Here is a group of kids playing math. Do they look engaged to you? Which one is the problem child? Which one is considered the genius child? In this pic you can't tell. These students are all around 10 years old.
Get them started off right by using base ten blocks. Here are a couple of students that by now I'm sure you recognize. People are of course amazed at their ability to do math in their heads, thus disproving the thinking that base ten blocks somehow lead to block dependency where they won't be able to do math without having the blocks in hand and other ridiculous ideas. In fact, I got the job teaching the kids you see above because these two were doing multiplication in their heads in a health food store (calculating simple stuff like if it costs $2.73 per pound and I buy 6 pounds of it how much does it cost?) and one thing led to another.
"This is back when I didn't know what anything was..." one of them remarked upon seeing this vid after not seeing it for a long time. Note how when they are young like this, how it looks is important in answering the question, "are they same?" This persists into adulthood and certainly into the teen years...2 + 1 = 3 does NOT look same because of the color of the blocks and on one side there is only one block and on the other two blocks...but in total number it is the same, and this is quickly understood. "The equals sign never lies" is an important math concept. Concept based math teaching with manipulatives speeds and eases the whole process. Very soon (a couple of years) and they are doing math like this. Everybody is so impressed. They think it's EASY because it is.
Meantime many students have lost track of what the symbol equals even means and somehow come up with the "the answer is" instead of same as...this one understanding has, I have been told directly by older students, made a huge difference in algebra, pre-calc, and trig, and of course calculus. Anyone will tell you x + 5 = 8 doesn't look same, but that statement says it is...IF x = 3. I was also reminded of how much things get lost and confused working with a AP calculus student...because math gets so segmented and compartmentalized they fail to see relationships.
Here is the "whole thing" for those of you interested. This lesson is also on the sample lessons page (I think) along with many hours more video of sample lessons with base ten blocks. These are actual unrehearsed lessons not scripted demonstrations: practice not theory. If you want theory I have about 3 hours of it up now on the parent teacher training page...with more to come. There's some short free stuff there now for you to check out if you want to get a better idea of the theory behind the method. And there are posts like this to help you understand more about the method and posts like this to help you get started using base ten blocks.
So of course now doing algebra like this is no big deal and neither one of them is even 10 yet. I keep telling them as they get older it's less impressive which is why this is funny on a lot of levels. It's kind of an inside joke. You can see him looking at the picture and being very careful to get it right...he looks at the picture YOU see the symbols.
If you have older kids or students, base ten blocks make math visually obvious for them too, the blocks level the playing field because they speak to all learning styles. Whether male or female, visual, kinesthetic, or auditory learners, ALL benefit from the use of base ten blocks. And younger really is better. So I made this to help get them started off right. Combine with this blog and website and your kids won't have to worry about common core mathematics, because they'll know math not just have some stuff memorized and jumping through the silly hoops on tests showing work or "number sense" won't be hard at all...all they may see the absurdity of it all.
"I have to tell you that when I first started to watch your videos I cried....after learning it myself in school (haha) then teaching my three daughters algebra using Saxon, Math U See and things from the Teaching Company, I never really had any idea of what I was doing. Watching the videos of you made everything make sense!!! I'm sure that this is a labor of love for you but I just wanted to say thank you! It is much appreciated." ~HS, Ohio, USA.
Having traveled the USA doing seminars I can tell you this was not an uncommon response when people finally understood a math concept and faced their math demons...usually revolving around algebra but sometimes with much simpler things like why invert and multiply--something most teachers have no idea how to explain and end up saying "just memorize it..." Avoid the problems in the first place it's never too late to break the cycle, start off with my book if you have young children.
Here is what it looks like when you give a young kid a head start with base ten manipulatives. YOU can do this too.
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