A model for nurturing and assessing multidigit number sense among first grade children

Abstract

ABSTRACT. Based on a synthesis of the literature and on the results of a two-year teaching program working with young primary children, a framework was developed, refined and validated for nurturing and assessing multidigit number sense. The major constructs incorporated in this framework were counting, partitioning, grouping, and number relationships. For each of these constructs, four different levels of thinking were established which, in essence, reflected a "learning apprenticeship" for multidigit number sense. At each level, and across all four constructs, learning indicators were developed and matched to distinctive problem tasks that went beyond the four basic operations.The framework was validated through data obtained from six case studies of grade 1 children. The thinking of these children was assessed and analyzed on the problem tasks for the four constructs and four levels. While the students were at different levels, all but one showed striking consistencies across the four constructs. Moreover, no student was able to solve a problem at a higher level when they had not solved a lower-level problem in the same category. The present framework for multidigit number sense covers only the lower primary grades, but research and instruction would benefit from an extended framework across the elementary grades.

A Framework for Characterizing Children's Statistical Thinking

“…Our previous research in formulating frameworks for number sense (Jones, Thornton, & Putt, 1994;Jones et al, 1996) and probability Tarr & Jones, 1997) demonstrated that students' thinking in number sense and probability was consistent with the SOLO model of Biggs and Collis (1991). Consequently, in formulating our framework for this study, we hypothesized that children's statistical thinking across the four constructs could be characterized in terms of the SOLO model.…”

A framework for assessing middle school students’ thinking in conditional probability and independence

“…Adopting the validation process used by Jones, Thornton and Putt (1994) and Jones, Langrail, Thornton and Mogill (1997), this study sought to: (a) refine the initial descriptions of the four levels of probabilistic thinking; (b) examine the profiles and stability of case-study students' thinking over the two constructs; and (c) illuminate the distinguishing characteristics of each thinking level within the framework. Qualitative analysis was used to address all three parts of the validation.…”

Acquisition and use of shortcut strategies by traditionally schooled children

“…Children's strategy variety has been studied in diverse mathematical domains, including the domain of multi-digit addition and subtraction (Baroody 1987;Beishuizen 1993Beishuizen , 1999Blöte, Klein, & Beishuizen 2000;Blöte, Van der Burg, & Klein 2001;Carpenter, Franke, Jacobs, Fennema, & Empson 1997;Carroll 2000;Fuson 1992Fuson , 2003Fuson et al 1997;Heirdsfield & Cooper 2004;Hiebert & Wearne 1993, 1996Jones, Thornton, & Putt 1994;Klein, Beishuizen, & Treffers 1998;Murphy 2004;Thompson 1999Thompson , 2000Torbeyns, Verschaffel, & Ghesquière 2006). These studies first revealed that children generally apply three types of strategies to mentally solve sums and differences in the number domain 20-100, namely decomposition, sequential, and shortcut strategies.…”