tag:blogger.com,1999:blog-5324120177673194522.post7980355607262462124..comments2017-08-08T18:51:20.293-05:00Comments on Math Without Tears: Why memorize facts?Concerned Teacherhttp://www.blogger.com/profile/06758529063793725123noreply@blogger.comBlogger1125tag:blogger.com,1999:blog-5324120177673194522.post-69942365928623992552008-07-11T13:54:00.000-05:002008-07-11T13:54:00.000-05:00Memorization does not go away no matter how high u...Memorization does not go away no matter how high up in math you go. It is not the mark of a backwards program if a math course requires certain formulae to be memorized. Certain trig identities for example are better off committed to memory, even though math reformers would have you believe that if you really need to know something, you can look it up. <BR/><BR/>Well, OK. Let's look at a typical problem in calculus. A gutter is to be made of a strip of sheet iron 3a inches wide, the cross section being an isosceles trapezoid. Assuming the base of this trapezoid is "a" inches wide, find the width across the top giving maximum carrying capacity.<BR/><BR/>First of all, this isn't some contrived 'real world' problem; it is a pretty good problem that oomes up in various engineering design situations. Second of all, it requires that you know a lot of things. You have to know what an isosceles trapezoid is. You have to know how the carrying capacity (volume) is calculated; specifically that is a function of the area of the isosceles trapezoid. And you have to know how to compute the area of a trapezoid. <BR/><BR/>You then have to set up a function to represent the various knowns and unknowns. If you are doing it based on angle of the bend, then you need to know your trig functions. And when you do your computation of area, and then differentiate, you will have to know your differentiation formuale, and how to factor appropriately to get it into proper form for solving.<BR/><BR/>The higher order thinking step is setting up the equation of area as a function of angle of bend. All the rest is "merely" algorithmic. I put "merely" in quotes because if you have to take the time to look up what reforms consider to be a bother, you will spend far more time than this problem should take. If you know your stuff, you can solve this problem in 5 or 10 minutes.Barry Garelickhttps://www.blogger.com/profile/01281266848110087415noreply@blogger.com