title: What counts as knowing? The development of conceptual and procedural knowledge of counting from kindergarten through Grade 2.
abstract: The development of conceptual and procedural knowledge about counting was explored for children in kindergarten, Grade 1, and Grade 2 (N = 255). Conceptual knowledge was assessed by asking children to make judgments about three types of counts modeled by an animated frog: standard (correct) left-to-right counts, incorrect counts, and unusual counts. On incorrect counts, the frog violated the word-object correspondence principle. On unusual counts, the frog violated a conventional but inessential feature of counting, for example, starting in the middle of the array of objects. Procedural knowledge was assessed using speed and accuracy in counting objects. The patterns of change for procedural knowledge and conceptual knowledge were different. Counting speed and accuracy (procedural knowledge) improved with grade. In contrast, there was a curvilinear relation between conceptual knowledge and grade that was further moderated by children's numeration skills (as measured by a standardized test); the most skilled children gradually increased their acceptance of unusual counts over grade, whereas the least skilled children decreased their acceptance of these counts. These results have implications for studying conceptual and procedural knowledge about mathematics.
authors.affiliation: Carleton University, Department of Psychology, Carleton University, Ottawa, Ont., Canada K1S 5B6. jo-anne_lefevre@carleton.ca
authors.forename: Jo-Anne
authors.initials: JA
authors.lastname: LeFevre
authors.forename: Brenda L
authors.initials: BL
authors.lastname: Smith-Chant
authors.forename: Lisa
authors.initials: L
authors.lastname: Fast
authors.forename: Sheri-Lynn
authors.initials: SL
authors.lastname: Skwarchuk
authors.forename: Erin
authors.initials: E
authors.lastname: Sargla
authors.forename: Jesse S
authors.initials: JS
authors.lastname: Arnup
authors.forename: Marcie
authors.initials: M
authors.lastname: Penner-Wilger
authors.forename: Jeffrey
authors.initials: J
authors.lastname: Bisanz
authors.forename: Deepthi
authors.initials: D
authors.lastname: Kamawar
mesh_terms: D002648:Child; D002656:Child Day Care Centers; D002675:Child, Preschool; D003071:Cognition; D003210:Concept Formation; D005260:Female; D006801:Humans; D007600:Judgment; D008297:Male; D008433:Mathematics; D012574:Schools