Is it any surprise, though? Math is taught in a manner that focuses very much on the how but rarely ever the why. And while Discovery Math/Reform Math/etc are lambasted for not teaching kids to memorize certain algorithms, they do something else that's very important: encourage students to use creative problem solving skills to develop their own solution algorithms.
I'm not going to advocate reform math in its current form, but I have to question traditional "drill and kill" teaching methods in today's modern world. If I can't remember how to find the area of a triangle, I just Google it. Drilling it into my brain would have made sense in the 1920's when there was no internet, no assurances my peers had the appropriate level of education to know such a thing, and possibly no ability to reach an "expert" via telephone to tell me the algorithm. I'd be completely reliant on my memory and (possibly) a math book if I was fortunate enough to have one with me. For all practical purposes, memorizing one half times base time height would have been the way to go in a pre-Internet era. Today, it seems like it's far more worthwhile to develop students who are solid problem solvers with strong information retrieval skills, as opposed to wasting precious time memorizing trivial algorithms that are readily available.
Is it any surprise, though? Math is taught in a manner that focuses very much on the how but rarely ever the why. And while Discovery Math/Reform Math/etc are lambasted for not teaching kids to memorize certain algorithms, they do something else that's very important: encourage students to use creative problem solving skills to develop their own solution algorithms.
The idea sounds really great, but everything i've ever seen is that the students just end up terrible at everything. I even tried to teach it some, and the material seemed great to me as a teacher, but the students just never got it. I feel like the discovery idea makes a lot more sense in hindsight, but when learning that way, doesn't work out like hoped.
However, I study applied math and I would say i learn in a more discovery way... But thats at the graduate level.
If students are ending up terrible at everything, then the problem is deeper than just tradition vs reform. What's likely occurring is we are much better at teaching plug-and-chug than we are at developing problem solving. That's to be expected, as it's significantly harder to develop problem solving skills than it is to simply memorize steps, grade, correct, and repeat until perfect. This is especially true when you consider most math teachers really aren't trained in the art of problem solving, and were likely taught in a traditional manner themselves. As such they have no real frame of reference to go off of when attempting to foster problem solving skills in their students.
Also with a triangle it can be easily shown how you arrive at 1/2 bh, and I agree teaching this is much more valuable than formula memorization. Throwing in some practical use cases school kids can actually relate to wouldn't hurt either. I mean, when you're in 4th grade, who gives a fuck how tall a light pole is.
I'm not going to advocate reform math in its current form, but I have to question traditional "drill and kill" teaching methods in today's modern world. If I can't remember how to find the area of a triangle, I just Google it. Drilling it into my brain would have made sense in the 1920's when there was no internet, no assurances my peers had the appropriate level of education to know such a thing, and possibly no ability to reach an "expert" via telephone to tell me the algorithm. I'd be completely reliant on my memory and (possibly) a math book if I was fortunate enough to have one with me. For all practical purposes, memorizing one half times base time height would have been the way to go in a pre-Internet era. Today, it seems like it's far more worthwhile to develop students who are solid problem solvers with strong information retrieval skills, as opposed to wasting precious time memorizing trivial algorithms that are readily available.