Every rule – even the craziest, most arbitrary mandate – has a reason rooted in this essential purpose...
And so it is in math class. If you understand slope not as “that list of steps I’m supposed to follow” but as “a rate of change,” things start making more sense. (Why is it the ratio of the coefficients? Because, look what happens when x increases by 1!)
You get to work a lot less, and think a lot more.
Now, conceptual understanding alone isn’t enough, any more than procedures alone are enough. You must connect the two, tracing how the rules emerge from the concepts. Only then can you learn to apply procedures flexibly, and to anticipate exceptions. Only then will you get the pat on the back that every robot craves.
Sunday, January 25, 2015
The "How" Is Rooted In The "Why"
Here's a great post explaining, with a robot analogy--and who doesn't love robots?!--why it's important in math not just to memorize things, but to understand why the rules you're memorizing make sense: