This study examined "backward transfer," which we define as how students' ways of reasoning about previously encountered concepts are modified when learning about new concepts. We examined the backward transfer produced when students learned about quadratic functions. We were specifically interested in how backward transfer may vary for…

Emergent graphical shape thinking (EGST) involves interpreting or constructing a graph as dynamically generated, which is useful across science, technology, engineering, and mathematics fields. Although evidence suggests that students as young as middle school can engage in EGST with support, other research indicates most college students and U.S.…

Considerable research has been conducted on the critical role of gesture and action in children's mathematical thinking. However, teacher professional development (PD) has not tended to include specific supports for attending to nonverbal student thinking. In this Brief Report, we argue for including supports for multimodal teacher noticing in…

A growing consensus holds that preservice K-8 teachers (PSTs) need to experience the modeling process as learners to understand it and envision teaching modeling in their future classrooms. We examine this recommendation by exploring how PSTs construct models and how collaborative learning practices influence them in revising and refining their…

This exploratory study investigated the behaviors and content of onscreen calculator usage by a nationally representative sample of eighth-grade students who responded to items from the 2017 National Assessment of Educational Progress mathematics assessment. Meaningful features were generated from the process data to infer whether students…

Studies have found that some teacher professional development programs that are based on Cognitively Guided Instruction (CGI) can increase student mathematics achievement. The mechanism through which those effects are realized has been theorized, but more empirical study is needed. In service of this need, we designed a novel measure of…

We investigated how the time elementary preservice teachers (PSTs) spent studying certain mathematics topics during teacher education coursework was related to performance on teaching-related tasks administered after graduation. In two studies, participants completed tasks assessing their specialized content knowledge (SCK) for teaching 12…

To design and improve instruction in mathematical proof, mathematics educators require an adequate definition of proof that is faithful to mathematical practice and relevant to pedagogical situations. In both mathematics education and the philosophy of mathematics, mathematical proof is typically defined as a type of justification that satisfies a…

This article introduces unit transformation graphs (UTGs) as a tool for diagramming the ways students use sequences of mental actions to solve mathematical tasks. We report findings from a study in which we identified patterns in the ways preservice elementary school teachers relied on working memory to coordinate mental actions when operating in…

This article investigates the implementation of inquiry-oriented instruction in 20 undergraduate mathematics classrooms. In contrast to conventional wisdom that active learning is good for all students, we found gendered performance differences between women and men in the inquiry classes that were not present in a noninquiry comparison sample.…

Generalizing is a critical aspect of mathematics learning, with researchers and policy documents highlighting generalizing as a core mathematical practice. It can also be challenging to foster in class settings, and teachers need access to better resources to teach generalizing, including an understanding of effective forms of instruction. This…

We use a narrative framework to investigate how mathematics textbook lessons can promote sustained student inquiry. Our analysis of four high school textbook lessons on the SSA congruence property, three of which contain explorations, reveals how explorations can promote problem-solving perseverance by inspiring readers to raise mathematical…

Early education is replete with debates about "academic" versus "play" approaches. We evaluated 2 interventions, the "Building Blocks" (BB) mathematics curriculum and the BB synthesized with scaffolding of play to promote executive function (BBSEF), compared to a business-as-usual (BAU) control using a 3-armed cluster…

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…

This article presents the results of a design-based research study related to slope that took place in a high school algebra 1 classroom. In the study, students explored situations related to making predictions. As students engaged with these situations, they reinvented and made meaningful multiple subconstructs of slope. I present the findings in…