Think about a concept you teach — any concept involving quantity, measurement, comparison, or proportion. Post here: Walk through the three augmentations for that concept: 1. Precision — What vague perception does this concept make precise? 2. Shareability — How does this concept allow students to communicate what they sense to others? 3. Testability — How does this concept allow a claim to be checked against reality? If one of the three augmentations feels harder to identify than the others, name that too. It may reveal something about how the concept is currently being taught versus what it could become.

In one or two sentences, how would you currently describe the purpose of mathematics to a student or a parent? Don't overthink it — just write what you would actually say. We'll return to your answer at the end of this course to see if anything has shifted.

Choose one of the four failures mentioned on Page 4 of the course. Find or create a concrete example from your own teaching context or your students' experience where this failure was at work. Post here: Share the example and then answer: What mathematical augmentation would help here? What tool, representation, or question would restore perceptual clarity? Is this something your students encounter — and if so, where in your curriculum might you address it, not as a lesson about math, but as a lesson about sensing more accurately?

Post your three magnitude moments here. For each one, share what you were sensing, what you were comparing it to, and whether precise numbers would have helped or not. Be honest — some moments genuinely don't need mathematics, and noticing that is just as important as noticing the moments that do. Then read a few other people's posts. What do you notice about the kinds of magnitude sensing that teachers do? Are there patterns?

Describe a moment where a child demonstrated the Sense of Magnitude without using any mathematics. What were they sensing? What were they comparing? What was the background against which they were judging "how much"? The goal is to see the sense that exists before the symbol arrives.