Thursday, January 27, 2011

Higher Orders of Math

*Thanks to CCMM Communications Director Jennifer Courtney for this guest post*

I used to tutor geometry. Every fall, about the time mid-term grades came in, my answering machine was full of calls from frustrated parents. Memorization is especially key here because your brain cannot memorize formulas, apply them by plugging in numbers, and prove that they are true at the same time.

I am convinced that these students would have been more successful if they had memorized the formulas for area and circumference and a few other simple things like the Pythagorean theorem long before they were asked to use them.

Then, when this knowledge is solid, they need to apply it by plugging in numbers and solving the equations.

Finally, they will be ready to graduate to the rhetoric stage of geometry which is proving that the theorems are true.

The same is true in Algebra. It’s difficult to think about mathematical formulas with letters when you haven’t learned how to think about them with numbers.

Students must be able to recite the multiplication tables in their sleep before approaching the abstract concepts of algebra. They would be helped by memorizing the laws that we memorize in Foundations.

Then, they can identify equations which use these laws. Then, they can plug in numbers and demonstrate that the laws hold true.

Finally, they will be able to write and solve equations with letters.

People only object to rote memorization when they conceive of it as cramming for a test and then forgetting the information or memorizing facts without going on to apply those facts to higher orders of thinking.

*To read more about the importance of memorization, check out A House With a Foundation. For more information about the Classical Conversations Foundations Program, visit*


Health Insurance Specialists said...

Speaking of Math, I have a son in Challenge 1 - Saxon 2, at what point is the calculator allowed to be an intregal part of the homework and test routine?
It's difficult to mark the entire problem wrong for silly addition errors that would have been caught with a simple calulator.

1 Smart Mama said...

I recommend using calculators only once a student reaches trigonometry, but the most important thing is to make sure your son is developing his brain's calculator even as he learns higher math. That means being able to do basic arithmetic quickly and accurately. Using a calculator may speed up the process as long as he has shown you he's capable of working the problems correctly and consistently on his own, but it shouldn't be a crutch for something he struggles with. Drilling the basics never ceases to be important.

Hope this helps!