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Homework Help: What should HS Students Know?

  1. Nov 28, 2006 #1
    As a high school math teacher, I would like to know if there are certain "everyday" facts that you think students should memorize while in high school? For example, should students be required to know the distance of a mile? The size of the smallest state - Rhode Island? How many pints are in a gallon? etc....

    If you feel that there are facts that students should know, be sure to include them (along with the appropriate numbers) in your reply.

    By knowing certain facts, will these students have a better understanding and feel a better connection with objects seen outside of the classroom?
  2. jcsd
  3. Nov 28, 2006 #2
    I do not think it is essential that students 'memorize' quantities of measurement. That's why there are tables. I think dimensional analysis is a more important skill.
    Last edited: Nov 28, 2006
  4. Nov 28, 2006 #3
    my 2 cents -- We went through the 1st 10 chapters of a college calc textbook my senior year of HS -- and it was VERY helpful in college. It also helped that we were able to access all of the answers to our homework in the class at any time (mostly). Most of the questions assigned our HS teacher had already worked out and had them in a notebook we could use anytime (as long as he was there). Through practice, the methods of solving problems became much easier.

    When I taught labs in college, I found students (who somehow qualified for calculus in college) that still couldn't follow simple algebra (such as manipulating equations). Practice, practice, practice.
  5. Nov 28, 2006 #4


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    Well, I would like to say that it is, indeed, advantageous for a student to have a rough understanding of how units of measurements relate together.
    (Like "how much" a gallon represents).

    However, I wouldn't say that maths should be the sole subject in which such an understanding is developed.
    Maths classes ought to focus on developing maths SKILLS, like the ability to convert from one unit of measurement to another.
  6. Nov 28, 2006 #5
    show them how to take derivates and integrate. i wish i had learned this before taking Calc.
  7. Nov 28, 2006 #6
    I had a physiology teacher that told us after the first test that when you get an answer for a diffusion coefficient that is something like 5000 cm^2/s, your BS detector should go off and you should redo the problem. So, I would agree that an elementary understanding of how basic quantities relate to each other is a skill every scientist/engineer should have.

    I have also come across situations in solving real-world engineering problems where one potential solution looks more promising than another, based solely on comparing ballpark figures. This saves a lot of time, and really lets the people around you know that you're not just a number cruncher, but that you understand how all of this relates to the real world.
  8. Nov 28, 2006 #7


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    Wnen I went to Cambridge Univ. (UK) back in the 1970s, they had an entrance exam for maths/physics which REQUIRED that you knew, or could estimate, the physical constants you needed to answer the questions. Something like "attempt 10 out of 50 questions" in 2 hours I think. No reference materials allowed. Typical sample questions were (1) Estimate the power of a traditional windmill. (2) A herd of elephants which was previously at rest stampedes along the equator travelling East. Estimate the effect on the earth's rotational speed. (3) A small pendulum clock keeps accurate time when it is at ground level in London. Estimate the change in accuracy if it is taken to the top of the dome of St Paul's Cathedral.

    Of course you didn't have to know EXACT values for every quantity you needed, but you were penalized for making seriously wrong estimates.

    You also needed to choose your own method - there was no "right way" to solve them. E.g. with the windmill question, you could work on the fluid mechanics, or else estimate the power to turn a millstone against friction.

    I think it's valuable to teach that you need to "actively" pick up and remember ball-park estimates of the important numbers in whatever field you are working in, so (as BNoelCMU said) you can look at the results from computer simulations or experiments and say "oops, that can't possibly be right" if need be. And in my experience in the Aerospace industry, the proper place to file the results of at least 90% of computer simulations and experiementals was in the trash can - so having a good mental BS filter is VERY useful :-)
  9. Nov 28, 2006 #8
    Ummm... Since that is pretty much the bulk of material taught in calculus, learning it before would be redundant.
  10. Nov 28, 2006 #9
    I would say that memorizing things like mile to km conversion factors and stuff is useless, knowing that a mile is around 1.5km is good enough and if a student needs exact numbers they can find it out fairly easily since most homes have access to the internet nowadays. Students should have a FEEL for quanities, but I think that memorizing exact values is not neccesary.

    Also, every student should know how to carry units in calculations! If there is one thing that I would say is "everyday" (in the academic sense anyway) it would be the ability to calculate with units in your equations. Also as someone said, dimensional analysis is nice. :)
    Last edited: Nov 28, 2006
  11. Nov 28, 2006 #10
    Bring in like a jug of water, ask them to estimate how much water is in the jug. Then poor all the water out into a measuring glass. Visuals are the best. The students can actually see how close their guess' are.
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