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
Milan F. Sherman, Charity Cayton and Kayla Chandler
This article describes an intervention with preservice mathematics teachers intended to address the use of Interactive Geometry Software (IGS) for mathematics instruction. A unit of instruction was developed to support teachers in developing mathematical tasks that use IGS to support students' high-level thinking (Smith & Stein, 1998). Preservice teachers used the IGS Framework (Sherman & Cayton, 2015) to evaluate 3 tasks, to revise a task, and ultimately to design a task using the framework. Results indicate that a majority of preservice teachers in this study were successful in creating a high-level task where IGS was instrumental to the thinking demands, and that the IGS Framework supported them in doing so. The article concludes with suggestions for use by fellow mathematics teacher educators.
Milan F. Sherman, Charity Cayton, Candace Walkington and Alexandra Funsch
Research has demonstrated that textbooks exert a considerable influence on students’ learning opportunities and that technology has the potential to transform mathematics instruction. This brief report provides a systematic analysis of how technology tasks are integrated into secondary mathematics curricula by analyzing a sample of 20 textbooks. The results indicate that across the entire sample, nearly 15% of tasks incorporated technology, and of those, 21% used it as a reorganizer of students’ mathematical thinking; calculators were the predominant technology utilized. Investigative textbooks were not more likely to incorporate technology than conventional texts, but algebra 2 texts were more likely to include technology than geometry texts. Implications for instruction and teacher preparation are discussed.