2003. When I started this study, students were just turned to Grade 9 year. In order to understand teachers’ and students’ long term teaching and learning experiences including their early Grade 7 and 8 years to shape their typical teaching practices. I need to adopt multiple research methods to evaluate and interpret their opinions (see Section 4.4).
The traditional school is referred to as School T in this study, and the experimental school, School E. The teacher in the traditional school is called Tom, while the male teacher at the experimental school is given the name Ed, and the female teacher is called Eve. The teacher (Tom) in the traditional school (School T) taught using the traditional direct teaching approach. The teachers (Ed and Eve) in the experimental school (School E) taught based on a constructivist view of learning. All three teachers taught the same curriculum and covered the same mathematics content.
The Traditional School (School T)
This junior high school is defined as a traditional school in this research. Based on observations of this school by the researcher for more than ten years, it was felt that the main aims of the school were similar to those of most schools in Taiwan. Teaching was focused on helping students successfully pass the entrance examination to the senior high school; it also focused on developing students’ moral values and other talents besides academic achievement. This is a rural school. The size of the school is relatively small when compared to other schools in Taiwan. There were about 23 class cohorts from Grade 7 to Grade 9 in this school during the academic year of 2002-3. In order to improve students’ achievement, each year this school - like other schools in Taiwan - offers opportunities for Grade 9 students to study late until 9:00 p.m. at the school. Every year there is one special talented class in this school.
Tom, the male teacher involved in this study, is considered a very good mathematics teacher by the school. Tom has been working for 24 years as a mathematical teacher in School T; when interviewed in 2002 (T1Ihp1Q1), he was a homeroom teacher and also taught four mathematics classes (T1Ihp9Q22). He normally would teach at least one special talented class cohort each year. Students in School T who participated in this study were in a special talented class in Grade 9 in 2002. Of the 27 students in this class, 26 participated in this research.
Evidence from my personal surveys held with other grade 9 students in 2001 had revealed that Tom helped students to better understand mathematics. Thus, it was expected that it would interesting to examine how this experienced and excellent teacher conducts his mathematics teaching.
The Experimental School (School E)
The experimental school, established in the end of 20 century, was a rare case of a school using alternative teaching approaches at the junior high school level in Taiwan. However, the junior high level of this school was discontinued in early years of 21 century, while the senior high level finished after three years. The goal of this school included giving back the ownership of learning to students while promoting students to collaborate and cooperate with other. Further examination of the school revealed that a constructivist teaching style was used in mathematics classrooms by a Bureau of Education. Two scholars in early years of the 21 century regarded that teachers of School E did not automatically give direct answers, so students could develop independent thinking abilities from multiple dimensions, and abilities to solve problems and to make judgements (references removed for confidentiality). Students could choose their homeroom teachers, arrange their own learning schedule, and learn at their own speed. They used a school court and discipline cooperatively structured by teachers and students, instead of school rules, to maintain justice on campus (references removed for confidentiality). Students normally took nearly two years to learn self- management, self-acceptance and responsibility in such an open environment (references removed for confidentiality). The Ministry of Education and the Ministry of Justice in Taiwan have commented that this school performed well in
democracy and law education. The Union of Education Reform for Secondary School Students recommended this school as the best campus with respect to respecting students’ rights (references removed for confidentiality). Students’ learning styles were consistent with the spirit of self-learning and cooperative learning. However, mathematics teachers in this school had been asked by the Bureau of Education in an early year of 21 century to provide more mathematical subject matter knowledge in classrooms (references removed for confidentiality).
Eve, the female teacher who engaged in this research, earned a Master’s degree in mathematics, had taught in primary school for seven years, and was a mathematics teacher in this junior high school for three year at the time of this study. (Of1Ihp1Q1t). Eve was also a homeroom teacher of one of the Grade 9 class cohorts (Of1Ihp14Q12m) and taught four mathematics classes for Grades 8, 9, 10 and 11, when participating in this study (Of1Ihp21Q21). Ed, the male teacher involved in this study, had been a mathematics teacher in an army school teaching mathematics at the junior high level (Om1Ihp9Q7e) for more than 20 years. Then he retired and came to this experimental school (Om1Ihp4Q1b). When Ed participated in this research project, he taught mathematics, science and sociology (Om2Ihp1Q1t). Further information on the schools, teachers and the coding systems used in this study are listed in Appendices N & O.