This work investigates the foundational mathematical concepts required for elementary school instruction and the pedagogical frameworks necessary to convey them effectively. Edward Griffith Begle, a prominent mathematician and director of the School Mathematics Study Group, utilizes his extensive experience in curriculum reform to analyze the logical structure of arithmetic and geometry. The text argues for a rigorous, concept-driven approach to teaching that prioritizes mathematical understanding over rote memorization.

Experts recognize this text as a significant contribution to the history of mathematics education reform in the United States. Readers frequently note the academic density of the prose, which serves as a technical resource for educators and curriculum designers rather than a casual instructional manual.