Thoughts on math homework in college
Moderators: gmalivuk, Moderators General, Prelates
 ImTestingSleeping
 Posts: 88
 Joined: Mon Dec 06, 2010 3:46 am UTC
Thoughts on math homework in college
Hi xkcd forum goers,
How do you think homework in math courses should be graded in college? Should it be graded if it is right or wrong? Effort based? Something else perhaps? Does the difficulty of the course matter?
Also, do you like homework due per week, per class, or something else?
Let me know! I'm a TA and I'm curious!
How do you think homework in math courses should be graded in college? Should it be graded if it is right or wrong? Effort based? Something else perhaps? Does the difficulty of the course matter?
Also, do you like homework due per week, per class, or something else?
Let me know! I'm a TA and I'm curious!
Re: Thoughts on math homework in college
Here's the opinion of a former student and TA and current professor  homework should primarily be graded on whether it's correct or not. Sometimes I throw in points for it being turned in on time, but usually it's based on whether it's correct  after all, someone who is not actually in the class and has absolutely no knowledge of calculus (for example) should not be able to get a 100% on a calculus assignment simply because they were able to write their name on top of the assignment. Depending on the course homework can play just as large a role in determining the overall grade as exams so do take stock of what class you have....
Also be considerate of students. When I was a student I was taking a math class. I got a 90 on a homework assignment. I'd taken my time on a homework assignment and got 90 out of 100 correct. The other ten I simply did not have time to do if I wanted to do the rest carefully. I was perfectly content with the grade until I saw a classmate's, who'd gotten a 100. They'd answered all 100 questions but only 20 of them were actually answered correctly. As a student I felt this was incredibly unfair. If you are not grading on whether something is correct (or exhibits some kind of class goals) you might as well simply just ask someone to write their name on a paper and turn it in  it would save you a ton of time on grading at least!
However you are in a delicate situation  when I was in elementary through high school EVERYTHING was graded as correct or incorrect so I expected the same in college. More and more I am finding students coming in from high school expecting homework to be graded as 100% simply if it is turned in on time, regardless of the content. No doubt you are experiencing the same questions  "will we be graded on this?"
Another however, though, that puts you in a less delicate situation, is that you are a TA. This must mean that you have a professor or professors that you report to. If you are unsure on the grading simply discuss it with them. Some of the profs I TA'd for just left me make up my own grading scheme (although one would always just change it after everything was graded) but another would sit through and grade about ten papers together with me so I could see how he wanted them graded. However, for all of them they wanted number grades. Hopefully you have a cool prof. you can talk to about this. In that case, bottom line if the students complain you can shrug and say, "Prof.  told me to do that, if you have a complaint make an appointment."
Also be considerate of students. When I was a student I was taking a math class. I got a 90 on a homework assignment. I'd taken my time on a homework assignment and got 90 out of 100 correct. The other ten I simply did not have time to do if I wanted to do the rest carefully. I was perfectly content with the grade until I saw a classmate's, who'd gotten a 100. They'd answered all 100 questions but only 20 of them were actually answered correctly. As a student I felt this was incredibly unfair. If you are not grading on whether something is correct (or exhibits some kind of class goals) you might as well simply just ask someone to write their name on a paper and turn it in  it would save you a ton of time on grading at least!
However you are in a delicate situation  when I was in elementary through high school EVERYTHING was graded as correct or incorrect so I expected the same in college. More and more I am finding students coming in from high school expecting homework to be graded as 100% simply if it is turned in on time, regardless of the content. No doubt you are experiencing the same questions  "will we be graded on this?"
Another however, though, that puts you in a less delicate situation, is that you are a TA. This must mean that you have a professor or professors that you report to. If you are unsure on the grading simply discuss it with them. Some of the profs I TA'd for just left me make up my own grading scheme (although one would always just change it after everything was graded) but another would sit through and grade about ten papers together with me so I could see how he wanted them graded. However, for all of them they wanted number grades. Hopefully you have a cool prof. you can talk to about this. In that case, bottom line if the students complain you can shrug and say, "Prof.  told me to do that, if you have a complaint make an appointment."

 Posts: 1
 Joined: Mon Jan 03, 2011 10:08 am UTC
Re: Thoughts on math homework in college
I had a TA this last semester who graded very harshly unless the answer was correct. It was jarring at first, but I ended up with a better grasp of the material than I think I would have had if he had given a lot of. Small errors in arithmetic don't matter so much, but a correct answer is important, in my opinion. If you do give partial credit, it should be a much smaller amount than full credit would be worth.
As for how often, this class had homeworks due every class, on Monday, Wednesday, and Friday. I liked that better than weekly, because it prevented me from procrastinating. That's just me, though.
As for how often, this class had homeworks due every class, on Monday, Wednesday, and Friday. I liked that better than weekly, because it prevented me from procrastinating. That's just me, though.
