My math students consider me a harsh grader. Is my teaching attitude wrong?

Question

I am a math major grad student at a big public school, and we need to do TA every semester.

I got assigned to lower level classes last couple semesters, and it's been quite difficult for me. Even though I am a pretty nice person in general, I have so much trouble tolerating my students' sloppiness, arguing for more points when they don't deserve, and just explaining very simple things to students again and again in general (for example, why log(a + b) is not equal to log(a) + log(b)).

I am sure many will think my attitude is wrong, and probably I need to hear that. I am also a "harsh grader", as my students would probably call me. The way I was raised, it's very hard to accept people not working hard, but feeling entitled to good grades. I have students coming to me asking how they can get extra points without doing any actual work. I feel offended by that.

Let me know what you think about teaching in general. I enjoy doing research in mathematics and want to be in academia in the future. However, I feel this could be a problem for me if I hate teaching so much. Should I think more positively about this?

Answer 1

Yes, you do seem to have a bad attitude toward it, but I suspect you knew that. I would suggest trying as hard as you can to put yourself in their shoes:

1. Not everyone enjoys the same things you do. What's a subject you had to take in school but didn't enjoy? Can you imagine not putting as much effort or showing as much respect to it as someone going to grad school for it?
2. It's totally rational for someone to try to maximize their grades. I think everyone finds it annoying when students push for every last point they can, especially when you don't feel they've earned it. I like to remind myself that it makes perfect sense to try to get the best grade you can for the least amount of effort. That doesn't mean you give in to their exhortations, of course, but if you understand where they're coming from then that's not incompatible with both helping them and keeping your sanity.
3. Everyone is busy. A lot of undergrads are adjusting to life away from home for the first time, are taking on responsibilities for the first time, and are probably swimming in social and extracurricular activities. That's what they're supposed to do; just keep in mind your class isn't the only thing on their plate.
4. The things you find easy, others find hard. You specifically gave some logarithmic rules as an example. To you, that's trivial. You can't understand how it's not trivial to someone else - I mean, you probably even just told them it was trivial! But I bet you can think of a field where you struggle with things an expert finds trivial. Foreign languages are a good example for me - I can hear how to say something in a new language repeatedly, and it just goes right out of my head a minute later.

That said, you suggested you "hate" teaching. If you really do, maybe it's not for you. On the other hand, you're here asking about it, so maybe you're interested in changing. To do that, try hard to put yourself in the shoes of your students, and remember that they're just trying to get by. Some will fail, and that's okay. But you can help all of them, even those who won't ever get your subject, without resenting them.

Answer 2

Yes, you should think more positive about this, and at least don't take it personal.

The students are sloppy, and you have to repeat stuff. This is how people learn, don't be surprised. If they would understand everything the first time they see it, no teacher would have a job. Don't take it personal. Additional tip: if a student wants to have points for something that's clearly wrong, they can go to your supervisor. Don't draw out the discussion.

The students want to have free points. Of course, everybody wants to have free stuff. Don't feel offended, and just grade the way you think is right. There should be no problem telling adults that they're not getting something.

The idea that this behaviour is unfair, offensive or disrespectful is just in your head. You cannot expect everybody to work as hard / be as smart as you are yourself. Think about how bad you would do in a Chinese language course (and what you would ask the teachers if you really had to pass this course).

Answer 3

Personally I found that it got better as the years went on. It was irritating when students barely a few years younger than me were complaining and begging for grades, but as you get older the students become so young that they're cute no matter what they do!

Also, you need to assess your situation objectively. If by large public school you mean Berkeley or Michigan or others of that calibre and you're one of the strongest grad students there, teaching might not matter so much in your career (it still matters, but there will be other things that make your job worth it) but if you see yourself as mediocre, teaching matters a lot in tenure-track hiring, so you'd better get used to it. Furthermore, even some top tier schools care very much about your teaching records, even at the postdoc hiring stages, so if you do a bad job you're cutting yourself out of some jobs.

