We introduce the Into Math Graph tool, which students use to graph how “into" mathematics they are over time. Using this tool can help teachers foster conversations with students and design experiences that focus on engagement from the student’s perspective.

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### Amanda K. Riske, Catherine E. Cullicott, Amanda Mohammad Mirzaei, Amanda Jansen, and James Middleton

### Bobson Wong and Larisa Bukalov

Parallel geometry tasks with four levels of complexity involve students in writing and understanding proof.

### Jason Lee O'Roark

After teaching high school mathematics in Maryland for three years, I began teaching sixth-grade mathematics in one of the best school districts in Pennsylvania (according to state test scores) and have been teaching there for the past six years. My high school teaching background led me to differentiate differently from my colleagues. I share my observations of the result of the differences in methodology and my conclusions from those observations, and I offer a plan to implement changes in the way that mathematics is taught.

### Alex Friedlander and Abraham Arcavi

Integrating procedures and thinking processes makes learning more meaningful.

### Daniel R. Ilaria

Students generally first encounter piecewise–defined functions in the form of a step function (perhaps the postage stamp function) in an algebra class. Piecewise–defined functions do not play a central role in mathematics before calculus although they can serve as challenging examples in the precalculus curriculum. Before the advent of the TI–Nspire, entering piecewise–defined functions on the calculator was time consuming and not particularly user friendly. That has changed.