Development of the Connection Between Fractions and Algebra Performance and Learning in the Post-COVID-19 Era

• In Event: The Importance of Mathematical Competencies: When and for Whom Do They Matter?

Abstract

1. Objectives or purposes
In the present study, we examine developmental and cohort-level differences in fraction magnitude knowledge, fraction computation knowledge, algebra feature knowledge, algebra equation-solving, and the relationships between these measures for students in grades 4-10.

2. Perspective(s) or theoretical framework
Over the past decade, researchers have established a predictive relationship between students’ fraction knowledge and algebra performance (Siegler et al., 2012; Booth & Newton, 2012), suggesting that supporting the development of students’ fraction understandings and skills may be critical for their later learning in algebra. In middle school, fraction magnitude knowledge is predictive of algebra skills (Booth et al., 2013), however, fraction computation knowledge predicts algebra performance for college students (Hurst & Cordes, 2018). It remains unclear whether and when different facets of fraction knowledge become more or less important for algebra, and therefore which supports should be implemented and when in order to maximize success in student learning of algebraic content.

3. Methods
Students in grades 4-10 taking part in an ongoing longitudinal study (N = 700) completed computerized measures in three subsequent years (Summers 2021 - 2023).

4. Materials
We measured student performance on fraction magnitude knowledge (fraction number line estimation), fraction computation (solving fraction arithmetic problems), algebra feature knowledge (conceptual understanding of features in algebraic equations such as the equals sign, negative signs, etc.), and algebra equation-solving (finding solutions to algebraic equations).

5. Results
Results examine developmental changes in student performance on these individual measures and on the relations between the measures cross-sectionally, longitudinally, and cross-sequentially. Fraction skills develop early and then stabilize in middle school and beyond, whereas algebra skills consistently improve between late elementary school and high school. Fraction computation skills are consistently predictive of algebra knowledge. Fraction magnitude knowledge does not often predict algebra equation solving but predicts algebra feature knowledge as students approach middle school. However, it becomes less predictive as students reach the grades in which they begin studying algebraic content (e.g., middle school and beyond; see Figure 1).

6. Significance
Algebra has long been considered a gatekeeper for later student success (Adelman, 2006). Understanding what factors lead to student success in Algebra is thus a key objective in education research. This effort is complicated in recent years as students’ educational careers were significantly disrupted by the COVID-19 pandemic. Reports to date indicate that student learning gains have been slower than normal, with mathematics learning experiencing a greater “COVID gap” than other content areas (Lewis et al., 2021). The timing of the present study allows us to investigate not only grade-level differences in the development and connections between fractions and algebra, but also cohort-level differences such as whether the importance of various aspects of fraction knowledge for performance and learning in algebra vary based on what type of mathematics content students were attempting to learn during the COVID-19 disruption.

Author

• Julie L. Booth, Temple University