The authors apply a research-based framework to a specific task and discuss how it can be used to revise the task with respect to goals for student thinking.
Milan Sherman and Charity Cayton
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.
Jennifer N. Lovett, Allison W. McCulloch, Lara K. Dick and Charity Cayton
In this article, we present a set of design principles to guide the development of instructional materials aimed to support preservice secondary mathematics teachers (PSMTs) examining student practices in technology-mediated environments. To develop design principles, we drew on the literature related to technological pedagogical content knowledge (TPACK; Niess, 2005), video cases as learning objects (Sherin & van Es, 2005), and professional noticing (Jacobs, et al., 2010). After presenting the design principles, we share a task created using these design principles. Finally, we share PSMTs’ reflections about changes in their own understanding after examining students’ practices. Their responses provide insights into the usefulness of the design principles for deepening PSMTs’ mathematical knowledge and knowledge of students’ understanding, thinking, and learning with technology.