On Jan 10, 2014, at 6:55 AM, Richard Strausz <Richard.Strausz@farmington.k12.mi.us> wrote:
> Also, what would your ideal book do to make use of technology for demonstrations and student use? > > Richard
Funny you asked this. On another (physics) thread the current discussion was about the applicability of log paper today. As you probably already know, log paper is graph paper but with one or both axis using a logarithmic scale instead of the conventional linear scale. There are many use cases that benefit from plotting things on a logarithmic scale, namely when the data is exponential in nature. One of the benefits is that exponential data becomes linear when plotted this way. The discussion was more or less about whether log paper is even needed in classrooms today, with the advent of spreadsheets and all. A parallel to the slide rule and its disappearance was made as well. The following was my reply to a point posed by one of the participants -
> Do students learn something in the process? Probably, but they'd learn similar things and a lot more using a slide rule and my guess is that few of us would deem that exercise worthwhile.
My reply -
There has to be a way to preserve the cognitive benefits of interesting use cases that our generation took for granted. I have no problem with replacing old use cases with new use cases, but they need to retain the pedagogical and cognitive effects. Technological advances run counter to that notion. And for good reason. Technology strives to make the ?task? simpler. But in cognitive pedagogy, the ?task? is usually not the point. The point of cognitive pedagogy is to make the student think better and to enhance their ability to unravel mystery. This almost always means to become more familiar with the underlying principles of the task, not the task itself. Aka, formal thinking.
Our precious takeaway from using slide rules and log paper wasn?t how to apply them to the tasks they applied to. It was how the damned things worked and as incredible as this might sound, those tools worked on the very same principles we were learning. This free and direct benefit does not exist with modern technology. The principles and theory behind calculators and spreadsheets is too advanced, too complex, and worse of all, not even relevant to the principles we are learning, unless of course, it is a class in computer science.
This discussion, others like it, and the misconceptions that abound with technology?s role in pedagogy, have inspired me to do a deeper dive into this problem. Essentially, when is a spreadsheet in a classroom as cognitively useful and pertinent as was a slide rule, or log paper, or many other use cases that have been displaced by modern technology.
A thought experiment that I have found useful in my analysis is quite simple. After I observe a class activity and what is expected of the students during and at the conclusion of the activity, I then imagine what that same activity would look like with 5th graders. If the 5th graders would achieve the same expected results as the much older students then the activity and its expected results are cognitively and pedagogically lacking. 3rd graders can use slide rules, but they cannot understand how or why they work. Thus, an activity involving slide rules designed only to require the use of slide rules is appropriate for 3rd graders, but not for 9th graders.
Modern technology changes things considerably. It isn?t possible for a 9th grader, or even a college student, or even a professional to understand how a spreadsheet works. And even if they did understand, that understanding is not relevant to the principles we are focused on. Which in this case is a more thorough and deeper understanding of the logarithmic function and its nuances, which underlies a lot of phenomena. Another interesting function, with its own nuances, that also underlies a lot of phenomena, is the sine function.
So the trick is to create spreadsheet activities that continue to reinforce the understanding of the logarithmic function and its nuances. An understanding which was easily and directly observable in older technologies like log paper and slide rules.
This isn?t an impossible task. It's just often confusing to many teachers. They confuse ?the task" with the pedagogical and cognitive goals. When new technologies emerge that do ?the task? better they forget that this wasn?t the pedagogical goal. Slide rules and log paper do both. They were designed on the very principles that you are trying to teach. It?s their nature. When you replace them with spreadsheets, then it is now up to you to replace what you lost with the older technology. You must design the activities such that they exhibit those same principles and challenge the students to understand them. Something that the older technologies did just siting on a table.