Examining the implementation of the mathematics strand of the Key Stage 3 Strategy: What are the bases of evaluation?

This article presents findings from a comparative case study examining the implementation of the mathematics strand of the Key Stage 3 Strategy in two contrasting schools—one using setting and whole‐class teaching, the other incorporating mixed‐ability grouping and individualised learning. A number of ‘outcomes’ of implementation are considered, including teachers' and students' experiences, changes in pedagogic practice and students' attainment. Whilst both schools achieved highly in relation to similar schools, higher attainment gains between Key Stage 2 and Key Stage 3 in the school using setting/whole‐class teaching were associated with increasing student disaffection and dependence on teachers. In contrast, the attainment gains at the school using individualised learning were associated with increasing enthusiasm and independence. The mixed picture of outcomes and their complex interconnections suggest that evaluations of implementation resting on attainment‐based outcomes are problematic in terms of longer‐term aims of increasing the proportions of students choosing to study mathematics and developing the skills of independent learning.     

Development in South African Primary Mathematics Teacher Educators’ Work with In-Service Teachers

This paper focuses, empirically, on the developments seen in a group of South African early grades’ mathematics teacher educators in the course of a university-provincial education department partnership project. This project sought to support the district Mathematics Subject Advisers to support, in turn, teachers to implement an intervention consisting of a sequence of four lessons focused on multiplicative reasoning. Outcomes based on pre- and post-tests administered by the Subject Advisers suggested substantial pre- to post-test improvement at the student level. Subject Adviser observations and reflections pointed to successes in engendering more dialogic conversations between mathematics teachers and mathematics teacher educators focused on mathematics and its teaching and learning. The ‘double move’ of increasing overlap between the subject adviser and teacher communities, coupled with evidence that implementing the intervention had enabled the Subject Advisers to develop their mathematical and pedagogical understandings, provides a useful way of considering development in the capacity of mathematics teacher educators to support mathematics teaching and learning.

     

Writing reviews: perspectives from the editors of Educational Studies in Mathematics

Educational Studies in Mathematics -     

Shape-shifting Davydov’s ideas for early number learning in South Africa

In this paper, we share details of a South African early grades’ number intervention informed by aspects of Davydov’s writing on early number teaching and learning. A key part of Davydov’s approach to early number teaching involves starting with attention to relationships between quantities rather than with counting. The Structuring Number Starters (SNS) intervention focused—over a nine-year period—on supporting early grades’ students to move beyond the calculating-by-counting approaches that are prevalent in South Africa. In attending to this focus, the intervention shifted increasingly towards an emphasis on relationships between quantities, though not in the same format or task sequence as advocated by Davydov. The contextual and cultural features that led to our adaptations—or shape-shifting—are highlighted in this paper. We interrogate key aspects of Davydov’s approaches to early number teaching in relation to key features typical of South African classroom mathematics teaching in order to understand the evolution of the SNS initiative. Quasi-longitudinal interview-based assessment data available from a cross-attainment sample of students in 2011, 2014 and 2018 indicate shifts over time from calculating-by-counting to calculating-by-structuring. These outcomes point to successes with moves into increasingly structured ways of working with early number, but suggest also that these successes may be contingent on some fluency with forward and backward number word sequences. The outcomes suggest that it is feasible to explore interventions directing attention to early number structure from the outset in larger scale studies.