The impact of fraction magnitude knowledge on algebra performance and learning

• Magnitude knowledge of fractions, not whole numbers, predicts algebra performance.
• Fraction knowledge predicts improvement in equation solving and encoding.
• Proportional reasoning may be crucial for predicting algebra learning.

Knowledge of fractions is thought to be crucial for success with algebra, but empirical evidence supporting this conjecture is just beginning to emerge. In the current study, Algebra 1 students completed magnitude estimation tasks on three scales (0–1 [fractions], 0–1,000,000, and 0–62,571) just before beginning their unit on equation solving. Results indicated that fraction magnitude knowledge, and not whole number knowledge, was especially related to students’ pretest knowledge of equation solving and encoding of equation features. Pretest fraction knowledge was also predictive of students’ improvement in equation solving and equation encoding skills. Students’ placement of unit fractions (e.g., those with a numerator of 1) was not especially useful for predicting algebra performance and learning in this population. Placement of non-unit fractions was more predictive, suggesting that proportional reasoning skills might be an important link between fraction knowledge and learning algebra.