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Closing the gap on the map: Davydov’s contribution to current early algebra discourse in light of the 1960s Soviet debates over word-problem solving

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Abstract

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.

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Notes

  1. In our paper, we use Russia and the U.S.S.R. (Soviet Union) when referring to different time periods and geographic zones. Prior to 1917 and after 1991, Russia is the most appropriate name whereas the period of 1917 to 1991 refers to the U.S.S.R. (Soviet Union).

  2. The U.S.S.R. (Soviet) educational system was constantly evolving in the second part of the twentieth century. In the first half of the twentieth century, formal schooling began in grade 1 at the age of 7 with no mandatory kindergarten. Elementary school was from grades 1–4, and secondary school was from grades 5–11. At some point during the 1960s, this changed to primary school grades 1–3 and secondary school, grades 4–10. Mandatory schooling was grades 1–8, with grades 9–10 being optional for general education, which could be further completed in other types of educational institutions. In modern Russia, the system was changed back to the 1–4 and 5–11 model (5–9; 10–11).

  3. The 1703 Arithmetic by Leontii Magnitskii is one the first Russian textbooks that set up standards for teaching elementary mathematics for centuries to come (see Freiman & Volkov, 2014).

  4. This word problem was originally cited by Bodanskii (1969/1991, p. 296).

  5. A genetic modeling experiment (“formiruyushchij”) refers to an “experimental method of studying the potentialities of the development of children and adolescents with the tools of education.” (Zuckerman, 2011, p. 45) This method, Zuckerman points out, was the driving framework of the El’konin–Davydov study, which has elevated their work “to the rank of the theory and practice of education.” See also Radford’s (2020) paper in this issue.

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  1. Université de Moncton, Moncton, Canada

    Viktor Freiman

  2. University of Ottawa, Ottawa, Canada

    Olga O. Fellus

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Freiman, V., Fellus, O.O. Closing the gap on the map: Davydov’s contribution to current early algebra discourse in light of the 1960s Soviet debates over word-problem solving. Educ Stud Math 106, 343–361 (2021). https://doi.org/10.1007/s10649-020-09989-6

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