“Hey, Mr. Kane, can I get a nerd search?” was the highlight of my day (see yesterday’s post).

I didn’t teach today because of state testing. Instead, I had lots of time to plan and think. Yesterday’s post got me thinking about a different type of number sense — using an atypical scale to get an idea of the size of an answer, in this instance on a coordinate plane. These are just rough thoughts, but I wanted to sketch out a few types of number sense that I want my students to have when they leave me.

A sense for relative size, using integers, fractions, decimals, roots, and powers.

The ability to simplify a complex problem by estimating using easier numbers.

A sense for the appropriate magnitude of an answer before calculating.

The ability to use structure (in particular commutative, associative and distributive) to break complex problems into simpler ones.

An intuition around the structure of linear relationships, including slopes and intercepts.

An intuition around the difference between linear, quadratic and exponential change.

A sense for appropriate sizes of geometric objects, including angles and relative distances.

A sense for the relationship between distance, speed and time.

This is just me spitballing. I’m not sure which of these go together, what I’m missing, and what is more or less important. I wish there was more time in the school day to teach number sense, and more time in the year for my current students to struggle with these ideas.

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howardat58Go for it! This is what math is about. Without this the rest is a purely academic exercise.