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Old 06-11-2019, 08:15 AM
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How many years of high school math do students need?


Back when I was in high school in the 80's in Missouri we only had to take 1 credit in math. Now my son takes 3 - algebra 1, algebra 2, and one other like trigonometry or geometry.

Granted in many fields like engineering you need these so you can go onto subjects like calculus then differential equations and so forth.

Do we need 3 years of high school math for a general student?

I propose we need math but it should be practical math such as accounting and understanding of business and finance such as how to analyze a loan and how compounded interest works. Why? Because no matter what field you go into you will need those skills.

What do you all think?

Questions:

1. How many years of HS math were you required to have?

2. How many years of HS math do you think we should require?

3. Would you prefer HS students take more practical math courses like financial math over math with more scientific applications like geometry?
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Old 06-11-2019, 08:31 AM
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1. If I'm remembering the system correctly, you got a half credit per semester of class, and we needed 3 math credits.

2. For most students, that seems like enough. If my high school was indicative, it's a struggle for a lot of students to pass three years of math (sad, I know).

3. I agree that practical, direct-real-life-application courses should be offered, if not mandatory. (But I do consider geometry to be "practical math")
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Old 06-11-2019, 08:56 AM
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I teach math in an Adult Ed program for our local community college. Basically, I teach GED prep courses for adults who had dropped out of high school at some point and now want to get their HSE.

Here’s my take on it. The U.S. education system is designed so that everyone leaving high school should, theoretically, be ready for either the workforce or college. However, most of the math that high school students have to learn have no “real-world” applications to speak of. Many can factor a polynomial or balance an equation—basic pre-algebra stuff—but don’t know the first thing about balancing their checkbook. They have no idea what FICA withholding is, how insurance premiums and deductibles work, or how to calculate intertest of any type—from basic compound interest to the actual money going out of pocket on a home or car loan with x% interest.

Now math, clearly, isn’t pointless. It not only teaches students actual math but it also hones critical thinking skills and helps them practice thinking “outside the box” a bit, as well as how to tackle problems systematically.

Having said that… yes, I think most high school students have too much math on their plate. Or perhaps I should say, they have the wrong kind of math. Making high school students take something like trig is pointless unless that student plans on going into a math-intensive field like engineering or chemistry. Hell, I took trig in college, I teach math, and have never used trig once since the day I took my trig final in 2013. Is it useful? Of course. Should it be mandatory? Never.

My students have to learn polynomials, functions, logarithms, linear and quadradic equations… there’s quite a list. But most (all, probably, unless we specifically teach it in class) don’t know how to balance their checkbook.

So I think high school math curriculums need to be completely axed and re-created from scratch using real-world math concepts and teaching students what they need to know to actually function in society. If they need calculus or trigonometry for their career, they can learn it in college. Take out that mandatory pre-calc class and add in a "how to compute and file your taxes" class. The 2014 revision to the GED test took a couple steps in that direction, but did not go nearly far enough IMO.
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Old 06-11-2019, 09:02 AM
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My answer is 'all of them'. The more math kids have, especially prob and stat, the more they'll be able to cope with the things they're presented with as adults.

It's easy to say, "What application does algebra or calc have" and blow it off. But the truth is what they teach are ways to approach problems and deal with them. Without that we have more people who will be confronted with problems they're not trained to deal with.

But I'm partisan. I finished all of my school's math curriculum by mid-sophomore year - it was a private school but not a great one - and they had to order special coursework for me. It's served me well.
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Old 06-11-2019, 09:16 AM
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Originally Posted by Urbanredneck View Post
1. How many years of HS math were you required to have?

2. How many years of HS math do you think we should require?

3. Would you prefer HS students take more practical math courses like financial math over math with more scientific applications like geometry?
1. 4, since I was in the Applied Sciences track. If I'd chosen Accounting as one of my optionals that would have been 2 years of financial math (it wasn't only plain book-keeping, but stuff such as running the calculations behind different types of financial products); I chose Draftsmanship.

2. Well, that depends on the track: trades vs humanities vs life sciences vs physical/applied sciences vs art vs...

3. Again it depends on the track. People aiming for careers in the sciences often could use a better understanding of statistics, which tradespeople don't particularly care about; people aiming for PoliSci or Economics… well, it's not so much that they could use a better understanding of stats as that the rest of us would benefit from them understanding stats better.


We didn't have checkbooks, but basic financial math was 5th grade. Compound interest, yay! Multiple fees, hooray! It's come handy many times; for example, when I proved to our company's well-meaning HR manager that the 401(k) being offered were shit: the fees were so high that they ate up amounts equivalent to several years' worth of interest.
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Old 06-11-2019, 10:26 AM
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My answer is 'all of them'. The more math kids have, especially prob and stat, the more they'll be able to cope with the things they're presented with as adults.

It's easy to say, "What application does algebra or calc have" and blow it off. But the truth is what they teach are ways to approach problems and deal with them.
Algebra and calc teach ways to approach problems and deal with them, _if you understand them_. But a lot of kids get on the "math is a class where you try your best to learn absurd patterns of incomprehensible actions"-track before or while they're in Algebra.

Maybe forcing all students through these classes at this tempo is the best way to ensure as large a number of them learn these things as possible, but I doubt it. I think offering more options to catch up later on when some actual application motivates the students to understand the math would be a much better use of resources. Make the students who struggle do extensive household math and math literacy (reading math problems for understanding) instead, and learn the basic understanding of algebra and statistics that way.
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Old 06-11-2019, 10:27 AM
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What do you all think?

