Poster #15 - Kindergartners’ ‘Smart’ Errors in Syntactic and Approximate Place Value Tasks Predict Their Second-Grade Multidigit Calculation Performance

• In Event: Poster Session 18

Abstract

Place value (PV) notation uses a complex symbol system (“24” stands for [2 x 10] + [4 x 1]) and has historically been assessed by exact, syntactic tasks (e.g., Base-10 Counting) and inexact, approximate tasks (e.g., reading/writing numbers—Transcoding). Children with stronger initial place value understanding demonstrate better performance in mathematics as they progress through elementary and middle school (e.g., Chan, Au, & Tang, 2014; Hiebert & Wearne, 1996). One way to better understand these longitudinal and causal associations is to explore not only children’s correct performance, but also, evidence of structural understanding in their error patterns.
In the present study, we focus on two such “smart errors” in children’s place value learning: (1) unconventional unit-boundary shifts in Base-10 Counting and (2) expanded errors on Transcoding. The Base-Ten Counting task (Chan et al., 2014) requires children to determine the number represented in line drawings of base-10 blocks by counting. Children sometimes shift their counting strategies at unit-boundaries (e.g., 100-to-10 and 10-to-1) despite using incorrect vocabulary that leads to incorrect responses (see Figure 1). These unconventional unit-boundary shifts seem to signify partial understanding of base-ten structure. In Transcoding, children may add zeroes to generate faulty, but arguably better alignment between written and spoken versions of multidigit number names (e.g., writing “two hundred and thirty-two” as “200302.” Kindergartners who produce either or both of these smart errors may be at a transitional stage of place value understanding, and thus may be better prepared to learn multidigit calculation and score higher on multidigit calculation assessed in second grade than their peers who are equally incorrect, but produce random errors rather than smart errors.
Kindergartners (N=279; Mage=5.76 years, SDage=0.55 ; 135 females) were administered two PV tasks mentioned above (Base-10 Counting and Transcoding). Children’s smart errors on both the Base-Ten Counting and Transcoding tasks were recorded. Two years later in second grade, children were administered the CMAT measuring multidigit calculation skills. In order to avoid grouping highly accurate children who made few smart errors with highly inaccurate children who made few smart errors, we excluded the nineteen children who scored above 80% correct on Base-Ten Counting from analysis.
The remaining 260 kindergartners were divided into 4 groups based on their smart errors: 1) neither unconventional boundary shifts nor expanded errors (n=16); (2) at least one expanded error, but no unconventional boundary shifts (n=42); (3) at least one unconventional boundary shift, but no expanded errors (n=78); and (4) at least one of each smart error (n=124). An ANOVA revealed a significant group difference, F(3,178)=7.23, p<.001 and pairwise comparisons showed that kindergartners who made either unconventional unit-boundary shifts alone or both smart errors together had higher second grade multidigit calculation scores compared to the other two groups (highest p=.010) (see Figure 2).
Thus, not only does accurate place value performance predict later calculation skill, but so does inaccurate performance that reflects partial structural understanding.

Authors

• Corinne A. Bower, California State University - Los Angeles
  Presenting Author

• Kelly Sue Mix, University of Maryland - College Park

• Lei Yuan, University of Colorado Boulder

• Linda B. Smith, Indiana University - Bloomington