CAREER: Predictors and Consequences of Early Understanding of Mathematical Equivalence

Principal Investigator: 
Project Overview
Background & Purpose: 

The purpose of the study is two-fold: (1) identify foundational skills in kindergarten that predict individual differences in understanding of mathematical equivalence in second and fourth grades, and (2) track the development of mathematics achievement and algebra readiness in children who do and do not demonstrate understanding of mathematical equivalence in second grade.


The study is being held in Michiana, which is a region on the Indiana/Michigan border in the U.S. One-on-one interviews with the participating children will take place in one of three locations: (a) the Cognition Learning and Development lab at the University of Notre Dame, (b) a quiet room in a local school, or (c) a quiet room in a local community center.

Research Design: 

The project uses a longitudinal research design and will generate evidence about factors that precede and predict the outcomes of interest [quasi-experimental using a fixed effects model and multi-level analysis for repeated measures data]. Original data are being collected on 140 kindergarteners and 130 2nd graders who are representative of children in the local community and who will be followed for five years using assessments of learning [achievement tests], observation [videography], and survey research [structured interviewer-administered questionnaire and semi-structured or informal interviews]. Instruments or measures being used include:

  • The Wechsler Abbreviated Scale of Intelligence (WASI) to control for baseline differences in IQ.
  • The Number Knowledge Test (Griffin & Case, 1997) and the Number Line Estimation Task (Booth & Siegler, 2008) to assess number sense in K.
  • Bruner and Kenney’s (1966) matrix reproduction task and Fuson et al.’s (1996) “matching” word problems to assess relational thinking in K.
  • The Advanced Dimensional Change Card Sort Task (Zelazo, 2006) and the Day-Night Stroop Task (Gerstadt et al. 1994) to measure cognitive flexibility and inhibitory control in K.
  • The Computation section of the ITBS to control for baseline levels of computational fluency in 2nd grade.
  • Equation solving, equation reconstruction, and defining the equal sign to assess understanding of mathematical equivalence (McNeil & Alibali, 2005) in 2nd and 4th grades.
  • The Indiana Statewide Testing for Educational Progress-Plus and the WJ-III Brief to assess math achievement in 3rd-6th grade.
  • The Iowa Algebra Aptitude Test (IAAT) and select items from the Transition to Arithmetic to Algebraic Reasoning (TAAR) Items (developed by Knuth, Alibali, and colleagues) to assess algebra readiness in 6th grade.

To analyze which skills in K are most predictive of understanding of mathematical equivalence in 2nd grade, researchers will use hierarchical multiple regression. To test if understanding of mathematical equivalence in 2nd grade predicts mathematics achievement in the long term, researchers will use both mixed-factor ANCOVA and HLM. To test if early understanding of mathematical equivalence in 2nd grade predicts algebra readiness in 6th grade, researchers will use hierarchical multiple regression. 


Findings will be posted as they become available.

Other Products: 

The study does not include an intervention, but results will be used to inform the design of an intervention on math equivalence.