Kindergartners’ Mastery of the Base-10 Representational System Predicts Place Value Understanding and Later Calculation Skills in Second Grade

• In Event: Beyond Accuracy: Children’s Correct and Incorrect Strategies on Early STEM Tasks Provide Insights into Cognitive Development

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, count+unit syntax tasks (Base-10 Counting, Which number has __?, and Expanded Notation) and inexact, approximate tasks (Number Line Estimation, Transcoding, and Magnitude Comparison). Children with weak initial place value understanding are likely to demonstrate poor 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 the mechanisms and origin of place value understanding.

Beyond PV task accuracy, an alternative window into children’s underlying place value understanding is examining their understanding of external representations that are specific to the base-10 representational system. One particular exact PV task that uses external representations is the Base-10 Counting task (Chan et al., 2014). Here, children are asked to count the number of small squares in drawings of base-10 blocks. Performance on this task has been coded in terms of accuracy or the presence of specific errors. In the current study, we ask whether children show evidence of noticing the boundaries between different units (ones, tens, hundreds) despite perhaps counting incorrectly (see Figure 1 for example), and how this awareness of base-10 unit boundaries relates to their 1) concurrent performance on exact and inexact PV tasks and, 2) calculation skills two years later. We hypothesized that for kindergartners who lack this awareness of unit boundaries, approximate understanding of PV will better predict later calculation skills; whereas, for kindergartners who exhibit awareness of base-10 boundaries, performance on exact PV tasks will better predict later calculation skills.

A total of 279 kindergartners (Mage=5.76 years, SDage=0.55 ; 135 females) were administered the six PV tasks mentioned above. Children’s performance on the Base-10 Counting task was recorded. Across Base-10 Counting items, there were 12 total switches in representational units (e.g., 100s-to-10s; 10s-to-1s). Children’s counting at each representational switch was coded as “0” for no switch in counting or “1” if there was a switch even if the counting words children used were incorrect. Two years later in second grade, children were administered the CMAT measuring calculation skills.

Because the distribution of boundary switches appeared bimodal, a median split was used to identify two groups: (1) poor boundary switchers and high boundary switchers. Multiple regressions tested whether each group’s performance on the six PV tasks were predictive of later CMAT performance, controlling for general cognitive ability. Results indicate that for poor-boundary switchers’, performance on two approximate PV tasks (Number Line Estimation, p=.030, and Transcoding, p=.039) significantly predicted later calculation, but for high-boundary switchers, accuracy on two exact tasks (Base-10 Counting, p=.004, and Which number has __?, p=.049) were the only significant predictors (see Table 1). Overall, in addition to early PV task accuracy, children’s deeper understanding of the base-10 representational system may play a role in what types of PV knowledge children rely on to progress their foundational, mathematical skills.

Authors

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

• Kelly Sue Mix, University of Maryland - College Park
  Non-Presenting Author

• Linda B. Smith, Indiana University - Bloomington
  Non-Presenting Author