Becoming more approachable and bonding with your students (which is much easier to do as a grad student) will also make it more fun.

Answer 4

Some comments, in no particular order:

1. I don’t think you have a bad attitude. And, high expectations are a good thing.

2. It's important to explain domains and codomains. Explain that log : ℝ_>0 → ℝ. Make sure the students understand that log(x) doesn’t mean “log times x.”

3. Not everyone’s brain is wired for mathematics. Some people need to see log₂(1)+log₂(1) = 0, log₂(1+1) = 1 a few times before it sinks in. It's worth spelling out the obvious: we've just seen that log₂(x)+log₂(y) = log₂(x+y) doesn't work for those particular values of x and y. Ergo, it's not a universal law. Okay - it doesn't hold for all possible value of x and y. So it's not a valid rule. So if we've got log₂(x+3) written down somewhere, we can't just replace it with log₂(x)+log₂(3), because we don't have a universal law available guaranteeing that these two expressions are going to be equal. You might find this discussion helpful.

4. If many students are making the same mistake, your job as a TA is to start the tute by explaining the stuff that people are getting wrong. And, you may have to do this repeatedly, and really spell it out. See (3).

5. Don’t be too hard on sloppiness. The reality is, it’s not just the students’ mathematics that is sloppy. Your mathematics is sloppy. Mine is, too! Unfortunately, the mathematical language we've inherited isn’t sufficiently excellent to produce non-sloppy mathematics. Maybe in 2066, things might be different. Probably, mathematics will be computer-formalized, and therefore every bit as precise as programming is now. But that’s not currently the case, and if I were sitting in one of your tutes, I could probably point out dozens of ways in which you’re being sloppy. So just go easy, okay? The idea is to teach, not to punish.

6. Never show any contempt for the student. Ever. Personally, I mainly reserve negativity/contempt for the textbook, the textbook writer(s), the notation, and the general sloppiness of mathematical convention. But I'm never contemptuous of the student. If need be, a firm "no, you need to work harder if you want better grades. I know you can do better" is all that's needed. Mathematics is already frustrating enough, so just be friendly, helpful, approachable, and if necessary, firm.

Answer 5

First, as others have pointed out, the students are behaving rationally according to their own preferences, in an "economics" sense. Unless they have sufficient incentives to do otherwise, why should they do otherwise? But this broaches a more genuine problem, namely, that it may seem disproportionate to give them bad-enough grades to communicate effectively... and thereby make them ineligible for their desired major program, students loans, etc.

Second, and relatedly, "teaching" required-course lower-division courses, and even some upper-division "required" courses for math majors and so on, is not really so much about the mathematics (although it is officially so), but about testing/filtering students for somewhat-broader purposes. "In real life", most students have no need of "pre-calculus" or "trig", but their major programs often require that they take such courses (and get a sufficiently good grade) as a filter on prospective majors in not-very-mathematical subjects. Not so that they'll know some odd bits of elementary math, but to see if they can show up on time, follow instructions, do things that are required even if they don't want to, and so on.

So, oddly enough, "mathematics teaching" is mostly testing the general competence (and perhaps willingness to conform to inexplicable rules imposed by authorities) of students.

And, notably, this function is what allows/causes math departments to be so large, and effectively underwrites the research we do. Seriously, the monetization of "research in math" is not so vigorous, but teaching lower-division math as filter is a reliably remunerative job. Supporting our "hobby" of research.

Answer 6

Here's how I've been able to ju-jitsu this situation for myself.

An enormous number of people are in great, desperate need for learning mathematics. It is a great challenge and responsibility and honor to help them, and instruct them in what real college learning is like. It's pretty clear that math is the hardest limiting factor in almost anyone's academic aspirations. I'd argue that almost any other subject can be watered down to meet an institution's desires, but not math. It is essentially a buzz-saw of truth. As JFK said, we do these things "not because they are easy, but because they are hard".

