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• Author or Editor: Nicholas H. Wasserman
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A Random Walk: Stumbling across Connections

Ideas in statistics, probability, stochastic processes, and algebra follow the steps of a wandering professor.

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A Rationale for Irrationals: An Unintended Exploration of e

The practice of problem posing is as important to develop as problem solving. The resulting explorations can be mathematically rich.

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Math Madness: Coloring, Reasoning, and Celebrating

Looking for a way to influence elementary school culture about mathematics prompted this author's use of graph-coloring problems in an activity with second graders.

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Opportunities to Learn From (Advanced) Mathematical Coursework: A Teacher Perspective on Observed Classroom Practice

This article explores secondary teachers’ opportunities to learn from an innovative real analysis course, as reflected in their actual classroom teaching. The course used cases of teaching as a site for applying mathematics and developing pedagogical mathematical practices. This article explores particular teaching moments in (N = 6) secondary teachers’ classrooms, and the attributions they gave for why they engaged in those teaching practices. Teachers engaged in instructional practices that exemplified course objectives, and their attributions for their actions contribute a teacher perspective on opportunities to learn in teacher education from (advanced) mathematical coursework. Results highlight cases of teaching and modeled instruction as catalysts of change and as opportunities to develop pedagogy from mathematical activity, and vice versa.

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Technology Tips: An Archimedean Walk

The circle, so simple and yet complex, has fascinated mathematicians since the earliest civilizations. Archimedes, a well–known Greek mathematician born in 287 BCE, began to unravel part of the mystery involving π by applying iteration to the circle. Building on Euclid's postulates and theorems, Archimedes used iterations of inscribed and circumscribed regular polygons to find upper and lower bounds for the value of π. These bounds are close approximations of the value of π, and one is still used today: 22/7 differs from π only in the third place to the right of the decimal (see fig. 1).

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Area-Preserving Transformations: Cavalieri in 2D

A 2D version of Cavalieri's Principle is productive for the teaching of area. In this manuscript, we consider an area-preserving transformation, “segment-skewing,” which provides alternative justification methods for area formulas, conceptual insights into statements about area, and foreshadows transitions about area in calculus via the Riemann integral.