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Glad to hear every month is like that in your class! For the record, the theme this year is Mathematics and Internet Security.
Oh the calculator debate. I firmly believe that there are basic math facts that everyone should know and this means without the use of a calculator. Multiplication facts would be one of them. Now in my little world, this basic fact list that should be known increases as one progresses through mathematics. For example, I don't expect anyone to know what sqrt(50) is to 2 decimal places, but I do expect one to know that it is a little more than 7. Not exactly a math fact, more of a number sense deal, but still I see it as calculator related for some.
Now I happened to be at OSU in the mid 80's, when graphing calculators hit the scene and OSU was ground zero for GC's thanks to OSU professors Frank Demana and Bert Waits. (I actually was at the right place at the right time!) What I found was that GC's were becoming a crutch just like scientific calculators can become a crutch for younger students. When a student looks at the equation 2x + 3y = 6 and can't state what the graph would look like without using their calculator, there is a problem. I expect my calculus students to know the general shape of quadratics, exponentials, natural log, sine, and cosine, to name a few, without the aid of a calculator.
Now I use the GC and require my students to have one for class. It is a tremendous tool, just like any other tool, to help in doing mathematics, but it is only a tool. It is far inferior to our gray matter! In my calc class on Friday, we started parametric equations. Hell yes we graphed them using the GC; it is quicker and more efficient and it allowed my students to get at the concept. To me, utilizing technology should be an aid to help understanding the concept at hand. On Monday and Tuesday, we begin polar equations and calculus of polar equations. This topic actually is a perfect marriage of brain power and technology. To determine an area enclosed by a polar graph, the difficult part is determining the limits of integration. Since polar equations are of the form r = f (theta), using the derivative (that almost no calculus book discusses which pisses me off), dr/d(theta), which gives the rate of change of distance from the pole with respect to theta, one can use this derivative to find relative extrema, which in turn can be used as theta (min) and theta (max) on the GC and "seeing" if these bounds for theta produce that region whose area is trying to be determined, hence the limits of integration. The power of calculus (from our brain) to figure bounds, testing on the GC to see if the correct region is graphed, then setting up the correct integral and evaluating,.......a perfect marriage of technology, brain power, and concept.
I seemed to have rambled a bit there Thump, but I have strong opinions about calculator usage. I don't deny it, I embrace it even, but I REFUSE to let it become a crutch for my students.
Now the texts I have written are actually GC optional. Again, a strong opinion of mine, but a text should not dictate to a professot when and where to use a GC; that is up to the professor and said professor's academic freedom. We are finding that there are more professors today that like GC optional texts than there were as recently as 5 years ago.
So at the level I teach, it seems that the great calculator wars of the late 80's through the 90's has cooled down. It seems that they are still going on in elementary and secondary school. Your students will be much better off Thump that you actually "make" them learn some basic facts and I hope as they go through school, they continue to have teachers who make them know other basic facts (like basic shapes of basic functions). These students are much better prepared for calculus!
A final bitch, what really grates me like sandpaper underwear, is people who "teach" trig and let students use cheat sheets for trig values, identities, etc. These "teachers" are so screwing their students for calculus!
A final bitch, what really grates me like sandpaper underwear, is people who "teach" trig and let students use cheat sheets for trig values, identities,
Our school has a class set of them.Buckeyeprof- You're a good man.
Graphing calculators should not be needed till a 200 math level (OSU standards)
Kids use them to do the most basic of things. You need to know how to do these things without outside assistance.
Don't really know what to make of this.A final bitch, what really grates me like sandpaper underwear, is people who "teach" trig and let students use cheat sheets for trig values, identities,
Our school has a class set of them.
We used them a little, in 9th grade. It was to graph some points and stuff, mostly the teacher showing us how to use them. But that was after we learned to do it, how should I say(?), manual way.
Again I realize this was Algebra 1 material. But it was a like once every month thing that we used them. Not like we pulled them out every day.
We learned some trig in Geometry this year, assuming it was going to be on the OGT. Never was.
We used to calculators when we had to find the sin, cos, and tan of the number.
My understanding of it was slim. I had some troubles with it, but started to get a grasp of it. Which may be why I don't understand really what aspect of the way trig is taught, that you are complaining about.