One of the many popular tropes of the internet is referring to someone who offers criticism of a piece as a “troll”. Not that there aren’t bellicose and baiting-type comments, but the word is often applied to any type of criticism as in : “If you don’t agree with this, you’re a troll.”
So I thought I’d provide some comments I received in private regarding the discussion following Keith Devlin’s piece in the Huffington Post, as well as what I wrote about Devlin’s piece in the post below this one. Chances are pretty good that these commenters would be viewed as trolls by many, so if what they have to say is disturbing, I won’t hold it against you if you want to call them that. If it helps you to ignore what they have to say, go for it! They won’t mind.
Troll No. 1:
With the consultants I’ve met, who always push this stuff and insist that kids aren’t fluent unless they can explain everything to you, it seems that they themselves just figured out that there are reasons behind procedures in math as adults. Then they’re angry that their teachers (supposedly) didn’t explain all these things to them. They’re certain that they would have liked math more and done better if only their teachers would have focused on understanding. So, their mission is to make sure that all kids are forced to explain their thinking at every step. Pure torture, really. Funny thing is, that the understanding piece is a lot more difficult for students. They generally don’t like it and it’s something that really comes with much experience and mathematical maturity. It won’t make students like math more if we spend more time on understanding…it will just confuse and frustrate them more. In my experience, I’ve found that students like step-by-step procedures and algorithms more than anything else.
Troll No. 2
Troll No. 3
Does what they do work? Can they even define what success means? I’ve seen no explanation. They don’t show how any sort of discovery for one problem translates into other areas. Discovery in basic fractions will help very little with factoring quadratics, let alone rational expressions. It also takes a lot of class time and few topics can be covered. What “deep” concepts helps students solve all of the variations of Distance/Rate/Time problems? Draw a picture? Think backwards? How about studying the governing equation, seeing how the variables relate, and doing a whole lot of individual homework problems of all sorts of variations?
In preparing for the AMC math competition, you don’t just study concepts or some general top-down process. You prepare by going to their web site and doing ALL of their past problems. There are tricks and understanding subtleties that will never be discovered with some general process. By working on all of these problems, you start at a much closer solution point when you encounter a new variations. This is how success for any highly-valued math test is created. You don’t have to have any conceptual knowledge if you can define the variables and equations. Just let the math give you the understanding.
The people pushing these new ideas need to show how a full curriculum based on their ideas works, not just some sort of small delta success for kids already damaged by fuzzy K-8 math curricula. They define their own version of success without regard to the needs of where these kids are going after high school. A local highly-regarded vo-tech school in our area requires the AccuPlacer test. Do the techniques of these reformers help those students do better on that test than a traditional process – done well?