I used to conduct math (teacher) trainings with "Julie." She was (is!) a phenomenal math teacher. But one day, while working with a group of 4th/5th grade teachers, the topic of multiplication table memorization came up. After a number of folks shared their ideas and perspectives--including their frustration with kids who just don't get it, Julie spoke, close to tears. She told us how she struggled throughout childhood with the fact that no matter what she did, she could not memorize multiplication facts. It became a huge point of anxiety. Yet mathematical thinking and strategies came naturally to her. She explained how at 40something, she still does not know her facts. BUT, her knowledge of math strategies is so great that she can compute quickly and easily.
As she spoke, I reflected on my own experience with memorizing facts. As a 4th grader, I was scholastically competitive. Surprising, I know. When the class multiplication chart went up, the race was on! I was eager to conquer the chart (and beat my classmates.) I memorized it quickly. To this day, if I need to recall a fact, I do this sing-songy thing in my head to find it. ("Nine times nine is eighty-one.") But here's the irony... I didn't have a clue what I was doing--what multiplication meant. I was great at memorizing, but it was really no different than memorizing a random list of words, letters, or numbers. It carried absolutely no meaning. Yeah, I could use them to do higher level multiplication and division, but my knowledge of the gamut was pretty limited because I'd done nothing more than memorize, first the facts and later the larger algorithms.
My friend Julie, in the meantime, fully understood the mathematical thinking behind multiplication. She had a wide range of strategies to pull from in order to figure out facts. I meanwhile, had none.
Which brings us to the concept of fluency. The definition of fluency is "good command." I would wager that as kids, Julie had excellent command of multiplication facts while I had relatively little. Today, Julie uses strategies to compute facts just about as quickly as I can locate them with my little sing-songy memory.
When I teach multiplication, my goal is fluency, not instant recall. I want kids to command multiplication--by thoroughly understanding what it is and being able to express their understanding through a wide range of strategies.
That sing-songy voice occasionally fails me. Julie's strategies never do. Her toolbox is loaded; mine has one unreliable wrench. ;)
In Salman Khan's book, The One World School House: Education Reimagined, he quotes from Nobel Prize-winning Eric Kandel, a neuroscientist:
"For a memory to persist, the incoming information must be thoroughly and deeply processed. This is accomplished by attending to the information and associating it meaningfully and systematically with knowledge already well established in memory."In order for something to be memorized [well], it has to make contextual SENSE!
For more thoughts on fluency, read "Teaching for Mastery of Multiplication."
P.S. I'm on the edge of my seat, waiting for the online version of Number Pieces to come out. When it's available, I'll show you some spectacular strategies for multiplication. (Even this 40something can add a few tools to the ole' toolbox!)