Student-teachers learning mathematics for teaching: learner thinking and sense making in algebra

Abstract

This is a qualitative case study that draws on Bernstein’s theory of the pedagogic device to analyse to what extent and how the discourse of engaging with learner mathematical thinking (LMT) is recognized and focused on in mathematics teacher education in Zambia, crucially in algebra that underlies progress towards further mathematics study. Four mathematics education teacher-educators and twenty of their final year student-teachers of a particular university in Zambia participated in this study. Moreover, a total of one hundred and five learners (45 grade 9s and 60 grade 12s learners) from a selection of four Government schools in a particular province of Zambia participated in the study. My study specifically explored three critical questions, which are: 1. What do teacher-educators select and privilege with respect to the discourse of engaging with learner mathematical thinking? 2. What are student-teachers’ recognitions and realizations of the discourse of engaging with learner mathematical thinking? 3. What is the relationship between teacher-educators’ discourses of engaging with learner mathematical thinking and that of their student-teachers, and how might this be explained? Semi-structured interviews were used to collect the data that enabled me to answer these research questions. These included three interview schedules that were used to: 1. carry out individual interviews with the teacher-educators; 2. interview the student-teachers in their respective two focus groups of 10 student-teachers in each; and 3. interview 8 pairs of student-teachers on 3 scenarios of common learner errors in algebra described in literature and the other 3 scenarios that were elicited from learners’ own working. The findings show that teacher-educators’ privileged selections of what entails LMT is weakly classified and framed, hence implicit messages being relayed to student-teachers. Whether teacher-educators’ focus is on developing in learners both relational and instrumental understanding, or learner errors, or creating an environment where teacher can listen to learners, there is a range of mixed messages being relayed, hence messages within them are spread out. That is, the criteria for what counts as LMT are weak because they are spread out. Moreover, it is also evident that across all the three major categories, LMT is a practical accomplishment as principles that would guide discussions around it are not so clear. LMT is talked about when focus is on principles that guide discussions on topics/courses in the mathematics education curriculum. The indication here is that the privileging by the teacher-educators while in these three domains, some of the big discourses in the specialized fields of mathematics education research and mathematics education are filtering through but in a very weak way. As expected, student-teachers’ realization of what entails LMT is also weakly classified and framed but they were able to recruit or take-up some of the messages from their teacher-educators with further elaboration in some cases. While there is attention to LMT in the courses and it is discussed as within the courses by both the teacher-educators and the student-teachers, neither seem to be informed directly by the literature. This suggests that the talk about error while it relates to the literature is not discursively organised. In terms of positioning of student-teachers/teachers/teacher-educators or learners or the curriculum, teacher-educators as well as student-teachers hold contradictory views in referring to what is there pertaining to LMT as absences or presences. I have also shown that given scenarios on common learner errors in school algebra, student-teachers hold contradictory views on what teaching and learning entails despite constructivism being the theory espoused in their mathematics education courses. They equate teaching to learning; hence a transmission view as well as have the understanding that learners are not empty vessels but come with prior learning to the teaching and learning situation. This suggests that focus on LMT in terms of the nature of errors and strategies for carrying out error analysis is not a principled focus in these student-teachers’ mathematics education courses. This is further confirmed in that student-teachers spoke in the everyday professional knowledge of teaching and learning. I have therefore argued that ways in which LMT ought to be explicitly structured and focused on in teacher education be sought, for example, to include use of discursive resources from research. I have also made methodological and theoretical contributions to the specialized field of mathematics education research. In particular, methodologically, I have extended the use of the notion of an evaluative event as a unit of analysis on interviews unlike before when it was used on assessment tasks and instruction in teacher education. Theoretically, I have shown how my study has been an attempt towards developing the internal and external languages of description concerning the discourse of engaging with LMT, an issue of potential future development.