One of the fun things for me about home schooling has been learning to teach elementary school math.Â Maybe “learning” is the wrong word since I’m not really studying anything, but through trial and error I feel that I’ve improved my teaching a lot in the last few years.

It is always difficult teaching a new subject for the first time because you really have a good feel for how other people think about the material.Â Even though the elementary school math is quite basic, not totally understanding what the kids aren’t understanding makes teaching the material tough for me.

In the last year I began to follow a bunch of math teachers on twitter.Â It has been an incredible experience learning from all of the ideas that they share.Â One of the most prolific writers is a middle school math teacher in California named Fawn Nguyen.Â How she has the time in the day to do what she does is beyond me (as are her blogging skills), but I use so much of her stuff that it is as if my kids are being taught by an east coast amateur impersonator of her.Â Â Â Seems like everything she posts turns into some sort of homework for the boys.

Today she posted a series of problems here:

http://www.mathtalks.net/nt-5-8.html

The first is a problem that I wouldn’t have appreciated before I started working with my kids.Â After seeing it today, though, I couldn’t wait to go home and try it out on them.

I didn’t let either of the kids see the problem before turning on the camera – the goal was really to see how they’d approach the problem rather than if they’d be able to do the multiplication correctly.

First up was my older son.Â He’s always seems to want to charge right into a problem with the first idea he sees, so I was curious if he’d simply multiply out the two expressions.Â He did, but in a way I wasn’t completely expecting:

I should note that he taught himself how to do basic arithmetic, so his way of adding, subtracting, and multiplying is definitely not standard.Â As his approach to arithmetic was perfectly fine,Â I never bothered to teach him now to carry, borrow, or do long multiplication the “normal” way.Â I’ve always wondered if I’ll regret that decision later.

Next up was my younger son.Â I also wasn’t sure what he was going to do.Â He’s only learned the basics of multiplication, so it didn’t seem likely to me that he’d want to multiply everything out.Â In the last couple of weeks we’ve been studying primes and factoring, and that was the approach he took to the problem.Â I’m sorry that so much of this video is him trying to figure out if 79 was prime, but I thought the process was fascinating.Â Even if I had to help him get over the last little hump.

This was a really fun problem to work through –Â Thanks Fawn!!