What can be done to instill good habits in students?

Question

This question might sound vague, but I'm really just looking for particular examples that worked for you.

From my experience, it seems like a large portion of "weak" students remain weak despite their best efforts. I understand that part of this is due to things that have happened earlier on in their lives. Perhaps they didn't learn a fundamental subject well enough and were passed anyway. Perhaps they have poor study skills that haven't been corrected: copy notes mindlessly, look at solutions before attempting the problem, don't memorize, etc.

Besides just reminding them and showing them by example, what can be done?

In particular, my question is this: What have you done in your classroom that has helped instill good study habits or good habits in general. Or alternatively, what have you done to break bad habits?

My go-to weapon is office hours. I can talk to individual students about their study habits, ask them to work problems in front of me, etc. but it seems very inefficient to have to deal with students on a case-by-case basis...and hard enough to get them to show up.

Is this a lost cause or can you teach an old dog new tricks?

Answer 1

One thing I have done is to have taken the courses I have helped with (Teaching Assistant, Course Assistant, Research Assistant, Instructor) very seriously. A summary of my approach to TAing and office hours (your "go-to weapon") can be found in an earlier MESE post here.

Of the approaches mentioned there, one that I would like to re-emphasize here is the importance of asking that students who would like assistance:

1. Give their questions due consideration before asking them, and

2. Indicate how they are thinking about their questions as a part of the asking process.

Some of the so-called bad habits that you cite can be addressed to a reasonable extent by ensuring that students are not viewing you, their teacher or even their peer, as a crutch, but rather as someone to help them in their struggle (ideally a productive struggle, cf. MESE 2) to learn the material.

Here is an actual email excerpt from a graduate student in mathematics education (previously a kindergarten teacher!) who decided to take a course in Topology for which I was the TA. (For the sake of clarity, I added in the TeX below.)

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Question: Are basis elements in $\mathbb{R}_d \times \mathbb{R}$ of the form $(a \times b, a \times d)$?

Here is why I'm guessing basis elements in $\mathbb{R}_d \times \mathbb{R}$ are $(a \times b, a \times d)$:

•$\mathbb{R}_d$ is the discrete topology. The discrete topology is the collection of all subsets of $X$, which means all subsets are open, which means $\{p\}$ is open for all $p \in \mathbb{R}$.

•For $\mathbb{R}$ we have the standard topology, which means open intervals $(a,b)$.

•So the basis of $\mathbb{R}_d \times \mathbb{R}$ is $\{p\} \times (a,b)$ or, written another way, $(a \times b, a \times d)$.

Is this correct? Is this completely wrong? I'm doing #9 p. 92 [in Munkres' Topology 2e] and if the above is correct, then the dictionary ordered topology on $\mathbb{R} \times \mathbb{R}$ and product topology on $\mathbb{R}_d \times \mathbb{R}$ have the same basis elements.

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I include the above excerpt not for the specifics, but rather because this student initially overwhelmed me with questions. Eventually I asked her to include her thoughts - even if wrong - whenever emailing me. In the above example, note that she includes a guess and her reasoning. In this case, they are pretty correct; moreover, from around this time, the volume of emails dwindled substantially as the student was able to gain a fuller sense of agency.

(The question of whether Topology should be taught in Mathematics Education programs is one I leave to another thread...)

Answer 2

Give frequent quizzes.

When I say frequent, I mean every day.

The quizzes should be very brief: one basic problem from the lesson of the previous day. The grading will not be too onerous if the quiz has just one basic problem.

Give the quiz at the start of class, after briefly answering questions.

Make the point value of the quizzes very small. Drop several of the lowest quiz scores at the end of the term. No matter how small the point value of the quizzes, students will take the quizzes seriously.

In order to instill good habits in students, you have to first decide exactly what good habits you want your students to have. Surely most of us agree that the best habit is for students to keep up with their work, and the worst habit is to fall behind and give up. Frequent quizzes help to instill the good habit of keeping up with their work.

Assigning homework is not enough by itself. If you assign homework but don't collect it, the good students will do the homework, and the other students will not. If you assign homework and do collect it and grade it, the good students will do the homework, and the other students will cheat off the good students. So in either case, the good students do the homework and the other students don't.

By giving frequent quizzes, more students begin to realize the value of doing their homework and keeping up with their work. And it is not easy for students to cheat on quizzes, if you are a good proctor.

No technique works perfectly to instill good habits in all students, but giving frequent quizzes is very valuable.

Answer 3

The causes are probably a hodgepodge of all of the above, and a few more. First step is clearly to find out the most important factor in each case... and that takes one-on-one time.

Is special tutoring (even in general math) available? If so, make sure the students go there.

Suggest/encourage/enforce studing habits:

• Take a look at the notes after each class
• Don't try to cram three days before the exam, it just won't work. It is my impression that some variation of this is at the root of most bad performance.
• Make up a regular schedule for studying, and stick to it. If no homework or other work, go through your notes, solve proposed exercises. Count yourself lucky, I didn't have the Internet to trawl for material...
• Leave a day off from studying each week (does wonders against ending all stressed out)
• Don't study for the exam the day before. You may study other subjects, but not for tomorrow's exam (the last day you won't learn anything new, you'll only make yourself nervous).
• Make sure you are well-rested for the exam (i.e., no allnighters the day before!)

With my TAs here we came up with the idea of proposing three problems for each weekly tutoring session: one solved by the TA (asking for input from the class), one to be solved by the class in open discussion (with hints/help from the TA), and one to be solved individually and handed in. Solutions to all are posted after the session. The problems handed in are checked just for rough relevance to the subject, not really graded, and their yes/no make up a 5% of the final grade. Seems to have made wonders in the one occasion we have used it up to here.

Give short homework, often. Keep them involved with the subject. If a week goes by without looking at the subject, reconnecting becomes very hard (even hopeless).