KINDERGARTEN AND FIRST-GRADE STUDENTS’ UNDERSTANDINGS AND REPRESENTATIONS OF ARITHMETIC PROPERTIES
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Young ChildrenArithmetic Understandings
Ramírez, R., Brizuela, B. y Blanton, M. (2020)Kindergarten and first-grade students´ understandings and representations of arithmetic properties. Early Childhood Education Journal
SponsorshipThis work has been developed within the project with reference EDU2016-75771-P, financed by the State Research Agency (SRA) from Spain, and European Regional Development Fund (ERDF) and the grant “Jose Castillejo” funded by the Spanish Ministry of Economy and Compet-itiveness. This research study was supported in part by the National Science Foundation under Grant No. DRL-1415509. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.
We present a study that explores Kindergarten and first-grade students’ understandings and representations of arithmetic properties. Sixteen students participated in a classroom teaching experiment designed to explore children’s algebraic understandings, including their understandings and symbolic representations of three arithmetic properties: additive identity, additive inverse, and commutativity. We characterized students’ understandings in terms of Skemp’s framework of understandings: rules without reason (instrumental) and knowing what to do and why (relational). Then, following Vergnaud, we analyzed the types of additive relationships (transformation, comparison, or combination) and representations used by students. Our findings show that students’ understandings developed in sophistication over time. We observed the least sophisticated understandings for the commutative property, particularly among Kindergarten students who exhibited instrumental understandings even after instruction