Re: Thoughts on math homework in college
For me, I really liked the way my multivariable calc professor did it last semester. He would assign us homework problems every couple of days, but rarely collect it. He told us when he collected it that it couldn't hurt us and could only help us. Basically, he would collect it to make sure we were still on track and knew what we were doing, but wouldn't penalize us if we didn't; he just told us that we needed to focus on things more (I presume, I never had problems with it). Also, every day after the homework was due he would ask us if we had any questions about it and go over the challenging problems. I especially recommend doing that part as a TA, as it has the potential to help students more by making sure you cover what confused them and not wasting their time on things they already know.
cjmcjmcjmcjm wrote:If it can't be done in an 80x24 terminal, it's not worth doing
Re: Thoughts on math homework in college
The problem with grading entirely on a correct/incorrect system is that sometimes that isn't a good reflection of the student's understanding of the work. If they get a very advanced problem wrong because they screwed up some arithmetic, the problem obviously isn't right, but they clearly have a better understanding of the concept they were meant to learn than someone who doesn't understand the basic steps to solving the problem.
If someone is told to find the area of a square with sides of length 2 and they give you the answer of 4 by added the length and width together, this shouldn't be marked correct.
If someone is told to find the area of a square with sides of length 2 and they give you the answer of 4 by added the length and width together, this shouldn't be marked correct.
 Magnanimous
 Madmanananimous
 Posts: 3491
 Joined: Wed Feb 17, 2010 7:11 pm UTC
 Location: Land of Hipsters and Rain (LOHAR)
Re: Thoughts on math homework in college
Math classes in high school are more about building a work ethic, frankly... But once students get to college (especially grad school), they pretty much know how to crank out a sheet of homework and hand it in. If you're in a highlevel math lecture, the whole point is that you learn the material.
I like the idea of evenly splitting points between the work and the answer. One point if you show your work neatly (maybe a halfpoint if you found the answer inefficiently), and a point for the circled answer at the bottom.
I like the idea of evenly splitting points between the work and the answer. One point if you show your work neatly (maybe a halfpoint if you found the answer inefficiently), and a point for the circled answer at the bottom.
Re: Thoughts on math homework in college
I assume this is something like calculus or diffeq where problemsolving is emphasized over proofs. I don't see why homework is even graded at all in college classes like that. If it were up to me, homeworks would be assigned, but not collected, and solutions would be provided about a week later. Make sure the students keep up with some brief quizzes either once a class or once a week, and make the grade about 20% quizzes, 80% tests.
What I like about this system is that students who already have a good grasp of the material (in lowerlevel courses, a good portion) aren't doing busy work. For students that are struggling, the TAs have more time to make kickass solutions and answer individual questions. The only people who will be worse off are students who refuse to do ungraded homework and end up taking tests and quizzes with no preparation. These last students probably don't belong in college.
What I like about this system is that students who already have a good grasp of the material (in lowerlevel courses, a good portion) aren't doing busy work. For students that are struggling, the TAs have more time to make kickass solutions and answer individual questions. The only people who will be worse off are students who refuse to do ungraded homework and end up taking tests and quizzes with no preparation. These last students probably don't belong in college.
This signature is Y2K compliant.
Last updated 6/29/108
Last updated 6/29/108
 Bakemaster
 pretty nice future dick
 Posts: 8933
 Joined: Fri Jul 06, 2007 2:33 pm UTC
 Location: One of those hot places
Re: Thoughts on math homework in college
ImTestingSleeping wrote:I'm a TA and I'm curious!
No offense, but you should really be asking your students, not us. Every group is different; rather than looking for an objectively correct or best way to assign or grade homework, you'd do better to look for the way that works for the group in question.
Where "the way that works" is defined as the method that best facilitates the learning process for those students who need the most help (excluding anyone who isn't prepared for the course to begin with, of course).
Personally, I can handle homework fine as long as the guidelines for its grading are clearly laid out at the beginning of the semester. I prefer to be given credit for having done the work as well as for doing it well; I sure as hell don't want to get the same grade for not turning in a homework as for doing every problem but arriving at all the wrong answers.
But again, you're not grading me. So my response may only be biasing you against the best method for your students.
c_{0} = 2.13085531 × 10^{14} smoots per fortnight
"Apparently you can't summon an alternate timeline clone of your inner demon, guys! Remember that." —Noc
 ImTestingSleeping
 Posts: 88
 Joined: Mon Dec 06, 2010 3:46 am UTC
Re: Thoughts on math homework in college
Bakemaster wrote:ImTestingSleeping wrote:I'm a TA and I'm curious!
No offense, but you should really be asking your students, not us. Every group is different; rather than looking for an objectively correct or best way to assign or grade homework, you'd do better to look for the way that works for the group in question.
I've found that asking students what they want is often not in their best educational interest. Instead, they'll ask for a system which allows them to be lazy and get a good grade on their homeworks with little effort. This ends up hurting them on quizzes and exams. You might argue that it is up to the students to put in the effort, and I completely agree, but most will be lazy if not forced to work.
