"Cherrelle, just out of curiosity, how do you teach math? Do you teach the common core math? And since you know more about education than I do, how would it impact a kid now to learn it the old way when they go to college (or any other furthering education)? I've wondered about this since I'm not sure I want to send my kids to public school..."
When I started tutoring, Common Core-based curriculum was just getting a foot hold. Most adults hated it (and still do) because they didn't (and still don't) understand it. At base, what Common Core actually is, is a set of standards that all kids in every state have to meet so that if their parents move from Alabama to New York, that kid isn't so far behind that they can't catch up or isn't so far ahead that they have to skip grades. Now, the implementation was undoubtedly poor, because Alabama is backwoods and borderline retarded, but the concept is sound. Anyway, when I first started tutoring, I decided that to be an effective tutor, I needed to learn what the kids were learning, the way that they learned it. I grabbed the Common Core Go Math! workbooks for 2nd-5th grades and actually worked through them, using the strategies that the books taught. It blew. my. mind. These kids are learning not just formula; they are learning math theory. They are learning concepts that I didn't see until my junior year of college. They are learning to see numbers as tools to be used and manipulated. They are learning that numbers are not set in stone, that they can be broken up and put back together so that you don't even need a pencil and paper to figure it out. Mental math is taught as a matter of course, not trick.
Not only did I see how the kids were learning, but it actually DRASTICALLY improved my performance in my 300 and 400 level math courses. I discovered that 4th graders understood mathematical theory better than I did, could apply it better, could do it faster, and could do it all in their head! From personal experience, I can say 100% without a doubt that any kid that learns the old way and does not have a natural talent in mathematics will find themselves at the bottom of the class when they go to college, because they have memorized a formula without understanding it and have not learned the process and manipulation of basic mathematical concepts.
As to teaching it, I've got a few different ways I do it. If I'm tutoring and picking up the slack for the public schools, I expand on what the teacher has taught in class and show the kids mental math tricks and formula application that they won't get in school. If a homeschool parent has a curriculum they want me to follow, I do basically the same thing with the materials they give me. If I have free reign, I take the standards we want to accomplish, check them with the state requirements and design lessons that mix real world application, mental math, and physical calculation.
If you are interested in furthering a basic idea of math, here's a few resources:
- For the type of mental math that is often taught to common core students: "The Secrets of Mental Math" by A. Benjamin and M. Shermer
- For an overall good way to learn middle/high school math concepts: "Demathtifying" by Ilan Samson
- For an understanding of why numbers are the way they are and behave the way the way they do : "Zero: The Biography of a Dangerous Idea" by Seife
- And as always, check out reddit: Mental Math
"If it was good enough for me, it's good enough for them, right?"
The biggest problem I see is that those people have a hard time passing that understanding on to others. It's like art. My brother can just DO it, you know? We can take the same class that shows the same techniques and what he ends up with will have soul. What I end up may technically look like is supposed to, I'll have memorized the technique, but it won't "speak" to anyone. It's just lines on a paper that I've drawn the way I was told I was supposed to. Because that's my brother's talent, he can take that memorization and his brain will automatically make the connections and develop the shortcuts, but mine won't. If your kids have that natural talent, they'll most likely end up developing and discovering the mental math tricks on their own over time. If they don't, the methods teachers started to use after Common Core was implemented will help their mind make those connections, as long as you are open to it, as well, and set a good example.