Wikipedia:Reference desk/Archives/Mathematics/2010 March 8

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March 8

Catching cheaters in a math class

Okay, so this isn't a math question exactly, but it is specific to math and people who have taught math. I am teaching Calc 1 right now and I assign homework from the textbook, some odds but mostly even. I just found that 9 of 35 students who handed in their last homework copied out of a solutions manual. There is a student solutions manual available with odds, but I'm talking about even problems. The papers of 2 are extremely obvious, word for word, and the other 7 all have several things, each of which by itself would be suspicious, so together make it pretty obvious. Basically they didn't copy as much detail, leaving out words here and there or whatever but it's still the same stuff in the manual and in the same order and all that.

This question is not about how I should handle the situation, like turn in cheaters or give them a 0 or whatever. That is going to be specific to the rules in my university and all that. But, what sort of things could I do to make sure I can catch such cheaters in the future? I want to be able to assign homework from the book because it is way easier than making it up myself. But, I don't want people getting free points. One thought I have, which may or may not work, is asking the author for an errata to the solutions manual. Then I could assign and grade those problems at least occasionally if not regularly. Then any one who copied from the manual would have the exact same mistakes as the manual and that could be a very easy way to at least clue me in to who is cheating. I may need more evidence than that to accuse them. I have emailed one author so I'll see if such an errata even exists.

Thanks for any suggestions/thoughts. StatisticsMan (talk) 16:36, 8 March 2010 (UTC)

One option is to simply not grade homework, so there's no reward for cheating in this way. You could still give smiley faces or something like that to show you appreciate them doing the homework. In this case, their grades are entirely dependent on quizzes and tests, so that doing their homework and learning the material will be rewarded. You could also have them do homework in class, and even on the board, to discourage cheating. This last option might be appropriate for those who you've caught cheating. StuRat (talk) 17:31, 8 March 2010 (UTC)

I agree. Having homework not count towards the final grade makes a lot of sense. It should still be marked and can even still be compulsory (when I was doing a maths degree, you would face disciplinary action if you didn't get at least a C on too many homeworks), but it shouldn't count towards your grade. Homework is very effective as a learning tool, but it is almost entirely useless as an assessment tool (in addition to the difficulty of dealing with cheaters, it is unfair on people that don't understand things straight away - their final grade should describe their ability as they leave the course, not their ability a week after each lecture). If you want to reduce the unfairness on people that are good at the subject but not at exams, you can set project work, which is far harder to cheat on. --Tango (talk) 18:08, 8 March 2010 (UTC)

I teach computer programming, which is rampant with students copying code from websites. I simply set up the grade system for the class such that cheating on the homework will cause you to fail if you don't learn the material. 10% of the grade is in-class work. It is really hard to download code in class when your name is called and you are asked to work something out. 40% is homework. If you cheat and get 100% on the homework, you only guaranteed a 40% in the class. 30% is exams (3 of them at 10% each). 20% is the final. Each semester, I get both extremes. I get students who do great on the homeworks and terrible on the exams - they fail. I get students who do great on the exams, but skip class and never turn in homework. They fail. I don't see why calculus wouldn't be the same. You can cheat on the homework, which will lead to failure on the exam if you don't know the material. -- kainaw™ 17:36, 8 March 2010 (UTC)

Why should students who do well on tests but poorly on homework fail ? Haven't they demonstrated proficiency ? Or do you suspect them of cheating on the tests ?

There is also a fundamental difference in computer programming: it's just about impossible to write a program of any complexity without bugs, which requires a more iterative testing and correction process than just about any other discipline (a typo in a program usually means it won't run at all, while a typo on an English paper is a minor mark down). Therefore, homework (as in writing code) is actually testing something different, their ability to debug, than a test (at least a test on paper). StuRat (talk) 18:28, 8 March 2010 (UTC)

Another idea is to assign homework from a different textbook (or better yet, several different textbooks). Of course, this is a bit more work for you, because you have to make handouts of the homework problems. —Bkell (talk) 19:50, 8 March 2010 (UTC)

Surely it would help if you set them homework questions that you wrote yourself rather than just a) choosing them out of a book or b) choosing them out of a book that has an Answer Book too? 78.146.208.26 (talk) 21:39, 8 March 2010 (UTC)

I agree with the general tenor of responses that homework in a university math class should not be part of the grade, or at least not a significant fraction of the grade. Part of the reason is that collaboration on homework ought to be encouraged (many students learn better in group efforts, provided they actually make an effort), but the line between collaboration and copying is fuzzy and hard to define, much less enforce. Plus you probably have other work to do than grading calculus assignments (of course it's different if the school is willing to pay for a grader; in that case it's a nice thing to help some undergrad have a little income).