Questions:

1. How many years of HS math were you required to have?

2. How many years of HS math do you think we should require?

3. Would you prefer HS students take more practical math courses like financial math over math with more scientific applications like geometry?
1. 4 I think?
2. 3 Probably.
3. Yes.

Quote:
Originally Posted by Lancia View Post
Many can factor a polynomial or balance an equation—basic pre-algebra stuff—but don’t know the first thing about balancing their checkbook.
I always chuckle a little when people bring up balancing a checkbook as a life skill that should be taught in HS. I imagine all these HS and early twenties pulling out their checkbooks at the grocery checkout, putting on their reading glasses, and saying to the cashier in a shaky voice "Now, how much is the total again honey?"
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Old 06-11-2019, 10:29 AM
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Students should be studying some kind of math, natural science, history/social studies, communications arts, and creative expression every year.
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Old 06-11-2019, 10:39 AM
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Northern California, graduated in 1987:

1. How many years of HS math were you required to have?

3 yrs for those on the college prep track; 2 yrs for those on the general track; I took 4

Kiddo, graduated in 2016, was required to take 4 years of higher math. He took pre-algebra, algebra 1 and algebra 2 in middle school; then geometry, trig, calcuclus and something else, maybe more calculus?

2. How many years of HS math do you think we should require?

Probably should take at least basic algebra and geometry; obviously should take what their desired college requires if they are college bound

3. Would you prefer HS students take more practical math courses like financial math over math with more scientific applications like geometry?

In general, I would like to see more life skills taught including practical math; but I also think basic algebra and geometry have a lot of practical applications.

Last edited by Rhiannon8404; 06-11-2019 at 10:40 AM.
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Old 06-11-2019, 10:42 AM
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I always urged my son and daughter to take as much math and science as they could, and I was able to demonstrate why I thought that was a good idea.

When I was cutting down a tall tree, I'd ask them how they would go about estimating the height of the tree to determine whether it would, say, hit the house. This would lead to a discussion of right triangles, trigonometry, etc. During a drive, I'd tell them my gas tank held 14 gallons, my gauge told me I had 1/4 tank, I averaged 20 mpg, so how far before we run out of gas? When we stopped for a meal, I'd tell them our check was $40 and I want to leave a 20% tip, how much do I leave?

For whatever reason, they played along with my silliness.

ETA: My daughter is now a nurse, and uses math all the time. My son is a prison corrections officer and jokingly gives me examples of using math at work.

Last edited by kayaker; 06-11-2019 at 10:44 AM.
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Old 06-11-2019, 11:21 AM
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ETA: My daughter is now a nurse, and uses math all the time. My son is a prison corrections officer and jokingly gives me examples of using math at work.
If you have an infinite number of cells, and all of them are occupied, but one day an infinite number of new prisoners arrive, what do you do?
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Old 06-11-2019, 11:39 AM
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Many can factor a polynomial or balance an equation—basic pre-algebra stuff—but don’t know the first thing about balancing their checkbook. They have no idea what FICA withholding is, how insurance premiums and deductibles work, or how to calculate intertest of any type—from basic compound interest to the actual money going out of pocket on a home or car loan with x% interest.
This stuff should definitely be taught to HS students, and perhaps could even replace some math, but I'm not sure it should be called a "math class". It should perhaps be called something like "practical finance", and it should strike a balance between understanding the principles of concepts like percentage, interest, deductible, etc., and just following procedures to calculate them.

Quote:
Originally Posted by Lancia
Take out that mandatory pre-calc class and add in a "how to compute and file your taxes" class.
IMO this is a terrible idea, at least as stated. Teaching kids how to collect very specific numbers to fill out a very specific form is just going to leave them bewildered when the tax forms change.

If we replace a higher math class like pre-calculus with something like the "practical finance" course I mentioned, it should be geared not to filling out specific forms, but to the general ideas of things like percentages, progressive tax rates for different tax brackets, using numerical tables, deductions, rounding, withholding, and so on. Filling out tax forms is an important application of such concepts, but it should not be the primary goal of the course.

Just filling out various financial forms is like drivers' ed: It's a necessary skillset and we should absolutely teach it to students, but it's a life-skills subject, not an academic one. Some aspects of academic subjects can help you understand hot to fill out forms, just like they can help you understand driving, but life-skills training per se should not replace academic subjects in the curriculum.

Yes to academic subjects like math incorporating more useful life-skills applications, but No to actually replacing academic subjects with task-specific life-skills training.

Last edited by Kimstu; 06-11-2019 at 11:39 AM.
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Old 06-11-2019, 11:40 AM
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You could as easily ask how much history do students really need or how much exposure to classic literature do students need. As a math major and stats PhD, I'm hopelessly biased, but I find that in terms of every day life, next to reading and writing, math is potentially the most useful subject you could learn in school. The more math you know and feel comfortable with, the more applications you see in every day life. I always note with wry amusement that the people who claim math has little application tend to be the same people who hated "word problems".

The problem with math, however, is that it is also probably the most unforgiving of subjects. Unlike something like history or writing, you can't sort of muddle through. A poor writer can still put words on paper and come out with a mediocre essay and get credit, and while you might not remember all of the dates on a history test, if you read the material you probably remember at least few. But with math, an answer is either right or wrong. If you don't understand the process, or your mind can't make the logical leaps, which rely more on instinct than rote memorization, then you are going fail. Also unlike other subjects, math builds very heavily on what came before it. So if you fall behind and miss one concept on the way up, its going to continue to hold you back in all future math classes. This is why math is one of the most hated/dreaded subjects and why I might be loathe to make hard requirements.

