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Much of this issue reaches for the picture or the physical thing behind a number fact. Sinha proves wordlessly that 1 + 3 + 5 + … + (2n − 1) = n², and Subramaniam and Thomas give a visual confirmation that two numbers’ product equals the product of their GCF and LCM. Butler turns Minecraft blocks into a manipulative for factoring composites and quadratics, then pushes the same idea into perfect-square trinomials and Pythagorean triples. Alhammouri and Al-Ouran hand students real data and an RStudio activity, with the code and datasets posted as downloadable links so a teacher can run it Monday.

The rest of the issue is about teaching and the road students travel through it. Schwan, a preservice high school teacher, answers people who question why she chose the classroom, and asks the rest of us to think harder about how we defend that choice. Pachnowski and Cannelongo lay out Ohio’s new high school pathways, the alternatives now opening up beyond Algebra II, where they came from, and how schools are meant to put them in place.


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