I expect you encounter some resistance from the students to this idea; many of them have learned to expect to be able to buffer possible bad results on tests via sufficient grunt work on assignments, whether they understood what they were doing or not. To that I think you just have to tell them that they're not in high school anymore, and this is the way it's done at university. I used to tell my students that homework does count — on the exams. Meaning that if they do the homework, they have a better shot at doing well on the exams. --Trovatore (talk) 21:50, 8 March 2010 (UTC)

At issue is what level of "university" are we discussing. I mentioned computer programming above, which is a Freshman level course. Freshmen are transitioning from high school to college. Homework is a necessity to help in that transition. If I were to use computer architecture, which is a much more advanced course, as an example, then I wouldn't expect as much homework to be involved. -- kainaw™ 22:04, 8 March 2010 (UTC)

It's not that you don't assign homework. You just don't grade it. The idea is that the student is responsible for learning and understanding the material, and then being able to prove that he/she understands it (this notion of "prove" being a bit problematic, but exams are more reliable than homework assignments in this regard). Then the homeworks are provided as an aid for the student to come to that facility, not as an evaluative technique in itself.

Programming is different, though — I'm specifically talking about math classes here. Programming classes need projects, which indeed should be evaluated. If results for the students were the only concern, and instructor time didn't matter at all, you could also have projects for math classes, I guess. I don't know how you would do a project for a cookbook class like calculus, but the idealistic answer is probably "restructure calculus so it's not cookbook anymore". --Trovatore (talk) 22:35, 8 March 2010 (UTC)

Personally I'd like to see more of them working together on a problem during a tutoring session. After all that's what people mostly have to do in life and it trains in cooperative work. Also I believe it helps if they try to explain problems to each other. Dmcq (talk) 09:52, 9 March 2010 (UTC)

I have mandatory homework assignments and have never had students complain about it. Actually I've had students tell me that they really appreciate having to do them. The way to prevent "cheating" is to legalize it. They are allowed to work together, and I don't care if their paper is identical to their friend's. If they're just copying, they might learn something minimal, and then they'll fail the exams anyway. (The exams are weighed heavily.) Everybody says that the way to learn mathematics is to do mathematics. If you really want them to learn mathematics, then make them do mathematics. It's work for me to grade, but you can't beat it for effective learning. Staecker (talk) 13:13, 9 March 2010 (UTC)

Your job as a professor consists of teaching and judging. Do your students look at you as a teacher or as a judge? A good teacher is inspiring and enthusiastic while a good judge is serious and fair and strict. The good teacher makes the students study with pleasure, while the judge threatens them to study. Pick your choice. Bo Jacoby (talk) 14:12, 9 March 2010 (UTC).

Thanks for all the comments. I think homework is very important for students. If I do not assign it, many college freshmen will not do it and will not learn anything. So, it has to be worth something. In fact, I make it somewhat easy to get the points.

I disagree with the comment that it shouldn't be worth much because it's the first time they're learning something. I am fine if they work with others. I am fine if they ask me questions and I will give them a lot of help. I will work through the entire problem with them and ask questions and make comments to try to make sure they understand what I am doing. I am fine if they go to the help room and ask questions. I tell them this. And, I give them most of the credit just for doing it and then only grade a few problems for 30% of the homework points. Then, even if they mess up quite a bit but are sort of on the right track they will get half of that. So, as long as they put in work, they will get a good score on the homework and learn from doing. And, they will learn from my feed back if they look at it. And, I put solutions to some problems on my web page as well so they can learn from that. If they have no idea what they're doing on the homework with all those options for help, then they're not going to know what they're doing when the quiz or test comes around any way so who cares if they lose points on the homework.