As to the OP's questions, I think I was required to have 2 or 3 years of math (I forget which), and I think that that is a reasonable requirement. As to what sort should be taught that is tricky. In order to consider any STEM career you are going need to be comfortable with advanced algebra, and analytic geometry before you get to college. But for reasons defined above, making that or anything approaching that an absolute requirement, will derail the academic careers of too many students who for one reason or another just don't "get" math. For them, couple of years worth of classes in finance, probability, and logical reasoning might be more appropriate. But this would require that a student make what amounts to a life long career choice at around age 13, a time when children are still in the process of learning who they are and what they like.
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Old 06-11-2019, 11:46 AM
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I took 4 as that was ‘strongly recommended’ for entrance to a Florida public college. I didn’t plan on going to a state school but ended up basically being forced to. I didn’t get algebra in 8th grade, so I took Algebra I, geometry, Algebra II, and pre calculus.

I think students need at least 3 years of math at the high school level. I believe we had a placement test for Algebra, you either took a pre-Algebra class, regular Algebra I, or advanced Algebra I freshman year unless you had it in 8th grade and did well enough to test out. I was in advanced Algebra I and there were definitely kids that had taken 8th grade Algebra but didn’t master enough to test out completely.

For those wanting to take AP calculus as a senior, there was an option to take Algebra II and Geometry concurrently in sophomore year, precalculus junior year, AP calculus senior year. Unfortunately for me, since I was in band, I couldn’t do this since I also had Spanish.
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I don’t think that schools need to feature practical math in a math class. Rather, they should do like my school did and have a weekly life skills class senior year. We did this during senior year American Government/Economics. Once a week, we’d have a special lecture about applying for college, how to register to vote, credit cards, dealing with homesickness at college. This was also the time for the usual anti drug and anti suicide lectures. My Government/Econ class was advanced, I believe they covered a few different topics in the non-college prep classes.
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Last edited by dalej42; 06-11-2019 at 11:48 AM.
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Old 06-11-2019, 11:53 AM
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1. Two years of high school math. Algebra and geometry were avoidable for a general diploma. I took algebra 1 and geometry.
2. Two years is fine, with general math courses being available for non-college bound diplomas.
3. Maybe, depending on whether they're going to college, trade school, or just out to work.

There has been a trend in Georgia for the last thirty years of piling on more and more requirements just to graduate high school. Algebra 2 or "its equivalent" is required now. I know academics here may disagree, but I really don't think it should be necessary just to graduate high school. I think the requirement just reduces the number of classes a kid can take because he wants to take the class. "The equivalent" amounts to two other year long classes, and that takes the choice of another elective away!
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Old 06-11-2019, 11:54 AM
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Back when I was in high school in the 80's in Missouri we only had to take 1 credit in math. Now my son takes 3 - algebra 1, algebra 2, and one other like trigonometry or geometry.

Granted in many fields like engineering you need these so you can go onto subjects like calculus then differential equations and so forth.

Do we need 3 years of high school math for a general student?

I propose we need math but it should be practical math such as accounting and understanding of business and finance such as how to analyze a loan and how compounded interest works. Why? Because no matter what field you go into you will need those skills.

What do you all think?

Questions:

1. How many years of HS math were you required to have?

2. How many years of HS math do you think we should require?

3. Would you prefer HS students take more practical math courses like financial math over math with more scientific applications like geometry?
Went to high school '89-'93

1) I believe it was 3. I took 4.

2) Dunno. Three seemed about right to me.

3) I don't necessarily know about "prefer," but I do think it would be more appropriate for some students than others. I mean, I did advanced algebra, geometry, pre-calc, and AP calc, but we did learn A=pert continuous compounding interest along the way. Basic compound interest was introduced pretty early on--probably my first year (but I did do an accelerated course, so probably year two for most.) So it's not like the more "theoretical" math classes avoid these topics.

Last edited by pulykamell; 06-11-2019 at 11:55 AM.
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Old 06-11-2019, 11:55 AM
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I always chuckle a little when people bring up balancing a checkbook as a life skill that should be taught in HS. I imagine all these HS and early twenties pulling out their checkbooks at the grocery checkout, putting on their reading glasses, and saying to the cashier in a shaky voice "Now, how much is the total again honey?"
Yeah—I was tempted to ask, facetiously, "What's a checkbook?"

Quote:
Originally Posted by Urbanredneck View Post
I propose we need math but it should be practical math such as accounting and understanding of business and finance such as how to analyze a loan and how compounded interest works. Why? Because no matter what field you go into you will need those skills.
When I was in high school, one of the classes we were required to take was "Consumer Education" or "Consumer Economics." That was a long time ago, and I don't remember what it covered, but I believe it included things like how checks work, how interest works, etc. (This was not classified as a Math class.)

I've never studied any accounting. For those who have, is it fair to call it "math"?
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Old 06-11-2019, 11:58 AM
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I took 5 years on math in high school.

I think we should require 4 years of math to graduate but i suppose that would lead to a lot of people not graduating after they failed a math class but generally I'd prefer to make a high school degree worth more not less.i understand the 3 year requirement but would prefer 4.

I think algebra is increadiby useful and commonly use geometry and trig in everything from building fences to measuring how much paint I need to buy. I would probably substitute probably and statistics for pre-clac for everyone. I've never balanced a checkbook so I'm not sure why people are so hung up on that being important hell I haven't written a check in a decade. Understanding interest and compounding is a part of algebra so I don't see why we need a special life skills math class we just need to make sure people understand the math we're actually teaching them.

