Recent scholarship around teaching elementary mathematics supports the learning of early algebra with 5- to 12-year olds. However, in spite of the recognition of the affordances of early algebra, issues about how to introduce it remain open. Within this context, Davydov’s work is often cited as a source of impressive demonstration of young learners’ capacity for algebraic thinking. This work requires further exploration in order to yield a clearer picture of a very particular teaching approach, which focuses on early abstractions and symbolic language. We argue that in order to fully understand how Davydov’s work contributes to current conversations and what Davydov was trying to do, we need to shed light on the context- and time-specific discourse of the 1960 Soviet educational reforms that made it possible for Davydov to develop his vision about algebraic thinking and to set in motion appropriate teaching approaches for young learners. In this paper, we look back to the Soviet debates that unfolded in Russia on the integration of early algebra in elementary school word-problem solving. Drawing on these debates and the results of Davydov’s school experiments, we lay out the developmental axes of capacity building. This can be done by emphasizing ascent from the abstract to the concrete using a variety of representational modeling tools to support the emergence of algebraic thinking while targeting particular habits of mind within carefully designed learning activities. We conclude with some insights about current arithmetic-algebra debates, and how these could be enriched and deepened by Davydov’s work, which yet remains open to future discussion and reflection.

中文翻译：

---

缩小地图上的差距：鉴于 1960 年代苏联关于解决单词问题的辩论，达维多夫对当前早期代数论述的贡献

最近关于小学数学教学的奖学金支持 5 至 12 岁儿童学习早期代数。然而，尽管承认早期代数的可供性，关于如何引入它的问题仍然悬而未决。在此背景下，Davydov 的作品经常被引用为展示年轻学习者代数思维能力的令人印象深刻的展示来源。这项工作需要进一步探索，以便更清楚地了解一种非常特殊的教学方法，该方法侧重于早期的抽象和符号语言。我们认为，为了充分理解 Davydov 的工作如何对当前对话做出贡献以及 Davydov 试图做的事情，我们需要阐明 1960 年苏联教育改革的语境和时间特定的论述，这些论述使达维多夫能够发展他对代数思维的看法，并为年轻学习者制定适当的教学方法。在本文中，我们回顾了在俄罗斯展开的关于将早期代数整合到小学单词问题解决中的苏联辩论。利用这些辩论和达维多夫学校实验的结果，我们列出了能力建设的发展轴心。这可以通过强调从抽象到具体的上升来实现，使用各种表征建模工具来支持代数思维的出现，同时在精心设计的学习活动中针对特定的思维习惯。