28

To start things off, some moments my students move around during class: I have given students tape measures and had them determine how much they would spend at the paint store if they wanted to paint the walls and ceiling of the lecture room (while projecting two images on the overhead: one of a paint can label, showing the number of square feet per gallon; ...


19

I'm a female who was often 'the only one' and later became a teacher in classes with 'only one' or very few females. When I was a student in a normal (say 100th-ranked university), I just worked hard (and screwed up the grading curve for everyone hehehe) and didn't notice the gender ratio or whatever. Then I moved to grad school at a really elite school ...


18

It has been nearly a year now since I've made this question, and I think I've discovered a 'magical cure'. This one simple trick has worked for all of my classes with great success (I am feeling more like a scam-advertisement as I am typing this), though I admit I don't fully understand why it works so well, though I do have theories. Simply kneel down ...


13

I prefer to think of lectures not as the worst way to teach but rather: A lecture is the worst way to teach, apart from all the other ways we've tried. That said, to understand when it is appropriate to lecture we have to understand what lectures do. At its heart, a lecture is a time-efficient way of communicating "stuff" from the lecturer to the ...


12

Two things that I had in mind, which prompted the question in the first place, are: A Pin Board (source: ptrow.com) This device demonstrates the emergence of normally distributed data from a large number of independent, random events applied in series. Image from http://ptrow.com/articles/Galton_June_07.htm An Adding Machine I'm currently building ...


12

The Hungarian Quicksort Dance demonstrates a computer science algorithm with dance. It's pretty advanced, but the idea is to have your students physically act out algorithms. Perhaps something similar can be done with a number line. Line your students up and have one walk down the line to demonstrate addition and subtraction, or take big steps for ...


10

Here are some examples of physical 3D-models of mathematical surfaces. They might give you some ideas. https://raisingcalculus.winona.edu/ (Raising Calculus to the Surface - Aaron Wangberg - Winona State) uses a plastic mold of a surface that students can study (and markup with a dry-erase marker). http://www.3dprintmath.com/ (Visualizing Mathematics with ...


9

I will try, though I am a biologist. The main difference between your question and the one linked in the comments seems to be that you want students to realize that articulating mathematics leads to better learning of mathematics. Not just being willing to answer questions, but talking. I would recommend a technique that can be done with either clickers or ...


8

Start calling on students individually without waiting for any one to raise their hand. For a long time I never did this since I am conflict avoidant and since I didn’t want to put students on the spot, but then I witnessed another instructor masterfully call on every student throughout the course of one class period. The key point to add is that when a ...


8

I think polyhedra and polyhedra-like objects are, although not exactly wall-mountable, quite pleasant to have around. Polyhedra are particularly easy to build with zometool materials (a professor of mine always had a complete set of zometool Platonic Solids laying around in his office; they were great), as this picture (from the zometools website) shows: ...


7

I've had a remarkable (remarkable to me) success in a different environment on a different topic, so I am not sure this will translate. But I'll mention in anyway. With one change, the same quiet "labs" turned into such lively conversations that I now have to raise my voice above the din to interrupt them with instructions. The change was from allowing ...


7

I'm not a natural extrovert, but I've found that this is less about social skills than about establishing clear expectations. For example, if I put up a question on the projector that says "Discussion question: ..." and tell the class we're going to discuss it, there's no real uncertainty about what is expected. On the other hand, when I observe other ...


7

I've taught about 100 biology discussions and get good interaction evaluations; you can decide if this advice applies to you and calculus. I am making some assumptions about your teaching environment: You have 10 - 30 students in the room Students had lecture elsewhere, so you don't need to lecture Nobody is telling you what you have to do in discussion (e....


7

This is a bit tongue-in-cheek, but it is good to lecture after students think they have mastered something via an active learning experience, provided the lecture is the result of long effort to find an efficient or beautiful path to a result. A lecture should be given with the disclaimer that such efficient and beautiful paths are the result of a long ...


6

In some of my graduate courses, my professors tried to get a 'post your homework solutions and other thoughts' page going. It didn't work, which is surprising considering we are graduate students massively interested in the topic. Here are my thoughts in no particular order: Pros: Encourages students to practice mathematical typesetting (latex, etc) Helps ...


