Strategies are proposed that promote use of an Integrated Applied Mathematics (IAM) approach to enhance teaching of advanced problem-solving and analysis skills. Three scenarios of 1-dimensional transport processes are presented that support using Error Function analyses when considering short time/small penetration depths in finite geometries.…

We introduce, motivate, and exemplify a proposed theoretical construct guiding the design and facilitation of collaborative geometry activities, conceptually generative perspectival complementarity (CGPC). Participants in CGPC activities learn content by negotiating their respective perceptions of situated features they manipulate to accomplish…

Although raised in the early days of research on teacher noticing, the question of context specificity has remained largely unanswered to this day. In this study, we build on our prior research on a specific aspect of noticing, namely teachers' analysis of how representations are dealt with in mathematics classroom situations. For the purpose of…

Teachers' questions shape the instructional environment and the direction of mathematics discussions in critical ways. This article is the product of a research study on the relationship between teachers' questions and student engagement in the Standards for Mathematical Practice (SMP) during whole-class discussions. Using classroom video gathered…

Productive struggle leads to productive classrooms where students work on complex problems, are encouraged to take risks, can struggle and fail yet still feel good about working on hard problems (Boaler, 2016). Teachers can foster a classroom culture that values and promotes productive struggle by providing students with challenging tasks. These…

This paper links educational psychology research about curiosity to teacher moves that are effective in an inquiry-based mathematics classroom. Three vignettes will show explicit teacher moves (staging disagreement, intriguing anecdotes, and creating a safe space) for different audiences (math majors, mathematics for liberal arts students, and…

I present a viable learning trajectory for prospective elementary teachers' number sense development with a focus on whole-number place value, addition, and subtraction. I document a chronology of classroom mathematical practices in a Number and Operations course. The findings provide insights into prospective elementary teachers' number sense…

This article describes the "mathematical criteria" employed by the International Skating Union (ISU) to identify potential judging anomalies within competitive figure skating. The mathematical criteria have greater sensitivity to identify scoring anomalies for technical element scores than for the program component scores. This article…

This paper describes efforts by the author to engage and motivate students in undergraduate research by giving them a large audience and engaging the media in disseminating their work. I provide an introduction to public relations from the point of view of a mathematics professor, and describe some lessons I have learned in my own attempts to…

This study used design experiments, specifically micro-cycle teaching experiments (MTE) as a catalyst for practice-based professional development. The MTE incorporated research-based characteristics of effective professional development: it was embedded in the teachers' daily work of planning and enacting lessons, co-constructed with the…

A Bayesian model formulation of the deterministic inputs, noisy "and" gate (DINA) model is presented. Gibbs sampling is employed to simulate from the joint posterior distribution of item guessing and slipping parameters, subject attribute parameters, and latent class probabilities. The procedure extends concepts in Béguin and Glas,…

For several years we have been teaching a one-hour class called "Longwood Seminar," a first-year seminar that is required as a general education goal and has much of its content dictated by Longwood University. During this time we have collected and used a series of mathematical vignettes to supplement the university-required material.…

This article explores the inter-relationship between the embodied processes of pattern generalisation and the visualisation of pictorial cues. A research framework is established for analysing pupils' multiple visualisations of figural cues in the context of pattern generalisation. The research framework centres on a novel combination of three…

In this article, we address how the design of educational scenarios can support teachers' adoption of both technology and open-ended projects indorsing creativity and innovation. We do that by describing how groups of teachers develop digital learning environments supporting using a combination of GeoGebra and Google sites. Both teachers and…

In this paper, we propose an approach to analysing teacher arguments that takes into account field dependence--namely, in Toulmin's sense, the dependence of warrants deployed in an argument on the field of activity to which the argument relates. Freeman, to circumvent issues that emerge when we attempt to determine the field(s) that an argument…