Hacker News Reader

Comment by WalterBright | Hacker News Reader

> believing that because facts or formulas or arguments are easy to remember right now, they will remain that way tomorrow or the next day.

This is sad, it confuses education with memorization. I was fortunate in winding up at Caltech, which had a policy of open book / open note exams. The idea wasn't to memorize formulae, it was to learn how derive the formulae and then apply them properly.

For example, in AMA95 one of the lectures went through deriving the fourier transforms. On the final exam one of the questions was to derive the hyperbolic transforms. If you understood the fourier ones, you could derive the hyperbolic ones. If not, well, you were lost.

In Physics 2, one lecture showed how the characteristics of magnetism could be derived from the idea of electric charges. An exam question was to show the characteristics of electric fields given the existence of magnetic monopoles.

Anybody can look up a formula in a book, and then misuse it.

View on HN

If you majored in physics, you'd probably come to find out this isn't specific to CalTech, but it's typically specific to hard sciences and engineering disciplines.

Probably 80% of the physics courses I've taken (and people that I know have taken) are almost all like this. Open Note and/or Open Note+Homework and/or Open Book (and occasionally open laptop), typically with a class averages of around 40-70% on the exam

I don't know about how other colleges do it. But I have run into a lot of "formula plugger" engineers who, as far as I could tell, did not understand where those formulas came from nor when the formulas were inapplicable.

I also majored in ME. Caltech requires 2 years of Physics for everyone.

That is no necessarily a bad thing though. When you are designing a bridge, you had better not be deriving equations. My grandfather was an flight repair manager. He always had the tables up on the walls for the guys, not even equations. His thinking was that if you remembered the torque on the wheel brakes, you could also mis-remember them. Therefore, 'Never remember anything!' was the motto. I can only assume this maxim came about after a very scary incident. This also applied to much engineering and design. Yes, it is sad to see and hear about minds gone to 'waste', but it is very necessary for life to not go to waste.

In my experience, when people used formulas with no understanding of where those formulas came from, nor what assumptions underlaid them, they misapplied them. All book formulas are based on models, which have limitations.

Would you really want formula pluggers designing life critical systems? Not me.

Book values, however, provide valuable feedback on whether an answer is correct or not. While the book may not provide the right formula for the job, it often provides formulas that "bracket" the right answer, and so can be used as a reasonableness check.

A central part of engineering design are reasonableness checks.

To speak on civil engineering, of which I have only observed from the outside:

They do use formulas and calculate things, but they do NOT recalculate the constants, even though they may be derived each time. The tensile strength for steel is just assumed, from what I can tell, even though it falls out of tests and formulas itself.

In fact, I would trust the computer better than the deriver. The guy that just plugs it in, in a proven system, is safer to my ears. The guy that recalculates everytime is bound to have false positives and negatives and whatnot in the calculations. A good aphorism is 'A man that has one watch knows the time, a man with 2 is never sure.'

I do agree on the standard values though, it does give a ball park, and that is valuable.

One thing to keep in mind is that the brain power required to do all these calculations simply does not exist. Physicists typically are less then 5% of a undergraduate class, I'd actually argue for less, but I haven't a source. These are the guys that can run the calculations through everytime. However, the need for the various jobs is FAR outstripped by the output. Hence you get engineering and the margin of safety, as we know you can't get the proper people in there, but you have to get someone to check at least something otherwise the people will just make it regardless of safety. And then boom, bob's your uncle, you get the casualty differences between Chinese earthquakes and the 6er in Napa.

Yes, it's not much, but it's better than nothing.

Yep at Univ. of Rochester as physics undergrads we were often allowed a single sheet of paper with anything on it (we were told no microfiche!). I did a few open book exams but still made the "cheat" sheet. We all spent a great deal of time preparing that sheet. You had to study to really know what to put on the sheet. I often found that I did not need the sheet in the actual exam because the process of preparing it helped to bring the concepts forward in my mind.

