Based on our experience in STEM programs over the past couple of decades, it's clear to us that there's very little M in STEM – with that morsel of math generally being used in service of science or computer science. In most cases, a teacher or mentor just tells the students the math they should use, perhaps with some hand-waving, and they incorporate it into their projects.

Some people put the M under the STE, indicating that math is actually the basis of it all, but often that just promotes the notion that math is a utilitarian subject, a tool for solving other types of problems. There is none of the sort of creative and often deep mathematical thinking we promote and teach in mathematical circles, just more blind implementation of techniques and algorithms. Standard approaches don't encourage (and sometimes actually discourage) mathematical thinking.

In this project, we're working with students to help them take the mathematical discoveries arrived at in math circle (or similar) settings, and explore, visualize, and apply them, using computer modeling, analysis, and programming tools. This approach could just as well be used to investigate mathematics that leads into investigation in other areas of science; the key point is that by starting with, and staying grounded in, the mathematical exploration, a deeper understanding of the physical or computational systems is possible.

We will be presenting our current work in this project on June 2^{nd}, at the 2017 NM STEM Symposium in Albuquerque, NM. For the presentation and links to the supporting materials, see The Missing "M" in STEM: A Math Circles & Modeling Approach.

Explore the surprising variations in conceptually simple sequences of numbers, constructed by applying one of two operations to generate each successive term. Can you make the sequence return to its starting value?

What happens when generous people sit in a circle, and share candy – under some conditions – with each other?

Fold a long strip of paper in half several times. Can you see a pattern in the creases formed along the length of the paper? What sorts of route do we trace if we use the creases to direct our turns along a path?

How does the circle leader keep spotting the lie?

Can you see the light? That is, can you see the patterns in light bulbs that are left on, after repeatedly following a simple rule to switch them on and off?