# Extend, Ontario!

Posted on May 7, 2021

I signed up for a MOOC but the timing is in relative down time so … looks like it will be happening.

## Executive Summary (or: TL/DR)

Multiplication is often not fully understood. See https://resourceroom.net/UDLMult/ for a way to teach it concretely and thoroughly.

Exponents are fun, too. Here’s a fun story in a two minute video.

## Long Version

First “assignment:” “Misunderstood.”

Three “misunderstood” concepts come to mind: Exponents, multiplication and … math in general.

First: misunderstanding what math/ math classes are about. I work with adults and most of them are experiencing math as a roadblock in their lives. They’re trying to get through and/or around it so they can move on.

In the math classes, math problems are things you have to get right to get through this rough part of the route. They’re not really related.

For our students landing below pre-algebra placement, we designed a course to build number sense.

There are several elements woven throughout. First, connections: concrete / visual connections. Also: Stories. The students loved it when Kathy would have the problems be about her and her family (she asked). Oh, I’m fibbing. First: connections… *with the students.*

The connections — lots of “connected representations” help get students away from “just copy the example and change the numbers” tho’ a person can figure out similar paths in lieu of understanding for Getting The Right Answers for … just about anything that has A Right Answer.

…. so that’s the meta part of this. Once again, I’ll need to find the little survey we have that asks questions about knowledge and feelings about math, and 3 or 4 diagnostic questions. But that’s the Big Thing If I Have Time. Option 2:

So, Exponents! that’s the littlest one — but one where a solid foundation opens up so many doors. It’s also Not As Abstract As You Think It Is.
There’s an awesome New Thing for multiplication called Building Fact Fluency that helped me label important elements of learning that, without even being aware of it… I usually do. One is to have a “rich image” to represent the idea. Another is to have a *story* — like in this example of another person’s “misunderstood” assignment. The other parts are more familiar when making lessons — connecting well to past knowledge, providing practice. “Connecting representations” is a big deal for this one, since the symbols for exponents look just like “count up to me” numbers but oh, my! They don’t mean the same thing at all. An analogy is … exponents have “higher powers” than ‘regular’ numbers. Here’s a two-minute Exponent Story (seems now I’d have to upgrade to embed it).

And the third thing that is not *fully* understood is multiplication. Analogies aren’t happening with this and… honestly, I don’t think they really work for these math ideas. The “rich image” and the story and making things look and feel right (what Graspable Math is about that I figured out when noticing that folks who didn’t remember ***anything*** else from math remembered how to make an improper fraction out of a mixed number… it has a look and a feel to it…)

For multiplication, this concrete, active introduction builds a visceral understanding.

Okay,