THROWBACK: MATHEMATICAL MATURITY & TEST SUCCESS

So, Steve, I think what's really interesting about the approach that you have taken in your books or series of books is this idea of levels, right? I mean, your books really do allow students to almost identify where they are and try to kind of...

raise the bar or achieve or kind of work their way up the level so can you share a little bit about like sort of you know where your thought process came from that or sort of you know um yeah

this is this is kind of just the way i always did things when students came to me when i was uh preparing them for sat What I realized is that you can't just teach them everything because students have to be ready to learn material of a certain difficulty level.

If they're not ready for it, then teaching it to them is a waste of time.

So the primary focus when you're tutoring a student or when they're learning on their own, whatever it is, they really need to focus on that sort of sticking point exactly where they are rather than trying to cover everything all at the same time.

So if they're struggling with level three geometry questions and you give them a bunch of level five geometry questions, that's really counterproductive.

So I tried to make my books map that out really clearly exactly where students should be working of specific ability levels in each specific subject area.

How many levels of mathematical maturity have you described?

Well, I mean, first we should probably talk about what mathematical maturity actually is.

Since that's number one, it's probably a term that many people, they may have heard of it or they may not have, but they probably don't really know exactly what it's referring to.

And a good reason for that is there's not really a well-defined definition of mathematical maturity.

If you ask two different mathematicians, what is mathematical maturity, they'll give you two different answers.

And there'll probably be some similarities and some differences, but everyone kind of has their own feel on what it actually means.

And because it's kind of a little bit of an abstract idea, then when you ask, well, how do you improve it, that becomes even trickier, right? Right.

So one definition that I like to use is, especially for high school students, which is probably what this podcast is targeted for, is it's one's ability to analyze, understand, and communicate mathematics.

So someone with a low level of mathematical maturity won't be able to do those things.

Right.

Right.

Someone with a very high level of mathematical maturity will be publishing papers in mathematics, right? So you can

start with a low one, but it can really go up to the stratosphere.

Right, right.

So there's a whole wide range of levels in between that.

You know, and it's funny, whenever I meet people for the first time and I tell them I'm a mathematician, a very typical answer I get is, oh, I'm...

I'm not a math person.

I don't personally believe in math people and not math people, but what they're basically saying, I think, is, oh, I have a really, really low level of mathematical maturity.