On Jun 30, 2014, at 11:34 AM, Joe Niederberger <email@example.com> wrote:
> Performance is just that - time spent mastering quickly and easily performing operation that you now know adequately well.
This comes from discussions in another forum geared more towards cognitive science than the discussions here, but consider that repetitive lessons are actually necessary for appreciation in order to allow us to do the lessor things without thought so that our attention can focus on the bigger things. It isn?t to do things faster, but to do things without conscious thought because the number of things we can consciously devote our thoughts to (our working memory) is quite limited.
> If a problem halts you in your tracks and you have to search for some new understanding to proceed, I would consider as being toggled back into appreciation (recog) mode. When you've gotten your "mini-ah-ha!" and can proceed again, you are back into performance track. > > Performance is doing arithmetic fluently, taking tests, working at the board etc. Working the exercises when they don't make you stop and think too much. Drills to increase speed and accuracy. The dreaded "rote" tasks. > Near effortless understanding of situations described in arithmetical terms is "recall" as well, or in my translation, performance. You've already "got it", you are just using by now established capabilities.
None of this though happens on the first or second exposure, right? Even something as simple as the times tables takes many weeks and many later weeks for an elementary student to master. And by master I mean without thought, not speed. To learn to the point of automaticity. Speed training would occur after that and I see very few cases of lesson plans geared towards speed.
I guess what I am saying here is that *fluency* is not about doing things fast but doing things without conscious thought. The only relationship fluency has to speed in pedagogy is that we know how fast someone would do something if they are doing it without conscious thought. For example, the 5 minute drill in arithmetic is not to get the students to do the problems in 5 minutes, then 4 minutes, then 3 minutes etc. It is just a convenient amount of time such that if a student does 100 arithmetic problems in 5 minutes then they are doing those 100 problems without much conscious thought. It is a test of fluency, not speed.
I don?t think you can separate performance from appreciation. The mind is amazing in its ability to use such a small working register on such complicated data but this is only possible because of fluency. If it were not for the process of fluency your mind?s CPU would max out in just a few seconds of exposure to even the simplest scenario, and stay maxed out. You would halt. Appreciation isn?t just *getting it*, there is a lot more that has to take place in that mental engine we call our mind to move forward and appreciate deeper things.
I think, and I am only suggesting here, that if people thought a bit more about the vast amount of background processing their mind?s rely on when they think (appreciate) on new problems, they would understand better what pedagogical development involves. When I here people say *rote* or *procedure* I sometimes think that the science of pedagogy doesn?t even exist. Which is odd, because it seems like a pretty damn simple science with pretty damn simple test cases. It isn?t like we are trying to fathom things we cannot see nor feel here.
In any event, my definitions behind the 25% and 75% are obviously different. The 75% includes all of the tasks and activities devoted to the development of appreciation (your version) and the appreciation itself. In my theory of pedagogy there is no appreciation without performance and the goal of performance isn?t performance, it is fluency, because fluency is necessary for appreciation. The 25% (what I thought was meant by appreciation earlier) is all the tasks and activities that are NOT devoted to performance/fluency/appreciation. These are activities done out of order and/or without (strict) regard to pedagogical development. They are done for inspiration, they are done for setting the mood, they are done for fun, and they are done for human nature. If I were to start a section on series for example, I might ask the class (who are familiar with trig) How does the sin button on the calculator work? Is there a table of sines in the calculator? And then I would demonstrat! e a couple series that converge to the value of sin(x), maybe even one that converges fast and one slow. Some discussion about how this technique is only possible because of how fast the chip in the calculator is and previously it was done with tables or slide rules. And then when video games appeared and (extreme) speed over accuracy was the issue, back to tables we went. That would be 25% material. Of course, if we did this activity later in the class , in its proper pedagogical order, then it also becomes 75% material as well.
Ironically, my 75/25 rule came from studying Dy/Dan. Way back in the early days when I was first studying Dy/Dan?s philosophy and noting that he was (deliberately) avoiding math, a poster by the (screen) name of Joshua noted that Dan once told him that his blog represents only 25% of the material and that the other 75% of the material was traditional algebra and geometry. Naturally that intrigued me and I set off looking for Dan?s other 75%, and I found it, and it is still available?
It isn?t very good. It is actually pretty sad. I realized then that the 25% is not the issue. The 25% it is easy to do and there are tons of examples of the 25% on the internet and some of Dan?s stuff is actually good 25% material. The issue is the 75%. Many teachers have enormous difficulty with the 75%. You can tell by the way they refer to the 75% as the *procedures*. As Lou suggested, many of them don't even get the 75% themselves. It is no wonder then that when they have the urge to improve their classes they choose the 25%, the low hanging fruit. My focus is on the 75% and I think we have all of the pedagogical science needed to deal with the 75%, within the limits of student preference and free choice. It?s strange that I had to spend 6 years finding the science across a dozen forums, dozens of books and millions of tests. But I am happy that I found it nonetheless. I even understand now why I didn?t find it the first place I looked, where they teach teachers. Because! education today is not about the science of pedagogy. It is an economic/political/religious activity that teachers and the public engage in. It is business and marketing and politics and almost no science. They invent words like ?learners? not to advance the science of pedagogy or make that science more accessible to teachers and people. They invent those words as part of a marketing strategy to cloud the science and the simple truths and to sell more education.