What kind of standard we need to maintain when preparing advanced level mathematics term test papers ?
In many cases I have seen test papers prepared using exactly past paper questions and in some occasions with slight changes in values and letters used in past papers . Since students have better chance of getting much exposure to past papers and answers they score higher marks when the papers also contains questions very much similar to those.
My opinion is we need to prepare students for the future and not for the past, therefore we should concentrate much on new type of questions and questions which cover the areas not considered in past papers. I suggest that is the better way to encourage students to learn the subject and not just to be exam oriented. What would you have to say about this?
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4$\begingroup$ I'm voting to close because this is just a request for discussion, not a real question. $\endgroup$– Alexander WooCommented Oct 29, 2022 at 3:39
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2$\begingroup$ Also, consider that many students have, for whatever reason, no problem solving ability - no ability to apply their knowledge to problems they have not encountered before, no matter how well they can recite their knowledge - and cannot reasonably attain a reasonable aptitude at problem solving within the duration of their studies. Now you have to decide, within the context of your educational culture, whether it is or should be considered fair for such students to be doomed to failure no matter how hard they study. $\endgroup$– Alexander WooCommented Oct 29, 2022 at 4:00
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3$\begingroup$ Stackexchange is a site for fact-based answers to questions that can be answered with facts. It is not a discussion site. Please take requests for discussion elsewhere. Of course this is an important question to discuss, but not every place is suitable for every purpose. $\endgroup$– Alexander WooCommented Oct 29, 2022 at 4:19
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1$\begingroup$ I’m voting to close this question because it is meant for discussion, not for factual answers. $\endgroup$– Sue VanHattum ♦Commented Oct 29, 2022 at 15:49
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2$\begingroup$ @AlexanderWoo "Stackexchange is a site for fact-based answers to questions that can be answered with facts." While I agree that not every question should fly, the description you give seems way too narrow for me, especially if we take into account that mathematical education is only half science and the other half is art, so there are hardly any "facts" there beyond the most trivial observations like "stick and carrot always work best when balanced correctly", while there are many bright (and dumb) ideas with a lot of controversy about them, which are open for discussion and trial. $\endgroup$– fedjaCommented Oct 31, 2022 at 11:06
1 Answer
I understand the desire to test a broad knowledge of the subject versus very select cribbed questions. All that said, study of past questions is not purely for the hope of seeing those questions again, but because they typify what is required knowledge. I would posit that it's actually pretty HARD to be able to perform well on several (say 3+) past final exams, including with changed numbers/phrasing and NOT have learned a butt-ton about the topic!
I would be wary of always pushing for something unique in that you start creating "puzzle" type questions that are testing more for intelligence (or even luck) rather than basic mastery of the subject. Yes, calculus is broader than just the subset of what questions you have time to ask. Yet, it's also a stereotypically familiar subject. So, the ability to answer TYPICAL questions is a feature, not a bug.
Think of teaching something more mechanical like carrier airplane landings or full-twisting double backs. Probably testing those should involve the exact task. Now, again, calculus (or most courses) are necessarily broader than there is time to ask about. That said, some reasonable correspondence to the course topics (and within that the most central and common and used ones) is desirable.
All in all, I think rather than scratching your head on how to make the kids scratch their heads, you should construct rather "normal" (commonplace) tests that correspond to the homework. And the drill works should correspond to what you test kids on!
Train the kids, get them over the hump. Don't worry, Nash and Ramunujan will emerge on their own, despite your not challenging them. The bigger issue in this country is getting F kids to C's. Getting C's to B's. And getting B's to A's. NOT getting A+ to A+++. Think about the number of kids you are teaching and their average capabilities.
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$\begingroup$ I'm not so sure. This should be taken with a grain of salt, because programmer productivity is hard to measure, but studies of programmer productivity have shown that the most productive programmers are 10-15 times as productive as the median programmers, who are in turn 10-15 times as productive as the worst programmers that could get hired (which means they look qualified on paper). Given that disparity in productivity, we really have a shortage only of A programmers. With the severe shortage, B programmers are useful, but C programmers are still basically useless. $\endgroup$ Commented Oct 31, 2022 at 1:53
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1$\begingroup$ The people paying the bills (taxpayers or students/parents) expect that a reasonable effort will be made to progress the average student. The nursing student taking business calculus. They don't want to see all that funding going into a course that is designed around releasing the reluctant John Nash. He needs to unleash himself on his own. Or not. Not everyone chooses to go down that path. That's life. $\endgroup$– guestCommented Oct 31, 2022 at 17:30