The way we have it now (I've been TA'ing a Calculus I and II course for college freshmen for a few years now) is that a homework set is due and assigned every class (class meets 3 times a week) and we grade based on a check/check minus system. Basically, a check is 100/100 and if I think you really made a poor effort, you get a check minus which is a 70/100. I'm generally rather lenient. Obviously, everyone does rather well on the homeworks, so we make them count for a very small portion of the overall grade (about 7 or 8%).
However, this doesn't seem to be ideal and we've been looking to change this. The posts so far have been very helpful! I'll have to steal some of these ideas.
 KestrelLowing
 Posts: 1124
 Joined: Mon Mar 22, 2010 6:57 pm UTC
 Location: Michigan
Re: Thoughts on math homework in college
For me, the best option was always the 'pick a couple problems and grade those' approach. Basically, homework is assigned and 2030% of those problems are actually graded, but the students don't know which. The rest are just looked at to see if you made a decent effort. Granted, I wasn't too fond of this when the one problem I couldn't figure out was the one problem that was graded, but I think it's a good compromise  the TA's don't have to grade as much, but the students do get some feedback.
Another option in the same realm is to assign just a couple problems to turn in, but suggest more as well. When I had that kind of assignment, I'd usually just do the ones I had to at the time, but before a quiz or test I'd do the rest. It worked well for me.
Another option in the same realm is to assign just a couple problems to turn in, but suggest more as well. When I had that kind of assignment, I'd usually just do the ones I had to at the time, but before a quiz or test I'd do the rest. It worked well for me.
Re: Thoughts on math homework in college
I had a professor that used a system that worked out pretty well in a beginning Linear Algebra class. She would give us a list of problems and about half of them would be graded for correctness and half of them would be graded for completion, and she told us which were which. She was a pretty stern grader, so students like me who had As on the final and in the class weren't strangers to getting in the 5575% range on homework assignments. The class met twice a week and she would assign something based on the lecture both days, and they would both be due the following Thursday, so we had a while to work on them, and she'd devote about half the lecture on Tuesdays to answering any questions the students had on the homework. I think homework counted for about 1015% of the final grade.
My calculus teacher in high school would assign homework and go over questions the next day in class, but would never collect it. I liked this, because I shine on exams but have a tendency to not do homework if I don't feel I'm learning from it, so I could do as much as I felt was necessary to understand the material. This worked out well for me and the most disciplined handful of the students, and those who were serious about pursuing math/science , but the majority of the class (particularly those who would major in something that doesn't require much math) ended up simply not learning the material, and failing the class (though the cuter girls never quite failed) and the AP exam.
So I really think you have to tailor to the student's abilities. If you have a class that is entirely bright students who care, as would probably only be the case in upperlevel classes at good schools, I relaxed grading policy might be the good thing, but if you're teaching a precalculus class at an average school, I would grade everything and make it a more significant portion of the grade.
(On a side note, the University I'm at is a Tier2 public school, and a vast majority of the math students are aspiring high school teachers. I think it's about 90%)
My calculus teacher in high school would assign homework and go over questions the next day in class, but would never collect it. I liked this, because I shine on exams but have a tendency to not do homework if I don't feel I'm learning from it, so I could do as much as I felt was necessary to understand the material. This worked out well for me and the most disciplined handful of the students, and those who were serious about pursuing math/science , but the majority of the class (particularly those who would major in something that doesn't require much math) ended up simply not learning the material, and failing the class (though the cuter girls never quite failed) and the AP exam.
So I really think you have to tailor to the student's abilities. If you have a class that is entirely bright students who care, as would probably only be the case in upperlevel classes at good schools, I relaxed grading policy might be the good thing, but if you're teaching a precalculus class at an average school, I would grade everything and make it a more significant portion of the grade.
(On a side note, the University I'm at is a Tier2 public school, and a vast majority of the math students are aspiring high school teachers. I think it's about 90%)
Re: Thoughts on math homework in college
In advanced classes that are mainly for math majors and others who want to learn the topic, I like the system of 5 points per problem. 5 means perfect. If the basic idea of the solution is correct, I take off 0.5 for minor errors (arithmetic) up to 3 for major errors. On the other hand, if there is a serious misunderstanding that leads to the solution not making any sense, I take off 3 to 5 points depending on how bad the mistake is. In addition, taking off points for sloppy proof writing (up to 2 points) can be a good idea (obviously, the score can't drop below 0 on a particular problem). The most important thing, though, is to explain the mistake so that the students can see what they did wrong. Of course, if you prefer a system with a different number of points per problem, the change is easy to make.
I'm not sure there is a good way to grade homework for classes that are required for everyone. This is because many of the students don't care about improving their understanding of the concepts. If you use the above grading method (which is workintensive for the grader) for those classes, you waste a lot of effort on students who don't even look at the explanations you gave. If you use a loweffort grading system like check/check minus, this is not so effective for the students who really are trying to learn, since they get less feedback.
Grading a subset of the problems, as KestrelLowing suggested, sounds like a decent compromise for these classes, though. I should try it out.
