Publications and Research
Document Type
Article
Publication Date
2025
Abstract
This article explores the instructional challenges faced by mathematics educators when addressing students’ limited background knowledge and underdeveloped mathematical maturity, two critical barriers to success in college-level algebra. Using the quadratic equation 2x2+x−3=0, which is reducible over the field of rational numbers ℚ ⊂ ℝ, we analyze how diverse solution methods—factoring, completing the square, and the quadratic formula—can support learning. An additional strategy, “Slide and Divide,” was introduced to promote procedural fluency and conceptual flexibility. To gain insight into students’ evolving mathematical maturity, an online survey was conducted to students at various levels of mathematics. The survey captured their perspectives on different methods and which techniques they found most effective as they progressed in understanding. Analysis of the responses revealed that exposure to multiple strategies, supported by classroom instruction and reflective practice, led to increased confidence and engagement with algebraic problem-solving. The findings highlight the value of incorporating diverse methods and student feedback to build mathematical maturity. Recommendations for instruction and directions for future research are discussed.
Comments
This article was published in MATHEMATICS TEACHING RESEARCH JOURNAL 1 SEASON 20XX Vol Y no Z Readers are free to copy, display, and distribute this article as long as: the work is attributed to the author(s), for non-commercial purposes only, and no alteration or transformation is made in the work. All other uses must be approved by the author(s) or MTRJ. MTRJ is published by the City University of New York. MTRJ on the CUNY Academic Commons