Student Strategy Choices on a Constructed Response Algebra Problem

• Published in: School science and mathematics 2011-12, Vol.111 (8), p.389-398
• Main Authors: Ross, Dan, Reys, Robert, Chávez, Óscar, McNaught, Melissa D., Grouws, Douglas A.
• Format: Article
• Language: English
• Subjects: Achievement Gains; Algebra; Cognitive Style; Critical Thinking; Educational Strategies; Elementary education; Grade 10; Grade 8; Grade 9; Learning; Learning Strategies; Longitudinal Studies; Mathematical analysis; Mathematical Applications; Mathematical Aptitude; Mathematical problems; Mathematics; Mathematics Achievement; Mathematics education; Mathematics Instruction; Mathematics Skills; Problem Sets; Problem Solving; School Districts; Secondary School Mathematics; Secondary school students; Student Improvement; Students; Thinking Skills
• ISSN: 0036-6803; 1949-8594
• DOI: 10.1111/j.1949-8594.2011.00104.x

A central goal of secondary mathematics is for students to learn to use powerful algebraic strategies appropriately. Research has demonstrated student difficulties in the transition to using such strategies. We examined strategies used by several thousand 8th‐, 9th‐, and 10th‐grade students in five different school systems over three consecutive years on the same algebra problem. We also analyzed connections between their strategies and their success on the problem. Our findings suggest that many students continued to struggle with algebraic problems, even after several years of instruction in algebra. Students did not reflect the anticipated growth toward the consistent use of efficient strategies deemed appropriate in solving this problem. Instead a surprisingly large number of students continued to rely on strategies such as guessing and checking, or offered solutions that were unintelligible or meaningless and not useful to the researchers. Even those students who used algebraic strategies consistently did not show the anticipated improvement of performance that would be expected from several years of continuing to study mathematics.