For me, I think of this like being a doctor (or at least a triage medic): Diagnosing what in the world has gone wrong in their heads. You'll learn to spot some common general patterns. But, there will always be rare and unique cases popping up with things you never imagined in your wildest dreams. I'm always learning and getting better at detecting what people don't know, or what incorrect bit in their brain caused a cascade of problems, and helping them fix it. I find it endlessly fascinating.

Personally, I have no problem with your being a "harsh grader" and not tolerating student sloppiness. I think that's well-phrased on your part, and is among the most important things we can help them improve at this level; attention to syntactic detail, and the fact that every symbol counts in our language and grammar (and, truth be told, every other language; perhaps we are the only discipline that assesses the student on structure in this way anymore). To me this sounds like you are maintaining high standards, and we need more people in education committed to that. The real frustration is if you get to an institution where administration doesn't want to allow that.

Now: I'm a dedicated lecturer and I don't have to do any research. I'm pretty happy with that position, and not sure how I would balance adding research on top of that (4 classes per semester). But the teaching alone became really fascinating once I came to view it as diagnosing a spectrum of crazy ailments.

Answer 7

There's a wide gulf in America between "good" math students like yourself, and "bad" math students (most others) and very little in between. Probably more than in other subjects.

That makes it hard to for the good math students to relate to the bad ones. Even so, having the good ones do "TA" is part of the drill of making sure the bad ones don't get even further behind. Once you realize that it's part of the "social contract" that helps fund your own studies, you will be able to deal with this better.

Answer 8

The most extreme case of arguing for another point on a homework, that I ever experienced, as a TA in a field that involved a lot of math and proofs, was in an upper level graduate course. I graded homework and exams, and was available for posted office hours. One day one of the best students in the class came to see me to get his grade changed from 99 to 100.

I have never seen such stubbornness as that student's.

I think it came from anxiety. He was an international student, from a country where he had had to prove himself to be the crème of the crème many times over in order to get to the U.S. for grad school. He was used to working very, very hard, and doing very, very well.

Okay, now on to what you can do, to be more effective in your teaching.

1. When a student comes to office hours unhappy about a grade, put the focus squarely on making sure the material has been well understood. Show that you are glad the student came to office hours. Encourage the student to come see you for help with the next assignment, before finalizing it and turning it in. You will earn students' trust if you show that you are available to help when they are struggling with the material.

2. You can walk the student through checking whether log(a+b) = log (a) + log (b). Don't do it on the blackboard in your office -- have the student do it on paper, with you giving suggestions as needed. You may write things down, but do so on paper, and make sure the student takes these notes home to be able to refer to later.

3. Elicit more student interaction during class. A correction made by you (e.g. log(a+b) <> log(a) + log(b)) is so much less effective than a correction made by a fellow student. (Of course, make sure that students are respectful with each other.)

4. Set the tone by being respectful yourself.

5. One way to elicit more student interaction is by having everyone write one of their homework solutions on the board. This works best if you have several blackboards in the room, and can have everyone write on a section of blackboard at the same time.

6. You can ask the students to create homework problems, and then assign the student-created problems to the whole class.

7. Sometimes, make an assignment that must be done in a small group. Don't wait until the semester is almost over to assign group work. The main point of this, in my opinion, should be to encourage the formation of study groups. When students are learning from each other, you won't have to repeat yourself so much.

8. Ask each student to hand in a short autobiographical sketch, to help you get to know your students. Ask them to describe their learning style in the sketch, to state what their strengths and weaknesses are, and to tell you about their life goals.

9. Don't wait until the end of the semester to do a class evaluation. You can do a short evaluation three times in the semester.

10. If you have lecturing duties, take the time to prepare well. (My son's Calculus II teacher would try to make up example problems on the fly. Sometimes he would have to abandon an example problem after wasting 20 minutes on it.)

11. Try videotaping yourself while teaching. When you watch the videotape, check to see if you are audible, if your chalkboard work is clear, if you are being careful not to stand in front of what you just wrote on the board, if your speaking voice is effective.

