Why do HS geometry teachers hate protractors, etc., that give easy and CORRECT answers? see text?

Question

Mathhater/phobe, so pls be patient and use itty bitty words in the explanation, at abt a 2nd grade level if you can.

WHY on earth did my HS teachers (years ago) have such a fixation on doing things the hard way? IIRC, they were insistent that we bisect angles with JUST a straightedge and compass (goodness knows why!). Or see if triangles were identical or congruent or whatever the heck it was with some weird angle-side-angle or angle-angle-angle arguments (every triangle I EVER saw had 3 angles and 3 sides; what the ^%^#$*# were they talking about, anyway?).

It's been years, and I'm **still** wondering. What's the practical reason for doing things in such a bass-ackwards, round-about way, instead of just grabbing a protractor or other doodad and just MEASURING the darned thing?

I'm being utterly serious here. If it's **that** important to bisect or trisect an angle, why not use reasonably accurate ("within tolerances") and readily available tools to do it?

Help!

Where were you guys, when I needed y'all years ago in school???? (OK, casualty of the New Math in the 1970s here.) Explanations? relevance?--what're those? It was just "DO these problems and pass the class---because you need at least 2 Carnegie math units to get into college".

UURRRRGHHHH!

Think we lost a generation of people to innumeracy that way....

Waiting a little more for additional answers, but I'm loving what's come in so far----thanks!

Answer 1

I'm not a HS geometry teacher, but I have taught math (calculus and similar courses, at the university level). In my calculus courses, students would frequently use graphing calculators to work out problems, instead of the analytical techniques covered in class, which is analogous to using a protractor to bisect angles instead of a straightedge and compass.

Based on my experience, if students were always permitted to solve these problems "the easy way", then they would learn very little except how to use those tools. If this were the case until they completed the typical requirements of taking at least some calculus course in college, then they would be woefully unprepared for any further experience in mathematics, and those who did not pursue math any further would have wasted their time and lost any potential benefit those classes may have provided.

What math courses can do, for those who do not plan to pursue further study in math, is help them learn to use their wits more effectively, for whatever it is they'll be doing. There are so many jobs out there that require paying attention to every little detail, employing abstract reasoning, constructing valid arguments (or spotting invalid ones!), the list goes on and on. Of the subjects that are taught in HS, none prepare you better for acquiring those skills than math.

That means having a deeper knowledge about the problems you face besides what it takes to employ some device to do the job for you. You never know when you're going to face a problem that may be similar, but just different enough so that you can't do that. However, if you have a thorough understanding of the problem, you can fall back on that and find a way to proceed. There are many cases in which I am unable to use all of the formulas I learned in calculus, so if all I had done was plugged-and-chugged with a graphing calculator, I wouldn't be able to do my job.

I'm not suggesting that everything your geometry teacher did was completely justified; I strongly feel that many math teachers do not do enough to help students understand and appreciate the importance of "the hard way", leaving them to feel as you do now. But it's not done just to make life more difficult for the students. It's done to make life easier for them down the road than it would have been otherwise, by forcing them to learn to use their wits in new ways. All the brainpower we have doesn't do us any good if we're not prepared to use it.

Answer 2

Because they are teaching you geometry with the thought that you will procede into higher mathematics. You are correct that if you are given a triangle and need to measure it the simplest way is to grab a protractor or ruler and measure. However, once you move into the higher maths or into engineering there are many cases where the triangle you are trying to measure is not a set of lines on a paper - it might be the bracket on the wall or the brace inside a buildings structural system. In that case, it is important to have an understanding of the relationship between the sides of the triangle and the various angles, because actually measuring it may be out of the question.

Further, using the various formulas is a way to get you used to the idea of algebra (or practicing it if you've already been exposed to it). It's also something that gets students really thinking about how to solve a problem instead of just following an order of steps. Which is why geometry and/or algebra are the classes where people truly decide to pursue math or not. Before this class, you can really fake your way through math without really understanding the concepts.

