Friday, January 20, 2012

Teaching an Honors Section of Discrete Mathematics

A few years ago I was assigned to teach the HONORS section of Discrete Math (a course for sophomores who have had a year of programming and a year a calculus). They told me it was up to me to figure out what to do to make it an honors course. (My section had 30 students, the non-Honors has about 60.) There were several options:
1. This could be taught separate from the non-honors course. Diff homework, diff exams.
PRO: the homework and exams can be more interesting since you do not have to worry about how they are for the non-honors student.
1. CON: If a student would have gotten (say) an A in the non-honors course, but gets a B in the honors section, that is not good. OR the teacher could grade inflate so that the students who got a B in the reg section gets an A in the honors section.
2. You could give the same exams and homework to the honors students but REQUIRE them to do more work- extra problems on the homework, extra problems on the Exams.
1. PRO: They will get to do more fun problems.
2. CON: They are being penalized for taking an honors course.
3. Same Exams and homework as the regular class. The regular class meets Tu-Th for 75 minutes. The Honors class meets MWF for 50 minutes each. What the Regular class does on Tu-Th, the honors class does on MW. On FRIDAY the honors class has an HONORS DAY- they work in groups of 3 or 4 on problems of more interest than usual. (example: For Logic devise a way to do do AND, OR, and NOT if the variables take on values BETWEEN 0 and 1 (including 0 and 1)). There is a LIGHT homework on this work just to keep them honest. But its not graded seriously.
1. PRO: They get to learn more stuff in a fun way.
2. CON: More work for the professor to make up these kinds of problems. (To brag- this is the sort of thing I am good at so not a problem for me.)
I did the last one and I think it worked, for some definition of worked. That is, the students liked it and found it interesting, but its hard to compare it to other ways of doing it. (Doing real studies that tell you things in the field of Education is hard.)

How have you, or would you, run an honors course in discrete math? How about for a programming course?

1. "If a student would have gotten (say) an A in the non-honors course, but gets a B in the honors section, that is not good."

[citation needed]

1. This is just my opinon, however here is why I have it: Some
cutoff. While they SHOULD say `he got a B in the course, but it
was the honors section' I suspect that many do not and just go
with the GPA or the Grade. You may say that I need a citation
for that comment, and you may be right, but I do not have one.
I have heard stories of such, but again that is not quite proof.

I very much do not want to punish people (with a lower grade)
for taking the honors section.

2. Honors sections at UMass are usually one-credit add-ons to regular (3 or 4 credit) courses. There some of the students, usually members of our Honors College, meet with the instructor weekly and do something supplemental. For the discrete math course, I have usually had my honors students read Godel, Escher, Bach, talk about it in the weekly seminars, do some of the exercises in there, and present some kind of project at the end. This term I am doing an honors section for the upper-level theory course using the Sipser book -- I'll present some extra stuff on descriptive complexity and algebraic automata theory, and have them make a wiki of the new material collectively.

If I could have a section of discrete math containing only the better students, I would probably keep the syllabus the same and do a lot more proofs and hard problems. I agree with you that I would want the grade scales of the honors and ordinary sections to be comparable.

3. I think the premise here is flawed. I think that the in the honors section there are students who won't getting anything more from extra material and that in the regular sections there probably are students that will get something from it. I wasn't in the honors program, but I did extremely well in your Discrete Math class, and having a Math class were I had to think, and the homework wasn't just tedious busy work to mechanically teach people the process of solving the sort of problems they will be tested on. I think if you do anything special you shouldn't torture the people who are only toiling away in honors sections cause it's what's their parents expect them to do and should cast a wide of a net as possible for the people that will appreciate your efforts and be nurtured by them.

But I've heard form enough students who have been split between a section taught by a professor and one by a lecturer that both used the same homework and tests, and the ones not in the test author's section felt that what was done in class did not line up with their assignments and that it was unfair to them.

4. What a coincidence; I'm teaching the first Honors section of our Discrete Math course this semester (about 15 students vs 50 in the regular section). The approach I'm taking so far:
1. I let them vote, after a discussion and nomination on day 1, how they will be graded. Ultimately they decided on 10% midterm/final, 90% homework (which can be reworked for earning half credit back on missed points) OR 60% homework and 30% group research project (they choose an advanced topic like QR Codes or Godel, etc. and produce a report/presentation at the end of the semester (they have until midterm to decide which
2. I plan on making the same homework and exams as a regular section
3. The "Honors" portion comes in two ways: I cover the material at about a 30% faster rate (reduce 3 lectures to 2) with fewer examples and the normal recitation section is gone (no GTA support). The expectation is that they will get it without reinforcement or will work examples on their own. The second "honors" portion comes in covering advanced topics later on (breadth) and/or covering related advanced topics throughout that are not normally covered (depth).

1. at our institution it's been found that Honors students are actually notorious for working together (not allowed) on homework assignments to make sure they get full scores

how in the world do you make the midterm and final worth a total of only 10% of the grade?

2. (Agree that HW should be a smaller part of the grade-
we usually do 10 or 15 percent, not just Honors students.
But thats a topic for another day.)

We do have a TA but since the students often
don't need extra help the Honors Discrete Math TA
is given other extra things to teach them.

I did in Monday-Wed (50 minutes each) what the non-honors
did in Tu-Th (1 hour 15 minutes each), we also coverd
it some percent faster. What percent? I'll get some honors
student to figure that out. :-)

The extra topics I did on fridays was usually related
to the material. (In a later post I may enumerate them.)

3. I'm not obsessed with enforcing "honesty". These are honors students, which I've found to be *more* honest, self-motivating, actually *wanting* to learn rather than getting a grade. I have no problem handing out A's like candy if I've felt that they've learned the material (which is the actual point of a course after all). Moreover, I explicitly allow team work in written homework assignments (which also carry a substantial amount of programming: Graph Isomorphism, Set operations, etc).

In-class midterms and finals under a time restriction are not a great evaluation tool and the type and depth of questions that you can fairly ask in them are limited.

4. You are naive if you think they are more honest. They are under more pressure to score an A and they will work together on homework so it's good that you allow it. If you are doing 90% of their grade on group work where you'll never really know who has learn what and you are happy with that, great.

5. Here at UMich (I'm a sophomore very much interested in computational/descriptive complexity theory), I usually take honors/advanced/grad-level math and physics courses for two core reasons:

1. They challenge students without having to rely on the horrendous amount of nonsense that comes from trying to weed students out or create a curve.

2. Less time is spent worrying about the grade. So the focus can be placed on doing interesting projects, independent readings that can be shared, and potentially pose new ideas or questions that students can collaborate on. Of course, all portions of the courses are valued, not just exams.

If things like this did not exist, I would simply be too bored with undergrad to really be motivated to pursue my education. I am willing to admit that this position may be quite naive, but there is not much that can question the fact that I learned more from these courses than anything else. I know this is not much, but hopefully someone here can gain some insight from it.