6

When dealing with students, especially more quiet and private ones, the most important thing is to build some sense of trust before trying to breach things that make them uncomfortable. If you just outright go up to them and tell them to show their work to you because you are the teacher it will only make them more uncomfortable and less likely to want to ...


5

Of the common teaching methods used in STEM, evidence from educational research strongly suggests that lecturing is the worst. A 2013 meta-analysis[Freeman] compared the effectiveness of lecturing with that of active engagement techniques. The metrics used were success rates and scores on standardized tests or other assessments. In all STEM subjects and by ...


5

I have many ways I have used technology in my math class to promote mathematical thinking. Here are five examples. Share a dynamic Geogebra applet at the front of the room, and ask students to share things they notice, and share things they wonder, and ask the person at the front to change the sliders. As students notice things, other students notice other ...


5

Here are some ideas: Try using shared vertical surfaces for doing problems. For example use whiteboards/windows. According to Peter Liljedahl http://www.peterliljedahl.com/publications/building-thinking-classrooms, having to share the writing space can encourage discussion. He suggests vertical non-permanent surfaces, but any shared space is better than ...


5

Am I just asking or expecting too much from this group? I empathize with your goals completely, and they are honorable. Bear in mind that sometimes, due to a conflation of factors, a particular class climate may be such that this just never gels no matter what you do. In my master teaching folder I have a half-dozen post-it notes for (hopefully very rare) ...


4

How about a Slide Rule: Also some wolfram posters: or:


4

You could hang posters of the 17 wallpaper groups, or the 230 space groups, hoping their presence will engender wonder and generate questions.                     (17 Wallpaper Groups.)                     (230 Space Groups.)


4

When I teach some basic graph theory, I explicitly mention (and include in the notes) that certain definitions and terminology vary from author to author, in some cases giving the alternatives. In fact, the field is notorious for this. Of course, there is a risk that students will use one of the alternatives instead of my preferred definition, but my ...


4

I am most happy about technology when it comes to dynamic processes. There is just nothing like seeing something actually move, whether you rotate a transparency or whether you move a point in Geogebra/Cinderella/etc. Another big subject class where visualization is extremely enlightening is asymptotics. I have let my students plot the prime counting ...


4

A technique I use a lot is to use software to put students in random groups, then have them do active learning activities in those groups. These activities are sometimes the "conceptest" technique created by Mazur, or think-pair-share. My set of conceptest activities for freshman calc are here (click through to "active learning resources"). The conceptest ...


4

To build intuition for the Cartesian plane, assign axes to the room (or to students, depending on how many you have and how they're arranged in the room). Then you can do things like: Stand up if your $x$-coordinate is 0, 1, 2 etc. Stand up if your $y$-coordinate is less than five. Stand up if your $y$-coordinate is less than or equal to five. Stand up if ...


4

My favourite is addition and multiplication by walking. This is my go-to activity when I talk at schools. $+2$ is two steps forward. Then we get to negative numbers, and $-3$ is three steps back. Multiplication scales and rotates- so multiplication by $-1$ turns you backwards (or rotates your "true north"), and $\times 2$ does something twice. Now we can do ...


3

It seems to me that there are two things that I would want in a teacher who is looking to improve their interpersonal skills: (1) ability to master the subject (2) ability to lead a flowing discussion. The first is not the question that I think you're really referring to, so I'll talk about the latter. I have had the discussion with a few teachers about the ...


3

While I do believe much of this is natural talent, there is lots you can learn, by looking at how more experienced colleagues do it, asking around ( e. g. here :-) , ... Much of the problem might be just nervousness/anxiety. Work on that: Get very familiar with the subject matter, see if you can (also) work in situations that are less threatening to you (...


3

My website lists a good many math words with two widely used meanings. It is at [dead link]. Search the index for "two meanings" and you will find a bunch of them. --Charles Wells Edit many years later: It may still be possible to find some things at an archive of this site; try perhaps: https://web.archive.org/web/20180831121859/http://www.abstractmath....


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