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In this article, a K-12 mathematics educator and a recent (2020) high school graduate discuss curricular work related to math trails, which are based around the idea of mathematizing potential discoveries along a physical walk. The intersection of math trails with the realities of schooling amid the COVID pandemic is described, along with ways in which math trail learning has ramified beyond classroom walls. This collaboration serves not only to draw attention to the under-researched topic of math trails, but also to exhibit how students and teachers can, in the language of Freire, work together as critical co-investigators. [ABSTRACT FROM AUTHOR]

In the first part of this paper, we provide an example of a project designed to foster mathematical creativity among students at an independent, all-girls school in the Northeastern United States. The mathematical motivator for the project is a polyomino proof by induction first formulated by Solomon Golomb. We explain how the project has been implemented over the past two years at the school's Innovation Lab in collaborative work between a mathematics instructor and an educational technologist, provide instructions and background information to facilitate the implementation of this project at other learning sites, and show examples of student work along with a discussion of their reactions and takeaways. We close by naming the practice of \mathematical code switching" and situate it within Rochelle Gutierrez's discussion of creative insubordination in mathematics teaching. [ABSTRACT FROM AUTHOR]

The article presents a lesson plan that teaches high school students techniques in enriching divisibility and in creating rich mathematical tasks in proving routine propositions in varied ways.

The article discusses an approach to solving mathematics problems that involves tame guessing, or guessing at a solution after finding it through other means, also known as looking back. Topics include how this reverses the four steps described by George Pólya in his book, "How to Solve It," how an educated guess helps develop mathematical intuition, examples of looking back on a known solution by guessing including partial fraction decomposition and the derivative of a quadratic function.