Studies on more simple problems, or fewer difficult problems?

Question

I'm a new adjunct faculty member. I haven't taught math yet (I'm teaching a related subject for now), but I've been thinking about my approach to teaching Calculus I should I be asked to teach it in the future.

One idea that has come to my mind is the possibility of fewer, more difficult homework problems that represent "real-world" practice (e.g., maximum likelihood estimation) over doing hundreds of computational problems (like what one would do through, say, WebAssign or MyMathLab for homework problems).

Have there been any studies that attempt something similar to what I've said here?

Answer 1

1. If you want to find academic studies, do an academic literature search. Didn't you learn to do this during your studies? Even if the results show little, if you give us the parameters that you searched with, it helps others to respond/add.

   I also recommend you not to expect too much from formal education research. Teaching is a complex affair, full of confounding factors. Many academic studies are poorly controlled, biased (both statistical and colloquial terms), and have low population counts. Sure, look for studies--why not? But realize the state of the subject.

2. The impulse to do fewer, more difficult, problems is a frequent desire by skilled academics moving from research to teaching. It tends to mimic their research. And is more intellectually interesting (to them). However, it ignores several possible traits of pedagogy that relate to more/simpler problems, such as progression and repetition. (Would you learn judo by fighting a match first thing?) Also realize that the typical student is weaker than his teacher (except maybe at Cal Tech) in terms of both aptitude and experience. Don't be blind to this difference. So my advice is not to replace drill for "project" style questions. Especially given your lack of either research or deep experience to support changing the traditional approach.

   This is not to say there is no value (motivational or conceptional) in more complicated problems. But make it the paprika in the goulash, not the meat and onions. Also realize the benefit even of the harder problems towarsd the end of a homework section. Even a "simple" (to you) word problem is complex for someone new to the techniques.

   Also realize humans are not computers. We have to do things several times to learn/master them. A computer can execute a program instantly and repeatedly, including one with a complex number of steps. Humans need repetition.

3. Get some experience teaching the traditional approach before deciding to try something different. Don't make your first rodeo an alternate rodeo. Even if you still want to change, you'll know more about why/what to change. But don't confound being a new instructor with teaching an alternate approach. If it bombs, you won't even know if the fault was you or was the approach (one equation, two unknowns).