multiplication as we make are way through the 20x20 matrix. The idea is not just to be able to do multiplication with symbols or blocks but to be able to do the multiplication quickly and easily in your head. In order to do this we need to be able to organize our thought and count very rapidly.
Manipulatives expedite this. The mind wants to work rapidly. The device it uses is the brain. Brain and mind are not same, just like computation and mathematics are not same. Computation is how we DO math. Mind uses brain, brain does not use mind. But I digress.
As I am doing this video I try to impart some concepts not just on the students but on the adult viewers who may be parents or teachers. Concepts like the stages to competence. Do you see the blend of drawing symbols and base ten blocks? Driving home the point that "no" needs to be removed from the lesson. I was going to make the point that they are building neuro-pathways and now that we know some neurophysiology, you understand it takes a little bit of time for the child to form the thoughts and then vocalize them. When they learn new things this takes up a lot of the brain and it takes a few seconds for the brain to process and compute and then make the information available for the mind verbalize. We are faster because the pathways have already been built. We are also going to use repetition to make the information available for instant recall and store it in the long term memory, but we are going to have FUN doing it. No muss, no fuss, no tears, no need for endless worksheets and drill.
The idea that the partial products model was supposed to be a way to help you count and organize thought and that it was a stepping stone to understanding multiplication and doing it fast was interrupted. Mortensen math uses the term "split and shift" to show this. Manipulatives illustrate partial products superbly, BUT here is a faster easier way to go about multiplication counting the big ones FIRST.
Already getting very positive feedback for this vid. People are stunned and amazed because one of the students is "only" six.
I make one error in this presentation I expect you will see it easily but it doesn't slow us down or make a difference to the lesson. The blocks show 18x13 when I am doing 18x12 with the symbols. There are a couple of other subtle errors I caught while I was watching this, perhaps if you find them you can put them in the comments below. Lets see if YOU are paying attention, LOL.
Problem is, things got a little muddled along the way and many students get bogged down in the algorithm and instead of it unleashing speed it actually hobbles them. As you can see I am training them to go left to right. Count the big stuff first, understand that we're counting hundreds then tens and then units...adding them up is SUPER EASY IF you understand your addends. The youngest boy needs some practice with addends. He is going to build pyramids NOT do worksheets.
Since this first post we have maybe practiced this for an hour over two weeks. Maybe. There has not been drilling or worksheets, there has been some play (playing algebra and building math towns and such) and some practice. Soon we will make a game of practicing all 400 facts.
Note the order...first we get single digits facts mastered. Then we do the single digit times two digit facts. WHILE we are doing this, we have been building squares all the way out to 20x20. This helps us practice addends, addition and single digit multiplication. We have played with 11's (and nines) so those are easy. Also played with 12's. As we do this we are now also doing two digit by two digit which of course includes square numbers, 11's, 12's and the "easy ones where the tens addends add up 100, which are 11x19, 12x18, 13x17, 14x16 and 15x15. We can play with the little one like 12x13 and all those where there are no tens "hiding" first. These are great for building confidence with the little kids because it makes them feel like they are doing big kid math.
Note that concurrently with learning addends, addition, and multiplication they are learning algebra which reinforces this...and also fractions, percentages and problem solving. You will also see compound lessons on square root and and the concept of square numbers tossed in as a matter of course.
I think you will agree they are making fine progress. And this is the way it works first you crawl, then you walk then you can jog and pretty soon you can run where you used to stumble and fall.
I hope you can hear the excitement. So much energy that many times I don't get to complete my thoughts...math learning should be FUN not done in silence to the scratching of pencils.
Raymond has his own page where you can track his progress. But you need a password. Great page if you have a five six or seven year old. Sarah's is a good page to visit if you are dealing with Autism. There are also tons of sample lessons and videos (free and password protected) on my site, and please come join me on Face Book.