**“The essence of metaphor is understanding and experiencing one kind of thing in terms of another.”**

-George Lakoff and Mark Johnson, *Metaphors We Live By*

As I explained on the Home page, I constructed metaphors to help me implement authentic mathematical practices. I wanted to see students engaging in genuine mathematical inquiry, for them to see the activity of problem solving as a creative process, and most importantly, for them to see themselves as mathematical thinkers.

I maintain that mathematics needs to be framed as a creative activity that people do, and is a subject that is worth talking about for its own sake. However, students will not agree with this sentiment if they are not provided with the experience of freely discovering the concepts in a safe environment. The mathematics that students study in high school is extremely constrained, in the sense that there are no other possibilities for points and lines to interact on a 2-D plane other than in Euclidean ways. Now, it may take different groups of students different amounts of time and they may take slightly different paths to come to the conclusions we know, but the conclusions still end up being the same. Just as an improv theatre troop may take stories and tell them in different ways each time they perform them, so too do my sections of students, when they are constructing the theorems from the problems that they are given. So, the metaphor "My classroom is an improv theatre" came to be.

I spent some time unpacking the language of the statement analytically, to see the types of activities that would be implied. I began by taking the two key words "improvisation" and "theatre", and wrote out all of the thoughts that come to mind when I think of them. Then, I wrote out their dictionary definitions and saw how they matched up with my thoughts. Lastly, I applied the words to more closely define the kind of environment and the types of activities that students would be engaging in through the viewpoint that this metaphor provides.

**Unpack: Improvisation**

My first thought is:

Jazz improvisation

Responsiveness

And what I think from that is:

Derivative of

Personal interpretation

Freedom

Creativity

Another thought is:

Improvisational Engineering

To take what is available and make due to make a new thing

Definition Merriam-Webster

: to speak or perform without preparation

: to make or create (something) by using whatever is available**Unpack: Theatre**

My first thoughts are:

Acting

Story

Performance

Frame

Stage

Play

**Apply: Implied Activities/Meanings**

If my class is *actually* a mathematics course, then the metaphor functions in the following way:

A mathematical thinker **Freely** discusses their thoughts and opinions on the problems that they are solving. Students must be **Creative** in moments when they are stuck, and share their **Interpretations** of the problems with their peers. In order to become good problem solvers, they must apply whatever prior knowledge they have, and **Make Due** to find the new concept that is embedded in the problem.

Creating this environment for my students means that I must be perpetually **Responsive** by providing new problems each night according to what is covered each day, and **Interpret** the lessons while they are being **Played** out.

**The classroom is an improv theatre.**

**The classroom is an improv theatre.**