Intermediate Participatory Stages as Zone of Proximal Development Correlate in Constructing Counting-On: A Plausible Conceptual Source for Children's Transitory "Regress" to Counting-All
Quantitative and qualitative analyses of 37 first-graders' solutions to addition problems were conducted to re-examine inconsistencies in children's progress from counting-all to counting-on. The study advances a novel, theoretical coordination among 3 frameworks: constructivist scheme theory with a focus on the notion of prompt, Vygotsky's sociocultural approach, and Siegler's Overlapping Waves Model, and provides a corresponding, threefold stance on mathematical tasks.
Tzur, R., & Lambert, M. A. (2011). Intermediate participatory stages as Zone of Proximal Development correlate in constructing counting-on: A plausible conceptual source for children’s transitory ‘regress’ to counting-all. Journal for Research in Mathematics Education, 42(5), 418-450.