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.