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Rote Drill has its place. Its a great tool. I highly recommend it.

By rote drill, I mean being able to solve a problem or recite a theorem on demand with no hesitation and at the fastest speed possible.

To survive Very Hard tests in college, I had to have some things down cold. I took advanced thermo and stats classes that required us to derive methods to solve general classes of problems then solve specific cases. All the math had to be second-nature. And we ended up using ALL our math skills - from calculus, diff-eq, Linear Algebra, theorems from RA, Stats, etc. Those kids who did could not slam out the math or reach for a theorem, were left behind.

The first week, the instructor told us we had to take this "easy" week to get up to speed. He told us how to do it.

I had already been doing rote drill for calculus and Linear Algebra prior to the semester to get warmed up. But he upped our game. Every night I spent 12 hours outlining all my other texts, categorizing problems, setting up flash cards, then just started going through it. I had over 200 flash cards with theorems and problems - both pure and applied - on them. Once I had all the subjects down, I shuffled the cards, then took 50 with me on the bus each morning. As the class progressed, I added cards from that class.

After I started this method, I usually finished the finals in one hour vs four most of the other students needed. It all came down to that rote drill. A friend of mine started using it when he was in the math program and from then on he got A+ in classes.

To this day, I can look at most applied math problems and do them in my head. And I can usually look at something that is not right and be able to grasp the theorem being used and which of its givens are being violated.

When you look at other human pursuits - such as sports or marksmanship or cqb - rote drill is a key part of the training method. Sure, there are unstructured problems - but the solution to them often involves pieces taken from actions which are down cold. Academics - and problem solving - are no different.

A mathy kid should start his or her set of flash cards by putting the hardest problems from the week on them. Its like baseball cards for math! On the front should be the problem statement. On the back should be the elements for the solution.

Another set of cards should have definitions and theorems on them. Name of the item on the front, the explication on the back.

This method can be explanded to other subjects as well.

Sorry, Austin, but rote drill would destroy my 7yo's interest in math. Like with a sledgehammer.

I'm not saying practice and even memorization don't have their place. I just don't think the place for the sort of drill you're describing is necessarily elementary school math...which is where most of it is currently located! Flash cards are about the worst way to teach my son. I know--we tried them!

Different kids have different needs, so different approaches suit them better. A lot of GT kids are concept kids, and drill-and-kill simply isn't the right approach for them. Especially for visual-spatial kids, they need to see the big picture first and then the details come more naturally to them.

One-size-fits-all just doesn't work.

I understand Kriston. Good point. I am a spatial learner, too. There were times I would take the whole deck and organize it in one big jigsaw puzzle just for fun.

The way I used the cards was to organize the information and then ensure the retainment of information once the knowledge was obtained. Once I had the stuff down, it got a few cards, then they went into the deck.

I did not use it to learn new stuff.

Yes, that makes sense. As a review tool or to build speed where speed is desirable, I think strategies like that can work wonders.

DS7 is not fast at anything except learning! And he probably never will be. I always say that there are (at least) 2 kinds of GT kids: the fast and the deep. DS7 is deep. He prefers time to mull things over.

I think that style difference affects learning strategies, too. Things like flash cards or even educational video games that require quick retrieval of info stress him out. We're working on it, but I'm pretty well convinced that we have to come at things that are typically memorized--like his times tables--from another direction or it will not be good for his love of math. He needs lots of concept, very little drill at this point.

Maybe that will evolve as he gets older. I guess we'll see...

Kriston - your post rang a bell for me. In "Re-forming Gifted Education" the author wrote about two different types of gifted kids. Those that need to learn fast and furious, more, more, more and those that need time to ponder, need to go deep, deep, deep.... those two types should not be in the same gifted program as they will frustrate each other.

Makes sense to me!

I am late to this post. Going back to TexasSummer comment about engineering math tgught him the "whys", engineering requires applied math. I started in premed and took calculus, but then switched to enginnering and had to take applied calcullus in the spring to make up.

I think teaching physics is a good way to teach applied math. My opinion. I think of physics as applied math, chemistry as applied physics etc. And there are many simple experiments to do in physics that help with math.

Ren