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The Most Common Errors in Undergraduate Mathematics (2009)
61–70 of 161 posts
Re: The Most Common Errors in Undergraduate Mathematics (2009)
#62I studied theoretical mathematics. The absolutely biggest and most common error and really the only one worth to be on list is not internalizing and understanding entirety of material as the course progresses. Everything else should be basically to achieve goal of understanding the entire course material. It is ok to forget later, as long as you are sure you understood it at least when there was a lot of discussion a…
I would agree, but qualify by saying that not all the blame lies with the student. Precisely because mathematics is so interconnected, beginning students really do require an experienced guide to navigate through the tangled web of concepts. A particularly bad or lazy professor can be worse than no professor at all.
> students really do require an experienced guide to navigate through the tangled web of concepts.
Consider how much people pay for education and don't get this, and how much some people are paid to be teachers who do not provide it.
Re: The Most Common Errors in Undergraduate Mathematics (2009)
#63Bad handwriting. At age 40 I started taking a masters in stats and had situations where I had exponents on exponents. This lead me to buy a higher resolution tablet for reading pdf's with tiny math. I also bought a finer point pen and this helped me improve my handwriting a lot . Closing loops on "o's" or backtracing the upward line of a cursive "t" to not make a loop. With the finer point, I was able to see my impre…
\tangent can you recommend what to look for in a tablet for mathematics? I've got a lenovo M8 - only 8", 800p, but I think that's OK; it's the insufficient contrast of IPS screen that makes my eyes tired (suggesting AMOLED or epaper) - but I don't know the cause for sure... What did you find?
Re: The Most Common Errors in Undergraduate Mathematics (2009)
#64Earlier quoted context omitted.
I would agree, but qualify by saying that not all the blame lies with the student. Precisely because mathematics is so interconnected, beginning students really do require an experienced guide to navigate through the tangled web of concepts. A particularly bad or lazy professor can be worse than no professor at all.
> students really do require an experienced guide to navigate through the tangled web of concepts. Consider how much people pay for education and don't get this, and how much some people are paid to be teachers who do not provide it.
Oh yeah, I'm with you there. Teaching quality at both my undergrad math program and my graduate compsci program was abysmal, with the exception of a handful of dedicated teachers. Both at well-ranked research institutions, which is the problem.
The whole system is crazy. Why on earth do we allow tuition money to be spent on anything else but full-time teaching staff?!
Re: The Most Common Errors in Undergraduate Mathematics (2009)
#65Earlier quoted context omitted.
> I would go to office hours and the teachers were seriously so helpful. As a grad student that taught undergrads I always encouraged students to attend office hours. Most instructors do want you to succeed and one-on-one time is one of the best ways to learn. Definitely take advantage of your instructors' office hours; ask questions about anything that you aren't 100% sure about!
> I would go to office hours and the teachers were seriously so helpful. This was the only way I survived. I learned that you don't have to be a 'numbers person' at all to be good at math. You just have to understand what's going on under the hood, and this may require lots of questions and outside help. But most importantly, you just have to practice I agree with all of this and it's how I got through extensive math…
> I made sure to get to the office hours and I was surprised that there was almost no one there most of the time.
One of my biggest regrets about university is not taking advantage of office hours. For me it was a combination of 1) social anxiety and 2) thinking that if I really belonged in this program (physics) I should really be able to figure everything out on my own. I know now that this is a stupid way to think but it's the way I felt at the time.
Re: The Most Common Errors in Undergraduate Mathematics (2009)
#66Most of these appear to be errors caused by stress or tiredness.
More lack of preparedness. My approach in setting exams was always that someone who actually understood the material well would find most of the exam quite easy - i.e. you'd be able to pass without focusing hard. Getting top marks would require deeper understanding. The basic idea here is that any student who genuinely understood the course material should definitely be able to pass even on a bad day, or a bad exam schedule, etc. If you can't meet that mark, you shouldn't advance.
Re: The Most Common Errors in Undergraduate Mathematics (2009)
#67To me the biggest problem was conversion of terms/formulars.
I knew all the rules, but when I needed to reach a specific form I somehow ended up running in circles.
Calculus felt more like learning chess than learning math. You needed to think three conversions ahead to get a result and that had to be practiced.
Re: The Most Common Errors in Undergraduate Mathematics (2009)
#68Earlier quoted context omitted.
> students really do require an experienced guide to navigate through the tangled web of concepts. Consider how much people pay for education and don't get this, and how much some people are paid to be teachers who do not provide it.
Oh yeah, I'm with you there. Teaching quality at both my undergrad math program and my graduate compsci program was abysmal, with the exception of a handful of dedicated teachers. Both at well-ranked research institutions, which is the problem. The whole system is crazy. Why on earth do we allow tuition money to be spent on anything else but full-time teaching staff?!
I'm now interested in a list of transactions ordered by participant dissatisfaction, like, paying for gym memberships and not getting the outcomes they want, therapy or medical attention to mostly be ignored by the provider, ISPs in the US, online shopping to get something wildly different.
Is education especially bad compared to these things? or just that it's such a large expenditure we just-world-fallacy ourselves into thinking it ought to work better?
Re: The Most Common Errors in Undergraduate Mathematics (2009)
#69My biggest problems as a math major at the undergraduate level were proofs. I could muddle my way through abstract algebra proofs but real analysis just didn't click. The oddity is that I could read proofs for both subjects: the reasoning made sense. But I couldn't develop a proof.
I had a similar experience doing my math minor. All the way through Caluclus classes and Diff EQ and up until the first half of Linear Algebra, everything is plug and chug. After the first half of Linear Algebra when proofs started making an appearance, I came to the realization that proofs are another type of mental activity entirely. Survey of Algebra, Basic Real Analysis, and even the dedicated proof writing cours…
>the dedicated proof writing course
What was yours like? The one I took didn't cover much on the actual writing of proofs. The professor accepted reasonable essays with high-school level notation. Instead, he gave us a toolbox for proving things: pairing terms in a series to find the sum, rewriting recursive equations, etc. It was mostly to show that clever tricks are how mathematicians prove new things. But that might've been because the professor was a guy who reveled in clever solutions.
Re: The Most Common Errors in Undergraduate Mathematics (2009)
#70I understood the mathematics, but made a lot of silly errors, e.g. misreading -/+. Messy handwriting, crammed layout and too many steps at once all contributed, but I also just made many mistakes.
It felt impoosible to fix and didn't seem worth it since the understanding was what I valued. But since I never felt confident in my results - checking the answer was always suspenseful - my mathematics was useless, to actually use, without an answer to check.
So I decided to methodically notice where I made errors, and to verify those particular places. "It might take me twice as long", I thought, "But at least I'll have the skill to do it, when needed, and be able to have results I can actually use!"
So I began this, and it did take twice as long, and it worked. That sense of suspense started to disappear, because knew I had the correct answer. I became more skilled at checking, so it look less time. And then a very strange thing started to happen...
I started to make those mistakes less often. I became attentive to them as I was making them. Then stopped making them. I didn't antipicate or account for this at all... I thought it was impossible for me to change - it was like magic.
In hindsight, this was "deliberate practice", with the key quality of not just repetitive practice (which eventually plateaus), but practice focussing on appropriate aspects, changing as needed.
An expert coach really helps here, both for identfying issues and psychological encouragement. Although I managed this particular one on my own, it was hard. But finding such a coach seems even more difficult! And I'm so obstinate, I'm not sure I would pay attention anyway...