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The development of relational thinking: a study of Measure Up first-grade students’ thinking and their symbolic understandings


This study is focused on the relational thinking of first-grade students following their first 3 months of instruction from the Measure Up (MU) curriculum, an adaptation of the El’konin-Davydov curriculum. Following Davydov’s outline of instructional material, the MU first-grade materials were designed to have students identify the quantitative attributes of objects, learn to designate the properties using certain symbols, and carry out elementary analyses of the relationships. Additionally, MU emphasized the use of specific, multiple concurrent representations so students could use concrete, diagrammatic, and symbolic ways to analyze comparisons and convey their findings. Our research focused on the characteristics of MU first-grade students’ thinking about relations without numbers. Additionally, we were interested in the role symbols had in their ability to communicate their thinking. We analyzed video recordings and transcriptions of six semi-structured student interviews and then reanalyzed the data for specific evidence of symbolic understandings. Recognizing MU as a symbolically structured environment, we connected our data to this paradigm. Our findings show that students were able to make direct and indirect comparisons and that they relied on symbolizing to explain their thinking. These results show further support for Davydov’s hypothesis––a non-numeric introduction to relational symbols can develop children’s theoretical thinking abilities by going beyond empirical ways of knowing.

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  1. Learning activity here is understood in the Davydov way as “uchebnaia deiatenlnost.”


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Correspondence to Linda C. H. Venenciano.

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Venenciano, L.C.H., Yagi, S.L. & Zenigami, F.K. The development of relational thinking: a study of Measure Up first-grade students’ thinking and their symbolic understandings. Educ Stud Math 106, 413–428 (2021).

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  • Davydov
  • Relational thinking
  • Symbolizing
  • Discourse
  • Curriculum
  • Symbolically structured environment