We report on an innovative design of algorithmic analysis that supports automatic online assessment of students’ exploration of geometry propositions in a dynamic geometry environment. We hypothesized that difficulties with and misuse of terms or logic in conjectures are rooted in the early exploration stages of inquiry. We developed a generic activity format for if–then propositions and implemented the activity on a platform that collects and analyzes students’ work. Finally, we searched for ways to use variation theory to analyze ninth-grade students’ recorded work. We scored and classified data and found correlation between patterns in exploration stages and the conjectures students generated. We demonstrate how automatic identification of mistakes in the early stages is later reflected in the quality of conjectures.
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Yael Luz and Michal Yerushalmy
Merav Weingarden and Einat Heyd-Metzuyanim
One of the challenges of understanding the complexity of so-called reform mathematics instruction lies in the observational tools used to capture it. This article introduces a unique tool, drawing from commognitive theory, for describing classroom discussions. The Realization Tree Assessment tool provides an image of a classroom discussion, depicting the realizations of the mathematical object manifested during the discussion and the narratives that articulate the links between these realizations. We applied the tool to 34 classroom discussions about a growing-pattern algebraic task and, through cluster analysis, found three types of whole-class discussion. Associations with classroom-level variables (track, but not grade level or teacher seniority) were also found. Implications with respect to applications and usefulness of the tool are discussed.
Dana L. Grosser-Clarkson and Joanna S. Hung
This Perspectives on Practice manuscript focuses on an innovation associated with “
Kuo-Liang Chang and Ellen Lehet
Defining a quadratic function through the slopes of its secant/tangent lines leads to the fundamental theorem of calculus (FTC) and an alternative way of understanding integration.
David B. Custer and Ksenija Simic-Muller
We reflect on recent presentations at the NCTM annual conference and articles in MTLT that address statistics, data modeling, and data science. We observe that such presentations and articles are increasingly common, and encourage readers to use them in their teaching and write about their own adventures with data.
Stephanie Casey, Liza Bondurant, and Andrew Ross
This Perspectives on Practice manuscript focuses on an innovation associated with “
Robert Powers and Michelle Chamberlin
Growing Problem Solvers provides four original, related, classroom-ready mathematical tasks, one for each grade band. Together, these tasks illustrate the trajectory of learners’ growth as problem solvers across their years of school mathematics.
Kym Fry and Lyn D. English
Grade 4 students engage in problem solving through inquiry in an agricultural science context.
Joanna Papakonstantinou
Students create clever mathematical Valentine’s Day cards.
Margaret Rathouz, Nesrin Cengiz-Phillips, and Angela S. Krebs
Issues of equity in mathematics classrooms existed prior to COVID-19. For many students, however, meaningful participation in mathematical discussions became nearly impossible in online settings during the pandemic. In this study, we note the diversity in and nature of participation in mathematical discourse in an online course for preservice teachers (PSTs). We investigate the influence of implementing two support strategies for discussion: (a) establishing a “rough-draft/revision” orientation to mathematical tasks; and (b) providing time and structure (tasks and prompts) in an online discussion board for PSTs to post their initial thoughts, react to peers’ solutions, and collectively revise their ideas. In this article, we highlight several benefits of these support strategies to equitable PST participation in a unit on number theory. For example, as compared with oral discussions where only a few PSTs offered their ideas, the written discussion format encouraged every PST to post their ideas. Using a rough-draft/revision stance in the prompts fostered sharing and revealed diverse mathematical approaches, perspectives, and ideas. We argue that giving students opportunities to interact with one another and the mathematics in a variety of ways promotes equitable participation.