In grad school as classes got more difficult, we had take home exams even. I always dreaded these because they were substantially more difficult than a regular exam. Generally if you didn't have the concepts down, having an entire library at your disposal was not helpful in that case.

One maths class we were only warned that we had to use Euclidean paper.

I did great in exams with cheat sheets, but poorly in the few truly "open book" exams, because I didn't know how to properly prepare for an open book exam. My silly undergrad brain thought "Woohoo, open book, I guess I don't have to study all this stuff, I can just look it up when I get there" which led to two hours of feverishly flipping back and forth in the book.

Yeah, big mistake thinking open book means one doesn't have to study. I know only one guy (Hal Finney) who could learn the material during an exam :-) As I wrote elsewhere, Hal was one scary smart dude.

The "cheat sheet" thing was common at my university too.

It often turned into an exercise in finding the extreme bottom limit to how small one could write (and turned me into a fan of Pilot Hi-Tec 0.25mm pens!), so I always wondered how carefully considered the limitation to one sheet was... did they actually try out different limits and choose the one that worked best?

More limitation forces students to think about what they're including instead of just copying the textbook onto paper, but even a slight relaxation to 4-5 pieces of paper would have really helped in many cases, and allowed us to focus more on the material and less on the physical chore of preparation...

My university was the same for most math classes, but some allowed printed notes.

Creating a LaTeX template that fits everything on to the sheet was an amazing time saver.

The engineering dept at UCDavis went well beyond a single page, and usually allowed anything you wanted as long as it was print-only, book included. (nothing electronic or networked, obviously)

The idea was 1) in the real world, you have reference material which you should know how to use, and 2) test length did NOT include any extra time to look things up.

If you knew the material and just needed a quick check of some detail, you could look it up without any problem because you didn't have to search. On the other hand, if you were trying to teach yourself some concept during the test, the wasted time would probably impact how much of the test you were able to complete.

I liked that system - it seemed rather generous coming from "nothing allowed" tests in earlier schooling, and it had a side benefit of reducing the number of profs that badly reused exam questions or lazily used textbook-provided questions.

/* Yes, this policy caused some of us to find the one printer on campus that printed on A3 paper with duplex support, so we could print an electronic-only reference book at 24 pages/sheet (if I remember correctly...) */

While the Physics courses at UIUC allowed us to bring in a 'cheat-sheet', the homeworks and the exams were pretty much 'plug-and-chug' multiple-choice questions.

Back in high school (in India), Physics used to be my favorite subject. It demystified the underpinnings of natural phenomena. In fact, Electromagentism was the main reason I decided to major in Electrical Engineering. Unfortunately, the Physics courses in college left a really bad taste in my mouth.

I'm sorry for your bad experience with college Physics. May I recommend "Einstein" by Isaacson for some really great prose about the wonder of what Einstein did and tried to do.

I feel your pain. Engineering Physics (or Chemistry or Math for that matter) in India destroys your love of the subjects that brought you in there in the first place.

> I was fortunate in winding up at Caltech, which had a policy of open book / open note exams.

I don't remember that as being policy. I definitely had several closed book exams, including one memorable pass/fail final first year that I failed by one question that I could have easily answered if I could have just looked for 5 seconds in the book. It was tempting...I was taking the exam in my room, with the door closed, and the book was sitting closed within arms reach on my desk from my pre-test study session. I knew exactly where to turn to in the book to get what I needed. But taking a peek would violate the Caltech honor code, so it was or course out of the question.

The only exam policy I remember was that exams were required to be take home exams rather than in-class exams. A professor needed to get special permission if he wanted to give an in-class exam. I never had an in-class exam at Caltech.

The only in-class exams I had there were organic chemistry.

