Mathematical skills and aptitude are best examined by oral examinations, not written ones. Discuss.

14 thoughts on “Weekend discussion”

For me the answer is yes. My favorite professor says that by listening to someone explain a mathematical concept, he can tell in 10 minutes if the person knows what he or she is talking about. By my own admission, my performance on written timed tests is abysmal. If I were judged solely on this measure, I would be considered a complete idiot. Yet, when I can stand in front of someone and explain a problem on the blackboard, I have no problem presenting the material. This is the method I prefer and it is fortunate that my professors are accommodating. Life is not a timed written exam and I see no benefit to trying to do math under time pressure. The interactive oral exam will reveal any lack of understanding of fine points on the part of the student fairly quickly, in my experience. I’ll get off my soapbox now…

Life is not a timed written exam and I see no benefit to trying to do math under time pressure

Speak for yourself. Only this morning, as part of my job in “the real world”, I was asked to build a smoothed particle hydrodynamics fluid solver from scratch as fast as I possibly can. Meanwhile I’m simultaneously busy finishing some convolution code that was due two days ago…

Do you mean that you do see a benefit? The requirement has always been there (e.g. the calculation by hand in Apollo 13, the movie), but I usually can tell if I’m forcing myself to do something faster than I reliably could.
I think it’s interactive vs non-interactive that we’re talking about (i.e. it doesn’t have to be oral; it could be on MSN messenger with mathml support, etc.). Then, I’d claim that dialogues are a superset of monologues.
However, if it’s oral skills we’re concerned with, then it’s a deeper subject. I can usually tell if a person is sloppy or rigorous in the first two minutes. You can also tell if he’s creative when he realizes that you’re having trouble understanding his concepts and invents clever examples.

I have to agree with sigfpe. In an effort to make education accessible to everyone, we over look the fact that the “real” world of business is not going to make the same adjustments. But that is a different subject.

As far as oral vs. written exams go, I much prefer a written exam when the subject is math. I can draft out my answers, check them over, and then write a well thought out response. It is far more difficult for me to speak sensibly without significant preparation.

The two approach have their own difficulties:
Oral examinations can better test if someone has a good knowledge of the subject, however from my point of view it is more difficult to reasoning with a cold mind.

Written test can permit a better atmosfere for the tested, but if the exercise is known it is more mechanical.

Oral exams are harder, and better gauge the candidate’s knowledge of math, because the examiners can make sure the person really understand and can prove the claims he makes.

I also don’t quite understand the discussion in the first few posts, because there is clearly no dichotomy between time pressure and oral exams. Examiners in an oral exam can take into account the time the candidate takes to solve the problems.

It is also possible to combine both forms of testing (that’s how math exams are done at my high school): the candidate is handed out the subject and allowed a certain amount of time to write down a preparation, and then has to present their answers orally at the blackboard, and examiners can ask additional questions (like asking the candidate to give a sketch of proof for a theorem they have used). I think this is the optimal solution.

The University of Cambridge Mathematics Tripos was an oral exam until the mid 18th century, when it became a written exam. This change was apparently introduced despite much protest from the Cambridge faculty. One argument made was that written exams could not assess students fairly, because they asked everyone the same questions. Asking a uniform set of questions would be like forcing everyone to wear the same-size clothes, which would be unfair to larger and smaller people. Only by allowing questions to be student-specific could the assessment be fair.

My colleagues from the countries of the former Soviet Union tell me that oral examinations in mathematical subjects are still the norm there for undergraduate students.

Oral exams are better if you know the material, since it becomes quite clear early on that you do, and you get to move on. Written exams favor angle shooters.

Actually, my oral examination experiences have been uniformly and simultaneously nerve wracking yet positive, since no one was interested in silly oversight mistakes like sign errors, etc.

I’m not sure written exams are that anonymous, unless the classes are very large. I review anonymous research papers, and I can usually tell who are the authors when the papers are in my own field. The same is true for anonymous reviews I receive on my own submitted papers. Likewise, with student exam scripts — either the hand-writing or the style of argument can give away the identity of the student to the marker.

I was an undergrad student with a guy who was a brilliant theoretical physicist and pure math’n, who used to write in his exams: “This question is beneath me!”. This was true, and both he and his professors knew it to be true. So he rarely lost any marks for doing this. So much for anonymity.

Peter : Exams should not be corrected by the same professor who train the students. In any case, you can always find a flaw in any system… The question is not which system is perfect but which one is the best.

