Recent reform movements have emphasized students making meaning of algebraic relationships; however, research on student thinking and learning often remains disconnected from the design of widely used curricular materials. Although a previous examination of algebra textbooks (Nathan, Long, & Alibali, 2002) demonstrated a preference for a symbols-first approach, research has demonstrated that Algebra I students' performance on verbally presented problems is better than on symbolic equations, consistent with cognitive theories suggesting the value of concreteness fading. The present study investigates whether current textbooks used in Algebra I courses demonstrate a formalisms-first approach using five different analyses. Results show that despite nearly 2 decades of research on student learning, the conventional textbooks used in most classrooms have been resistant to change and emphasize manipulation with symbols prior to making sense of verbal scenarios.
Milan F. Sherman, Candace Walkington and Elizabeth Howell
Mitchell J. Nathan and Kenneth R. Koedinger
Mathematics teachers and educational researchers ordered arithmetic and algebra problems according to their predicted problem-solving difficulty for students. Predictions deviated systematically from algebra students' performances but closely matched a view implicit in textbooks. Analysis of students' problem-solving strategies indicates specific ways that students' algebraic reasoning differs from that predicted by most teachers and researchers in the sample and portrayed in common textbooks. The Symbol Precedence Model of development of algebraic reasoning, in which symbolic problem solving precedes verbal problem solving and arithmetic skills strictly precede algebraic skills, was contrasted with the Verbal Precedence Model of development, which provided a better quantitative fit of students' performance data. Implications of the findings for student and teacher cognition and for algebra instruction are discussed.
Milan F. Sherman, Charity Cayton, Candace Walkington and Alexandra Funsch
. , & Howell , E. ( 2016 ). A comparison of symbol-precedence view in investigative and conventional textbooks used in algebra courses . Journal for Research in Mathematics Education , 47 ( 2 ), 134 – 146 . https://doi.org/10.5951/jresemtheduc.47