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.

     

When each one has one: The influences on teaching strategies and student achievement of using laptops in the classroom

In this study, we examined the educational effects of providing fifth-, sixth-, and seventh-grade students with 24-hour access to laptop computers. Specifically we examined the impact of laptops on classroom activities, and on student use of technology and their writing and problem-solving skills. Participating teachers received computer integration training using the iNtegrating Technology for inQuiry (NTeQ) model to develop problem-based lessons that engage students in critically examining authentic issues, and strengthen research and writing skills. A matched treatment-control group design was employed, in which classes taught at the same grade levels in five participating schools served as the laptop (1 computer per student) and control (5+ computers per class) contexts. Participants included students, teachers, and parents from the two groups. Although systematic observations revealed relatively few differences in teaching methods between laptop and control classrooms, laptop students used computers more frequently, extensively, and independently. Writing assessment results showed substantial and significant advantages for laptop over control students, with six of eight effect sizes exceeding +0.80. Results also showed significant advantages for the laptop group on five of the seven components of the problem-solving task.