For me the answer is yes. My favorite professor says that by listening to someone explain a mathematical concept, he can tell in 10 minutes if the person knows what he or she is talking about. By my own admission, my performance on written timed tests is abysmal. If I were judged solely on this measure, I would be considered a complete idiot. Yet, when I can stand in front of someone and explain a problem on the blackboard, I have no problem presenting the material. This is the method I prefer and it is fortunate that my professors are accommodating. Life is not a timed written exam and I see no benefit to trying to do math under time pressure. The interactive oral exam will reveal any lack of understanding of fine points on the part of the student fairly quickly, in my experience. I’ll get off my soapbox now…

Speak for yourself. Only this morning, as part of my job in “the real world”, I was asked to build a smoothed particle hydrodynamics fluid solver from scratch as fast as I possibly can. Meanwhile I’m simultaneously busy finishing some convolution code that was due two days ago…

Do you mean that you

dosee a benefit? The requirement has always been there (e.g. the calculation by hand in Apollo 13, the movie), but I usually can tell if I’m forcing myself to do something faster than I reliably could.I think it’s interactive vs non-interactive that we’re talking about (i.e. it doesn’t have to be oral; it could be on MSN messenger with mathml support, etc.). Then, I’d claim that dialogues are a superset of monologues.

However, if it’s oral skills we’re concerned with, then it’s a deeper subject. I can usually tell if a person is sloppy or rigorous in the first two minutes. You can also tell if he’s creative when he realizes that you’re having trouble understanding his concepts and invents clever examples.

I have to agree with sigfpe. In an effort to make education accessible to everyone, we over look the fact that the “real” world of business is not going to make the same adjustments. But that is a different subject.

As far as oral vs. written exams go, I much prefer a written exam when the subject is math. I can draft out my answers, check them over, and then write a well thought out response. It is far more difficult for me to speak sensibly without significant preparation.

The two approach have their own difficulties:

Oral examinations can better test if someone has a good knowledge of the subject, however from my point of view it is more difficult to reasoning with a cold mind.

Written test can permit a better atmosfere for the tested, but if the exercise is known it is more mechanical.

Oral exams are harder, and better gauge the candidate’s knowledge of math, because the examiners can make sure the person really understand and can prove the claims he makes.

I also don’t quite understand the discussion in the first few posts, because there is clearly no dichotomy between time pressure and oral exams. Examiners in an oral exam can take into account the time the candidate takes to solve the problems.

It is also possible to combine both forms of testing (that’s how math exams are done at my high school): the candidate is handed out the subject and allowed a certain amount of time to write down a preparation, and then has to present their answers orally at the blackboard, and examiners can ask additional questions (like asking the candidate to give a sketch of proof for a theorem they have used). I think this is the optimal solution.

as someone who’s about to take his orals in a week and half, i can only say that i wish they’d never been invented.

The University of Cambridge Mathematics Tripos was an oral exam until the mid 18th century, when it became a written exam. This change was apparently introduced despite much protest from the Cambridge faculty. One argument made was that written exams could not assess students

fairly, because they asked everyone the same questions. Asking a uniform set of questions would be like forcing everyone to wear the same-size clothes, which would be unfair to larger and smaller people. Only by allowing questions to be student-specific could the assessment be fair.oral approach are the most sutisfactory

My colleagues from the countries of the former Soviet Union tell me that oral examinations in mathematical subjects are still the norm there for undergraduate students.

Oral exams are better if you know the material, since it becomes quite clear early on that you do, and you get to move on. Written exams favor angle shooters.

Actually, my oral examination experiences have been uniformly and simultaneously nerve wracking yet positive, since no one was interested in silly oversight mistakes like sign errors, etc.

Oral exams allow discrimination. Written exam don’t if they are anonymous.

I’m not sure written exams are that anonymous, unless the classes are very large. I review anonymous research papers, and I can usually tell who are the authors when the papers are in my own field. The same is true for anonymous reviews I receive on my own submitted papers. Likewise, with student exam scripts — either the hand-writing or the style of argument can give away the identity of the student to the marker.

I was an undergrad student with a guy who was a brilliant theoretical physicist and pure math’n, who used to write in his exams: “This question is beneath me!”. This was true, and both he and his professors knew it to be true. So he rarely lost any marks for doing this. So much for anonymity.

>So much for anonymity.

Peter : Exams should not be corrected by the same professor who train the students. In any case, you can always find a flaw in any system… The question is not which system is perfect but which one is the best.