I'm not sure there is a good way to grade homework for classes that are required for everyone. This is because many of the students don't care about improving their understanding of the concepts. If you use the above grading method (which is workintensive for the grader) for those classes, you waste a lot of effort on students who don't even look at the explanations you gave. If you use a loweffort grading system like check/check minus, this is not so effective for the students who really are trying to learn, since they get less feedback.
Grading a subset of the problems, as KestrelLowing suggested, sounds like a decent compromise for these classes, though. I should try it out.
 ImTestingSleeping
 Posts: 88
 Joined: Mon Dec 06, 2010 3:46 am UTC
Re: Thoughts on math homework in college
++$_ wrote:Grading a subset of the problems, as KestrelLowing suggested, sounds like a decent compromise for these classes, though. I should try it out.
I like that idea a lot as well and will talk to my professor about it. Having a 5 point per problem system as you suggested while grading only a portion of the problems would be a great way to give feedback and keep the integrity of the homework (also it wouldn't have me grading for hours and hours). I think I'll suggest that homework remain a relatively small portion of their overall grade though.
Thank you all so much for your input. Really, it has been very productive!
Re: Thoughts on math homework in college
A tad late, but hey ho. What I do is try to assign a grade to a question based on how much knowledge of the subject I think the student has demonstrated in answering it. That's a tad wishy washy, so some provisos:
It's not a quick marking scheme, but fortunately I'm usually only dealing with a smallish group at a time, and find I can get a lot done on the train.
 Each question gets a set maximum number of marks, indicated along side it on the paper.
 Where possible I then try, when marking, to subdivide the question up into modular parts and assign a set max number of marks to each of these. They can then be marked separately as mini questions. These marks sometimes add up to less than the total amount available for the question (often out of necessity), so I've a few spare marks hanging around to give to really good overall answers.
 To get full marks a student should have exactly the right answer calculated in a suitably rigorous manner.
 I do give follow through marks  i.e. if in a multi part question part a student makes a mistake in part a), but then uses the result of this to perform exactly the right calculation in part b), then they get full marks for the answer in b)  provided that their erroneous answer didn't make the latter stages of the question easier. If it did then I try to make a judgment call on how much knowledge they have demonstrated, erring on the pessimistic side if they've changed the question so fundamentally that it's hard to tell. People who check their answers (back substitution, spotting eigenvectors are not orthogonal when they should be, etc) and realise that they've made an error usually recover a few marks
 Where an answer is not right on account of one or more silly mistakes (arithmetic error or similar) but the method is roughly right I start of at full marks and then gradually whittle them down as I go through the answer, depending on how many/what kind of errors I find. Usually this gets them a score above 50% (not always).
 Where the method is entirely wrong I start at zero and gradually add marks, depending on how many little parts I can find which are correct and relevant to the problem. This is usually below 50% (again not always, though I can't recall any specific counter examples).
 One thing I have found is that after finishing marking I usually need to quickly flip through all the student's answers to each question, to make sure I've been as consistent as possible across the board as to what counts as a 'good' answer. Whether an error indicates to me a complete lack of understanding or a simple slipup can vary quite surprisingly according to whether it was marked late at night or not . This often results in me twerking a mark here or there so that students who've made roughly comparable errors get roughly the same score.
It's not a quick marking scheme, but fortunately I'm usually only dealing with a smallish group at a time, and find I can get a lot done on the train.
 Yakk
 Poster with most posts but no title.
 Posts: 11128
 Joined: Sat Jan 27, 2007 7:27 pm UTC
 Location: E pur si muove
Re: Thoughts on math homework in college
The grade you get from homework in most math courses I took as an undergrad was trivial (there was one exception, but I dropped that course). 10%20% of the final grade at best.
The point of grading the work is to give the student feedback on "are they doing it right". Students don't magically know this. The point of making the grade matter is to give the student incentive and reward for putting work into it that is more direct and immediate than "getting feedback on am I doing it right".
Marking for "handing it in" and the like doesn't do this. So I'd strike that out immediately.
With unlimited resources, you'd want to sit down with each student and go over each line of each question and discuss ways to do it better, or what went wrong. Resources are not unlimited.
How close to unlimited are the resources relative to the number of students?
I find a 3 pass system  "effort checking" 5/12, "quick checking" 5/12, and "fully checking" 2/12, for 1 3 and 10 marks respectively, to be an interesting model (total mark /40). If the questions are all equally easy/hard, buy a 12 sided die and randomly pick which are full and which are not (roll twice, reroll one die on duplicate), then flip a coin for top/bottom for effort/quick, and mark everyone consistently using that scheme. But this could result in perverse behavior in your students as randomness tends to.
If you want to have fun, you could even allow students to request a full review of 1 question on their assignment. You do a full marking on it, but it doesn't count towards their marks unless it was selected randomly for marking for all students. This lets students say "I am not comfortable with my skill at this question, could you give me feedback" in a very passive way. And with 1 question/assignment, and most students not bothering to make the request, it shouldn't increase your workload much. It also gives the students a feeling of "you want the marker to give you feedback, as you are asking for the feedback". But maybe I'm a romantic.
(Then again, getting such a quirky system past your professor might be interesting...)