12. When you draft an exam, ask a colleague to take the exam to test it out.

13. Observe other instructors and keep a journal, noting what you see the instructor doing, what you see the students doing, what's working well and what's not working well.

14. Work very hard to catch any glimmer of a good attitude, good work ethic, or creativity, in a student, and provide positive feedback. In other words, catch the person acting like a good student, the sort of student you can enjoy working with, and reward that behavior.

Answer 9

Honestly, as a current mathematics student, I really needed the tough graders. When the graders would give me unreasonably high scores on the homework, I thought I was doing okay, but would fail the exam. On the other hand, after receiving several very low homework grades, I'd learn where I can improve and this reflected in high grades in the exams.

In mathematics, it's quite difficult for a first year undergraduate many times to understand where they went wrong and how to write a proof. Therefore, tough grading is a must in my opinion.

Answer 10

(On phone so there might be some formatting quircks)

Personally I don't have any problem with you maintaining a high standard. "If you don't work for it, you don't deserve a good grade" seems fair and can be a valuable lesson. People have to start working for something at some point in their lives, and if that starts at high school in math class, it seems like the perfect place.

That being said, you indeed sound harsh. The example you gave ( log(x + y) ) can be really hard for some people. Not every person has a brain that works in such a way that they can solve plain, boring stuff like that.

E.g. I was one of those people, I almost dropped out of high school because of mathemathics, even though I worked my back off and took way more math classes than I was supposed to. Now 5 years later, I'm a junior PHP software engineer (how ironic), make a decent salary and can even start thinking about buying my own home. Just because a student can't solve an assignment, doesn't mean he doesn't work to do it.

I've met a Dutch math teacher who would punish mistakes, but still grade answers alright if the calculation with the errors was correct. For example, you can earn 5 points per assignment and there are 10 assignments. A student accidentally flips an operator ( + -> -), but completes the assignment without further errors. That teacher would then give 3 out of 5 points: minus one for wrong answer and minus one for sloppiness. But since the student has shown he knows how to do the calculation, he still gets more than half the points.

Maybe this could be some solution?

Answer 11

(Continuing the thought of @stanri.)

When I was studying, I took lectures and seminars sometimes without getting points, grades, or certificates, just for the purpose of learning something exciting. Do try to motivate your students similarly. Tell them the following story, for example:

• Don't mind the grades too much; they measure your progress with respect to the expectations of a huge machinery called the state.

• Do mind what you have learned.

• University time is the unique opportunity to study; in general, there will be no second chance. Use this time.

Later, when I was a TA and the students asked me for better grades without doing something, I viewed it as my fault: I have not motivated them enough. You could think of doing the same.

Answer 12

Teaching in general: I do feel like you need to focus on the students more, - having to explain things "again and again" just means you didn't explain clearly a process - Complaining about this - is complaining about doing your job (To teach)

You need to make math accessible to them through language and logic in a way THEY understand, giving them the math tools to break problems down. You haven't achieved this if they don't get it (so stop punishing them for this with your attitude) roll up your sleeves and find a new way to explain

Math can be interesting for everyone when the steps are clear enough and the teaching versatile enough to be able to communicate the same process to appeal in many ways

People love to learn - You have a skill at math. But the genius of being a teacher its to find many ways to impart the same skill, requiring a great depth of knowledge and versatility in communication skills.

I would suggest to maybe look into Micheal Thomas, a really great teacher - his advice to students, and I believe it to be true -

There are no bad students only bad teachers This is a very important part of the Michel Thomas Method. Full responsibility for learning lies with the teacher, not with the pupil. This helps to ensure they can relax, and feel confident, so allowing them to learn effectively. (His course deals in teaching french) but the same is true for any skill - when something is well explained - then it is learnt. (If a student cant remember it - it wasn't learnt or understood as a concept)

https://www.youtube.com/watch?v=P8jhy7ZQC38

On grading - grade for what they have achieved, it is to show what concepts they are having trouble with and what the need you work on with them)