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.

中文翻译：

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变形达维多夫关于南非早期数字学习的想法

在这篇论文中，我们分享了南非低年级数字干预的细节，这些干预是由达维多夫关于早期数字教学和学习的写作的各个方面提供的。Davydov 早期数字教学方法的一个关键部分包括从关注数量之间的关系而不是计数开始。结构化数字起始者 (SNS) 干预在九年的时间里侧重于支持低年级学生超越南非流行的按计数计算方法。在关注这一焦点时，干预越来越多地转向强调数量之间的关系，尽管与达维多夫所倡导的格式或任务序列不同。本文重点介绍了导致我们适应或改变形状的语境和文化特征。我们询问了与南非课堂数学教学的典型关键特征相关的 Davydov 早期数字教学方法的关键方面，以了解 SNS 计划的演变。从 2011 年、2014 年和 2018 年的跨学科学生样本中获得的基于准纵向访谈的评估数据表明，随着时间的推移，从计算计算到结构计算的转变。这些结果表明，采用越来越结构化的早期数字工作方式取得了成功，但也表明这些成功可能取决于对前向和后向数字词序列的一些流畅性。结果表明，在更大规模的研究中探索从一开始就关注早期数字结构的干预措施是可行的。