One of the most effective teaching strategies in lower division service courses like pre-calculus, calculus, mathematical thinking etc. is to assign a good amount of homework. A good amount tends to be an individual call. You know it is a good amount when some, but not all, students complain.

Well, perhaps all will complain! So let’s call it an effective, but unpopular, teaching strategy.

It is definitely a time-intensive teaching strategy since students must get feedback on what they do. One way to save time while assessing routine homework is to check just a few of the problems. For example, in a homework set of 15 problems on solving linear equations, if the student knows how to solve an equation with variables on both sides, and brackets, and fractions, then the student knows everything else and it doesn’t matter if there are a few errors here and there. I tend to be generous in grading homework and I accept late homework. I take off a nominal amount for errors and lateness, but then allow them to earn it back at the end before the final exam.

I am, however, firm about students completing and turning in all their homework even if it is late. Mostly I do this by getting to know the students and asking them about homework throughout the semester.

The reward is captured in the following scatter plot of data from one of my lower-division classes last semester (Mathematical Thinking). The figure has homework scores on the x-axis and final exam scores on the y-axis. The correlation coefficient is 0.7. The cluster of point near 100 on both scales speaks for itself. (I gave students 6 bonus points on the final in case anyone notices that a couple of the exam scores are over 100.)

What about you? Do you assign homework? If so, is there any correlation between homework scores and final exam scores in your classes?

Of course, correlation does not imply causation and this is well illustrated in one of my favorite tongue-in-cheek books How to lie with statistics by Darrell Huff. Nonetheless, it is interesting to get some solid evidence to back-up favorite teaching strategies.

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4 Responses to Homework

  1. Hi Jinko, I think it is a great idea to assign homework before starting a topic. Thanks for sharing. It will motivate students to read over the material and get a head start. Even if all the students don’t do it, it sets an expectation. Combined with generous checking policies it encourages students to take responsibility for their learning.

  2. Jinko Kanno says:

    Hi, Sandra,

    I completely agree about assigning and checking homework is very important. One of my colleague assigns homework and only check if they did or not. I took his way but I did a little more extreme than his method. I even do not collect homework, just glance and mark in my roll sheet if they tried or not.

    As you do, I will take late homework up to a final. For junior and senior, I assign homework before I teach the topic. They are shocked at first, but if they can follow my way, they will succeed. Also, I have learned that if a student did the homework before the class, the student can take a better note in class. Yes, the correlation is very strong for both freshman and seniors.

    Oh, sorry I forgot introducing myself. I met Sandra at the AMS sectional meeting last Saturday in Oxford, Mississippi. I teach calculus and discrete math at Louisiana Tech University in Ruston, Louisiana.

  3. Thanks Jonas. Looks like I can put together a post every couple of weeks, instead of every week…

    The correlation/causation story is hard to forget and it illustrates the point so well.

  4. Jonas Reitz says:

    Sandra – welcome to the CUNYMath Blog! Great post. The practice of mathematics — wrestling with the problems! — is so important, and it’s constantly amazing to me how few students will do it without some external reward (like making it part of the grade). Hat’s off to you for collecting & grading homework — I have tried this, but I just can’t manage the workload. I have been experimenting lately with online homework systems — I have great hopes that this could be a way for technology to help with the burden of homework-grading, while still providing feedback & points to students. However, the systems are all a little clunky. Still looking!
    ps. I don’t think I have lice, and I’m beginning to worry that my health may be in danger

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