If we're dropping classes from the curriculum I'd shit can English down to two years and free up room in the schedule that way.
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Old 06-11-2019, 12:00 PM
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Also unlike other subjects, math builds very heavily on what came before it. So if you fall behind and miss one concept on the way up, its going to continue to hold you back in all future math classes.
At least in the case of things like algebra/pre-calculus/trigonometry.

Part of the reason these are stressed so much in high school is that, although not everybody needs them, some people really do, and it's a lot easier to take them in sequence than to try to catch up on them later. Taking these classes keeps some doors open that would otherwise be closed.
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Old 06-11-2019, 12:08 PM
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I graduated in 1969, New York. I don't know how much math I was required to take, but I took AP Calculus in senior year, along with a computer class that was taught out of the math department.

The problem with two tracks of math is that you are forcing kids going into 9th or 10th grades to decide on their future. Not teaching algebra means they can never go to a tech school. Why limit them.

I'm all for a life skills class, but you can teach a kid how to balance a checkbook in junior high. It is not like this takes anything but simple arithmetic - assuming that anyone actually still balances checkbooks when the graduate. A life skills class can teach this and the financial stuff that has been mentioned, and how to evaluate ads and simple contracts and political claims. Some simple probability and statistics also.

If I ruled the world I'd replace geometry with prob and stat, but I hated geometry, and trig functions are very important. Still, if you got rid of one current math class, replace it with prob and stat.
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Old 06-11-2019, 12:12 PM
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Are there high schools where absolutely no algebra is a possibility? I didn’t go to a fancy pants school, but even the lowest track of students—there were four tracks— had to take some basic algebra courses.
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Old 06-11-2019, 12:16 PM
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The problem with two tracks of math is that you are forcing kids going into 9th or 10th grades to decide on their future. Not teaching algebra means they can never go to a tech school. Why limit them.
Because it is obvious some students are not getting through high school with the math knowledge needed for tech school anyway. By trying to not limit their choices we make them waste a lot of time practicing quickly forgotten rote learning of tricks and techniques to "pass a math test". They leave high school with a disdain for math, and with poorer grades in subjects they actually care about.

Rather than "not limiting" them by making them take inappropriate classes in high school the system should have options to change your mind. Building understanding in math requires students who are motivated by a desire to learn math, not just a motivation to not fail.
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Old 06-11-2019, 12:20 PM
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If I ruled the world I'd replace geometry with prob and stat, but I hated geometry, and trig functions are very important. Still, if you got rid of one current math class, replace it with prob and stat.
A good argument could be made that everyone should have some familiarity with the basics of probability and statistics.

But geometry is useful too, not just for its practical applications, but because it's a way of teaching logical reasoning and deductive proof, by working with concepts that (1) can be drawn and visualized, and (2) are noncontroversial and not obscured by emotion.
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Old 06-11-2019, 01:05 PM
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They need one beginning middle school math class that teaches:

1) Solve for "X" for fairly basic 1 variable equations. Move things around and manipulate the equation to solve for X.
2) Use that knowledge to do basic SOHCAHTOA trig. Give them 2 things and they should find the rest.
3) Expand on that knowledge for basic carpenters geometry.

After that you can have different classes or higher level classes or different directions. We do a disservice to the students by treating these skills as the entry skills of these huge math disciplines and not the culmination of arithmetic.
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Old 06-11-2019, 01:28 PM
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I took everything through Calculus in high school and have used virtually none of it in the intervening 45 years beyond basic algebra/geometry. Most students would be much better served by a practical math class that folded in probability and basic statistics.
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Old 06-11-2019, 01:38 PM
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They need one beginning middle school math class that teaches:

1) Solve for "X" for fairly basic 1 variable equations. Move things around and manipulate the equation to solve for X.
And please teach them that you can solve for anything, not just for X, and that your "variable" can have a long-ass symbol, and that you can always say "you know what, since this variable's symbol is kind of clunky, I'm going to rename it 'x'". Or 'chocolate'. Or '©'. The biggest problem most of my chemistry students had wasn't with chemistry, it was with not knowing that you could solve for [HCO3-]
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Old 06-11-2019, 02:03 PM
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All the math taught by teachers who actually understand what they are teaching.

Every time I see someone moaning about new math, or about not understanding the practical applications of what they are learning, I know they have not had a good teacher.
(Do we demand the practical applications of writing 1,000-word essays? No, because we all get that it's about learning how to understand a text, analyze a problem, and express yourself.)

Math is about problem solving in a ruthlessly logical fashion and being able to apply this to other aspects of your life, be it felling trees, repairing escalators, or figuring out how much dirt to buy to fill a garden box.

In practical terms I tell high schoolers to take the most advanced math they can handle otherwise they'll end up like a relative of mine who finished high school knowing she wanted to be a dentist for a living. She then had to spent two years doing catch-up math courses in order to enter dental hygienist school (at which point she stopped. Happy!).
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Old 06-11-2019, 02:26 PM
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Quite frankly, unless a HS student plans to go into some field like science or engineering, they shouldn't have to learn anything beyond algebra. I'd much rather see high schoolers be taught a lot more practical math related to personal finance, household budgeting, etc. these days; there's far more need for that.
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Old 06-11-2019, 02:29 PM
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I'd much rather see high schoolers be taught a lot more practical math related to personal finance, household budgeting, etc. these days; there's far more need for that.
For those who are advocating this: I'm wondering what specifically you think high-schoolers should be taught. Can anyone either spell out or link to specifics?
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Old 06-11-2019, 02:32 PM
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I teach math in an Adult Ed program for our local community college. Basically, I teach GED prep courses for adults who had dropped out of high school at some point and now want to get their HSE.

