The Learning Gains studies investigate the impact of teachers’ participation in professional development (PD) on learner attainment. The Learning Gains I study (2013) showed that Grade 10 learners taught by teachers who had participated in the Transition Maths 1 course outperformed learners, in the same schools, taught by teachers who had not participated in the course. The gains were statistically significant with an effect size of d=0.21. In 2017 the gains made by Grade 9 learners taught by TM1 teachers were not statistically significant in relation to the comparison group. In 2018 we compared the performance of Grade 9 and 10 learners taught by teachers who had been on the course in 2016 or 2017, with learners taught by teachers who had no previous contact with the project. Initial results show that the Grade 9 and Grade 10 learners taught by TM1 2016 teachers made statistically significant gains over the other two groups, with effect sizes for Grade 9 and Grade 10 groups of d=0.68 and d=0.50 respectively. However, the gains of the group taught by TM1 2017 teachers were not statistically significant in relation to the comparison group. This, together with the 2017 results, supports the international findings that the impact of PD on learner attainment is delayed.
The overarching research question for the WMCS project is:
Can improving teachers’ mathematical knowledge for teaching through professional development (PD) lead to improving the quality of their mathematics teaching and consequently their learners’ learning?
The goal of all mathematics teacher professional development (PD) is to impact learning in the classroom. Linking a particular professional development intervention, the practices of participating teachers, and their learners’ learning is not trivial. Over ten years, we have carried out two sets of studies:
- A quantitative, quasi-experimental Learning Gains Study on the impact of the PD learners’ learning.
- A range of qualitative studies illuminating instructional practices, using an empirically grounded, developmental and theoretically informed analytic framework called Mathematical Discourse in Instruction (MDI)
These two strands of research and their related qualitative and quantitative studies combine to answer the overarching research question pursued in the WMCS.
Sitting within the qualitative studies of practice, is our Lesson Study project. We carried out cycles of Lesson Study, using a specifically adapted model, to both work with teachers on studying teaching, and to strengthen the MDI framework.
The MDI framework for describing and interpreting teaching also informs all our teacher development work. We have reworked it into the Mathematics Teaching Framework (MTF) that functions as a resource for teachers to plan and reflect on their teaching. As described in Adler 2017, MDI/MTF is a boundary object in the project – bending flexibly to suit the purposes of both research and the development of teaching practice.
Mathematical Discourse in Instruction (MDI) and related research
A first key task for our research was to construct a framework for describing mathematics instruction. The framework needed to be:
- empirically grounded in the realities of teaching and learning in the majority of South African secondary classrooms AND
- theoretically informed by relevant research and literature on mathematics teaching and learning on the international terrain AND
- developmentally oriented to enable us to work with teachers to make recognisable progress in key aspects of their teaching.
MDI is socio-cultural in its orientation to mathematics, teaching and learning. It follows that mathematics is viewed as a network of connected scientific concepts; learning is understood as goal directed and teaching as mediated activity. MDI is comprised of four key elements of teaching, that work together towards the mediation of mathematics. These are:
- The object of learning: what learners are to know and be able to do
- Exemplification: the example set, tasks and representations that can bring the object of learning into focus
- Explanatory communication: the way words are used, and mathematics concepts and procedures are justified
- Learner participation: what learners do and say
MDI and research on teaching
In Adler & Ronda (2015; 2017a), Adler (2017) and Ronda & Adler (2019) we describe the framework and its elements, and communicate its analytic use for describing and interpreting shifts in teaching. Specifically, in the 2015 and 2017 papers we use case studies which show that teachers improve their exemplification practices relatively easily. However, improvements in the quality of mathematical communication and learner participation are a more complex learning process. The research reported in 2019 focuses on a sample of teachers, with data on their knowledge of algebra as tested in the TM1 course; and video data of their teaching of algebra. Results supports the hypothesis that “stronger mathematical knowledge correlates with better quality teaching”, and thus the underlying assumption of the WMCS project: that improving teachers’ mathematical knowledge for teaching was a critical first step for our PD intervention.
Earlier work on MDI, with particular focus on connections and coherence (Venkat & Adler, 2012) and exemplification and explanatory communication (Venkat & Adler, 2014) laid foundations for the full development of MDI as an analytic research tool for describing and interpreting teaching practice. Enhancing these studies is the learner tracking study that illuminates mathematical connections and coherence at the level of learners
MDI and research on textbooks
In Ronda & Adler (2017) we show that MDI can be used and extended to analyse and then compare the quality of different textbooks.
MDI and research on teaching identity
In Ntow & Adler (2019), we explore teacher learning through the lens of “identity”. We study teachers’ take up of “practice-linked identity resources” as offered in the Transition Maths 1 course – where the MDI/MTF is a key ideational resource for teaching.
MDI and research on Lesson study
Adler & Alshwaikh carried out a systematic study of Lesson Study cycles with teachers from one cluster of project schools. In Adler & Alshwaikh (2019) we describe the WMCS Lesson Study model as a particular case of Lesson Study in South Africa, and confirm research elsewhere that progress with lesson planning, teaching and reflection is a function of co-participation of teachers and researchers. We also provide evidence in support of arguments that learning through Lesson Study is enhanced by the use of theoretically informed resources (like the MDI), and participation of “knowledgeable others”.
In Alshwaikh & Adler (2017a and b) we show the co-learning of teachers and researchers through collaboration in Lesson Study (2017a) and how there are tensions and dilemmas for teachers and researchers as they do this collaborative work (2017b).
The Learner Tracking Study (2010-2013) investigated changes in learner performance in algebra and function. We tracked 250 learners in 9 project schools from Grade 9 to Grade 11. Learners demonstrated low algebraic proficiency in Grade 9 which improved gradually in Grades 10 and 11. Typical learner errors included conjoining, difficulties with negatives and brackets, and inappropriate application of exponential laws and the distributive law.