A student who scores highly on a Calculus exam may be generally good at Calculus, or maybe they know a couple exam-specific algorithms to succeed and got a little lucky besides.
A student who fails a Calculus exam is nearly guaranteed to be poor at Calculus.
To say exams have no predictive power is to ignore the obvious.
Student A that passes a Calculus exam may be be more likely to know Calculus than student B that fails but so what?
Passing a Calculus test doesn't necessarily predict if the student can apply their knowledge to production to generate new ideas and widgets which make our lives better, it just predicts that Student A can follow rules and learn something _when required by an authority_.
I think this sentiment is similar to how people feel about Leet Code interview questions. So what if an engineer can invert a binary tree if they can't formulate new, useful ideas and convince others to work on them?
Perhaps student A is more likely be create new, better widgets than student B but I think academicia/LC cannot test this directly, which is what people are getting at when they criticize tests.
>Passing a Calculus test doesn't necessarily predict if the student can apply their knowledge to production to generate new ideas and widgets which make our lives better
It actually does though, because if he fails, then you can be completely certain that he can't.
I know this isn't true because of my own experience.
I've always been bad at math, I failed precalculus multiple times in both highschool and college, I never got past my first year of calculus in college, I wasn't able to pass descrete maths, and I never took an algorithms class but, never the less, I am applying statistics to novel problems at my day job and people are lining up to work with me and my career growth is accelerating faster than those around me who certainly got better marks than I did.
How is this possible? I'm not entirely sure, however, it indicates that academic tests don't actually measure ones ability to apply themselves and their knowledge to real problems that people actually have outside of an academic setting (i.e the real world), which I believe is the primary point in the "anti-testing" narrative.
If you can't do calculus in a stressful situation, you can't do it, anymore than you can understand french if you can't understand it when people speak it at full speed.
Huh? How often is calculus ever done in stressful situations outside of tests? Seriously this seems like a bad example...
I feel like you're making my point here. I can speak french and be spoken to, order off a menu, etc. but I can't understand when two native speakers are conversing. Are you saying I don't understand french?
When the deadline for your papers are approaching, when your competitors are closing in and about to scoop you, when you're using calculus in order to make financial trading decisions, etcetera.
Yeah but not to the same degree or in the same way. Having to sit in a room with no sources for an hour and shit out some test answers is not really same as having weeks to apply yourself with access to appropriate resources, references, and guidance from more senior coworkers.
The way I see it, you should be able to do calculus without pen or paper, so certainly without references or guidance.
If you want to be creative the first step is to put the problem in your head so that you can actually ponder it. If you have to pour over references and look things up, then you're not in the game any more than you can play chess if you have to look up the rules as you play.
This doesn't align with my experience writing software and applying maths to engineering problems. I am working a lot with statistics in my current role but if you asked me to take a stats test, I would almost certainly fail without references. Does this mean I am bad a stats? Perhaps? Does it matter? No.
> If you want to be creative the first step is to put the problem in your head so that you can actually ponder it. If you have to pour over references and look things up, then you're not in the game any more than you can play chess if you have to look up the rules as you play.
It seems like you are confusing the problems with the solutions. If you can understand the problem well enough, the solution will become obvious, even if you never took the math class--at least that's how it works for me. I do best when I have an actual real-world problem to solve, not a conceptual one created by an instructor.
So you have all the Laplace transforms memorized just in case some internet person asks you how to model a wheel going up a ramp at the origin?
Everyone on my engineering course did this question, but my guess is zero of us could solve it right now from memory. A fair portion would be able to solve it with some references available.
But you're making the other guy's point for him here. It's a waste of your mind to have test-taking skills memorized.
No, it's completely against my philosophy to memorize things just to remember; and things like Laplace transforms you look up in 'Beta: mathematics handbook' which you're typically allowed to bring to tests in engineering and in applied physics, at least here in Sweden.
What I mean is that if you know calculus you can do it fluently, like a language. You don't remember the solution, you calculate it, preferably in your head.
Edit: Though, back at my university tests took five hours, and I understand one or two hours is normal in America, and I could imagine that those shorter tests mean that there's more memorization and less sensible study.
It's acceptable to look things up that don't matter.
The way I see it, you should have the machinery in your head, so that you can derive things if pressed, and you should have the ability to work largely in your head and actually ponder things, but you shouldn't necessarily memorize formulas.
