How do blue book exams translate to real world problems the students will encounter?
Why not open book + AI use exams, because that's what students will have in their careers?
How do blue book exams translate to real world problems the students will encounter?
Why not open book + AI use exams, because that's what students will have in their careers?
There are many subskills that you must be proficient in without tools, before you can learn more interesting skills. You need to know how to do multiplication by hand before you rely on a calculator. If you can't do multiplication with a calculator, you're not going to be able to make sense of the concepts in Algebra.
Algebra has nothing to do with long hand multiplication, people who say otherwise can't do either.
We know, because we taught computers how to do both. The first long multiplication algorithm was written for the Colossus about 10 minutes after they got it working.
The first computer algebra system that could manage variable substitution had to wait for Lisp to be invented 10 years later.
Baby rather than Colossus. Colossus wasn't programmable.
>Jack Good, a veteran of Colossus practice at Bletchley Park, later claimed that, if appropriately configured, Colossus could almost have carried out a multiplication but that this would not have been possible in practice because of constraints on what could be accomplished in a processing cycle. We have no reason to doubt this, though it would presumably have required special settings of the code wheels and message tape and been, even if possible, a rather inefficient alternative to a desktop calculator. This fact has been offered as proof of the flexibility of Colossus, which in a sense it does attest to: a device designed without any attention to numerical computations could almost have multiplied thanks to the flexibility with which logical conditions could be combined. Yet it also proves the very real differences between Colossus and devices designed for scientific computation. Multiplications were vital to computations, and a device that could not multiply would not, by the standard of the 1940s, be termed a “computer “or “calculator.”
https://www.sigcis.org/files/Haigh%20-%20Colossus%20and%20th...
The limitation seems to have been physical rather than logical.
There are also many subskills not worth learning to some people. Sometimes traversal is what's needed and not understanding. (Though I'm never going to knock gaining more understanding)
Tools allow traversal of poorly understood, but recognized, subskills in a way that will make one effective in their job. An understanding of the entire stack of knowledge for every skill needed is an academic requirement born out of a lack of real world employment experience. For example, I don't need to know how LLMs work to use them effectively in my job or hobby.
We should stop spending so much time teaching kids crap that will ONLY satisfy tests and teachers but has a much reduced usefulness once they leave school.
Yes, totally. Relevant study: https://www.media.mit.edu/publications/your-brain-on-chatgpt...
I doubt they’re talking about entry level maths.
Why should other subjects be any different?
Are multiplication and long division by hand really necessary skills?
I never need to "fall back" to the principles of multiplication. Multiplying by the 1s column, then the 10s, then the 100s feels more like a mental math trick (like the digits of multiples of 9 adding to 9) than a real foundational concept.
Exactly, this is the reason why I struggle with this sort of solution to the problems we are all facing in education currently. On the surface it seems to make sense, but the blue book exam is entirely artificial and has basically no relationship to real world skills (subconsciously, even the quality of student handwriting handwriting could influence how graders assess blue books). Even leaving AI aside, anyone writing anything nowadays is using Google and Wikipedia and word processors, so why constrain those?
Oxford and Cambridge have a "tutorial" system that is a lot closer to what I would choose in an ideal world. You write an essay at home, over the course of a week, but then you have to read it to your professor, one on one, and they interrupt you as you go, asking clarifying questions, giving suggestions, etc. (This at least is how it worked for history tutorials when I was a visiting student at an Oxford college back in 2004-5 - not sure if it's still like that). It was by far the best education I ever had because you could get realtime expert feedback on your writing in an iterative process. And it is basically AI proof, because the moment they start getting quizzed on their thinking behind a sentence or claim in an essay, anyone who used ChatGPT to write it for them will be outed.
It really boils down to: are universities trying to teach abstract knowledge, or are they trade schools?
If they are trade schools, yes teach React and Node using LLMs (or whatever the enabling tools of the day are) and get on with it.
Not sure how it is these days, but at Cambridge, supervisions (what Oxford calls tutorials) did not contribute to our examination / tripos scores. They were just a learning aid.
> Even leaving AI aside, anyone writing anything nowadays is using Google and Wikipedia and word processors, so why constrain those?
And the library, and inter-library loan (in my case), and talking to a professor with a draft...
As a CS student I rather enjoyed the blue book essay exams in my classics courses.
And it did teach and evaluate skills I’ve used me entire career.
For the same reason I wasn’t allowed my extremely powerful SAT solver calculator in my maths exams (for high school and first year uni where it would’ve helped):
Because I was demonstrating that I understood the material intrinsically, not just knew how to use tools to answer it.