The point of grading the work is to give the student feedback on "are they doing it right". Students don't magically know this. The point of making the grade matter is to give the student incentive and reward for putting work into it that is more direct and immediate than "getting feedback on am I doing it right".
Marking for "handing it in" and the like doesn't do this. So I'd strike that out immediately.
With unlimited resources, you'd want to sit down with each student and go over each line of each question and discuss ways to do it better, or what went wrong. Resources are not unlimited.
How close to unlimited are the resources relative to the number of students?
I find a 3 pass system  "effort checking" 5/12, "quick checking" 5/12, and "fully checking" 2/12, for 1 3 and 10 marks respectively, to be an interesting model (total mark /40). If the questions are all equally easy/hard, buy a 12 sided die and randomly pick which are full and which are not (roll twice, reroll one die on duplicate), then flip a coin for top/bottom for effort/quick, and mark everyone consistently using that scheme. But this could result in perverse behavior in your students as randomness tends to.
If you want to have fun, you could even allow students to request a full review of 1 question on their assignment. You do a full marking on it, but it doesn't count towards their marks unless it was selected randomly for marking for all students. This lets students say "I am not comfortable with my skill at this question, could you give me feedback" in a very passive way. And with 1 question/assignment, and most students not bothering to make the request, it shouldn't increase your workload much. It also gives the students a feeling of "you want the marker to give you feedback, as you are asking for the feedback". But maybe I'm a romantic.
(Then again, getting such a quirky system past your professor might be interesting...)
One of the painful things about our time is that those who feel certainty are stupid, and those with any imagination and understanding are filled with doubt and indecision  BR
Last edited by JHVH on Fri Oct 23, 4004 BCE 6:17 pm, edited 6 times in total.
Last edited by JHVH on Fri Oct 23, 4004 BCE 6:17 pm, edited 6 times in total.
Re: Thoughts on math homework in college
You should see the system one of my profs used. HW's are worth 100%, unless you fail really really hard (the he gives you a final, but you won't ever get a good grade this way). You only need to do 3/4 of the questions to get a really good grade. You are given 5 tries per question, and with every wrong try, he hands it back to you, usually with some comments. You will only get marks on the question if you get it right. Your mark on the question is given by (6  try #).Yakk wrote:(Then again, getting such a quirky system past your professor might be interesting...)

 Posts: 103
 Joined: Wed Oct 27, 2010 12:44 am UTC
Re: Thoughts on math homework in college
Calc 3 professor I had last semester did it best, imo. We don't get a homework grade. Instead, it's used as extra credit:
Out of a set of 1520 problems, he picks 2 or 3 to be graded (each worth one point), and, at the end of the semester, every 3 points adds a percentage to our total grade. Ended up being a potential for somewhere around 116%, but his tests were scaled accordingly (and it wasn't very easy to get a point on a homework). More on your topic, the problems not only needed to be correct, but a reasonable person would have to be able to follow the work. This whole system, I think, is the best grading system I've encountered (for math, at least).
Out of a set of 1520 problems, he picks 2 or 3 to be graded (each worth one point), and, at the end of the semester, every 3 points adds a percentage to our total grade. Ended up being a potential for somewhere around 116%, but his tests were scaled accordingly (and it wasn't very easy to get a point on a homework). More on your topic, the problems not only needed to be correct, but a reasonable person would have to be able to follow the work. This whole system, I think, is the best grading system I've encountered (for math, at least).
Qaanol wrote:Actually this could be a great idea. See, you just have to bill the mission to an extrasolar planet as a mission, and then let all the fundamentalists from all religions be the missionaries.
Re: Thoughts on math homework in college
My math teacher (high school, but we were doing calculus) graded the problems by looking at 2 different things.
1 Does the student use the proper method for getting the answer?
2 Did the student get the right answer?
The first one makes sure that the student understands the concepts and knows what they are doing. In theory, if 1 is true, 2 should also be true. If that isn't the case (1true, 2false), it's usually because the student made an arithmetic mistake. She gives most of the points based on 1, but you really need the right answer if you want full points.
For example, on a question worth 5 points, you could get 4 points for the right method, and 1 for the right answer. Or maybe get full points for the method, but lose 1/2 a point for every arithmetic mistake. That way, you only lose lots of points if you don't understand the concepts involved.
On the other hand, if you have a big group of students and lots of homework to grade, I'm sure this gets to be really timeconsuming. Maybe assign a fraction of total worth to method (more than half, like 2/3?) and a smaller fraction for the right answer.
1 Does the student use the proper method for getting the answer?
2 Did the student get the right answer?
The first one makes sure that the student understands the concepts and knows what they are doing. In theory, if 1 is true, 2 should also be true. If that isn't the case (1true, 2false), it's usually because the student made an arithmetic mistake. She gives most of the points based on 1, but you really need the right answer if you want full points.
For example, on a question worth 5 points, you could get 4 points for the right method, and 1 for the right answer. Or maybe get full points for the method, but lose 1/2 a point for every arithmetic mistake. That way, you only lose lots of points if you don't understand the concepts involved.
