Journal of Mathematical Behavior最新文献

Mathematics lecturers frequently ask questions in their lectures, and these questions presumably play an important role in students’ thinking about and learning of the lecture content. We replicated and developed a coding scheme used in previous research in the US to categorise lecturers’ questions in a sample of 136 lectures given by 24 lecturers at a research-intensive UK university. We found that the coding scheme could be applied reliably, and that factual questions were predominant (as in previous research). We explore differences in the lecturers’ use of questions – both between our UK sample and the previous US work, and between individual lecturers in our sample. We note the presence of strings of related successive questions from the lecturer, which we term ‘question chains’. We explore the nature of these, examine their prevalence, and seek to account for them in terms of the lecturers’ possible intentions.

In this research, we investigated how a summative assessment of creating and sharing metaphors for linear algebra concepts supported undergraduate students’ affective, behavioral, and cognitive engagement. All seven research participants were enrolled in an introductory linear algebra course designed to develop students’ geometric understanding of linear algebra concepts in R² and R³. Using embodied cognition and an engagement framework, we analyzed students’ written responses and video-taped their focus group discussion. Our findings suggest that this summative assessment (a) privileged mathematical aesthetics and the affective domain of learning, (b) engaged students in binding formal aspects of linear algebra concepts with metaphors that they enacted via embodiment, and (c) was an opportunity to demonstrate learning and higher-order cognition. Thus, illustrating that assessments can focus on aesthetic and affective domains of mathematics while simultaneously integrating serious mathematical cognition. We conclude by offering adaptations of this assessment for other mathematics courses.

Informed by Realistic Mathematics Education, we designed a hypothetical learning trajectory on graduate students’ guided reinvention of reducible and irreducible elements in rings. We created experientially real context problems for use in a teaching experiment, in which secondary in-service and pre-service teachers used algebra tiles as an emergent model of factoring integers and quadratics in $Z\left(x\right)$. In their mathematical activity, this became the teachers’ model for abstracting the shared structure of (ir)reducible elements in $Z$ and $Z\left[x\right]$, which they used to formally define (ir)reducible elements. In this paper, we discuss the progression of the teachers’ reasoning and defining activities that were evident as they reinvented the definitions of reducible and irreducible elements of integral domains.

Teachers who use student thinking to make instructional decisions tend to create more positive learning experiences for students and support conceptual understanding. Looking at student work is one way college instructors learn about student thinking. We interviewed eight calculus instructors to investigate what they noticed when examining student work. Reflexive thematic analysis allowed us to classify instructors by the stance they adopted when looking at student work. Instructors who adopted an evaluative stance responded by providing examples or explaining how to solve the problem, often taking on the intellectual work of solving the problem. Instructors who adopted an interpretive stance responded by providing examples or asking guiding questions informed by the student’s thinking. We then extended our analyses to illustrate two instructional archetypes (Interpreter and Evaluator), to highlight how the stance taken when examining student work can serve as a proxy for how instructors engage with student thinking more broadly.