Connection to students' individual interests helps imprint mathematics concepts.

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- Author or Editor: Candace Walkington x

### Milan F. Sherman, Candace Walkington and Elizabeth Howell

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, 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.

### Caroline (Caro) Williams-Pierce, Elizabeth L. Pier, Candace Walkington, Rebecca Boncoddo, Virginia Clinton, Martha W. Alibali and Mitchell J. Nathan

In this Brief Report, we share the main findings from our line of research into embodied cognition and proof activities. First, attending to students' gestures during proving activities can reveal aspects of mathematical thinking not apparent in their speech, and analyzing gestures after proof production can contribute significantly to our understanding of students' proving practices, particularly when attending to dynamic gestures depicting relationships that are difficult to communicate verbally. Second, directing students to produce physical actions before asking them to construct a mathematical proof has the potential to influence their subsequent reasoning in useful ways, as long as the directed actions have a relationship with the proof content that is clearly meaningful to the students. We discuss implications for assessment practices and teacher education, and we suggest directions for future research into embodied mathematical proof practices.