I rather suspect that what we are seeing is a question which is designed to mimic how students are being taught. If so I doubt the presentation is really a significant issue. I'd be willing to change my mind if someone can demonstrate objectively that there's some general detriment to being taught this way. For example if you could show that someone taught to frame problems this way significantly limits or hinders them from grasping something else of obvious higher value.
An example of that might be that who seeing a six on a line drawing of a cup couldn't comprehend how it might not mean "6 cups" or "6 units of coffee". If that inability is due to their education then clearly it produced some limitations - doesn't sound like it's holding our engineer friend back in his work though. So at least he has that.
Now if this isn't a question very close to the way students were taught then again it might still be a useful diagnostic. I tend to think that, in the real world nothing looks like a textbook question and math doesn't need to be *applied* to a problem so much as mathematical problems need to be *extracted* from situations. Often that involves being creative. Chaitin often refers to math as being as much art as science. I tend to agree. Steven Levitt isn't well-known because he was a human calculator. Levitt is well-known because he was able to extract mathematically solvable problems from the real world and derive some interesting and counter-intuitive results.
So my standard, at least for now is that math needs to be taught in ways that help people to recognize opportunities to use it. If your math fails to do that, such as making you incapable to recognize a simple subtraction problem. Blame the question all you want, I'd still say that this is a sign that there's a significant gap in your ability to use your math.
Then again perhaps in some part of the world people like our engineer are rewarded not for solving problems but for whining and complaining that the world presents it's data in a way that is significantly different from the way they were taught in school.
I found the question quite confusing and laughably complicated.
Remind me again why that is necessarily anyone's problem but yours? Better yet just pontificate and call people who don't agree idiots...oh wait...
it was a poorly written question, and did not test kids on their subtraction knowledge.
This is more a pontification than an actual argument. Sometimes we call this an argument from implied anonymous authority. Also if a question is not a test of an educational outcome then it should be answerable without that knowledge. Are you saying that someone with no concept of subtraction (which seems unlikely) would be likely to answer this question correctly? So I'm thinking you need to do some more thinking.
you're confusing being educated on mathematical concepts and being educated on how to answer test questions.
In a lot of cases that's a distinction without a difference.
I said that someone coached to approach a problem in a certain way will more readily answer a question posed in that way. In my grade eight class we were being taught to solve simple systems of linear equations by substitution and/or "subtraction". Someone schooled to approach them as a matrix would probably solve the same problem less quickly and someone who's only exposure to solving systems of linear equations was with Cramers rule (this would be unlikely, but at least theoretically possible) would not have been able to solve any of them.
The grade eight student is being educated on how to answer the test questions they will be given on a test. Likewise a 1st year LA student is being educated in how to answer the questions they will be given on a test. Both are being fed from a very specific pool of representations of the problem space.
I think my example of calculus was even more clear. Why should it matter what the variable is? It's just a placeholder. However clearly, people are coached to, at least on a test look at the Greek letter theta as a measure of an angle and that made it hard for them to answer the question correctly. So was this a good question? If all you want to know is if they can replicate what's in the textbook - then probably not. However, personally I don't think that's what I'd like to see in math education.
from the descriptions it sounds like the classroom education is tricks for taking the test,
As I illustrate above an awful lot of math education is exactly that and I suspect it would be a bad idea to remove it on that principle alone.
Considering that the problem wasn't hard for me or my daughter - In a couple of weeks I'll be hanging out with a large group of friends, all with university math of some sort. I wonder what they would say. I really doubt that this is nearly the deal you are making it out to be. Perhaps you're just sore that you missed it and need to artificially inflate the complexity of the problem in order to avoid dissonance? Because the problem can't possibly be with you. Right?
the only way my math education "failed me" is it did not prepare me to take stupid tests mandated by the federal government.
And somehow mine didn't fail me like yours did. I wonder why?
and yet I can still get by as an engineer!
*sigh* Yes, I figured you were an engineer. Both the sheer number of engineers and the impairment that often comes from studying a tiny part of an enormous field were indications of that.
it's amazing those cars don't fall apart while driving on the freeway.
If there's even a hint of seriousness in that then your problems extend all the way down to first-order logic.
This is the exact point! We should be teaching children to do subtraction, not to respond to tortuous question formats!
Um...you're being obtuse. What I stated was
a) The question was both obvious for myself and someone of the targeted age group. How exactly is something both objectively obvious and tortuous?
b) That people educated in a particular way will respond to a question posed in that way more readily than those who weren't. That doesn't necessitate that the question being posed in a *generally difficult* way. Someone in a particular context will attempt to solve a system of linear equations by using Cramer's rule. Another context might simply attempt to reduce the matrix. Which approach is the most feasible on a test depends on the context. A very large matrix might be more easily solved using Cramer's which would of course be useless for a non-square matrix.
the simplest question type should be used!