Your HS teachers should have told you this, and explained what they were doing. Instead, they try to just teach you rules and spend no time on making any of it relatable or interesting.

Good luck!

Answer 3

It is a great shame that teachers just teach what is in the curriculum without explaining why they are teaching it and giving real examples of how you might use it.

I can give you an example of where all these various "tricks" in geometry are useful. I do some wood working at home for fun (it also useful around the home). I use power tools such as table saws and routers because I am lazy. I do not buy the most expensive tools because I cannot justify the expense. The tools that I buy have calibrations for length and angles. These calibrations are rather crude and cannot always be relied upon to be repeatable (because the tools are cheap). I can set up the tools ( for example a table saw ) to make cuts at 90degrees to the table. If I want to cut at other angles or adjust the depth of cut, I need to make myself one or more jigs so that I can accurately repeat the cuts. To do this I need to be able to use basic geometry such as bisecting angles and so on. I have spent money on accurate linear measurement and a good right angle, and, using these I can construct any angle or shape that I require.

What I do, I do at reasonable cost. I am an engineer, and my definition of an engineer is "someone who can do for $5 what any fool can do for $50".

Answer 4

There are a couple of reasons. One is that math instruction in general is not intended to provide specific facts you need later in life; it is intended to teach you how to think and solve problems in many ways. Suppose for example that you need to lay out a perfect rectangular tennis court. Your dinky little protractor will give you a tiny right angle. But what if it's bent, off by even 0.1 degree? By the time you get 100 feet away you'll be way off. So you would use a construction with long pieces of wire or rope to represent the compass. Believe me, you'd never even be able to line up the bases in a softball field with just a protractor.

Answer 5

In math ans science, we humans are VERRRRY bad at measuring things because sometimes what we have to measure, things that we can barely see with out own eyes. So they are training you early on to learn to find quantities without the use of protractors that will 100% give you an wrong answer.

What I mean by that is that even if you answered correctly in estimation (sure, it's 10 degrees), you will never be able to identify if it is, 10.000000... degrees, or 10.00005 degrees. In some fields, this difference is all the difference in the world.

But yeah, that's why they wanted you to become we equipped with the math instead of the protractor.

Answer 6

Here is some clarification.

Giving yourself many different ways of interpreting and understanding the same thing broadens the way you can look at things and solve problems. I understand your frustration, I was in the same boat when learning those things at first, but when I started doing independant studies of things such as magnetohydrodynamics and graphic design and natural movement, there could be one concept that is involved in each of them if thought of in a slightly different way.

So in short, if you can understand something simple in so many ways that it becomes complex, then that is where knowledge begins. Once we think we totally understand something, it becomes boring and childish. There is much more to a simple angle than most people realize.

Answer 7

Well, alot of jobs don't have the benefit of doing it the "easy way". For example, Air traffic controllers do alot of equations in thier heads and don't have time to sit and write something out and/or grap a protractor and try to use it. Doing things the long way makes it so you understand the equation when you do it the short way. It's like when you first learn how to talk. Your parents can't talk for you. They'll sit there and shout words and you'll mimic what they say, but until you understand the words, all you are doing is spitting out words that don't make sense.

Answer 8

What a laugh! You're still in grade 9, so why throw them away, when you'll need them for class on Monday. Oh sorry, Tuesday, because you skipped on Monday to post this brilliant and thought provoking query on Y/A. Along with many others, I'm sure. Keep studying. Maybe you can graduate by the turn of the NEXT century.

Answer 9

Ok so you use tools, but how were those tools developed ? How were they made ? What were the principles behind them ?

If we take things for granted and use things without understanding them we will be not better in anyway than cavemen.

"THAT IS BACKWARD"

Answer 10

Just in case your in a situation you might have to use your brain to figure when the instrument you were using broke, maybe they thought you didn't want to appear stupid. Or may be they wanted to touch er us.