I also disagree with legalizing cheating. The fact is, some of these cheaters are people who are doing very well in my class. They have probably had calculus before and do well on tests so they are not ever punished for the cheating if I do not do it myself. On the other hand, if they do very well on homework and then do only alright on everything else, they will still end up passing the class. I would be dishonest if I allowed people to cheat the entire way through the semester and then gave them a C and said they did satisfactory work. Especially when there are other people who don't cheat on the homework and get low grades and then do alright on the tests and those people end up with a D. So, the cheater would literally win in that situation compared to a noncheater. I am not going to allow that to happen. That would be terrible. And, the cheater who passes will then continue the same thing in Calc 2 and Calc 3. And, I guarantee most professors are not going to catch the cheating like I did because most people do not pay attention to detail as much as I do. So, this may be the only time they ever get caught doing this and I need to stop them in hopes that they actually do the right thing for the rest of their college careers. If they don't in other classes, that's not my concern but in my class it is my concern.

The comment about using problems I make up on my own is fine except the point is I don't want to go through that extra work. I assign around 20 to 30 problems a week. I do not want to make up 20 to 30 problems. That's a large part of the point of textbooks. And, the comment about using another textbook is a suggestion a professor here gave me. It may be a good option. I still might have to type up all the problems or something and it's still a large amount of work. He suggested I could just copy the exercise pages and put them on my web page. I guess I could do that but I don't know if that's legal. StatisticsMan (talk) 16:11, 9 March 2010 (UTC)

Well, making up problems (plus TeXing them) is fast, compared to grading them. Unless you have a grader? (Or, a small class?)

One thing I usually did (though I didn't always tell the students about it, at least not "officially" on the syllabus), was have multiple grading formulas, and give each student the grade from the formula most beneficial for that student. So for example the final exam would always count heavily, but midterms and quizzes might count only for those students they helped. If you go with "homework counts only if it helps, and even then not very much", that would considerably reduce the benefit of cheating, while still giving them a direct incentive to do the homework.

Seriously, though, you might consider if it isn't time for them to learn that sometimes you have to do things you don't get directly evaluated on, because they affect things you do get evaluated on. They're legal adults; might as well be now. --Trovatore (talk) 19:19, 9 March 2010 (UTC)

Well, just to knit-pick :) some of my students are not legal adults. One person told me she was 16 and another 17, both graduating from high school early. But, most would be and it still makes sense that they need to learn that lesson. As far as making up problems, if I have to TeX up 20 or 30, that would take me a while. I am a fast typer but I am somewhat of a perfectionist so I take too long on things like that. Right now, I spend about 3 minutes picking out the problems in the book. TeXing would take 15 minutes just to copy them out of some other book and 1 hour or more if I have to actually make up problems, especially word problems. I don't want to add an hour of work time to every week. Especially if I some day am teaching 3 classes at a time, then it is an even greater time. StatisticsMan (talk) 20:45, 9 March 2010 (UTC)

One more data point: at the UK university I teach at, homework for 1st years is compulsory but is worth nothing. I mark it carefully, we go over it together, but the mark they get in their 1st year is based almost entirely on exams. The advantages are obvious: the students know that cheating or copying is a waste of their time, and also the problem sets are a tool for learning things and not somewhere to try and scrape every last mark even if you don't really understand what's happening. The disadvantages are equally clear: some people are strong mathematicians but are not good at written exams, these people may not get the results they deserve.

If you really don't have the time to write your own problems, perhaps you could just make trivial modifications to existing ones (i.e. change a few constants, or even just variable names). It shouldn't cost you too long to solve the new questions, and you'll catch some people so foolish that they copy solutions to the old versions. Tinfoilcat (talk) 16:41, 9 March 2010 (UTC)

I think I like this idea somewhat. Instead of making it 0 points though, I think I will just lower the percentage of points. Perhaps I would make homework 10% of the grade. This is my first time teaching my own course and I'm still learning, so I made homework 25% of the grade. Now, with this situation, it definitely seems like I should have made it lower. Another thing is I want to be clear ahead of time what the punishment for cheating is so that at least some students will be scared from doing it in the first place. StatisticsMan (talk) 18:10, 9 March 2010 (UTC)