Here’s my take on it. The U.S. education system is designed so that everyone leaving high school should, theoretically, be ready for either the workforce or college. However, most of the math that high school students have to learn have no “real-world” applications to speak of. Many can factor a polynomial or balance an equation—basic pre-algebra stuff—but don’t know the first thing about balancing their checkbook. They have no idea what FICA withholding is, how insurance premiums and deductibles work, or how to calculate intertest of any type—from basic compound interest to the actual money going out of pocket on a home or car loan with x% interest.

Now math, clearly, isn’t pointless. It not only teaches students actual math but it also hones critical thinking skills and helps them practice thinking “outside the box” a bit, as well as how to tackle problems systematically.

Having said that… yes, I think most high school students have too much math on their plate. Or perhaps I should say, they have the wrong kind of math. Making high school students take something like trig is pointless unless that student plans on going into a math-intensive field like engineering or chemistry. Hell, I took trig in college, I teach math, and have never used trig once since the day I took my trig final in 2013. Is it useful? Of course. Should it be mandatory? Never.

My students have to learn polynomials, functions, logarithms, linear and quadradic equations… there’s quite a list. But most (all, probably, unless we specifically teach it in class) don’t know how to balance their checkbook.

So I think high school math curriculums need to be completely axed and re-created from scratch using real-world math concepts and teaching students what they need to know to actually function in society. If they need calculus or trigonometry for their career, they can learn it in college. Take out that mandatory pre-calc class and add in a "how to compute and file your taxes" class. The 2014 revision to the GED test took a couple steps in that direction, but did not go nearly far enough IMO.
Echoing Kimstu here, but the problem with the argument that we need more "real world" math is that the reason why most people struggle with those real world examples (taxes, balancing books, understanding loans/mortgages/hospital bills etc) is not because they require difficult math, but because they require sophisticated problem solving, excellent language skills, and complex understanding of many moving parts that are in a constant state of change, and may require active management of many different communication streams.

I'm a "smart" guy who took all the advanced math classes in high school and did some more advanced calc in college. Doing taxes or managing my medical bills is complicated and difficult not because I can't do the math, but because the systems are not designed to be user-friendly, are ever-changing, and are in fact developed to meet the needs on the entities administering them and not the needs of the end user.

Also, I have to ask, with no snark intended, is trig really required or is that just a made-up statement? In my experience, which I concede is now 20+ years out of date, trig was only "required" if you were in an advanced, college-placement math track. In which case we're not talking about general education at all.
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Old 06-11-2019, 02:59 PM
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Frankly I have always thought a students basic education should end by 10th grade and after that, most school time should be spent on what they want to do in life. So in some kids cases that might be all automotive. For others, lots of math. For others lots of biology.
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Old 06-11-2019, 03:36 PM
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Many can factor a polynomial or balance an equation—basic pre-algebra stuff—but don’t know the first thing about balancing their checkbook.
I've never met anyone who could factor a polynomial but couldn't balance a checkbook. (Met plenty who didn't balance their checkbooks - but not because they couldn't understand the math.) What I see is kids failing to understand factoring polynomials because they can't factor numbers.

Ideally, algebra teaches you a method of solving problems (take the information you have, manipulate it into figuring out the information you're looking for using a few rules). Geometry teaches how to start with a situation and some true statements and use logic to prove other true statements about that situation; it also teaches how to spot faulty logic.

I'm also not sure why accounting is considered more practical than figuring out how much butter you'll need (and whether you need to buy more) when you have a cake recipe for a 13"x9" pan, but all you have are 8" round cake pans (because your 13"x9" is where you're cooking the lasagna - speaking of which, two of your guests are vegans, so how do you change this entree that serves 6 into an entree that serves 4? and what time does it need to go into the oven so that everything is ready to eat at the same time since they all have different baking and resting times?)

1- I don't remember
2- 3-4 years of math seems about right.
3- As a separate class, no. But, I do suppose checkbook balancing could be part of learning how to add and subtract. And I am surprised that compound interest isn't covered when kids learn about exponential functions.
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Old 06-11-2019, 03:38 PM
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I don't remember how many classes I was required to take, because I took them as electives after they stopped being required.

Like others, I'm all for a "life skills" class and I've seen some of the schools around here have them (I was a substitute for a couple of months, so I could see what different schools needed a substitute for in the district I worked in)

How I view learning math as a necessity and the people who say "they've never used it" - I think that math is in part like the football player training that involves running through tires. No football player has ever run through tires when they're actually playing football, but doing that trains necessary muscles.

Or, you know, like the kid painting the fence in Karate Kid...

As far as actual classes - I think they need algebra, and more statistics & probability than I got (with a whole section on how people use statistics to lie). And computer programming, which is probably now taught in most schools. But there are probably thinks I learned in geometry and pre-calc that I don't realize that I use, but I do use.
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Old 06-11-2019, 03:44 PM
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Because it is obvious some students are not getting through high school with the math knowledge needed for tech school anyway. By trying to not limit their choices we make them waste a lot of time practicing quickly forgotten rote learning of tricks and techniques to "pass a math test". They leave high school with a disdain for math, and with poorer grades in subjects they actually care about.