On the other hand, if you have a big group of students and lots of homework to grade, I'm sure this gets to be really timeconsuming. Maybe assign a fraction of total worth to method (more than half, like 2/3?) and a smaller fraction for the right answer.
He has told us of the darkness,
He has shown us deepest night.
The rage inside a burning sun,
The calmness of its light.
He has shown us deepest night.
The rage inside a burning sun,
The calmness of its light.
Re: Thoughts on math homework in college
That isn't going to work, since you are still grading on the method, and you still need to read it, not saving any time at all. Even if the method is worth 0.01 out of 5 and the answer 4.99, you are still going to have to read it. (chances are, you will probably be lazy and skim at that case, but still, my point is there)Ambermutt wrote:On the other hand, if you have a big group of students and lots of homework to grade, I'm sure this gets to be really timeconsuming. Maybe assign a fraction of total worth to method (more than half, like 2/3?) and a smaller fraction for the right answer.
Re: Thoughts on math homework in college
achan1058 wrote:That isn't going to work, since you are still grading on the method, and you still need to read it, not saving any time at all. Even if the method is worth 0.01 out of 5 and the answer 4.99, you are still going to have to read it. (chances are, you will probably be lazy and skim at that case, but still, my point is there)
True. What I actually meant was to just see enough of the method to make sure they're not completely off base (as in, if they're trying to find the volume of something, make sure they're not using a formula for the area). If the work is done neatly, this should really only take a glance, and not much more time than checking the right answer.
I guess the best way to save time is right answer/wrong answer with no further explanation, but if you really want to teach something, method is more important (IMHO).
On the other hand, I haven't actually taken a college math course.
He has told us of the darkness,
He has shown us deepest night.
The rage inside a burning sun,
The calmness of its light.
He has shown us deepest night.
The rage inside a burning sun,
The calmness of its light.
 doogly
 Dr. The Juggernaut of Touching Himself
 Posts: 5531
 Joined: Mon Oct 23, 2006 2:31 am UTC
 Location: Lexington, MA
 Contact:
Re: Thoughts on math homework in college
I assigned homework as a means of teaching rather than a means of assessment. A little bit of grading let the kiddies know it is actually important to do and if they are on the right track, but banging your head against meaningful, hard problems is how you learn (not by listening to me, sadly.) So the grades on the homeworks were not so stellar and were not a big part of the final grade score anyway (generally 10%). The real assessment comes on exams.
If I were teaching a more upper level course I would probably swap philosophies. I've had grad classes where exams were just not things that happen at all, everything was hw.
If I were teaching a more upper level course I would probably swap philosophies. I've had grad classes where exams were just not things that happen at all, everything was hw.
LE4dGOLEM: What's a Doug?
Noc: A larval Doogly. They grow the tail and stinger upon reaching adulthood.
Keep waggling your butt brows Brothers.
Or; Is that your eye butthairs?
Noc: A larval Doogly. They grow the tail and stinger upon reaching adulthood.
Keep waggling your butt brows Brothers.
Or; Is that your eye butthairs?
 ImTestingSleeping
 Posts: 88
 Joined: Mon Dec 06, 2010 3:46 am UTC
Re: Thoughts on math homework in college
This thread has run its course for my original purposes (the semester is already well under way). However, it is always interesting to hear about different grading systems.
I for one am interested in people's thoughts on exams now that you bring it up, doogly.
It seems that the US education system operates under the assumption that standard paper and pencil exams are a good way to monitor student's understanding. I'd have to argue that these types of exams, at least in mathematics courses, are a terrible way to test a student's understanding. The thing I love so very much about mathematics is that I can play around with a specific troublesome problem for weeks and find myself coming at it at different angles. That process of coming back to a problem over a period of time is how I find myself learning best. Math shouldn't be rushed. You can't do a student justice by evaluating them after an hour or two of paper and pencil examination. To me, that promotes a type of rote learning, even at higher levels, which has become destructive to the US system.
If I didn't spend so much time studying for my exams, I feel like I could spend more time actually learning.
Feedback and evaluation are important things, but as a student I have become very good at studying for and sitting exams, but I don't feel I'm learning as effectively as I could be. In a way, I feel cheated.
[Edit]: That escalated into a rant, but what do you think about math exams? What types do you like? Have you run into or taught any courses which you felt were better than the traditional set up?
I for one am interested in people's thoughts on exams now that you bring it up, doogly.
It seems that the US education system operates under the assumption that standard paper and pencil exams are a good way to monitor student's understanding. I'd have to argue that these types of exams, at least in mathematics courses, are a terrible way to test a student's understanding. The thing I love so very much about mathematics is that I can play around with a specific troublesome problem for weeks and find myself coming at it at different angles. That process of coming back to a problem over a period of time is how I find myself learning best. Math shouldn't be rushed. You can't do a student justice by evaluating them after an hour or two of paper and pencil examination. To me, that promotes a type of rote learning, even at higher levels, which has become destructive to the US system.