If there weren’t differences between the educational environment and the workplace, that would be the same as if you just dumped people straight into the workplace with no education. For education to be useful at all it has to be distinct from the “real world” and optimized for learning. One way of optimizing for learning is to make the student solve the problem the hard way, so the student understands the entire process and not just the parts that are harder to optimize.
most exams aren't about solving a problem, it's about demonstrating that you've learned something.
Sadly, I think that's what's going to be lost in the switch back to exams: the ability to assess someone's ability to iteratively solve a problem or craft a thesis.
Would you let a second grader take their spelling test using a word processor with a spell checker?
They’re proof you learned the topic well enough to coherently write a very-few pages about it. That’s what they’re for.
Making them open book + AI would just mean you need “larger” questions to be as effective a test, so you’re adding work for the graders for basically no reason.
Because a tradeoff of relying on calculators means the average person can't do simple math on their own. It would be bad for society if a crutch for general thinking dulls those skills the same way calculators dulled home economics skills. In theory people could pull out a calculator at the grocery store but I've never seen it happen.
I don't know what you mean by "home economics", but to me, that encompasses things like balancing a checkbook and making a budget and taxes and understanding how savings and debt and compound interest works how to choose when to save and when to go into debt. The sort of money matters that apply to any schmuck trying to live in the world. The reason so many people lack those skills is that for the most part we don't teach them in high school. Calculators have nothing to do with it.
Thank god we still teach quadratic equations, complex numbers, hyperbolic trig functions, and geometric constructions though. I don't know what would become of the world if most people didn't understand those things when we set them loose in the world.
The problem is not that a student can ask AI for answers. The problem is that the student has to have an idea what questions to ask.
For that, the student must have internalized certain concepts, ideas, connections. This is what has to be tested in a connectivity-free environment.
In fact, why teach the material at all?
Can’t use AI on a date, or at a dinner party, or during a board meeting.
Faking intelligence with AI only works in an online-exclusive modality, and there’s a lot of real world circumstances where being able to speak, reason, and interpret on the fly without resorting to a handheld teleprompter is necessary if you want to be viewed positively. I think a lot of people are going to be enraged when they discover that dependency on AI is unattractive once AI is universally accessible. “But I benefited from that advantage! How dare they hold that against me!”
> Can’t use AI on a date, or at a dinner party, or during a board meeting.
Challenge accepted. One possible solution: https://github.com/RonSijm/ButtFish
Cheaters are universal no matter what social boundaries are defined, and neither high-bandwidth wireless signals nor onboard acoustic processing can be reliably performed within the human rectum to any reasonable degree of fidelity. If one would externalize basic critical reasoning skills, I encourage finding another location to store one’s supplemental cranium :)
>Can’t use AI on a date, or at a dinner party, or during a board meeting.
I get the same "you won't always have a calculator with you" vibes from 90s teachers chiding you to show your work when I hear people say stuff like this.
I wouldn’t equate trigonometry, which underpins the classic parabolic example you’re referring to, with critical reasoning in human conversation. One is situationally useful at best; the other is mandatory to prevent exploitation by malicious people. Mental quadratics may be appealing, but the ability to reason is the bare minimum. Besides: if you’re using a calculator or AI in a board meeting, you’re likely unprepared for the board meeting.
I'm not sure how you did proofs in trigonometry with a calculator.
I ran my school district out of math to teach me in the 80s and ended up focusing on sysadmin in the 90s rather than repeating trigonometry or pursuing formal math at the local college. Sorry I can’t be of more use to your argument! Perhaps someone else will have applicable experiences.
You say that like those teachers were incorrect. They were correct, and still are correct. You don't always have a computer to hand, and you do in fact need to be able to do basic math.
It's pretty rare that I don't have quick access to a calculator. Which really reduces the basic math I need to do in my head.
It's more likely I will not have paper and writing implements than not having a calculator.
Besides, most people have room for fast arithmetic or integrals; fast arithmetic would be more useful, but I'm not putting the time in to get it back.
Also LLMs have fairly well proven that even if you have calculator you probably should have ability to do some sanity check on the answer. In case you hit wrong button for example. With LLMs they can be confidently wrong and unless you are able to tell you are out of luck...
Plus all about capability to actually retain whatever you ask from the model...
Ironically, America finally automated one of our oldest workplace specialties: grifting! People overconfidently declaring made-up nonsense in board meetings is a classic executive behavior. I suppose it’ll be interesting to see what happens now that everyone has one in their pocket. Will their patter improve from exposure alone, or will they more easily detected because their skills weaken from disuse?
If I don't have access to my phone the power grid has been down for at least two days and by that point I've got more pressing issue than showing my work when doing basic math.
So we just give up on direct reading comprehension and critical thinking?