Rather than "not limiting" them by making them take inappropriate classes in high school the system should have options to change your mind. Building understanding in math requires students who are motivated by a desire to learn math, not just a motivation to not fail.
Here's a counterexample. My son-in-law is German, and they track kids early there. Because of various reasons he got put into a vocational track for high school. He then got it together. He was blocked from going to a regular college because of this, and had to go to a secretarial college to get the classes needed to eventually go to a regular college. He got a Masters in International Business and is now making tons of money.
9th grade is way early to decide this stuff. If a kid demonstrates that they can't handle regular math, sure, track them into a simpler math class. But there should always be a path back.
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Old 06-11-2019, 04:16 PM
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Here's a counterexample. My son-in-law is German, and they track kids early there. Because of various reasons he got put into a vocational track for high school. He then got it together. He was blocked from going to a regular college because of this, and had to go to a secretarial college to get the classes needed to eventually go to a regular college. He got a Masters in International Business and is now making tons of money.
9th grade is way early to decide this stuff. If a kid demonstrates that they can't handle regular math, sure, track them into a simpler math class. But there should always be a path back.
That's not a counter example, it's an anecdote of a system that works like I suggested. Your son-in-law has a Masters and makes tons of money, so obviously the system worked for him, even if it was not perfect. Note I specifically wrote that early sorting requires a system for changing your mind later.

Meanwhile practically every high school math class at the slowest and lowest possible level for students is full of students who're not learning math, they're learning how to pass math class. The idea that not teaching them about factorising polynomials is taking options away from them is evidence of a broken system, not of a system that is the only way to ensure kids have opportunities to use their talents.
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Old 06-11-2019, 04:44 PM
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For those who are advocating this: I'm wondering what specifically you think high-schoolers should be taught. Can anyone either spell out or link to specifics?
I would start with how interest rate and loan repayment work, and why it takes years to pay off a high interest CC making minimum payments. The class should also cover how insurance works, and the basics of the payroll and income tax systems. Top it off with saving for retirement and the basics of the stock market.
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Old 06-11-2019, 05:59 PM
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For those who are advocating this: I'm wondering what specifically you think high-schoolers should be taught. Can anyone either spell out or link to specifics?
I think the math program should build to a knowledge of how to handle probabilities in a logical fashion.

For example, I'd be over the Moon if the average person on the street could work out what they need to know to answer this question: "If there's an X% chance of A happening given B, what is the probability of B happening given A?" That is the kind of mathematical question which has some real implications for the lives of humans living in the world, regardless of what specific jobs they take on.

Presently, our math curriculum at the high school level builds to integral and differential calculus. That's why algebra leads into trigonometry, and why logic isn't really treated as its own subject, and why statistics is taught as an application of fractions as opposed to something worthwhile. That is what's pointless, and saying that calculus builds better brains an infinite number of ways doesn't save it: Probabilities are much more likely to be useful even if the kid grows up to be a civil engineer.
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Old 06-11-2019, 08:09 PM
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For those who are advocating this: I'm wondering what specifically you think high-schoolers should be taught. Can anyone either spell out or link to specifics?
1. A lot more focus on debt - just how much your credit-card debt swells with interest, or how staggering a burden student-loan debt can be in college. Mortgages, investments, etc.

2. Things like 401ks, Social Security, etc. How contributing a thousand dollars in your 20s grows to much more than contributing a thousand in your 50s.

3. Budgeting - how much various things cost.
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Old 06-11-2019, 10:08 PM
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On the same track, mental math and using mental references to calculate distance and volume.

For example, have the kids walk across the room in a way that over time and with practice, they can pace out a yard. Then they divide by 3 and have a distance in feet. Do it again diagonally and multiply and you have square feet. Now they can figure the area of a room or the front lawn.

Or by measuring their fingers (or 2 of them) figure out about which finger is one inch across.

I mean we use "length of 2 football fields" because most people can relate so why not teach some other useful measuring references.
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Old 06-11-2019, 11:36 PM
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I'm also not sure why accounting is considered more practical than figuring out how much butter you'll need (and whether you need to buy more) when you have a cake recipe for a 13"x9" pan, but all you have are 8" round cake pans (because your 13"x9" is where you're cooking the lasagna - speaking of which, two of your guests are vegans, so how do you change this entree that serves 6 into an entree that serves 4? and what time does it need to go into the oven so that everything is ready to eat at the same time since they all have different baking and resting times?)
Accounting isn't really math - it doesn't require anything other than arithmetic. It's comparable to doubling a recipe to make 2 - 9 inch layers rather than 1. Deciding which accounts to debit or credit has nothing to do with math or even numbers. On other hand,adapting a recipe meant for a 8 inch round pan to be used in an 9 inch round pan requires actual math- by which I mean not the actual arithmetic operations , but knowing which operations to use and which measurements you need. It might appear that the pans are close in size*, but the first step in adapting the recipes is knowing the volumes of the two pans . Change that - the first step is knowing that you need to know the volume of the two pans.



*The 9 inch pan is about 25% larger by volume.

