Here you will see students as young as 4 and 5 years old doing algebra and "advanced" math, without ever knowing it's supposed to be hard.
You are invited to learn how to use this method...

Thursday, May 24, 2012

Using Math Materials To Best Effect

I would Like to introduce you to this woman who has started making vids on Vimeo.

Seriously. Could these kids be any cuter?
And it's even more important to teach girls early because they need every advantage. Our culture puts females at a disadvantage when it comes to math starting very early on.

Here is her channel, Education Unboxed. She has opted to use Cuisenaire Rods, I am hugely biased toward Mortensen Math base 10 Blocks/Manipulatives but she is correct that they are pricey and many parents already have Cuisenaire Rods because they are cheaper. (They are cheaper for a reason IMO.) With just a little work, a few "mods" as geeks and nerds like to say, they can be quite serviceable for teaching math beyond just addition and place value. Her point is to make vids that parents/teacers/homeschoolers can use to put the materials they may already have to better use. I highly recommend her channel and vids and hope she one day makes a blog and website too.

If you can't afford Mortensen math materials, perhaps you can afford a set of the Cuisenaire Rods...and you can get started teaching your kids math and learning math right along side them...with all the FREE suport you get from The House Of Math and this blog and now her vids too you can't afford not to get started and have very few excuses left.

She says she is "just a mom" who wants the best for her kids and wants to help others help their kids too. Even more I want to promote her because so many make excuses that they can't do it because they aren't good at math or don't have a degree or what have which I reply: "just get started." You won't fail and you won't hurt or damage your kids. Errors can be corrected if you make them and can be turned into teachable moments.

My comments and critiques are for her improvement NOT to put her down or denigrate what she is doing. Her point and so is mine that if she (we) can do it SO CAN YOU.

Another great vid!

OMG: your kids are so cute it brings tears to my eyes.

Fine job removing no from the lesson and telling them what they have. Play a game with yourself how to I remove the negative completely. Instead of it's not 11, show me it's 11 or Hmmm, what's this side called again? (Answer is x, and then plus one.)

Improve your x² by putting a stip of paper over the sides because her observation that it is 10x is correct in this case you can clearly see it. I made a video about this...and it is a common question. Is 10x = x²? And the answer is a little complex involving 10, -10 and multiples of 10; they are after all base 10 blocks. That lesson would be best saved for another day...

Just telling them it's x when they can see it is 10 is usually not sufficient. Solve that problem with a strip of paper. I realize you are improvising with the tools you have and you are doing a FINE JOB.

This; however, is pretty important. Math concepts aren't because mom says so. lol

There is a Montessori concept called "visually obvious." It is visually obvious that that one side is must be visually obvious that that side and all sides is/are x.

A few side notes. At one point the younger child made and x to the second not an x square, which is good: it was one by could point that out in a later lesson. x² doesn't always have to be square! Especially if you are doing third power algebra...x³ dosen't have t be a cube fact it will make higher power algebra impossible to present if you try and stay in three dimensions. You may casually mention this if she does it again...that way it's a natural discovery and not a "lesson".

Also they are never wrong. They are just getting more information. (You know this I am just reiterating for those reading.) You are a patent and gentle teacher. You may want to direct them a little more and let them figure out some of their mistakes on their own instead of just showing them so they can have their own ah-ha moment. You accomplish this by asking good questions using control of error and putting them in a situation where they can not fail...each one of those is a full dissertation and they are covered lightly on my concepts page.

Good questions:
Does yours look like mine? How could you make your square look like my square? Show me. How are they same, how are they different, what's the name of this. Etc.

You can also avoid and control error with use of the three period lesson.

Lastly you casually mention they are completing the square when they are in fact completing the square. That is great! You could take a second to ask how they do it...the answer you are looking for is by taking the x and splitting into two parts...this seems small but it's huge. Later when they do the quadratic the (b/2)² will make sense...

I would like your permission to your vids on my website or blog once in a while where they will get more exposure and hopefully encourage others to get started teaching their own kids math. I would also like your permission to put links in these comments because I have covered a lot of this in detail in other places.

Third please contact me via is at my website. Just click the contact tab.
I am a master trainer. I was certified by Jerry to train trainers to train other trainers...not just train teachers to teach kids. The difference is understanding the why of things. You could be a mighty teacher if you wanted to be. You never know where teaching ends...somebody could see your vid and be inspired to do more...a kid could stumble across it and have an're making a positive difference.

One more time: FINE JOB.

Education Unboxed:

Yes, I absolutely do need to cover the sides with paper. I'll be doing that soon!

I THINK I understand what you are saying about "x squared" (not sure how to get the little 2 up there!) not having to be a square. Though I just learned last year that "squared" actually means a square! So, now you're saying that it doesn't HAVE TO BE in a square shape, right? Just that 9 is a square number because it COULD be made into a square? And when it's not in a square shape, then we call it "x to the second?"

Yes, please feel free to post my videos anywhere you'd like. The only reason I made them was to help other people (so they wouldn't have to do the hours and hours of research and reading I've done over the years). And, yes, links in the comments are fine.
I will contact you through your website. Thanks!!!

Then as you can see in this next vid she does...

A couple of notes for ALL teachers including myself: REMOVE THE NO FROM THE LESSON. Migrate to good habits early, but don't worry about doing it wrong if you are wrong just correct the mistake. Some students can be migrated to the correct way just by modeling, they see you doing it correctly so they change to make theirs the same as yours. Occasionally you get the child that wants to be different from you just to be different. These minds are to be encouraged but certain rules are not up for debate, we read left to right for example your blocks should mirror are my comments so far:

Many comments to make. This is great.

Remove the no from the lesson.

Need an equals sign instead of a solidus...

We read left to right...the girls need to be (gently) corrected to put the units in the upper right. It doesn't really matter ( 3 + x )( 4 + x ) = ( x + 3 )( x + 4 ) however ( x + 3 )( x + 4 ) is more correct because we count in descending order. (Count the big ones first.) Also (minor details) move toward putting the parenthesis closer together. Again they aren't wrong they are acquiring more information...and you are simply moving them to more correct notation and mathematical syntax.

Also DRAW pictures. This is the bridge in the mind between the concrete and the abstract. A blend of symbol and blocks is great...
Will add more later.

Keep up the GREAT work.

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