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Research

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.

More detail with links to research articles on MDI research, including Lesson Study, and the Learning Gains Study follows.

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:

  1. empirically grounded in the realities of teaching and learning in the majority of South African secondary classrooms AND
  2. theoretically informed by relevant research and literature on mathematics teaching and learning on the international terrain AND
  3. 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:

  1. The object of learning: what learners are to know and be able to do
  2. Exemplification: the example set, tasks and representations that can bring the object of learning into focus
  3. Explanatory communication: the way words are used, and mathematics concepts and procedures are justified
  4. 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).

Learning Gains Study

The Learning Gains studies investigate the impact of teachers’ participation in professional development on learner attainment. In particular we have focused on the impact of the Transition Maths 1 course which has been completed by more than 150 teachers from approximately 80 secondary schools in Gauteng.

Learning Gains 1 Study (2013)

The Learning Gains I study, conducted in 5 project schools in 2013, showed that Grade 10 learners taught by teachers who had participated in TM1 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 which translates to approximately 3 months of additional progress by learners.

The sample size was relatively small, and the comparison groups were drawn from the same schools so the results were treated as “evidence of promise” that the TM1 intervention can make an impact at the level of the learner. Further details can be found here. (ref: Pournara, Hodgen et al)

Learning Gains II Study (2016-2019)

The Learning Gains II study has built on the previous study, using a more rigorous test instrument and a much larger sample of teachers and learners. The new test instrument was designed and piloted in 3 cycles in 2016.

In 2017, 11 teachers who had completed the TM1 course in 2016 participated in the study. Data was collected with 991 of their Grade 9 learners. We also collected data with 988 Grade 9 learners of 15 teachers in the same 9 schools who had not done the course. There was strong evidence to show that the TM1 course had impacted the mathematical knowledge for teaching of the 11 teachers. However, the results of the learner testing were disappointing. There was no statistically significant difference in the gains in the learner test scores (pre-test to post-test) between the comparison group and the TM1 group. When we looked more carefully at the teachers’ profiles, we saw that the TM1 group and their colleagues had, on average, been teaching mathematics for a similar number of years. While the TM1 group had more experience teaching at Grade 8 and 9 levels, their colleagues had considerably more experience teaching in Grades 11 and 12.

This suggests that participation in the TM1 course did not make up for years of teaching experience at senior secondary level in the first year after doing the course. A different interpretation of the results might argue that, based on the learner results, participation in TM1 enabled the teachers to do “as good a job” in teaching Grade 9 Mathematics as their colleagues who have more experience in teaching higher grades. We also need to bear in mind the claims in the research literature that the impact of PD on learner attainment is not immediate. To read more (ref: Pournara, Barmby 2019 - Saarmste)

In 2018 we included teachers from the 2016 and 2017 TM1 cohorts. We tested their learners in Grades 9 and 10. We also tested learners in comparison schools where teachers had no previous connection with the WMCS project.

There was strong evidence of the impact of the TM1 course on teachers’ mathematical knowledge for teaching in both the 2016 and 2017 groups. Initial analysis of learner performance shows 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. Once again this supports the international findings that the impact of PD on learner attainment is delayed. To read more (ref: Pournara, Barmby 2019 - PME)

Further analysis is in progress and results will be made available soon.

Related Publications
  • No significant impact on learner attainment - really?
  • Can improving teachers’ knowledge of mathematics lead to gains in learners’ attainment in mathematics?

 

Learner Tracking Study

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. In October each year we administered a diagnostic algebra test to these learners. The test was based on the original Concepts in Secondary Mathematics and Science (CSMS) Study of the late 1970s and on its follow-on, the Increasing Competence and Confidence in Algebra and Multiplicative Structures (ICCAMS) Study of the early 2000s.

The CSMS algebra items are diagnostic and include items which are not directly linked to the curriculum. The test items were piloted in 2010 and were shown to be appropriate for project schools. The overall findings of the study indicated that learners demonstrated low algebraic proficiency in Grade 9 which improved gradually in Grades 10 and 11. While the trends are similar to the UK findings, there were substantially more SA learners who did not achieve minimum levels of algebraic proficiency and the range of learner errors was wider than in the UK.

Further error analyses showed a wide variety of errors even on simple algebra items. Typical errors included conjoining (e.g.), difficulties with negatives and brackets, and inappropriate application of exponential laws and the distributive law. Although such errors dissipated in the higher grades, this happened later than expected. Further details of this study can be found below.

Related Publications
  • Learners’ errors in secondary algebra: Insights from tracking a cohort from Grade 9 to Grade 11 on a diagnostic algebra test.
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