I have three classes to teach this semester:
The Mathematics of Games and Gambling - a distribution level course. There is a mix of freshman through seniors in the course. Class size is 18. There is one math major in the course (a senior who needs credits).
Calculus I - Section A - Mostly upperclassmen, about a third of which had me for a previous class. Class size is 21.
Calculus II - Section B - All freshman (except two). Only one student had me for a previous class. Class size is currently 15 - it could potentially rise to 20 by the end of the week (though I doubt it).
With that in mind, let's see what the students claimed as the qualities of a good math teacher (divided by class).
Mathematics of Games and Gambling student responses:
- Fun & Interesting
- Thorough, patient
- Interactive, knows the material, is excited about the material
- Explains well, takes time, offers homework to help prepare for tests
- Helpful & receptive to questions I may have; Makes subject matter interesting
- Multiple ways to find a solution
- Patient, eloquent, sense of fun
- Explains lessons and hands on
- Understanding, approachable
- Knows what he is talking about; Is clear when explaining steps
- Explains well and is hands on
- Answers students' questions
- Knows math; Gets the students interested in math (Texas Hold 'em? Yes please)
- Strict, but fun, explains things, not everyone's BFF
- Explanation skills, patience
As you can see, there is quite a diversity in what makes for a good math teacher. However, the one word that appeared a lot is patience. By my count 7 of the 16 respondents either named patience outright or alluded to patience in their qualities. The other attribute that was named a lot was fun or excitement (four out of the 16 alluded to fun in their comments). For a distribution class, I thought the comments were quite telling! The students want to see why the subject of math is interesting or fun, but they want to be shown in a clear, precise, (and perhaps slow) manner. If I had to try to summarize this class' thoughts into a single sentence, it would be: A successful (distribution) math teacher has a love for the subject which they can translate into thoughtful, fun, and well-structured lessons.
Moving out of the distribution course, I have a pair of Calculus I sections. First up, the (mostly) freshman section of Calculus and their thoughts on makes for a good math teacher.
- Understanding of info, communication
- Interactive, Hands on
- Engaging, able to make course interesting and fun
- They can somehow make class fun and not all lecture
- Gives a lot of problems to practice with
- Helpful, insightful, explains things well and goes over things extra times
- Funny, helpful, smart
- Can teach a topic in different ways to help better understand something
- Organized, smart
- Explains/teaches well, interactive, approachable
For my (mostly) freshman section of Calculus I, the differences in what makes for a good teacher (as compared to the distribution course) were quite stark. The idea of being fun wasn't nearly as prevalent. The idea of patience was essentially non-existent. Instead, words like "smart", "insightful", and "organized" make an appearance. Since the majority of the students in the class hadn't had more than one college class (as in, a single meeting of one class since this class meets in the morning), it seems that many of the qualities are a direct response to the stereotypical college professor.
Finally, my second section of Calculus I (a class in which there were only a couple of freshman and plenty of students who have had me for previous courses) had this to say about successful math teachers.
- Able to fully answer questions & visibly demonstrate answer; able to make learning fun
- Explains everything
- Patience, intelligence
- Funny, respectful, patient
- Someone who explains well and works problems on the board
- Explains new material in detail
- Goes at a good pace and is clear
- Funny, helpful, interesting, knowledgeable
- Patience, clarity, authority
- Good at math
- If they can teach me, they can teach anyone
- Answers every question
- Interactive, entertaining, available
- Doesn't assume we remember how to do everything from precalc*
*not one of my former students for the record!
I wasn't surprised by the across the board responses from this class based on the heterogeneous mix of students in the course. The freshman all said things to the freshman in the previous class while the upperclassmen usually went with something along the lines approachable or explains things well.
Can you make any broad assumptions or observations from my data? I don't know (well, you can make assumptions but how accurate are they)? If you put all the responses into a single list, it's interesting how much higher "fun" and "patient" rank as compared to "knowledgeable". Even more telling, I teach at a liberal arts college so the answer of "prepares me for a future job" was essentially non-existent!
Do you ask your students anything along the lines of what I did? Or, if you are a non-student reading this, what qualities do you think a good math teacher should exhibit?