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Topic: Assorted Grants Available
Replies: 19   Last Post: Jan 12, 2014 3:05 AM

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Robert Hansen

Posts: 11,345
From: Florida
Registered: 6/22/09
Re: Assorted Grants Available
Posted: Jan 12, 2014 3:05 AM
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On Jan 10, 2014, at 6:55 AM, Richard Strausz <> wrote:

> Also, what would your ideal book do to make use of technology for demonstrations and student use?

As far as using technology operationally, to do presentations and demonstrations, I have no qualms. The teacher has to figure out what works for them what is available to them. I would use a computer, iPad, projector and white board. I?m not thrilled with smart boards. I would use various presentations and resources in class. That is my setup here at home and I use it all the time with my son. Some topics are more prone to presentations than others. You need to know when and not when. Would I use a Dan video? Something similar, but with more math and formal development involved. And a little more exciting. Like a real car trying to beat a real train.:) Or a car jumping a row of buses (parabolas).

I guess digital versions of the textbooks count as operational as well. I don?t necessarily like them but its going that way anyways.

The rest of my post has to do with student use.

In mathematics pedagogy we are primarily interested in cognitive and functional development. Thinking and doing. Technology affects the later of those two goals, the doing. Technology removes the chore of doing. That is the point of technology?s point. The problem is that much of cognitive development is tied up in the chore of doing and when technology removes the chore of doing it interferes with cognitive development. An example from the past was using calculators in grade school to replace the chore of arithmetic. But the chore of arithmetic accounts for most of the cognitive development in young students. In fact, in young students cognitive development and functional development are mostly the same thing. What the student knows is basically what the student does. When they get older and their cognitive skills become more mature, that situation changes. But the chore of doing continues to play a critical role in cognitive development. Even in advanced mathematics (gradu!
ate level) the student must do the work to get a good imprint. The best strategy in such classes is to do every problem in the book.

The rule is simply that you not do anything that interferes with cognitive development.

Technology interferes with cognitive development when it removes the chore of doing and that chore had a role in cognitive development.

This all depends on the age of the student and the level of the material. We don?t remove the chore of arithmetic in a class in arithmetic but we can remove the chore of arithmetic in a class in calculus. The chore of arithmetic is no longer playing a role in cognitive development in a class on calculus.

It is actually a pretty simple rule. The reason it gets broken usually one of the following -

1. Teachers don?t respect the role that the chore of doing has in cognitive development.
2. Teachers get confused or forget that a particular task had a greater pedagogical purpose than just doing the task.
3. Teachers are so awe struck with technology that they think it can do things that it can?t.

While we have seen many examples of (1) and (2), I think the most common is (3). All of us are awe struck with software like Mathematica on our first exposure. It is only natural that we think ?this changes everything?. That is, until you actually use Mathematica to do mathematical work, and find out it changes very little. You soon realize that it just a another tool like any other tool. I know exactly what 99.9% of all the copies of Mathematica ever sold are doing right now. Nothing. They are on a computer sitting next to a stapler, that is also doing nothing. They are just tools.

My guidelines -

1. Do not interfere with or skip cognitive development.
2. When you use technology, it can only be used as a tool.
3. The student must be cognitively ready for the tool.
4. Make a big deal about it.

I have already explained (1) and (2). (3) is basically a combination of (1) and (2). It means that you can?t use fancy use cases like numerical methods when the student hasn?t developed far enough yet to appreciate them. And finally, you should make a big deal about it when you turn them onto technology. It is a big achievement for them.

That?s it.

What that means in my algebra 1 class is -

1. Calculators are in big time (actually, a year ago probably).
2. Graphing, maybe, something like geogebra.

The problem with graphing is that you have to spend a lot of time doing it manually first. There is so much involved in the activity, like signage, quadrants, slope and interpolation. Personal familiarity with these things is so crucial. What have you observed? How fast do the students generally get good at those things?

I can?t think of anything else. There is so much to do in algebra 1. Spreadsheets I think would be more of a distraction than a benefit at this point, but I would certainly use them in front of the class for tables and exploring expressions numerically. If I felt we could fit them in then I might add them the second half.

Bob Hansen

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