Source: Australian Journal of Teacher Education, 45(1)
(Reviewed by the Portal Team)
This paper draws on data generated as part of the Strengthening Mathematical Thinking and Reasoning Proficiency in Primary Teacher Education (MARKITE) project (Cooper, Cowie, Furness, Peter & Bailey, 2017).
The MARKITE project aimed to foster pre-service primary teacher awareness of mathematical and statistical thinking across the breadth of teachers’ work, as a way to support their understanding of the role and breadth of such thinking.
In this paper the authors examine the research question:
To what extent do pre-service primary teachers become aware and/ or more aware of the breadth of mathematical and statistical thinking within the wider professional teaching role over the course of their year-long graduate teacher education programme?
In the paper the authors set out findings from mentor meetings from two pre-service teacher cohorts, and a series of focus group discussions with a small number of volunteer pre-service teachers from one cohort.
Over a period of three-years the Strengthening Mathematical Thinking and Reasoning Proficiency in Primary Teacher Education (MARKITE) study in New Zealand aimed to enhance pre-service teacher awareness and understanding of the role of mathematical and statistical thinking across the curriculum and the breadth of teachers’ professional work.
Preservice teachers in the one-year Graduate Diploma of Teaching (Primary) programme were the participant group for the project in each year.
During each of the project’s three years data was collected from pre-service teachers in a variety of ways, including an assessment of their mathematical and statistical thinking, and associated confidence at the beginning and end of their one-year programme.
This assessment and confidence data is not the focus of this paper (see Cooper et al., 2017).
Preservice teachers were offered an opportunity to meet with a mentor to discuss their assessment results.
During the mentor meetings, which were held after the pre-service teachers’ first practicum, pre-service teachers were also asked about their perceptions of the role of mathematical and statistical thinking beyond mathematics classes, i.e., across teachers’ wider professional role.
Some pre-service teachers attended these mentor meetings in small groups, and some followed up on the mentor meetings by sending emails with further ideas and/or comments to the researchers.
These mentor discussions constitute the first set of data reported here.
Focus group discussions with volunteer pre-service teachers were held before and after the second practicum in the second and third year of the study, before the third (final) practicum in the final year of the study, and at the end of the programme in the second and third years of the project.
For all practicum placements pre-service teachers were full time in schools from four to seven weeks.
They worked alongside certificated teachers gradually taking more responsibility for teaching and learning.
Focus group discussions centred on pre-service teachers anticipated and experienced examples of teacher mathematical and statistical thinking outside the teaching of mathematics and statistics.
With researcher prompting, the discussions ranged over the three domains of interest in the MARKITE study: cross curriculum, data literacy, and administration and management.
As might be expected the initial focus and subsequent direction of the discussion varied depending on who spoke first and about what.
Typically, all participating pre-service teachers contributed to discussions, sometimes prompted by the authors but often encouraged by their peers to share their experiences and thoughts.
In the final year of the project the team recruited and retained the involvement of nine pre-service teachers.
All mentor meetings and focus group discussions were audio-taped, transcribed and field notes taken.
Focus group discussions in the second and third year of the project, along with data from the mentor meetings in those years are analysed in this paper.
Analysis of Mentor Meetings and Focus Group Discussions
First, the transcripts and researcher notes from the mentor meetings early in the year were read and analysed deductively for reference to and examples of the three domains of interest to the study: cross curriculum, data literacy, and administration and management.
Next the authors looked more closely at the data, viewing the conversations during the mentor meetings as reflecting a process of example-generation as described by Zaslavsky and Zodik (2014).
The authors viewed the examples of mathematical and statistical thinking pre-service teachers contributed in the focus group discussions as an indicator of their understanding as well as a catalyst for educating or raising individual and collective awareness of the role of mathematical and statistical thinking in teachers’ professional work.
Results and discussion
All of the pre-service teachers who participated in the project Year-3 focus group discussions reported that their involvement in the research alerted them to the existence of mathematical and statistical thinking across the curriculum, in the analysis of student achievement data, and in administrative and management tasks.
That is, for these pre-service teachers the mathematical and statistical thinking used across the breath of their professional work was no longer invisible.
Time and again during the focus group discussions the authors witnessed pre-service teachers’ awareness change as a result of another pre-service teacher’s contribution to discussion.
Hence, the data indicates that sharing and discussing examples was a useful strategy for raising the awareness of the pre-service teachers of the presence and role of mathematical and statistical thinking outside of mathematics classes.
The discussions (in mentor meetings and focus groups) served as a productive means for extending the personal example space the pre-service teachers had to draw on when considering the presence and role of mathematical and statistical thinking.
This finding echoes the assertion by Watson and Mason (2002) that deliberately prompting students to generate examples can be a powerful tool for alerting them to the role/s mathematical thinking has, or might play, in a context.
The data showing an expanding example space and awareness of the wider role of mathematical and statistical thinking opens the possibility that pre-service teachers will be better prepared to support student learning.
In particular, during the final focus group discussion in the project Year-3 pre-service teachers spoke of collecting and using data, offering a more integrated programme (i.e., being aware of mathematics across the curriculum) and being able to engage critically with the use of statistical data: all actions likely to enhance their future teaching practice.
Whether this happens in practice is yet to be investigated.
The authors note that if we value the role of mathematical and statistical thinking as an important aspect of well-being and active participation in democratic society, then the question for us as preservice teacher educators is how best to embed discussions that make visible and extend preservice teachers’ personal example spaces.
Literature on the teaching and learning of transversal concepts, or concepts that run across the curriculum such as assessment has identified a number of models for teaching these ideas.
These models range from dedicated elective courses to dedicated compulsory courses to programmes that embed ideas across all curriculum areas, courses, and an institution (DeLuca & Lam, 2014; Evans, Stevenson, Lasen, Ferreira, & Davis, 2017).
Indications from the wider MARKITE study are that teacher educators making visible and paying attention to any mathematical thinking embedded in their courses can be productive (Cooper et al., 2017).
Further research is needed to explore in detail the benefits of this experience, and how and if such discussions support beginning teachers to make deliberate use of this thinking across their professional work.
Cooper, B., Cowie, B., Furness, J., Peter, M., & Bailey, J. (2017). Mathematical reasoning and knowledge in initial teacher education. NZCER: Wellington, New Zealand.
DeLuca, C., & Lam, C. (2014). Preparing teachers for assessment within diverse classrooms: An analysis of teacher candidates’ conceptualizations. Teacher Education Quarterly, 41(3), 3–24.
Evans, N., Stevenson, R., Lasen, M., Ferreira, J., & Davis, J. (2017). Approaches to embedding sustainability in teacher education: A synthesis of the literature. Teaching and Teacher Education 63, 405–417.
Watson, A., & Mason, J. (2002). Extending example spaces as a learning/teaching strategy in Mathematics. In A. Cockburn & E. Nardi (Eds.), Proceedings of PME 26 (vol. 4, pp. 377–385). Norich, England: University of East Anglia
Zaslavsky, O., & Zodik, I. (2014). Example-generation as indicator and catalyst of mathematical and pedagogical understandings. In Y. Silver & S. Li (Eds.), Transforming mathematics instruction: Multiple approaches and practice (pp. 525– 546). London, England: Springer.