Last edited by doreen; 06-11-2019 at 11:36 PM.
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Old 06-11-2019, 11:55 PM
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The problem with math, however, is that it is also probably the most unforgiving of subjects. Unlike something like history or writing, you can't sort of muddle through. A poor writer can still put words on paper and come out with a mediocre essay and get credit, and while you might not remember all of the dates on a history test, if you read the material you probably remember at least few. But with math, an answer is either right or wrong. If you don't understand the process, or your mind can't make the logical leaps, which rely more on instinct than rote memorization, then you are going fail. Also unlike other subjects, math builds very heavily on what came before it. So if you fall behind and miss one concept on the way up, its going to continue to hold you back in all future math classes. This is why math is one of the most hated/dreaded subjects and why I might be loathe to make hard requirements.
The same happens with Chemistry or Physics (both of which rely heavily on math), but at least in Spain you're a lot more likely to get a math teacher who doesn't understand the subject than a science teacher in the same situation. Sadly this is a vicious circle: you get teachers who don't explain it well, so their students who eventually pass and get the associated degree don't understand it well, so they can't explain it well... Here at least, Phys Ed and Math seem to collect the worst teachers either in terms of not understanding the subject or not understanding the students; Phys Ed also gets a lot who don't give a shit (which I haven't encountered in Math).
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Old 06-11-2019, 11:58 PM
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Or by measuring their fingers (or 2 of them) figure out about which finger is one inch across.
Not any on MY hands... unless you're willing to accept a 20% difference, that is. Just don't try to call that an acceptable error level when filing your taxes.
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  #43  
Old 06-12-2019, 12:48 AM
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How are kids supposed to know what they are good or bad at if they're not given the opportunity or even pushed into different types of math?

I was rolling through school kicking ass at everything until I crashed and burned at Algebra 2. I also crashed and burned at AP Chem. I was able to get out of those classes, and realized my passion was English and went on to a degree in journalism.

My best friend was rolling through school with his finger up his nose, not excelling at anything, no encouragement from his family, until he landed in Algebra 2 and it all clicked for him. He kicked Calculus's ass too. He discovered his love for math and his ability to be a good student, and went on to a degree in Computer Science.

You can't say "no one uses that stuff" because some people use that stuff. Don't tell me trades don't use that stuff! My dad went to sheet metal school as an adult and found HIS love for Trig (after being a highschool dropout and a factory laborer for 20 years).

Button-pushing laborer jobs are going to be a thing of the past, and STEM is on the rise. We need to give kids the opportunity to figure out if advanced math is something they can do and enjoy.

I don't think Calc & Trig need to be mandatory to graduate (thankfully, they weren't mandatory for me - I took Spanish instead) but I don't think we need to shut them down or discourage kids from trying them. You never know when the next kid is going to have her "eureka!" moment and find themselves on a path to NASA.

Also, kids have 12 years to learn math skills. I don't know if it's useful to just toss in a "here's all the math you'll need in your daily lives" class some time around 11th grade. Why not sprinkle those sorts of lessons throughout their entire school career? You can learn to make change and calculate income tax deductions as part of existing lessons.
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Old 06-12-2019, 12:53 AM
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I'm also not sure why accounting is considered more practical than figuring out how much butter you'll need (and whether you need to buy more) when you have a cake recipe for a 13"x9" pan, but all you have are 8" round cake pans (because your 13"x9" is where you're cooking the lasagna - speaking of which, two of your guests are vegans, so how do you change this entree that serves 6 into an entree that serves 4? and what time does it need to go into the oven so that everything is ready to eat at the same time since they all have different baking and resting times?)
I think it's hilarious that this is presented as multiple math problems. You don't have to change the cake recipe, you just eyeball your pans and cook it for less time. There's no reason to make less food because you just eat the leftovers - better use of your time to make more food than make less. The only math problem here (barely) is baking everything to finish at the same time, except, in normal cooking, you would never need to the cake and lasagne near one another in preparation in the first place. The cake is done well in advance. Sounds more like you listed a bunch of life skills (learn how to be flexible in cooking, budget your time wisely, and proper task management) than actual math. Moving on, though...

We had 3 years of required math. Even though I learned a lot of worthless stuff because my final classes were calculus and I never used that, I'd still recommend that many years of math. But practical math. As mentioned before, less of the solving matrices and logarithms stuff, more of the calculating compound interest stuff. I don't know how anyone here thinks there's any possibility of not learning algebra in school though. Our standard school system had everyone learning basic algebra at age 11. Well before high school. If anyone's not getting to that by the end of high school, they're definitely laughably underprepared for life and their school system has failed them.

The main problem with high school math classes is they may teach you important things, but never give you their practical applications, which is stupid. Kids would beg teachers all the time to tell them why this stuff was important or when they'd ever use it, but even if we were being taught something useful the teachers never explained how or why it was. We'd be taught probability, but not what that means in playing the lottery or gambling. We'd be taught exponential equations, but not told that this was useful for understanding and calculating compounding interest. We'd be taught geometry, but it was always weird proofs and never about how many garden soil bags we need to fill a 5 foot by 10 foot trough. We were given all the tools but how or why we'd be using them was always kept from us like it was some kind of "you'll get it when you're older" thing. Thank god I did retain the useful stuff and figure out WHAT it was even useful for. It makes me mad even to this day that there's a hundred ways to make math practical, and explain why it's useful, but all the math teachers would just splutter and say that we needed it if one day we thought we'd want to be a scientist. Nothing actually useful. You could've taught us how to find the best deal at a grocery store! How to arrive places on time! How loans work! But instead they couldn't be assed to even let us know what we were learning was useful after all.

I learned a lot of useful stuff. But I also learned so much crap I've never had to think of again. A whole year, wasted on teaching us how to plot sine waves on our calculators. I could do it, but who knows why. And if a person isn't a logical thinker by high school, no amount of logic proofs is going to teach them how to start that late in life. I watched the other kids. The only reason they found math so hard was because for some reason they couldn't follow simple directions. High school math is just following directions from A to B. You don't need to know why. I watched them fight with teachers over physics, asking how these problems resulted in those answers, when that didn't even matter. You follow the directions, you get the answer. Every time. They're not asking us to make new equations or discover quantum physics. They are just asking us to re-solve problems solved a million times before. We're not going to prove the physics teacher wrong about how gravity works. And this followed through to my adult life. Seems like not a single damn person can follow simple directions. You can give them a numbered list of 3 things to do in order and they just can't figure it out. They can't read and just do what it says. They'll say they couldn't figure out what they had to do. It's absolutely mind-numbing. Theoretically our school system is designed to create exactly these sorts of mindless cogs who can follow a simple direction, and yet somehow they aren't. That's a mystery I'd like solved.

