More on How to Decide What People in a Culture Should Know

[lhynard]

Last week was crazy busy. I had started posting this, but it included another poll on your opinions that got far too long.

My last public entry did not really trigger much debate on this actual question. I think the science poll distracted everyone (except for jeltzzRather than trying to poll you on each and every possible topic one could teach to those

Comments

[themadcow]

Math: Is calculus compulsory now? I graduated from high school 11 years ago and subsequently attended a state university. I took calc in high school as well as college but only because I chose to in the former case and my degree required advanced mathematical skills in the latter. I'm with you here, though, for the most part. I do, however, think that educated people should understand how calculus works even if they do not understand how to work calculus (if that makes sense). Many scientific principles--especially in the physical sciences--require at least a rudimentary understanding of calculus to completely grasp. I don't believe that all students should have to be able to derive and integrate complex functions, but they should understand what derivation and integration mean in a practical sense.

Languages: Ditto.

History: I agree with you about chronologies. It is useless to remember what general fought such-and-such a battle and what day the battle was fought and what the casualties were on each side. All one needs to know is time frame and significance. I'm sure there are some situations where details are important and I give those caveat status. The best history professors I ever had held this same philosophy. As far as "importance" goes, I think a general knowledge of events significant to the context of the student's situation should be taught.

Science: My girlfriend teaches Earth Science on the 6th grade level and I agree with her philosophy of teaching an overall understanding without getting bogged down in irrelevant details. In chemistry, for example, it is useful to have an understanding of atoms and elements and how they are made up and how they form into molecules--but not to the degree of determining what energy levels the electrons are on. A chem major needs that, not your average student. The same can be applied to most scientific knowledge and I completely agree with your premise of teaching method over minutia.

Art and music: Fine. In moderation. But maybe I'm just too left-brained.

[lhynard]

Is calculus compulsory now?

No. I took it in high school, but it's not required. I'm just being hypothetical, in general, about what should and shouldn't be.

You make good points about people understanding "how", but I'm not sure if that's practically possible. Maybe it is; I'm not sure.

If you were to tray an explain derivatives to someone as an overview, how would you personally do it?

[themadcow]

The best way I know to explain derivatives in a practical sense is to show how we calculate area under a curve (be it a real-world curve or a mathematical one). We could show how we can approximate the curved area with a number of rectangles with a given width. Obviously, the more rectangles we use--and thus the shorter their widths--the closer to the actual value we get. Therefore, if we could somehow use an incredibly high number of rectangles (such that their width approaches zero) we could get a highly accurate idea of the area under that curve.

One might also be able to use real-world examples of Newton's Laws, but I haven't given much thought to that.