**This is Day 31 of 31 Days of Math Learning Success – THE FINAL DAY! See all the days here and check out others that are wrote for 31 days here.**

*I’ve never thought of acting as rocket science – you put on the costume, get your hair cut, and that’s it, really.*

~Marc Warren

There’s only a handful of actors in “math world.” Depending on the show, they play different parts.

For instance, Ignatius P. Identity will play **Zero** in *The Addition Show* and **One** in *The Multiplication Show*.

In *The Function Show*, Ignatius plays .

And in *The Matrix Show*, he plays .

Depending on the episode, Ivey McInverse may play or .

Or even , the soul mate of .

Ivey McInverse only plays inverses.

### They’re not Method Actors.

The “actors” in math are popular. You can’t see a show without spotting them.

The key is to figure out the actors and then watch the shows closely.

Every actor behaves the same way. Kind of like how Bruce Willis always acts like Bruce Willis.

There are some slight differences, sure. But overall Bruce Willis plays Bruce Willis. Just like Ignatius P. Identity always plays an identity element.

### In other words, it’s all the same stuff.

If you learned anything in math, ever, you mostly know everything.

The challenge is figuring out how the new stuff is like the old stuff. Who from last night’s math show is playing whom in today’s math show.

And what parts of the story line are the same.

### Math isn’t hard, it’s just detailed.

Like a great Quentin Tarantino movie, it’s deceptively simple. Or deceptively complex.

It’s funny, frightening and at times confusing.

But it’s worth the ride.

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I’ve often thought the key to math is doing a lot of it until it becomes second nature. I tell my students to compare it to learning to walk. Watch a toddler and see how much effort it takes to learn, but you haven’t given it a thought in years.

How do you get that number sense? With our games we try to have lots of different activities of different types, so that students see the same concept over and over but in different situations.

However you do it, I agree, number sense is a foundation too many people do not have, and just like in construction, you can’t build very high without a foundation.

Thanks for your thoughts, AnnMaria.

Repetition is important, but only if the foundation gives you the ability to make it compress. Otherwise you’re just trying to be a computer running a gazillion subroutines!

Great illustration, Bon. The only thing I’d suggest is to replace is the “younger” vs “older” labels in your comparison with “novice” vs “expert”.

Have you read any of David Tall’s stuff about mathematical thinking (http://homepages.warwick.ac.uk/staff/David.Tall/themes/three-worlds.html) ? He says that as expertise in math develops, processes become encapuslated (aka: compressed) into what he calls “procepts” — “thinkable concepts” or hybrids of process + object which can be manipulated in their own right.

Working memory (WM) is known to have a very limited capacity (newer research has lowered this from 7 plus/minus 2 items to 3 plus/minus 1). Without encapsulization/compression, WM fills to capacity with the calculations and single steps which all must be juggled individually and sort of held in suspension there until they can be assembled into a problem solution.

When students have to deliberately recall and then ‘drive’ each little step in a more complex process, WM capacity is exceeded and cognitive overload ensues. Some of the little pieces may be displaced by other little pieces which need attention. Unable to recall how the individual steps contribute to the solution, the student may become lost inside the bigger process. Unable to ‘see’ a solution taking shape, the student may shut down.

Developing fluidity is essential, and facility in fractions especially is now seen a sort of bellwether of future success in math.

Very nicely articulated Sue!

I had no idea that working memory was so small. I was still back on the 7.

My brain just realized that it can’t take much more and is wanting to shut down. Time for coffee!