Thursday, July 06, 2017

So-called Rote Memorization In Math

It used to be fashionable in some math circles to believe that students don't need to memorize anything.  They can look it up!  Anyone with more than two operational brain cells can tell you that that's a ridiculous idea, but some people still cling to it.  Here's one less reason to cling:
Between 1995 and 2010, most U.S. states adopted K–12 math standards which discouraged memorization of math facts and procedures.  Since 2010, most states have revised standards to align with the K–12 Common Core Mathematics Standards (CCMS).  The CCMS do not ask students to memorize facts and procedures for some key topics and delay work with memorized fundamentals in others. 
Recent research in cognitive science has found that the brain has only minimal ability to reason with knowledge that has not previously been well-memorized.  This science predicts that students taught under math standards that discouraged initial memorization for math topics will have significant difficulty solving numeric problems in mathematics, science, and engineering.  As one test of this prediction, in a recent OECD assessment of numeracy skills among 22 developed-world nations, U.S. 16–24 year olds ranked dead last.  Discussion will include steps that can be taken to align K–12 state standards with practices supported by cognitive research.


Jamie said...

My favorite part was "discovery and misconceptions". It resonated with me having spent the past two (frustrating) years teaching from a textbook called "Discovering Advanced Algebra". Worst two years of my 19 year career. I jokingly told people the only thing the students discovered with how much they hated math. :( Finally scrapped the book altogether in January. Burned through a lot of worksheets but was the best decision I could have made.

Niels Henrik Abel said...

No duh, Sherlock. Even with "looking it up" (or allowing a "cheat sheet" or 3 x 5 with formulae on it), the students still have no clue how to use that information to solve a problem. You should hear all the B&M-ing whenever I tell them that yes, you DO have to "memorize" (I usually say "know and correctly apply") the trig identities, for example.