Mathematical Structure and Error in Kindergarten

While contributing to that literature, this article focuses on choices educators make and draws attention to a little-recognized benefit of children's errors-errors can reveal strengths worth preserving, not just weaknesses to fix. Similar situations arise frequently in mathematics too, and these errors can reveal not just what students don't know, but also what they do know. [...]teachers can use children's ability and inclination to generalize and find patterns as an ally in teaching. Ruth: Attending to structure but inventing an incorrect one At the very end of kindergarten, a year in which the children learned about addition and subtraction, the children all create small thank-you cards for a regular visitor. Seth draws a blue square with what looks like a red lollipop stuck to it (below, left), his representation of a wonderful logic puzzle. About the authors E. Paul Goldenberg has taught mathematics from early elementary through graduate school and now develops mathematics curriculum at Education Development Center (EDC), in Waltham, Massachusetts. For more ways to make math engaging, challenging, and fun, visit ym.edc.org. kreed@edc.org Authors' note: The work reported here was funded in part by The National Science Foundation (award numbers 1119163 and 1348564) and by the Heising-Simons Foundation (award number 2015023). In Teaching Mathematics through Problem Solving: Prekindergarten-Grade 6, ed. National Council of Teachers of Mathematics.