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Sickle cell disease is a very common disease throughout the world. We used it to contextualize probability for upper elementary school students. Using Punnett squares, activities guide students' evaluation of inheritance using theoretical probability. Then, students perform trials using tools to compare theoretical and experimental probabilities.

“More weight, longer shadow,” a student predicts before we begin measuring the lengths of our objects' shadows. Another third-grade student conjectures, “Standing-up objects make the shadow longer, and lying-down objects make the shadow shorter.”

This article encourages optimization skills and development of winning strategies in grades 3–6 students via some game-based activities with dots and lines. Contributors to the iSTEM (Integrating Science, Technology, and Engineering in Mathematics) department share ideas and activities that stimulate student interest in the integrated fields of science, technology, engineering, and mathematics (STEM) in K–grade 6 classrooms.

Scoliosis, the curvature of the spine, is a medical condition that often affects youth. This article provides students with an opportunity to explore the geometry behind the spine's curvature. Students will first develop a method for measuring curvature and then compare their method to the commonly used Cobb method. Contributors to iSTEM: Integrating Science Technology Engineering in Mathematic share ideas and activities that stimulate student interest in the integrated fields of science, technology, engineering, and mathematics (STEM) in K–grade 6 classrooms.

This study examined the structure of two preservice teachers’ understandings of educational software in mathematics using repertory grid techniques. Specifically, the study focused on how teacher educators can enable preservice teachers to discern the features of mathematics software, and develop pedagogical goals that reflect the affordances and constraints of available tools. Results showed a deepening of knowledge and a differentiation of knowledge following experiences of exploration, evaluation, and comparison of different types of software. Results imply that directing preservice teachers’ attention to utilizing the functional characteristics of software for developing plans and for the design of instruction may be fruitful for more effective integration of software in their future teaching. However, participants’ preexisting content knowledge and their pedagogical worldview tempered this effect.

Anchored instruction is designed to present problems in a meaningful context to allow for investigations into real life environments. The Jasper Project was created to allow students to investigate mathematical dilemmas using anchored instruction techniques. This study uses case study methods to examine the perceptions that preservice teachers have toward the use of anchored instruction after having the opportunity to investigate and evaluate a Jasper predicament as a group. The guiding research questions were: 1) Through exploration and evaluation, are preservice teachers able to determine significance of using anchored instruction with their future students? And if they see significance, 2) How do preservice teachers envision student learning and mathematical growth using anchored instruction? Four individual cases were evaluated, specifically examining the features of anchored instruction each preservice teacher described. The preservice teachers were optimistic about the utilization of anchored instruction and described features that support student learning and growth.

Using stories in mathematics helps students situate mathematics within a context. This chapter presents an activity for the integration of stories and word problems into an algebra course designed for pre-service teachers. The pre-service teachers designed and created stories using technology (digital cameras and PowerPoint) to support algebraic explorations at the elementary and secondary levels based on the Common Core Standards. A balance of technology, language arts, and mathematics content is possible with these stories. The activity can be extended beyond the university classroom by guiding secondary students in creating their own algebraic stories in the classroom.

As there has recently been an onslaught of video cases being developed and implemented with preservice teachers, it is important to evaluate how we should use these cases. This research investigates the features elementary preservice teachers consider valuable when using video cases in mathematics education. The researchers used hierarchical cluster analysis to create a dendrogram that displayed statistically significant features. The study revealed two primary clusters— (a) cross-subject lessons emphasizing adaptations and techniques to reach a variety of learners and (b) problembased lessons with students in groups supported by lesson analysis—as well as (c) a small third cluster of collection and distribution of materials. Ultimately, such findings can be used to guide the design and incorporation of tools for using mathematics-based video cases. (Keywords: video cases, tool-based instruction, preservice teachers, technology use)

Technological tools available on the Internet can be used to support teachers’ understanding of how to teach mathematics to their students. This paper outlines a method for using algebraic tools in mathematics with teachers to help them discover features to facilitate student learning and understanding with the support of statistical software. The teachers first investigate algebraic tools and then analyze features of the tools and how they support or limit student learning. Personal Construct Theory (Kelly, 1955) is used to first help teachers create and self administer repertory grids and then generate dendrograms for cluster analysis. The model described can help others implement technology in a similar manner making use of both web-based applets and statistical software in an authentic context.