Being fluent in a topic and having concepts and facts memorized can greatly increase your ablity to conceptualize harder problems within a domain. Wouldn't you agree that even if every bit of knowledge were available for instant access through some massive google/wolfram ai database, people who internalize knowledge would have more, better, ideas on average, and more quickly, than people who had to constantly look everything up?

Of course. Oddly enough, look things up enough and you wind up inadvertently memorizing it! For example, I used to know by heart all the trig identities, not because I ever attempted to memorize them, but just by using them in practically every class.

That's a 'nice-to-have', but shouldn't form the basis of the course.

Not really nice to have. Memorizing is essential part of learning.

That the data are also out there, available in books and on the internet doesn't matter much.

Let's put it this way: a surgeon is someone that has, through training, memorized and internalized all sorts of facts, procedures and notions to be able to perform (and respond to anything that might go wrong).

The fact that I have full access to all the kinds of books and info that he had read, doesn't make me a surgeon.

And it's not just practice either. E.g. I wouldn't sit on the table of some surgeon who doesn't know the necessary stuff of his trade by heart but "can look it up on his iPad if he needs it".

I would argue otherwise. I think it's more important for surgeons to focus on understanding how different organs of the body work with and affect each other, so they can improvise when something goes off-track during a surgery, than on memorizing the name of every bone in the human body.

When you understand something, it prepares you better for the situations you haven't faced before, since you can formulate results for the new set of conditions. Also, when you look up something frequently enough, it's going to get committed to your memory automatically.

While I agree that the medical profession requires a higher degree of memorization, the context of my comment (and most others here I'm assuming) is more geared towards engineering. For example, if I was developing a course on programming, my focus wouldn't be on making the students memorize syntax and language quirks, since they can always look those up, and internalize them over time. My focus would be on developing their way of thinking, what's the right data structure to use for this problem, should I move this piece of code out as a reusable function, should I return the reference to this object or a copy, etc. This is based on my personal experience - I hardly remember anything from the 'plug-and-chug' classes which forced memorization.

tldr: the focus of education should be to cultivate and encourage understanding concepts, not rote memorization of facts and figures. Some memorization is nice for that extra bit of efficiency, but that is going to happen automatically, so no point going out of your way to do it.

>I would argue otherwise. I think it's more important for surgeons to focus on understanding how different organs of the body work with and affect each other, so they can improvise when something goes off-track during a surgery, than on memorizing the name of every bone in the human body.

That's not a real dichotomy though, as to know the different organs and how they work with each other, he also has to know their names, and memorize tons of information about them (namely, how they work with each other).

And of course, he would have to describe it to some other assistant on the operation, and "you know, that boney thing that is on the middle of the leg, and is kinda curved, and serves for stabilizing body pressure is cracked" doesn't really cut it compared to "the X bone is cracked".

I think the premise of the article is even more relevant for material that requires analysis and application, not just memorization. It's easy to get yourself in a situation where you think you know the material because you have some formulas memorized, but it's not until you get to the exam that you realize you don't understand the contours of how to apply the rules you learned.

Unfortunately all of the science referred to in the article is about memorization and not analysis, so this claim is hard to justify.

I had the same experience when I was studying in France. All of my exams were open book and I found that the exams actually reflected understanding of the subject instead of rote memorization.

I was an exchange student at RIT (Rochester Institute of Technology) and was very disappointed by the number of exams that graded rote memorization. Glad to see that Caltech is not like this.

When I worked at Boeing on gearboxes, I did some work to calculate the loads when the gear drive ran into the stops. To do that, I had to calculate the rotating moment of inertia of the gear train.

Another engineer looked over my work, and asked "what book did you get these formulas from?" I said the shape of the gear wasn't in a book, so I had to derive it.

He was shocked. I was shocked that he was shocked :-(

Wow. That's like the opposite of the exams I took in France, which were closed choice multiple choice questions asking for memorized facts.

I was in a grande école and it was their policy not to have multiple choice questions and for all of the exams to be open book. I do believe that there are differences between schools and universities in France and I was pretty lucky to be where I was.

