A comparison of mathematics and the other STEM fields.
I’ve been putting together a teaching/learning philosophy for a new program we are developing and I’m trying to raise the elements from ‘it sounds good’ to ‘there’s research that supports this’. So, I’ve been going through various reports on teaching and learning studies, especially those that focus on the STEM fields. I’ve not been through much yet, but I’m starting to formulate a question, and am going to use this space to ask it and start thinking about answering it:
From a learning point of view, does Mathematics fit with the rest of the STEM fields in higher ed?
The practical version of this question is:
Can we use the results of STEM (not math) education research or K12 math education research to inform higher ed math education?
(If I start feeling generous, I’ll change the ‘Can’ to ‘How’, but for now I just want to do a comparison.)
A disclaimer: I’m not a science or engineering educator and I’m not a professional math-ed researcher. I can only claim experience in teaching math, and thinking, talking and reading about teaching math.
I’ll write STE for STEM without math, although I don’t think much is about T, so it should really be just SE vs. M.
A list of comparisons:
- STE has observations, M has stipulations (I sometimes say science is limited by reality)
- STE defines based on observations, M focuses on sharp (human-made) definitions
- STE uses induction, M uses deduction
- STE has the Scientific Method, M has proofs
- STE works more with specifics, M more with abstractions and generalizations
- STE has more history in current content, M treats most content as brand new
- STE has more vocabulary, M has more symbols
- Both emphasize process, but STE more towards application, M more towards understanding
- STE has more facts, M has more processes
- Many study STE for it’s own sake, most study M for it’s use in STE and elsewhere
- STE K-12 results are relevant for higher ed, M K-12 results don’t seem to be as relevant
- When I look at education research for STEM, they usually don’t include many/any examples from math, and the examples they do provide from STE seem to favor the aspects of STE that are quite different from M.
- I think maturity plays a big role in learning mathematics; I don’t know if it is needed more in M than STE, but it is a big part.
- One data point: We have Supplemental Instruction (SI) on campus and they cover math, some sciences and other areas. If you go to the SI website (just search for it; the international headquarters is in Kansas, I think), you’ll see in the data that they include math, but that the results are quite as good. Locally we get the same results: lower attendance in math sessions than other, and less of an impact. There are probably lots of reasons why this is so, but one is that the SI sessions focus on the SI Leader helping the students help each other. It is not a review or tutorial session. The example I remember from the training/promotion was for psychology, and a student expressed some confusion about some topic, and the other students were encouraged (and able) to use the book and their notes to help the student understand. I can see how this wouldn’t work in math, as a student will say they didn’t get the right answer to some problem or got stuck, and either the other students can’t help because they don’t know or they were assigned a different problem, or they just give the student the answer. There’s no discussion and no learning about learning.
That’s it for now. When I’ve progressed more on my teaching/learning philosophy, I’ll post it. And, if I figure out more how M fits with STE, I’ll do an updated version of this. However, for now, this is all I have: just a question and some ideas.