Earlier Understanding of Mathematical Equivalence in Elementary School Predicts Greater Algebra Readiness in Middle School

Does the timing of children's formal understanding of mathematical equivalence matter for algebra readiness? A change-resistance account (McNeil & Alibali, 2005) predicts that it is beneficial for children to construct a formal understanding of mathematical equivalence in the early grades before overly narrow operational patterns become entrenched. This hypothesis is consistent with theories of development suggesting early skills beget later skills. However, other theories posit no benefit or even possible harm of teaching children concepts and skills that are beyond their developmental level. A 5-year prospective, longitudinal study was conducted with a sample of 84 children from a mid-sized city in the Midwestern United States (M-age [second grade] = 8;1) to examine whether earlier understanding of mathematical equivalence predicts algebra readiness in middle school. As hypothesized. earlier understanding of mathematical equivalence in elementary school predicted greater algebra readiness in sixth grade, even after controlling for math fluency, IQ, gender, and paid lunch status. It also uniquely predicted mathematics achievement, but not reading fluency, across the elementary school grades. Findings support the recommendations of mathematics education scholars who have called for increased focus on pre-algebraic concepts like mathematical equivalence in elementary school.