Last edited by Macca26; 06-12-2019 at 12:58 AM.
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Old 06-12-2019, 05:30 AM
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I took two years of math, Algebra in the 9th grade and Geometry in the 10th.

Trig and Calculus were offered for students (science majors) that needed it for college.

I didn't do well in Geometry and didn't take any more math until forced to in college.

Last edited by aceplace57; 06-12-2019 at 05:31 AM.
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Old 06-12-2019, 06:07 AM
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I think there should be four years of math, but I think there should be a much slower option for kids that need it: spend two full years on what we now call Algebra one, then geometry and Alg 2.

I've been watching high school kids learn math for nearly 20 years. Math, more than anything, is something almost anyone can learn given adequate time. I also have seen that the problem, more than anything, is a wobbly understanding of the fundamentals of Algebra. So do Algebra 1 SLOW. Work in lots of repetition and application. Then build on that. But don't rush them through Alg 1 when they aren't ready to go that fast, then make them do it again when they fail. Do it slow, do it right, make sure they get it.
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Old 06-12-2019, 06:08 AM
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Quite frankly, unless a HS student plans to go into some field like science or engineering, they shouldn't have to learn anything beyond algebra. I'd much rather see high schoolers be taught a lot more practical math related to personal finance, household budgeting, etc. these days; there's far more need for that.
What about the kid who, in 9th grade dreams of one day being a rodeo clown, then, with graduation looming realizes he wants to be an astronaut?
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Old 06-12-2019, 08:00 AM
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I think there should be four years of math, but I think there should be a much slower option for kids that need it: spend two full years on what we now call Algebra one, then geometry and Alg 2.

I've been watching high school kids learn math for nearly 20 years. Math, more than anything, is something almost anyone can learn given adequate time. I also have seen that the problem, more than anything, is a wobbly understanding of the fundamentals of Algebra. So do Algebra 1 SLOW. Work in lots of repetition and application. Then build on that. But don't rush them through Alg 1 when they aren't ready to go that fast, then make them do it again when they fail. Do it slow, do it right, make sure they get it.
Along with that, it's weird on makeup grades.

In Kansas if a kid gets say a D in a class, then retakes the class to learn it better and gets a B, the D still goes down in the grades. Only if a kid gets and F can that F get changed.

So if a kid has a terrible Algebra 2 teacher who gives them a D in first semester and and F in second semester, they can retake the course in summer school but only get the F changed, not the D.
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Old 06-12-2019, 08:58 AM
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The main problem with high school math classes is they may teach you important things, but never give you their practical applications, which is stupid. Kids would beg teachers all the time to tell them why this stuff was important or when they'd ever use it, but even if we were being taught something useful the teachers never explained how or why it was.
I very much agree and appreciate your rant on this. I remember when I was in geometry class, very likely (with adult hindsight) my school was of poor quality because the entire semester of geometry consisted of drawing each shape on a page of a notebook and writing the proof below it. The notebook was graded at the end of the semester as sort of a final "exam". At the time I thought it was fun and easy because it was just drawing and copying the proof from the textbook into my notebook. It never once occurred to me that I was learning logic. In hindsight I can see the logic, but still don't think it was the best way to teach it at all.

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Seems like not a single damn person can follow simple directions. You can give them a numbered list of 3 things to do in order and they just can't figure it out. They can't read and just do what it says. They'll say they couldn't figure out what they had to do. It's absolutely mind-numbing. Theoretically our school system is designed to create exactly these sorts of mindless cogs who can follow a simple direction, and yet somehow they aren't. That's a mystery I'd like solved.
This is a very interesting observation. I suspect it has more to do with the way people process information, which may also be in complete conflict with how they're taught math and logic. I've worked with people like the ones you describe who couldn't follow simple directions. If they made a list of tasks to get done, I would observe that they'd tackle the list in random order and never get to some of the items, then they'd make a new list, etc. and eventually they had a handful of lists of tasks all in various states of completion.

Another example: I noticed that they'd create a spreadsheet and type in column headers for things they wanted to track, for example item number, task name, date started, date completed. Over a few meetings where we'd update the spreadsheet, I noticed that they'd forget about the column headers and end up typing comments into the date started cell for one task, type comments into the task name for another task, put the completion date for a task into it's task name cell, etc.

What I noticed is that these people did not have a methodical way of thinking about things, they were creative/impulsive/random thinkers. I'm exceedingly logical and methodical but I'm not sure their way of thinking is bad. It's just different. (and frustrating to work with at times because of the natural conflicts that occur, but... eh, as they saying goes "it takes all kinds") Are these people unable to think methodically because they failed at elementary/high school math? I don't know, to be honest.

Last edited by JcWoman; 06-12-2019 at 09:01 AM.
  #50  
Old 06-12-2019, 09:53 AM
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What about the kid who, in 9th grade dreams of one day being a rodeo clown, then, with graduation looming realizes he wants to be an astronaut?
That kid is unlikely to learn much through being forced to go to math classes he's not interested in and might not be mentally suited for yet. He'll have spent his Algebra classes doodling bulls and clowns, and is better served by a system for doing remedial math for motivated young adults.
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