process, yes. have it your way, no.

To my latest, Myrtle Hocklemeier said:

Since the mathies in my life have always said that math is "justification, justification, justification" rather than simply the answer, I always thought that THAT sounded remarkably like fuzzy math.

But there is a difference and maybe in some future post you can expand on that.

Yes, there are several differences. But first, let me tackle an issue that grates on me. There are a number of concepts/methodologies/terms that have been hijacked by the educrats, and as a result, reasonable people react negatively to them. Portfolios. Rubrics. And yes, process.

Here's the first difference: The educrats say process is more important than the solution. I do not. The second difference is that educrats are speaking of what I call Burger King math (Have it your way!), where any old way students can think up to arrive at a solution is equally great. I, on the other hand, am speaking of a process that has been taught since Aristotle -- or has been until recently -- a process that is designed to teach us to think clearly, linearly, sequentially, and logically.

I understand Ricky's frustration with formalism. I was the same way. I lost points on math assignments because I was good at math, and I skipped steps (when I was in school, you lost points for that). So let's say I was supposed to solve (3x - 1) / 4 = 5. Here's what I was supposed to turn in:

(3x - 1) / 4 = 5
3x - 1 = 5 * 4
3x - 1 = 20
3x = 20 + 1
3x = 21
x = 21 / 3
x = 7

Instead, I would do something like this:

(3x - 1) / 4 = 5
3x = 21
x = 7

It's the right answer, of course, but I didn't get full credit, and I shouldn't have (though at the time, I thought I should have). This was in the space race/New Math era, so the focus was not only on the correct solution, but getting us to understand what we were doing. But as a student, the only justification I could think of for this anal retentive insistence on showing every tiny step was to make sure you hadn't copied your answer from somebody else.

Being on the other side of the desk changed my perspective.

Cheating control is a small part of it, yes. Another part of it is learning to follow instructions (something I have come to appreciate as one of the most important lessons we should learn in education -- because so few of my students can follow simple directions). But mostly, it is about learning to think.

If one of my students hands in an assignment with just the correct answer and no work, he gets no credit (for the first two reasons above). If one of my students hands in an assignment with the correct process (work), but the wrong answer, he gets partial credit -- because by showing the work, he has shown that he has learned something, even if the answer is incorrect (no, not lots of partial credit, but partial credit nonetheless), and because learning the process is a big part of our educational mission.

Note that I'm not saying process is everything, or that the correct solution isn't important. Note that I'm not saying estimation, but solution. And note that I'm saying the process, and not just process.

There is a right way to approach a problem -- sometimes more than one right way, particularly as you get more advanced -- and then there are wrong ways to approach a problem, ways that might in some instances get you the right solution, but will in many other instances lead you to the wrong solution -- or worse, an "estimation" instead of a solution. The other problem with wrong ways to solve a problem is that they do not discipline the mind in that admittedly boring, sequential, logical thought process that has applications to ever aspect of our lives, and not just mathematics.

That's my biggest objection to Burger King math -- and I have many.

I realize this is a conservative point of view, but there is a reason something has been done since Aristotle, and tossing something out merely because it is traditional is madness.