It is generally agreed that mathematics teaching in South Africa could and should be improved (The Centre for Development and Enterprise, 2013) and at the same time there is a body of literature to suggest that the effective use of formative assessment has the potential to improve teaching and learning (Black & Wiliam, 2009). It could therefore be argued that it makes sense to promote the use of formative assessment within South African mathematics classrooms. One way to do this might be to develop resources to support teachers as they try out new ways of using formative assessment. This is the goal of the Formative Assessment in Science and Mathematics Education (FaSMEd) project, which is an international project aiming to encourage the use of formative assessment in classrooms in nine different countries, of which South Africa is one, by developing a ‘toolkit’ for teachers to use.
FaSMEd is a three year project and at the time of writing has been running for two years. The toolkit is therefore not fully formed, but the classroom interventions that will inform the toolkit have been completed. This paper reports on the emerging findings from the classroom interventions in South Africa. It begins by explaining the theoretical framing of the project and then outlines what has been done, and why, and finally presents the emerging findings.
Formative assessment, which is the process by which ‘evidence about student achievement is elicited, interpreted, and used by teachers, learners, or their peers, to make decisions about the next steps’ (Black & Wiliam, 2009, p. 9), is at the heart of the FaSMEd project’s theoretical underpinning in terms of the teaching and learning of mathematics at school. Further, learning is theorised, following social constructivist theory, as the creation of concepts, together with others, as language and tools are used and internalised (Vygotsky, 1980). The implication, for FaSMEd’s classroom interventions, is that an active learning approach, which emphasises formative assessment, is adopted. This approach means that learners work collaboratively to build their understanding (Swan, 2008).
Whereas social constructivism and formative assessment inform the sorts of classroom interventions adopted, the design of the toolkit, which is the ultimate aim of the project, adopts a design-based research approach. Design-based research in this context means that tools are developed together with teachers in iterative cycles of design, classroom use, reflection and improvement (Edelson, 2002; Gravemeijer & van Eerde, 2009). This paper is concerned with the ways in which teachers used the tools in their classrooms and what can be learned from the interventions to inform the development of the toolkit.
Twenty secondary school teachers in and near Cape Town volunteered to take part in the project. All but one of the schools are government schools, and they range widely in terms of the socio-economic status of their learners. The teachers in the schools chose classes to work with in Grades 8, 9 or 10 (aged about 13 in Grade 8). The classroom interventions, in which teachers used the tools, took place in between January 2015 and December 2015. Most teachers used three tools; one in each of the first three terms of the school year. All lessons were observed and video recorded and the teachers were interviewed after the lesson.
The tools used by the teachers were lesson plans: classroom mathematics tasks and detailed guidance for the teacher. Most, but not all, of the tools were developed by the Mathematics Assessment Project (MAP) in the UK and USA and they were chosen because they are aligned with the theoretical framing adopted by the project: they are designed to support teachers in the use of formative assessment in their classrooms and to promote collaborative small group work. They can be described as active learning lessons. Very often this means that students are given sets of small cards to sort or match (e.g. equations and descriptions, such as ‘ax = 25’ and ‘the apples I bought cost R25’). The lessons are ‘formative assessment lessons’ in that they provide opportunities for teachers to gather information about their students’ current levels of understanding and the guidance suggests a) how they can gather this information and b) how they could respond.
The findings relate to the teachers’ responses to the lessons: what they chose to do and why. Overall, they made very few adaptations to the main classroom activity (e.g. card sorting) although some teachers requested some changes to the cards themselves, such as reducing the number of cards or simplifying the language. There was more variation in the ways in which they introduced the activity, with some spending some time on whole class teaching on the topic, some modelling the activity using big versions of the cards, some describing to the students what needed to be done and one handing out the cards and saying ‘Go!’. In terms of ending the lessons, teachers in this study all included some discussion on what the correct solutions were or could be. In some cases, this whole class activity was cut short because the lesson ended. In many cases big versions of the cards were used to support the discussion.
However, what the teachers do in the lessons is beginning to feel less important than what they say about what they might do if they were to teach the same, or similar, lessons. Their own ‘lessons learnt’ might prove to be the most valuable aspect of the toolkit. As stated, the findings are emerging and the toolkit is still in the early stages of development: as a research team, we need to find ways to use the classroom intervention data in creative ways to develop something really useful for teachers.
Black, P., & Wiliam, D. (2009). Developing the theory of formative assessment. Educational Assessment, Evaluation and Accountability, 21(1), 5–31.
Edelson, D. (2002). Design Research: What We Learn When We Engage in Design. Journal of the Learning Sciences, 11(1), 1–24.
Gravemeijer, K., & van Eerde, D. (2009). Design Research as a Means for Building a Knowledge Base for Teachers and Teaching in Mathematics Education. The Elementary School Journal, 109(5), 510–524.
Swan, M. (2008). A Designer Speaks : Malcolm Swan Designing a Multiple Representation Learning Experience in Secondary Algebra. Journal of the International Society for Design and Development in Education, 1, 1–17.
The Centre for Development and Enterprise. (2013). Mathematics Outcomes in South African Schools: What are the facts? What should be done ? Johannesburg.
Vygotsky, L. S. (1980). Mind in society. Cambridge, Mass: Harvard University Press.
This project was funded by the European Union under the Framework 7 programme.