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The Most Common Errors in Undergraduate Mathematics (2009)

math.vanderbilt.edu

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Re: The Most Common Errors in Undergraduate Mathematics (2009)

#121

Post by hintymad »

lmilcin wrote: post #47

I 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…

Maybe college-level math is different from math taught in a maths depart? Either way, the common errors mentioned in the article appear to be, well, elementary. I'd imagine 6 or 7 graders make those mistakes, but college students? Shouldn't they make mistakes like "there is no function that is everywhere continuous but nowhere differentiable", or "isomorphism of factors implies isomorphism of quotient groups"? The webpage says a lot about the quality of the K12 education in the US.

Re: The Most Common Errors in Undergraduate Mathematics (2009)

#122

Post by hintymad »

bmitc wrote: post #99
lmilcin wrote: post #47

I 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…

The problem exists in the educational methods, in my opinion. It seems most, not just in mathematics, feel that learning is the same as if the student can simply be played a tape that cannot be paused or rewound but can sometimes be sped up. Nearly nothing works like this, and it’s just that the penalties in mathematics are greater. I think of the ideal learning path as a sort of circular, recursive path that bends b…

I thought this was what university did. For instance, there's a little stats in calculus courses, then there's stats in mathematical stats courses, then in queuing theory course, then in networking course, and of course in all kinds of statistical learning and machine learning courses. By the time you finish those courses, you will get a pretty good grasp of basic stats.

Re: The Most Common Errors in Undergraduate Mathematics (2009)

#123

Post by lmilcin »

hintymad wrote: post #122
bmitc wrote: post #99

Earlier quoted context omitted.

The problem exists in the educational methods, in my opinion. It seems most, not just in mathematics, feel that learning is the same as if the student can simply be played a tape that cannot be paused or rewound but can sometimes be sped up. Nearly nothing works like this, and it’s just that the penalties in mathematics are greater. I think of the ideal learning path as a sort of circular, recursive path that bends b…

I thought this was what university did. For instance, there's a little stats in calculus courses, then there's stats in mathematical stats courses, then in queuing theory course, then in networking course, and of course in all kinds of statistical learning and machine learning courses. By the time you finish those courses, you will get a pretty good grasp of basic stats.

As long as we are talking math, you can take a bunch of books and learn the same without need for university. You can even go to talk to somebody who will tell you what books to take and in what order.

What university does is help you connect with other people who study the same, to observe or work with them when solving problems and to have access to people working the cutting edge of the discipline you are studying who you would not normally have access to.

Also, it gives a little bit pressure which might be important for some or most people.

Oh, and official credentials.

Re: The Most Common Errors in Undergraduate Mathematics (2009)

#124

Post by ac42 »

mattbk1 wrote: post #37
commandlinefan wrote: post #34

Earlier quoted context omitted.

That's what my (junior in high school) son keeps saying when he makes simple arithmetic errors that cost him points on tests. I disagree, actually - these mistakes are made by lack of practice. If you've practiced solving enough integrals, it doesn't really matter how tired you are, you're going to get the right answer just as you won't read words incorrectly if you're tired.

I read words incorrectly when I'm tired. Is this abnormal?

At the least, you're not alone.

Re: The Most Common Errors in Undergraduate Mathematics (2009)

#125

Post by kmill »

konjin wrote: post #111
ubercow13 wrote: post #73

Earlier quoted context omitted.

I honestly never found this an issue. Shorthand and type coercion is used a lot but at least when taught, it's usually made very explicit what notation means and when things are being excluded. After that point, the notation is the least challenging part.

It is not an issue until you start trying to teach any sort of fix point theorem, at which point the wheels fall off because the notion can't deal with higher order functions at all.

I use the mapsto arrow frequently for higher-order functions, and it seems to work fine for me.

Re: The Most Common Errors in Undergraduate Mathematics (2009)

#127

Post by vitus »

ghaff wrote: post #103
kkylin wrote: post #60

Earlier quoted context omitted.

Not arguing with your point, because it has merit, but do want to add that part of the problem with math education (at least here in the US) is structural: for most students, to start with what they know when they enter and to graduate in 4 years with a engineering / science / math / CS degree that means something, there is just too much to "cover." So we tend to cover "methods and tools," e.g., calculus first, with…

>It used to be (this tells you how old I am) Why do you say that? Maybe it's atypical but MIT seems to have the same calculus and physics sequence, taken in parallel, that they did ages ago.

At Berkeley, for instance, there were multiple Physics sequences: engineering + physics + chem majors took the 7 series ("Physics for Scientists and Engineers"), which used calculus; for most other majors (e.g. premed), the 8 series ("Introductory Physics") sufficed for degree requirements.

http://guide.berkeley.edu/courses/physics/

(Also, note that this is similar to the split between the AP Physics B and C courses that high school students might take. Physics B has apparently been replaced with Physics 1 / 2, both of which are algebra- rather than calculus-based.)

I think ultimately this is a function of where you went to school, more than anything.

Re: The Most Common Errors in Undergraduate Mathematics (2009)

#128

Post by Izikiel43 »

opnitro wrote: post #40
woliveirajr wrote: post #18

Earlier quoted context omitted.

When I was 9 I failed some question about fractions because I saw one 6 and it was just a bad written 5. At that age it took me a while to understand where the problem was and too late to ask my teacher to reconsider it. Well, was so intense that I remember it until today, 30 and some years later.

Ever since I failed similarly I write my sevens with a line through them to prevent them being confused for ones

I always do that, but people confuse 1 with 7 anyways, even when both are written in the same number.

Re: The Most Common Errors in Undergraduate Mathematics (2009)

#129

Post by Izikiel43 »

mcguire wrote: post #102

" Loss of invisible parentheses. This is not an erroneous belief; rather, it is a sloppy technique of writing. During one of your computations, if you think a pair of parentheses but neglect to write them (for lack of time, or from sheer laziness)... " " The great number of sign errors suggests that students are careless and unconcerned... " Sounds like someone thinks they should have a better class of students.

I had a recurrent error to add extra parenthesis at the end I think

Re: The Most Common Errors in Undergraduate Mathematics (2009)

#130

Post by godelski »

magicalhippo wrote: post #100
godelski wrote: post #45

Earlier quoted context omitted.

I find this concept of being a numbers person weird to being good at math. Most math is about symbol manipulation and numbers are really only at the end.

> Most math is about symbol manipulation and numbers are really only at the end. During the first semester at uni, the math prof was going through some non-trivial (at that stage) "real-world" example involving definite integrals. After what felt like 10 minutes of manipulating integrals and such we got to the final "x = ..." equation, upon which he turned away from the blackboard and said "and then you can just plug…

Middle School / High School: "What are these letters doing in my math?!"

Post University: "What are these numbers doing in my math?!"

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