How To Memorize Without Drilling
Is drill the best way to learn something? Absolutely not, says cognitive scientist Daniel Willingham, who draws a useful distinction between drilling and memorizing:
“‘Drilling’ connotes repetition for the purpose of automaticity, using the technique of thoughtless repetition.
‘Memorization’ connotes the goal of something ending up in long-term memory with ready access. . . but the word does not imply anything about the technique one uses to achieve that goal.
Students might drill in an effort to learn the multiplication table, but I hope they would not. It’s hard to think many school-related tasks that would be well-served by drill. Perhaps a very basic motor skill, like a particular run when playing the guitar? Again, this would be repetition without thought.
Much more common would be memorization: activities undertaken in the desire to commit something to memory so that it is readily accessed. This would include deep processing (i.e., thinking about meaning), generating cues for oneself, etc. A student who wants to memorize a poem, for example, could try to do so by drill, but it’s a terrible way to learn something. Much better to think about the meaning of whatever it is you’re trying to remember, and tie it to things you already know.” Read more of Dan’s blog post here.
I especially like Dan’s point that drill is “repetition without thought”—but that it’s actually the thought, the deep processing, that helps us remember things!
But, Dan—if you’re out there and want to comment on this—multiplication tables might be one of the only things that I would think would be suited to drill—because there’s no deeper meaning to think about, and not much other knowledge to tie it to. Rather, the goal is simply to achieve automaticity, as you put it: to get to the point where the answer pops into your head without effort. Would Dan, or anyone else out there, care to comment?
When you need to learn something that doesn’t have any meaning to you (those instances ought to be rare), that the time to use a mnemonic. Mnemonics help in for more than one reason, but lending meaning to otherwise meaningless content is one way they can work.
Thanks, Dan! Anyone have ideas about effective mnemonic devices for memorizing the multiplication table?
I wonder if the multiplication table is the mneomic device.
when asked for recall of 4×6 do you go to 24 as the answer or do you do the little song in your head 4×3=12, 4X4=16, 4×5= 20 then say the answer?
When working with my 5 year old son he starts somewhere in the chain then works to the answer. I wonder if that’s how adults recall it as well, it just works so fast that they don’t realize it?
Rob, I personally just recite them in a staccato rhythm but it is in the same way I learned them as a child. If I try to change the rhythm it becomes difficult though. Very interesting!
Hi Annie,
I disagree that the multiplication table has no meaning. The patterns and inter-relationships between the numbers is interesting and beautiful (see this image: https://plus.google.com/photos/111294772089064103270/albums/5772106108786252321?authkey=CNfb64yqkKvszQE). This is how I learned multiplication because rejected the drilling in school.
I think we live in the post-memorization era. We need to understand the meaning of things so that we can find and use information rather than just storing it in our heads.
Adam
Yes, I agree with Adam. While times tables are important to achieve what is called number sense, they do have meaning. It’s often (incorrectly) thought of as repeated addition, although scaling across the number line is more accurate. Annie, some good resources for conceptual multiplication are:
http://betterexplained.com/articles/rethinking-arithmetic-a-visual-guide/
http://www.maa.org/devlin/devlin_01_11.html
http://www.maa.org/devlin/devlin_06_08.html
How we commit ideas/facts/knowledge to long-term memory in the digital age is a fascinating subject…some argue there is no need to memorize anything, because your Smart Phone can access it in a few seconds. However, I’m not sure you can effectively use digital communication tools without having facts and ideas to draw on in your long-term knowledge.
Correct me if I’m wrong, but in Dan Willinghams book from 2009 he explains in fact we do need to have quite some knowledge to be creative, to look something up,…
Multiplication does not necessarily need drilling too. I couldn’t learn it that way so when my teacher told me while learning the 8 times table..”you know 8*3 but not 8*4, just add 8 to the result of 8*3 to get that of 8*4 and so on”. Then it made sense because I thought about it.
You’re right, Pedro, Willingham did write that. This is more about HOW you commit that knowledge to memory.
Great post and discussion.
Willingham’s point about the difference between memorization (a learning outcome) and drill (one of a number of possible processes for getting that outcome) is really important and frequently overlooked.
The *timing* of different kinds of learning processes is also an important consideration that hasn’t been raised yet. Trying to learn addition by jumping from drilling on number flashcards to drilling on addition problems (which is common in apps that are labeled “educational”) is a terrible way to learn about addition–it can be a punishing experience for the learner (basically trying to badger the brain into retaining something that has no obvious relevance), and it is incompatible with how brains learn-so it tends to produce fragmented, brittle, inert knowledge that is not very usable in the short term. It also does not lay down a strong foundation for future learning (of multiplication and subtraction, for example, which have deep conceptual ties to addition). Why is it incompatible with how the brain learns? Because there are regularities to addition as a system but the brain can’t easily identify these underlying relationships and patterns from a bunch of randomly chosen addition problems (“drills”).
If a child first understands addition (as the joining of quantities, for example) and then practices lots of math problems with feedback to develop fluency and automaticity, then there is a base of understanding that is being consolidated through the same process as would have produced poor quality learning if it had been used right from the beginning.
It’s not just *what* processes we use to support learning that matters – *when* we apply them in the learning process is also important.
We’ve been thinking a lot about these very issues in early math, in fact, as we are applying learning science to develop our “Native Numbers” app that will teach Number Sense to children.
When I taught third grade, we used songs to teach multiples as one way to learn the multiplication facts. Example: use the tune “Jingle Bells” to practice the multiples of three, from 3-33. You can also keep track on your fingers as you say each number, ie, when I say “3, 6, 9,” I tap my index finger, then middle finger, then ring finger. I can easily see that 3X3=9. For a more concrete representation, students can point to groups of counters (beans, buttons, etc) as they sing the song. Musical connections help us learn many things we need to memorize. How did you learn the letters of the alphabet?