DEVELOPING MATHEMATICS FOR TEACHING THROUGH CONCEPT STUDY: A CASE OF PRE-SERVICE TEACHERS IN TANZANIA

This descriptive qualitative case study investigates the question “In what ways does developing mathematics for teaching through concept study contribute to the professional knowledge and skills of pre-service teachers?” The concept studies were conducted in a classroom driven by five conditions: internal diversity, decentralized control, redundancy, neighbour interactions, and organized randomness (Davis & Simmt, 2003) that underpin complex system. Data was analysed using Davis and Renert’s (2014) concept study model that includes realizations, landscapes, entailments, blending, and pedagogical problem solving, and Ball and colleagues (Ball, Thames, & Phelps, 2008) model categories of mathematical knowledge for teaching (MKT). The study involved a group of ten pre-service teachers who were in their second year of the diploma in secondary education mathematics in a teacher college in Tanzania. They were majors taking one of the combinations: mathematics and physics, mathematics and chemistry, or mathematics and geography. Prior to the research, these pre-service teachers had only eight weeks teaching experience in their first year Block Teaching Practice (BTP). The pre-service teachers participated in 4 full day concept study sessions which involved three phases: pre-questionnaire, concept study workshop, and post questionnaire. Prior to the first concept study, the face-to-face interviews of all ten participants individually was conducted for the research to begin to shape a holistic understanding of them and their context. Four different concept studies of ratio, rate, proportion, and linear function were conducted for the group at an interval of a month from one concept study to another, with the researcher’s facilitation as an emphatic second-person observer (Metz & Simmt, 2015). An empathic second-person observer is an observer that becomes a member of the social group while acting as a facilitator as he or she knows the kind of experience the participant is talking about. The study reveals pre-service teachers’ deep understanding of mathematics concepts from the school curriculum, and mathematics for teaching (MFT) was built through group interactions in the concept study. Explicitly, concept study provided the pre-service teachers the opportunities to learn the meaning of the targeted mathematics concepts, their symbolic and iconic representations, their applications outside the school environment, how they are related to other mathematics concepts, and it served to correct participants misconceptions of the mathematics concepts at hand. The study demonstrates the value of mistakes in understanding the mathematics concept and the value of collaboration in pre-service teacher education programs. The study illustrates how through collective work the participants enhanced their mathematics for teaching across Ball’s MKT categories of common content knowledge and specialized content knowledge as subject content knowledge, and knowledge of content and teaching and knowledge of content and curriculum which fall under pedagogical content knowledge, with the exception of horizon content knowledge and knowledge of content and student. Although concept study reveals different emphases with pre-service teachers from in-service teachers the researcher illustrates concept study is a potentially viable strategy to use with pre-service teachers in Tanzanian teacher colleges/universities to enhance pre-service teachers’ mathematics for teaching both knowledge and skills. Key words: Concept study, Mathematics for Teaching, Mathematics teachers’ professional knowledge, Teacher education