Here is a video of a young student playing math. For us this is a pretty formal lesson. I need to get some video of the boys just playing because as I look over the vids I have, they are not exactly representative of play time. Problem is play is fun and spontaneous and getting the camera out changes that. Observing a thing effects a thing.
I enjoy this vid because you can see him throwing me some attitude. He wanted to play Legos not make a math a vid. He was also sick... Note the ease with which we breeze through lessons from subtraction to negative numbers.
Listen for the word "no"; it is replaced by me with show me or what do you have etc. We always start in the concrete and we skipped from blocks to symbols without drawing pictures then we went onto multiplication with 7's...
And this inspired a story about the numbers being happy. 7's have to go all the way to 10 before they get happy, 5's get happy after just 2...most get happy after just 5...the "hard" ones don't get happy until 10...3's, 7's, and 9's...
Then when we count all the way to 105 with 7's we get momentarily confused...but we keep counting...the point is we are playing math and we go through the basic operations of subtraction, integers and multiplication in one "lesson." This is the problem with traditional teaching of the mathematics to young children a lesson on math will be ONE lesson. No flow. Just a compartmentalized lesson on subtraction with borrowing and counting backwards, no movement to integers not shifting gears into multiplication...can you see the "subtraction" that goes on in multiplication when were counting 7's? Seven takes the three out of the next seven and and we get fourteen...etc.
Math. One language.
It has been noted that youtube constantly takes down the vids for multiplication rock. So go to youtube directly and search the vids...or better yet go buy the vids off my page.