What program were you in? I was an RIT Computer Science undergrad and (given this is one of the programs that RIT is known for) this was not my experience at all.

I failed a number of exams and classes, but none of them which I can recall were because they gave me way too many things to memorize. I failed Physics because I failed Calculus... I failed Calculus because the professor had a thick Hungarian accent until she went out on maternity leave and was replaced by a man with an even thicker Hungarian accent. In fact maybe I'm just not good at Calculus...

I failed Programming Skills electives because I had moved off campus and got a crappy part-time job, eventually lost my car, and no longer had the time to "live the life" and learn the lessons you learn from diving into the labs and the projects, working them over for dozens of hours until you get all of what ideas you are supposed to get. Actually I had a lot of 4.0 quarters until I moved off campus.

I got A's across the board in all of my Arabic classes (ok, one B) which is the only place I remember having to memorize a lot of things, except for one or two Art History classes. I had one professor in particular who I wound up grading for later, who was a master at writing tests that made you prove your actual understanding of the subject matter. He was also a master lecturer, we would often say "you only have to show up to Phil's classes and listen to be able to pass the exams."

I studied at RIT for 6 months as an exchange student in the Software Engineering department. The worst classes in term of rote memorisation were AI, Graphics Programming, Cryptography (the teacher was actually quite good though, just the exams were really bad) and Networking.

I remember one of the exam in Computer Graphics asking me when the OpenGL consortium was formed and other bit of useless trivia.

That said I did have a few interesting classes with much more interesting exams but they were in the business department.

Ah... there you have three elective classes I don't think I took, and one I did fail (AI). For the record I don't like memorizing things either.

While I do not want to distract from your main point, I think it is important to discriminate knowledge from rote memorization. Memorization and understanding are _not_ mutually exclusive, in fact, if you don't memorize/know anything, you don't have anything to work your understanding on.

I am a graduate student in Physics, and admittedly not in Caltech or one of it's peers, but I find that "memorization" (or, as I would put it, familiarity) is very important for understanding. I can't spend my time looking up formulae, I have to be able to just pull it out, or visualize it, at least. As the content I work with becomes more complex, I need to have more and more of the things I'm working on as part of my knowledge, ie., I need to memorize. If it isn't in my head, how can I put it all together?

You're right that understanding implies some level of memorization. But memorization does not imply any understanding, any more than a textbook "understands" anything.

You get from students what you test for. Testing "what is the formula relating volts vs resistance vs current" means the student can regurgitate V=IR. Understanding what that formula means is something else entirely.

I used to think I could get by without committing much to memory, but I find that I am more efficient if I add more to memory than I was willing to in undergrad.

Nonetheless, you are right to persecute those who emphasize memorization over understanding, formula plugging over understanding what a formula means because that seems to be the direction of education that is most threatening nowadays. And yes, memorization is easier than understanding.

>I was fortunate in winding up at Caltech, which had a policy of open book / open note exams

There is a widespread miscoception that openbook exams are somehow more better and forward thinking. You don't have memorize the exact formula but you still have to memorize where that formula is, one is just memorizing different kind of information.

Learning is about learning how to learn a particular subject . A good exam should test you on weather or not you can pick up/learn a new (slightly advanced) topic on your own based on your current knowledge. It should test you on what you can learn not on what you have already learnt. Open book exams don't address this fundamental flaw.

> you still have to memorize where that formula is

I don't recall a single exam question that was merely "plug the numbers into a formula and write down the answer" which is what you seem to be implying.

What were you using open book for?

The same thing you'd use open book for on homework problems.

Open book / open note changed the focus of trolling (studying) for exams. Instead of using flash cards to memorize formulas, one made sure one understood all of the homework solutions and previous exam solutions, A-Z.

Many of the formulas were far more complex than one could conveniently memorize anyway, such as the equations for jet turbine performance. And like I mentioned, none of the exam questions required mere formula plugging or had answers one could pluck out of the notes or book.