What does "simplest" mean? Students get the question right more frequently? My vector calc prof told me a story about how he once produced an exam using their bank of questions but on just one question they changed all the variables from "x" to "theta" - the average performance on that question dropped significantly when compared with prior years and the rest of the exam. Did these people "understand the concept" or not? Clearly there are questions that the same body of people would have likely performed better on but clearly they didn't really understand that the greek letter theta doesn't actually have any magical properties. Which prompts us to ask the question: "What is the learning outcome we are testing?" Is it the ability to regurgitate the chain rule or the ability to solve a problem even if it doesn't look exactly like a textbook question? The answer to that really has to do with what you think education is actually *for*. While I think there are times and places for questions that essentially spoon-feed you the answer and can be performed by someone who doesn't really understand what they are doing. To me, anyway the actual outcome you are trying to achieve is the ability to do math even when something doesn't look like a textbook problem. In which case, I'd argue that your "never anything but the simpilest question type" rule achieves the opposite.
regardless of how you feel about equating pennies to teacups.
Actually, I think you give a good example here of how your math education failed you.
How can you subtract 5 pennies from a cup of 6 units of coffee? You can't, and that kind of check will be important in a few years once they move onto using that maths for real-world calculations where dimensional consistency is important.
Nothing like an engineer to exemplify how poor math education is. Yes, units are exceptionally important. I'd argue that even more important is being able to correctly extract information (like say units) from some arbitrary situation. Sort of what you just failed to do....
did you even look at the test question? theres a link in the summary. on the left you have five pennies, and on the right you have a teacup marked with the number six. the teacup is apparently full of liquid. tea, perhaps? you know that this is a puzzle, and you need to decipher it for some clue. has the riddler been here? where's batman!
Apparently I looked more closely than you did. Five pennies yes, and a cup (looks more like a measuring cup to me) with "6" on it. Beneath the pennies are the words "part I know" and under the cup is the word "whole".
It was obvious to me, and my daughter that the cup contains/represents the "whole" amount which is six but what I can see is five pennies. What we are being asked for is what is missing? What is missing from 5 to make 6? Really not *that* hard.
This is probably even more obvious to a child which has been trained using these specific terms.
i'm not gonna argue about the importance of solving word problems as a skill. all of life is word problems!
I'm not talking about word problems. In fact I'd argue that all of life is the opposite of word problems. Life is filled with data you need to figure out how to structure it into something you can manipulate.
when you ask a simple question in a simple way, you test a child's ability to understand concepts. When you ask a simple question in an overly convoluted and distorted way, you test a child'a ability to follow directions.
Possibly. You could also be testing the child's ability to recognize a problem in a context. It could be a familiar one - which is what I expect in this case. However even an unfamiliar context is testing a degree of mastery that is pretty important, I frequently deal with people who have spent years studying math but still can't apply it unless the problem is formatted as if it's from a textbook. The writers nephews wife who teaches calculus sounds exactly like this...and to a point so do you. One reason you don't just give students a long list of questions in the form of X + Y = Z is that the only place you actually see a real problem framed that way IS in teaching materials.
That said, I don't find this terminology all that difficult. Nor did my six year old who regularly figures out these problems.
Let me know when you recover from blaming other people for your problems. Perhaps when you're 45?
I went through a similar experience. School was largely busywork, even in the gifted program. However it didn't take much to see that any work at any level anyone would be willing to give me is going to be the same. So I simply did the minimum required and turned my attentions to other things that interested me.
This caused problems when the work actually started to become challenging.. My issue, and probably yours was not having a coping strategy for busywork (assuming this was actually the problem). My coping mechanism was clearly better than yours but with a little more parental involvement I probably could have avoided the whole mess.
Ultimately though it was my decision not to simply push through the busywork and get the job done.
Busywork is a significant part of any job almost regardless of payscale. Meetings are busywork, charting is busywork. Strategy sessions are busywork. Recording results is busywork. Reading and signing documents is busywork.
As a parent even teaching your children is pretty close to busywork. It's always miles below your ability and often repetitive.
In fact given your rant above, you come off sounding like someone who has to be constantly stimulated in your job. Which to your supervisor sounds a lot like we have to be constantly working to keep you entertained. No offense but I'll just hire the next guy who can handle being bored from time to time without blaming me for destroying his "love of work"
Well i) That's a theoretical argument making an imposition on reality and ii) your wrong as I hear that you can't write a computer program which deterministically can predict if an arbitrary computer program will halt.
The law of conservation of energy?
You're an idiot. The human body isn't a simple machine where an easily accountable amount of energy going in will produce a given amount of work.
Most people can do the simple experiment of eating exactly the same thing this month as they did last month with the same amount of activity. Make one change - this month divide that daily food intake into 8 equal parts and have 8 small meals at even intervals throughout the day. Same energy in, same energy out, and you WILL lose weight.
Actually yeah there is an exceptional amount of correlation between what you eat and a few variables about you and your resulting weight. BMR can be reasonably reliably derived from age, sex, weight, height. If people really were so radically different you couldn't actually create a regression from the data (or the coefficients would be small or align by chance). There are lots of things which can affect weight gain but they are all needfully small compared to your caloric input vs your BMR + the energy you use day-to-day.
But y'know what? Jobs was a fucking genius,
I always wonder why people say this. It's unclear exactly how much of what Apple produced was Jobs's idea and how much help he had. We probably will never know since it's currently in Apple's best interest to keep the myth alive.
Oh, and y'know... he's dead. Those wars are over, asshole.
Think so? I think when a prophet dies is a sign that the wars are on their way