If I didn't spend so much time studying for my exams, I feel like I could spend more time actually learning.
Feedback and evaluation are important things, but as a student I have become very good at studying for and sitting exams, but I don't feel I'm learning as effectively as I could be. In a way, I feel cheated.
[Edit]: That escalated into a rant, but what do you think about math exams? What types do you like? Have you run into or taught any courses which you felt were better than the traditional set up?
 doogly
 Dr. The Juggernaut of Touching Himself
 Posts: 5531
 Joined: Mon Oct 23, 2006 2:31 am UTC
 Location: Lexington, MA
 Contact:
Re: Thoughts on math homework in college
Exams of the traditional style (in class, closed notes) seem to work for me for the intro courses I teach. The two questions I want to evaluate the kiddies on are "Can you solve hard problems?" and "Do you firmly grasp the principles?" The former is best checked with homework, and the process is more important than the final answer. I expect them to work over time and not get every question right. The latter I do think you can check quickly.
For example, I teach probability now. We spent a class talking about Monty Hall, and another on the Birthday Problem. (we meet for short periods.) These are big tricky things. Not too intuitive. We discuss them at length and make sure everyone is on board. On the exam I want to see you find the probability of rolling a 5 on 2d4. If your knowledge of the principles is secure this is quite easy, but that is what I want to see.
If the class becomes more about proofs, then an open book take home exam starts to make more sense.
A closed book take home and an open book in class seem to me to be atrocious mismatches, but some people do seem to like them. But, yuck.
For example, I teach probability now. We spent a class talking about Monty Hall, and another on the Birthday Problem. (we meet for short periods.) These are big tricky things. Not too intuitive. We discuss them at length and make sure everyone is on board. On the exam I want to see you find the probability of rolling a 5 on 2d4. If your knowledge of the principles is secure this is quite easy, but that is what I want to see.
If the class becomes more about proofs, then an open book take home exam starts to make more sense.
A closed book take home and an open book in class seem to me to be atrocious mismatches, but some people do seem to like them. But, yuck.
LE4dGOLEM: What's a Doug?
Noc: A larval Doogly. They grow the tail and stinger upon reaching adulthood.
Keep waggling your butt brows Brothers.
Or; Is that your eye butthairs?
Noc: A larval Doogly. They grow the tail and stinger upon reaching adulthood.
Keep waggling your butt brows Brothers.
Or; Is that your eye butthairs?
Re: Thoughts on math homework in college
While a take home exam is a good thing in some sense. Unless you have only 1 student, you are going to run into certain uncertainties, especially if it is a class of 1st years. Anyways, I agree with the other poster about closed book pencil/paper exams being a way to measure whether the student has utterly failed to understand the material.ImTestingSleeping wrote:This thread has run its course for my original purposes (the semester is already well under way). However, it is always interesting to hear about different grading systems.
I for one am interested in people's thoughts on exams now that you bring it up, doogly.
It seems that the US education system operates under the assumption that standard paper and pencil exams are a good way to monitor student's understanding. I'd have to argue that these types of exams, at least in mathematics courses, are a terrible way to test a student's understanding. The thing I love so very much about mathematics is that I can play around with a specific troublesome problem for weeks and find myself coming at it at different angles. That process of coming back to a problem over a period of time is how I find myself learning best. Math shouldn't be rushed. You can't do a student justice by evaluating them after an hour or two of paper and pencil examination. To me, that promotes a type of rote learning, even at higher levels, which has become destructive to the US system.
If I didn't spend so much time studying for my exams, I feel like I could spend more time actually learning.
Feedback and evaluation are important things, but as a student I have become very good at studying for and sitting exams, but I don't feel I'm learning as effectively as I could be. In a way, I feel cheated.
[Edit]: That escalated into a rant, but what do you think about math exams? What types do you like? Have you run into or taught any courses which you felt were better than the traditional set up?
The best course I had uses this weird system.
HW's are 100% of the grade.
~80 problems are given each term. Undergrads are expected to solve 40 of them, grad 60.
If you screwed up solving a problem, it gets handed back to you, and you can resubmit it again. You have up to 5 chances per problem, each time you fail 20% is deducted from the problem.
How on earth does the first part work!?doogly wrote:A closed book take home and an open book in class seem to me to be atrocious mismatches, but some people do seem to like them. But, yuck.
Re: Thoughts on math homework in college
achan1058 wrote:ImTestingSleeping wrote:How on earth does the first part work!?doogly wrote:A closed book take home and an open book in class seem to me to be atrocious mismatches, but some people do seem to like them. But, yuck.
I've seen it done by having the students sign something saying they didn't receive any outside help (including other students, the internet, or their book). Now if that actually works is an entirely different question.
double epsilon = .0000001;
Re: Thoughts on math homework in college
I like the way my (high school) calculus teacher gives homework. Our grade for the class is like this:
10% "In class grade"  This is given for being in class, participating in discussion, and having homework sets done when we go over them. It's an easy 10 points if you do at least some of the homework and aren't sleeping.