> It should test you on what you can learn not on what you have already learnt.

I'm not sure if this is the right approach, either, especially when materials get harder. It sometimes takes a lecture or two to fully teach a concept. You don't usually have that kind of time when you write an exam.

What I really enjoyed are my fluid dynamics exam. We learned all the theories in class + a handful of example scenarios. The exams had radically different scenarios than what we are used to (although if you look through it, it's the same and you apply the same principles to solve them).

I don't know if that's the right approach either, but it was fun to think about.

at that level, I think it's better to have a harder test and test understanding with open notes/books, etc.

the best professors at my school made the tests hard and the average scores pretty low. It wasn't graded on a curve but more of an "I expect A level grades to be around here, B level around here, etc...".

This only works for certain classes. You can't study history without memorizing things.

To some extent. History can be more focused on knowing concepts than factoids and dates. "Explain the role the industrial revolution played in the rise of the British Empire" is a way better exam question than "When was the British Empire founded?".

Both of those questions require memorization.

everything requires memory. You are being obstreperous. Memory alone against considered, analyical skills is the issue here.

If you want to define the debate in that way then sure, memory plus considered analytical skills is better than memory without analytical skills, but I don't think anyone was questioning that. People are more likely to question the importance of memorising things (because it's "boring") than of considered analytical skills.

One question that pops into my mind: can considered analytical skills actually be taught? I'm not sure they really can, they might be just plain old innate, in which case perhaps classes should focus on the thing that can be taught, which is stuff.

> can considered analytical skills actually be taught?

Yup. I came out of college far better at that than going in.

I'm being serious. You need to memorize a lot more facts to answer those "why" questions than you do do answer what year some war started.

Memorizing things certainly helps in every discipline.

Why having to look things up makes a bad historian, but not a bad physicist?

If you work with things a lot, you wind up memorizing them without any particular effort to do so.

Physics can be more abstract. E=MC^2 regardless of exactly how fast C is. You should have a general idea that "mass and energy are interchangeable", but you can look up the exact equation, and then look up the value of C.

This is incorrect. The interesting thing about history is not what/when, but why. Asking exam questions like "Why did Caesar's conquest of England fail, and what could he have done differently?" and "Why did the American Revolution not result in a reign of terror?" are much better.

And both of those "why" questions require memorization.

Depends. If the "why" was covered in the class material, then probably you're expected to memorize/regurgitate it. If not, if only the facts were covered, then it takes some thinking skills to select and distill the facts into a "why" narrative.

There also is no one "why", it's subjective. For example, what were "Hitler's biggest mistakes"? Ask 5 historians, and you'll get 5 different answers. A grade would be based on how well and insightfully you justified your answer.

To formulate a "why" answer you need the context, which requires some degree of memorization of previous events. You can't derive the events from first principles, but you must derive your conclusion from some knowledge.

You still have to study. You just don't have to memorize.

And you still need to have memorised things like what America is or who Hitler was.

Maybe you knew those things already before you started the class, which is nice, but no doubt there's a lot of other facts out there which you could have memorised which would help you in piecing together the historical narrative.

People criticise the rote-learning approach to things, but I think it's possible to go too far in the other direction. If, for instance, you teach your eight-year-old kids to memorise the capital cities of all the countries in the world, then that's not a huge deal of information right there, but at least you can guarantee that they've heard of every country on Earth, which puts them ahead of most adults.

Furthermore, they'll have noticed a bunch of patterns, like all the places starting with "San" or all the places ending with "-town" which can help them piece together things like which countries were Spanish or British colonies, which leads to an understanding of the history and culture of these countries, and so forth.

But you need to memorize a lot more facts to answer "Why did the American Revolution not result in a reign of terror?" than to answer "What year did the American Revolution begin?"

Reply on news.ycombinator.com