A Learning Progression for Elementary Students' Functional Thinking

Stephens, Ana C.
Fonger, Nicole
Strachota, Susanne
İşler Baykal, Işıl
Blanton, Maria
Knuth, Eric
Gardiner, Angela Murphy
In this article we advance characterizations of and supports for elementary students' progress in generalizing and representing functional relationships as part of a comprehensive approach to early algebra. Our learning progressions approach to early algebra research involves the coordination of a curricular framework and progression, an instructional sequence, written assessments, and levels of sophistication describing students' algebraic thinking. After detailing this approach, we focus on what we have learned about the development of students' abilities to generalize and represent functional relationships in a grades 3-5 early algebra intervention by sharing the levels of responses we observed in students' written work over time. We found that the sophistication of students' responses increased over the course of the intervention from recursive patterning to correspondence and in some cases covariation relationships between variables. Students' responses at times differed by the particular tasks that were posed. We discuss implications for research and practice.


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Blanton, Maria; İşler Baykal, Işıl; Stroud, Rena; Stephens, Ana; Knuth, Eric; Gardiner, Angela Murphy (Springer Science and Business Media LLC, 2019-10-01)
We share here results from a quasi-experimental study that examines growth in students' algebraic thinking practices of generalizing and representing generalizations, particularly with variable notation, as a result of an early algebra instructional sequence implemented across grades 3-5. Analyses showed that, while there were no significant differences between experimental and control students on a grade 3 pre-assessment measuring students' capacity for generalizing and representing generalizations, experi...
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Citation Formats
A. C. Stephens et al., “A Learning Progression for Elementary Students’ Functional Thinking,” MATHEMATICAL THINKING AND LEARNING, pp. 143–166, 2017, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/42907.