Kindergarten and First‑Grade Students’ Understandings and Representations of Arithmetic Properties Ramírez Uclés, Rafael Brizuela, Bárbara Blanton, Maria Young Children Arithmetic Understandings 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 2020-12-03T08:56:01Z 2020-12-03T08:56:01Z 2020 journal article Ramirez Uclés, R., Brizuela, B.M. & Blanton, M. Correction to: Kindergarten and First-Grade Students’ Understandings and Representations of Arithmetic Properties. Early Childhood Educ J (2020). https://doi.org/10.1007/s10643-020-01128-3 http://hdl.handle.net/10481/64635 10.1007/s10643-020-01123-8 eng open access