I have said it before, algebra is just generic math. It has many uses for teaching math at various levels. Here is the same exact problem with two very different students:
Note how it is nicely color coded but this is NOT sufficient, even the drawing is not sufficient many reading this may still not "get it" completely. I found as I traveled the USA that the only time we got 100% comprehension in workshops was when everybody had blocks or manipulatives. If you only have symbols or drawings some people get lost. They have to be able to get there hands on it. Now we can start off with manipulatives and then stop sing them over time but the concrete is ALWAYS where you start off. And one or two examples does not cut it it takes MANY before you can move to drawings only and then symbols only and this process often takes months and years.
Here is vid one with an older student:
Here is a much younger student doing the same exact problem notice it takes much longer and more patience with the younger child:
Note the difference in emphasis between the students. The older student's focus is the distributive theory of multiplication in preparation for problems that have negative coefficients. The younger student is learning to count up things that are SAME and as you can see because the x² are not the same shape even though they are color coded the same he has a bit of trouble and because the x are different color again he has a bit of trouble...but he can see what he is doing and it makes sense. Later more understanding can be added. Meantime adding up and counting in algebra isn't scary or hard and it's kind of fun this is enhanced because he knows older kids do this stuff and I tell him some of them find it scary and hard and he thinks I'm teasing him...but then they met some students that assured them that this isn't how they were taught in school and indeed algebra can be quite scary and hard.
Look for a future post where I go into a little more detail on adding layers of understanding. Hopefully I will remember to link it here.
Now some people comment that having the little kids do algebra shames the older students. Only if they have poor self esteem brought about by poor parenting skills. My students know that the point of showing them that little kids can do it is not to shame them but to emphasize that algebra is so EASY it is child's play. Even advanced algebra is no big deal, just more counting. And that if a little kid can get it they can get it. And so can YOU.
Algebra can be quite useful for teaching basic operations, that is addition, subtraction, multiplication AND division. As can be seen with the younger students they get experience with adding or combining like terms and counting as well as multiplication when the factors are positive and combining like terms that are negative and positive as well as multiplication when they have negative factors or coefficients. Further how do you teach multiplication without teaching http://www.crewtonramoneshouseofmath.com/division.html at the same time.
This is a lot more fun than memorizing multiplication tables or doing endless worksheets on addition or multiplication...yes they need practice and LOTS of repetition but don't turn it into drudgery. Be careful with worksheets. I tell my students as with sports you don't throw the ball a few times and become a pro you throw the ball a many times a day for many days and you still will need practice. That's why in textbooks you often see the problem sets labeled practice.
Here is another video with young students where I use algebra to teach counting skills like multiplication and addition:
And more "higher algebra" for the same purpose:
If you want to see the negatives you need a password.
Also people say I don't put enough posts up on my blog. That may be. But i can tell you that I post on my math page over on facebook everyday. If you want a steady stream of vids and math etc like this page:
Also you may want to do some searches with crewton ramone in them because there are now MANY videos showing how to use algebra to teach math. Too many teach algebra all by itself as a subject unto itself thus adding to the confusion by cutting the mathematics up into too many segments that seem unrelated to each other.