45% quiz grade  We receive a few quizzes a week, worth between 10 and 30 "points" each, all points you earn are totaled and divided by the total possible points.
45% test grade  One, sometimes two, tests per marking period (=six weeks, we have six marking periods.) These tests count as much as all the quizzes combined.
Homework is assigned every day or every other day, and is rarely collected. However, everyone in the class still does the homework. The way the teacher runs the class makes us afraid to be unprepared for class, so we do the homework either because we want to learn it, or because we don't want to look like a fool We go over the homework in class, with students showing their work on the projector and the professor correcting/ explaining as we go.
Optional homework allows the students who need practice the opportunity to practice, and the students who understand it quickly don't need to spend time on busy work.
For anyone that dislikes how much quizzes and tests count in this system: he will take minor points off for arithmetic errors, then check to see if you continued on correctly, even though you had a stupid mistake early on. He tells "I am not grading you on whether you can do arithmetic or not, I'm grading you on whether you can do calculus or not."
10% "In class grade"  This is given for being in class, participating in discussion, and having homework sets done when we go over them. It's an easy 10 points if you do at least some of the homework and aren't sleeping.
45% quiz grade  We receive a few quizzes a week, worth between 10 and 30 "points" each, all points you earn are totaled and divided by the total possible points.
45% test grade  One, sometimes two, tests per marking period (=six weeks, we have six marking periods.) These tests count as much as all the quizzes combined.
Homework is assigned every day or every other day, and is rarely collected. However, everyone in the class still does the homework. The way the teacher runs the class makes us afraid to be unprepared for class, so we do the homework either because we want to learn it, or because we don't want to look like a fool We go over the homework in class, with students showing their work on the projector and the professor correcting/ explaining as we go.
Optional homework allows the students who need practice the opportunity to practice, and the students who understand it quickly don't need to spend time on busy work.
For anyone that dislikes how much quizzes and tests count in this system: he will take minor points off for arithmetic errors, then check to see if you continued on correctly, even though you had a stupid mistake early on. He tells "I am not grading you on whether you can do arithmetic or not, I'm grading you on whether you can do calculus or not."
 doogly
 Dr. The Juggernaut of Touching Himself
 Posts: 5531
 Joined: Mon Oct 23, 2006 2:31 am UTC
 Location: Lexington, MA
 Contact:
Re: Thoughts on math homework in college
Poorly. Definitely poorly.achan1058 wrote:How on earth does the first part work!?doogly wrote:A closed book take home and an open book in class seem to me to be atrocious mismatches, but some people do seem to like them. But, yuck.
LE4dGOLEM: What's a Doug?
Noc: A larval Doogly. They grow the tail and stinger upon reaching adulthood.
Keep waggling your butt brows Brothers.
Or; Is that your eye butthairs?
Noc: A larval Doogly. They grow the tail and stinger upon reaching adulthood.
Keep waggling your butt brows Brothers.
Or; Is that your eye butthairs?
Re: Thoughts on math homework in college
doogly wrote:A closed book take home and an open book in class seem to me to be atrocious mismatches, but some people do seem to like them. But, yuck.
Yeah, that first one is basicly a joke. If the questions are at a closed book difficulty, then I should very much expect everyone to get 100 as they use their books, and depending on the level, potentially work in groups too. Open book inclass isn't so bad though, especially when the alternative is 'make your own formula sheet', since some people will write tiny and basicly have the whole book crammed on anyway, while some people (like me) write huge and barely have enough room for the essential formulas. Although for math courses, I might be inclined to think that you should actually know most/all the formulas anyway, so you shouldn't need anything like that to begin with.
re math homework: Something one of my prof's tried that I liked, was where the assignment solutions were made available before the due date, so after spending a lil under a week trying to figure things out on your own, you could then look at the solutions and then try to make sense of it. You would still need to write up your own solutions to hand in though, and in the view of my prof that process forced enough understanding to be worthwhile. Of course, homework only counted for 40% I believe, with the rest being midterm/exam, so those who blindly copied the solutions without understanding them still did relatively poorly. By having the solutions provided in advance too, the marker should be able to use a fairly rigid marking scheme, without that leading to lots of docked points since everyone should be getting a 100 (or even mark on a 'completed' versus 'not completed' basis).
In my personal case, I think that works great, since I won't write something down if I don't know where it came from, and as such will stare at provided solutions until it clicks (in terms of the overall method, not just the specific question). Having the same problems but solutions provided only after the assignment has been handed in tends to not recieve the same attention, since they (feel like they) won't matter until the exam. Providing practice problems+solutions similarly doesn't work terribly well without the explicit points to make them worth doing.
I wouldn't think that the above method would work in general though. I know lots of people who wouldn't feel compelled to try to understand anything if solutions were provided, and theres tons of people who love practice problems, and of course there is some utility to forcing people to be careful with their work and not lose minius signs or make addition mistakes. It's not something I like (as someone who probably lost more marks in calc 2 due to arithmetic than calculus errors...), but I can appreciate theres value to it.
Who is online
Users browsing this forum: No registered users and 8 guests