Early Math Skills and Enrollment in Algebra in Ninth Grade

• In Event: 34.027 - Access to Accelerated Mathematics Course-Taking in Middle School and Beyond

Abstract

It is not well understood whether early math skills related to later course selection in math. The current study attempts to identify whether early math skills relate to enrollment in Algebra in 9th grade, which is an important indicator of college enrollment after high school.

Siegler’s (2016) integrated theory of numerical development focuses attention on children’s development of symbolic numerical knowledge, highlighting counting and quantities as primary mathematical cognitive foundations. Thus, these foundational math skills are important as building blocks to more complex skills that are needed for advanced mathematical coursework. Siegler et al. (2012) showed that knowledge of fractions and early division was critical for being successful in Algebra, but what was not clear in this paper was what earlier skills were needed to be successful in fractions and early division.

Data were examined from 1,364 children in the National Institute of Child Health and Human Development (NICHD) Study of Early Childcare and Youth Development (SECCYD). Time points of interest were the assessments at 54 months and grade 9 math course-taking based on high school transcripts. Based upon questions from the Woodcock-Johnson Revised Applied Problems, factor analyses revealed three numeric competencies at 54 months—counting, arithmetic operations using visual object representations, and abstract arithmetic operations. Diagnostic classification models then identified four skills groups based upon these numeric competencies: (a) mastery of no skills, (b) mastery of counting only, (c) mastery of counting and arithmetic operations with visual representation, and (d) mastery of all three skills.

Among children who entered school with no mastery of early math skills, none had taken Algebra II and only 10% had taken Geometry as their highest math course in 9th grade. In contrast, among students with mastery of all three early math skills, 14% had taken Algebra II and 45% had taken Geometry as their highest math course in 9th grade. In other words, early math skills at 4.5 years of age strongly predicted advanced course-taking one decade later in 9th grade. In addition, results revealed racial and ethnic differences at 4.5 years of age. Black and Hispanic children were 43% of those with no mastery of early math skills, but only 4% of those who had mastered all three skills.

Our findings demonstrate that mastery early math skills are important for enrollment in later mathematical courses that are indicators of college-track students. Thus, it is important to understand how early math skills are developed in order for parents, teachers and practitioners to effectively intervene and train the foundational skills needed to take advanced math course work in high school. In addition, these stakeholders should evaluate equity interventions for minimizing the effect of early racial/ethnic differences on later access to high-quality opportunities for learning advanced mathematics.

Authors

• Pamela E. Davis-Kean, University of Michigan

• Thurston Domina, University of North Carolina - Chapel Hill

• Megan Kuhfeld, NWEA

• Alexa Ellis, University of Michigan - Ann Arbor

• Elizabeth Gershoff, University of Michigan