University of Illinois Urbana-Champaign

Characterizing exact arithmetic abilities before formal schooling

Jang, Selim

Content Files
JANG-DISSERTATION-2021.pdf

Permalink

https://hdl.handle.net/2142/113908

Description

Title
Characterizing exact arithmetic abilities before formal schooling
Author(s)
Jang, Selim
Issue Date
2021-12-03
Director of Research (if dissertation) or Advisor (if thesis)
Hyde, Daniel
Doctoral Committee Chair(s)
Hyde, Daniel
Committee Member(s)
  • Baillargeon, Renee
  • Fisher, Cythia
  • Federmeier, Kara
  • Berteletti, Ilaria
Department of Study
Psychology
Discipline
Psychology
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Date of Ingest
2022-04-29T21:34:50Z
Keyword(s)
  • Exact Arithmetic
  • Subtractive Negation
  • Nonsymbolic Arithmetic
  • Cardinality
  • Verbal Number Recognition
  • Symbolic Number Knowledge
  • Counting
  • Preschoolers
  • Mathematical Cognition
  • Cognitive Development
Abstract
This thesis explores the exact arithmetic abilities of children before formal schooling. Recent studies suggest that children have core arithmetic abilities even before learning formal arithmetic concepts, including approximately estimating arithmetic results. However, few studies have been undertaken to systematically investigate preschoolers’ ability to add or subtract exact, discrete quantities and how it is affected by the conceptual resources (i.e., acquired and core number abilities) available to them. To systematically test the exact arithmetic performance and its related factors before formal schooling, a preliminary study (Study 1) was conducted with preschoolers (N = 207; aged 3- 4.5 years); tested in the United States). Based on the findings of Study 1, a preregistered replication study (Study 2) was conducted to analyze a new sample of preschoolers (N = 136; aged 3-6 years, tested in Italy). All the participants in the two studies were administered an exact subtraction task, assessments of number knowledge (cardinal number knowledge, visual number recognition, and count list knowledge), a core number ability of the approximate number system (ANS) acuity task, and a linguistic ability test. In the exact subtraction task, participants were asked to choose a possible answer (0, 1, or 2) of an exact subtraction problem (e.g., 3 - 1) presented as non-symbolic (dot) arrays. In both studies, children showed above chance level performance on overall arithmetic problems with a size signature (better accuracy on smaller minuend (i.e., 1-3) problems than larger minuend (i.e., 4-6) problems). These findings indicate that preschool children can perform exact subtraction based on foundational, core numerical abilities with limits, as the size signature has shown poorer performance for larger (vs. smaller) arithmetic problems. Moreover, cardinal number knowledge predicted the exact subtraction performance when the answer size was 0 (i.e., subtractive negation problems) in both studies. Cardinality principle knowers (CP-knowers: the children who know the cardinal principle of counting that the last number word in the counting process stands for the number of items) showed above chance level performance of subtractive negation. However, subset knowers (SS-knowers) who do not know such a principle exhibited below chance level performance. These findings suggest that CP knowledge may be a prerequisite for successful performance on exact subtraction problems when the answer is 0. Concerning developmental changes, ANS acuity did not predict the exact subtraction performance in Study 1 but uniquely predicted exact subtraction problems in Study 2. Interestingly, this unique predicting effect of ANS acuity was only shown in children in Study 2 older than those in Study 1 and who were also CP-knowers. Moreover, the older group of children in Study 2 displayed more behavioral signatures using the ANS representation to perform exact arithmetic problems involving larger numbers. These findings indicate that the ANS becomes more involved in understanding exact arithmetic contexts as children become more experienced and acquire more symbolic number knowledge. Overall, the findings elucidate the characteristics of core arithmetic abilities and how such abilities interact with the core and acquired numerical abilities.
Graduation Semester
2021-12
Type of Resource
Thesis
Permalink
http://hdl.handle.net/2142/113908
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Copyright 2021 Selim Jang

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