Yeah it would probably be helpful to make an announcement now to the class that you've noticed some people are copying their answers from the book and that's really not what you are looking for, and if you see it anymore there will be consequences. You don't have to name names, but make it clear that it's pretty obvious. You might also try to explain why doing the homework for real is important, for whatever that's worth. Rckrone (talk) 19:16, 10 March 2010 (UTC)

Why not set the occasional homework yourself (or one question on each assignment)? Then you could weight the results of these special homeworks (or questions) so that they count more towards the final grade. You will still have the problem that some students will copy from others, or get someone else to do the work for them, but at least they can't just copy from a solution manual. Dbfirs 08:26, 11 March 2010 (UTC)

Ideally all work done by the student ought to be assessed by an objective and independant third-party. Teacher and student then unite with a common purpose. There ought to be "homework" that is marked but does not contribute to final grade, since people do learn and improve with practice and feedback from marks or teacher comments is an essential part of learning. It would be unfare to allow zero practise in a skill they are trying to learn - you are trying to teach them, not merely assess whatever knowledge they came to the course with. 89.243.212.29 (talk) 15:10, 11 March 2010 (UTC)

Easy free software for drawing (phase space) graphs from statistical time-series data?

I would like to draw some graphs to explore what I think is called the phase-space of time series data. I have searched around the internet but have only been able to find software that will draw from a formula only.

Is there any preferably easy to use freeware that people would recommend please? I would like to be able to make simple transformationms of the data in order to show various aspects or kinds of the phase-space. (I'd be interested to know how many different kinds of phase space graphs there are).

Supplemental question: I have R installed, but I have not used it yet. Where should I start in learning to use its graph facilities? Thanks. 78.146.208.26 (talk) 21:37, 8 March 2010 (UTC)

Calculating eigenvector for beginners

I'm trying to write up a description of calculating eigenvectors for a paper to be published in a medical journal - so it has to be VERY light on mathematics. Does anyone here have links to pages that effectively dummy down the calculations so I can get some ideas of how to phrase this with the least amount of matrix mathematics as humanly possible? I'm on revision 23 and I'm still being told it is complicated. -- kainaw™ 23:05, 8 March 2010 (UTC)

You calculate the eigenvalues by calculating the appropriate determinant and solving the polynomial and then you get a system of simultaneous equations to solve for the eigenvectors. So basically you need a simple way to solve polynomials and then a simple way to solve simultaneous equations. What size are the matrices in question? If they are a fixed size (especially if that size is 2 or 3) then there are simple methods of doing that. There is a limit to how simple it can get, though. Can you not tell them to use a computer? --Tango (talk) 23:17, 8 March 2010 (UTC)

Due to the nature of the research, the matrix is always 4x4. I end up with four equations to solve for. I'm a bit flustered because my last attempt was sort of faked. I used a 4x4 matrix with only non-zero values in the upper left 4 positions. So, it was mostly zeros. The reviewers all said it was more confusing. -- kainaw™ 23:31, 8 March 2010 (UTC)

Tango's method is going to be quite painful for a 4x4 matrix (at least the "finding roots of the characteristic polynomial" bit). In practice you would use something like the QR method or the Lanczos method. Do your medics really need to know *how* to calculate eigenvalues, or is it not rather *what* eigenvalues are?213.160.108.26 (talk) 23:33, 10 March 2010 (UTC)

I think I found a way to make this easier for doctors to understand. -- kainaw™ 01:23, 9 March 2010 (UTC)

Don't know if it's appropriate, but you can tell people to use Mathematica or Maple or similar. (Do medical types really need to know how to do it by hand?) For people who don't use this software, they can do them on Wolfram Alpha like so: http://www.wolframalpha.com/input/?i=eigenvectors+of+{{2,2},{4,3}} Staecker (talk) 13:06, 9 March 2010 (UTC)

I'd use just a 2x2 matrix and calculate the eigenvectors and eigenvalues by hand and show what they mean. Plus show a couple of funny cases which don't have two eigenvectors. Then I'd say the 4x4 ones are too much bother to do by hand but can be solved by various different methods using a computer which will be programmed to deal with any quirks. Dmcq (talk) 12:11, 11 March 2010 (UTC)