Procedures or intuition?
Math students often fall into one of two camps: those who memorize
approaches to every possible problem, and those who trust their
intuition. The article Procedural
vs Intuitive Approaches argues that this is one of life's false
choices.
Students need both approaches. And both approaches have their limitations.
Our intuition is not always correct. And students can only memorize so many procedures, and sometimes even knowing when to apply a particular procedure can be difficult. And of course, sometimes there is no single procedure that will work on a challenging problem.
The intuitive approach can often be used to understand why various procedures work. Having a good toolbox of trusted procedures can help improve a student's intuition about a problem. The best approach is often a hybrid of the two: using intuition to know which procedures to use to crack open a challenging problem.
And in geometry, this hybrid approach is often the only approach that will work!
Students need both approaches. And both approaches have their limitations.
Our intuition is not always correct. And students can only memorize so many procedures, and sometimes even knowing when to apply a particular procedure can be difficult. And of course, sometimes there is no single procedure that will work on a challenging problem.
The intuitive approach can often be used to understand why various procedures work. Having a good toolbox of trusted procedures can help improve a student's intuition about a problem. The best approach is often a hybrid of the two: using intuition to know which procedures to use to crack open a challenging problem.
And in geometry, this hybrid approach is often the only approach that will work!
