A quick addendum to my recent post on the role of facts in learning.
The point of that post was that students do need to memorize certain facts in the content areas if we want them to be able to do more cognitively difficult work. Another NYTimes article today about habits reinforces this point. In one study at MIT, rats are put into a maze and they start meandering, apparently aimlessly. Their brains, however, are bursting with activity. The cognitive challenge of learning the patterns of the maze is setting their brains off. As they learn the correct way through the maze, and as they develop the ability to navigate it faster and faster-- their brains stop working so heavily. Part of moving efficiently through the maze involves memorizing certain features and patterns of the maze.
To me, it seems obvious that something like multiplication facts work the same way. If you want students to develop higher order math processing abilities, you can't load their brain with activity everything they stumble across 3x4. You can ask them to turn to their calculator everytime they stumble across a simple math fact, but that's adding a time lag and a modest cognitive load as well. Really, if you want people to get good at multiplying exponents, factoring equations, interpreting log-odds in a statistical model, and all kinds of other things, it's really helpful if they can just do 3x4 in their head.
Someone tweeted back to me after my original post "If you can Google it, do something else." That wasn't my point. My point was that there are lots of things that you can Google that you really ought to memorize (if you want a reductio ad absurdam, how about the definitions of words). It's very difficult to learn more sophisticated concepts without mastering some of the underlying facts-- you spend to much cognitive energy sniffing around like a mouse in a maze.
The challenge, however, is that 50 state curricula (interpreted differently by 14,000 districts) tend to put too much emphasis on simply acquiring facts that are never used for deeper learning. It's a curriculum designed, and in some ways designed poorly, for an information scarce world. However, being in an information plentiful world does not mean that we should no longer store information in our heads in a robust, durable way. It means we need to think very carefully about what information we should store in our heads (and more importantly, in the heads of our students) in a robust durable way. What facts are freeing students to run faster through our academic mazes, or to invent and draw their own mazes, and what facts are we stuffing in their heads because 19th century textbook authors thought it was a good idea?