For example, I haven't even memorized the formula for the quadratic equation, I just complete the square in my head every time.
I think it's important to end up knowing them and to end up being able to calculate with paper and pencil to some degree and because calculus is very basic it's something one should be able to do in that way.
You should be able to imagine a right angle triangle sitting on the hypotenuse of another right angled triangle and figure out the x and y coordinates of the corner and how to get the sum of angles formulas from that, or to in general imagine things from calculus, like how the product rule can move what what is differentiated from one function to another etcetera.
I've never worked in a company where we were time constrained or stressed. I could always tell my boss "it's not going to be done by the deadline" and he'd have to come up with a way to do plan B.
Then it's not necessarily a "deadline", but a suggestion.
Most of the time it's better to do something the right way than to artificially hurry developers to hack something together that will bite you later in the form of bugs
Yes, although in this I was thinking less about software and the like as such and more about things like pricing derivatives contract that somebody wants and things like that, and of course, then you must do the right computation.
> Again, though, if creating new, better widgets requires calculus, student A may not have what it takes, but student B almost certainly can't do it.
I'm not so sure about this. What if student A was just better suited to learn Calculus when they were tested while student B bored by the class and teacher and stopped going/caring but, if given the chance to apply themselves in a non-academic setting working on real problems that affect people's lives, student B would learn Calculus twice as fast as student A and deliver a better widget in less time?
There are many more scenarios here that I could list but I think the primary point is that the context around the students, their lives, and the testing environment matters a lot and this is something that cannot easily be accounted for using numerical test scores
> But they also require some solid skills, and those skills are testable
Maybe badly. Leet Code is supposed to do this but is famously criticized. Probably better than nothing I suppose
I am trying to point out that the methods we use to "determine who is a genius and who is not" are deeply flawed and rudimentary, letting people fall through the cracks and preventing people with different learning styles for succeeding.
Like I said in another comment, I am terrible at testing and failed my way through school but I am still able to have a successful career as a software engineer applying maths to engineering problems that other people are excited about and want to work on. The reasons for this are complex because I am complex, like all people, but not like numerical test scores.
> But that method will need to be able to predict future events that shape the person
I think individuals are capable of qualitatively assessing a person's ability and trajectory given enough information, time, and context. Humans may come to the wrong conclusions a lot of the time but so do academic tests...
Because while tests arent perfect, then they are the best available method that is transparent/fair at scale
If you want the change, then propose an improvement.
________
>I think individuals are capable of qualitatively assessing a person's ability and trajectory given enough information, time, and context. Humans may come to the wrong conclusions a lot of the time but so do academic tests...
Ive heard countless stories like teacher telling student that he will be not even close to being successful due to not giving a damn about school and yet they manage to do fine
So no, i dont think people of school are capable of this at scale
You would need smart and open minded and up to date people to at least try to do that reasonably
> If you want the change, then propose an improvement.
I don't need to have a solution to have valid criticisms of an existing system. I am just sharing my experience with testing, how it has affected my life, and why it didn't work for me.
That said, I do think we can improve our ability to assess (not test) people by:
* Putting less emphasis/focus on tests and more focus on long form project work and interpersonal relationships with peers and instructors
* provide more flexibility to students when testing them (like access to resources/notes, more time, allow them to ask questions etc).
> You would need smart and open minded and up to date people to at least try to do that reasonably
I would certainly hope that the people teaching the next generation were smart, open minded and up to date. Testing doesn't control this anyway, a bad teacher will be unfair and have bad curriculum regardless if they test their students formally or not.
>I don't need to have a solution to have valid criticisms of an existing system.
I agree.
>I would certainly hope that the people teaching the next generation were smart, open minded and up to date. Testing doesn't control this anyway, a bad teacher will be unfair and have bad curriculum regardless if they test their students formally or not.
Hmm, I originally didnt think about those people as a teachers, but as if they were some kind of examiners.
But thats fine, they could be teachers too
Yet, I do believe that the bias would be too big :(
At every level of eduction except higher teachers were visibly biased towards students
Some benefited from it, some had harder time due to that.
I remember doing so well in calculus until the 3D graphing unit.
I think I ended up with a D or worse on that one units test. My friend was like "oh bro you just add a pi to everything". This isn't thanksgiving and it's more complicated than that!
A student who fails a Calculus exam is nearly guaranteed to be poor at Calculus.
To say exams have no predictive power is to ignore the obvious.