# Tag Info

45

This is a small tip based on the obvious idea that it needs to feel safe to answer questions. Suppose you need to take the derivative of x sin x, but you want students to speak up about it in the flow of lecture. Here are three ways to do it: "Now I need the derivative of x sin x. What should I do first?" "Now I need the derivative of x sin x. Which rule ...

42

First, a little background. I switched to slides a few years ago when teaching a 3rd year course at my university. Because of how teaching works at my university, this course is one of the first where as a lecturer I can assume that the students taking it are interested in mathematics as a subject in its own right. That is, they aren't students from ...

34

One important point to make is that you should ensure that interaction is part of the culture of your lectures. It isn't enough to pose a question now and again and expect them to suddenly leap in to action to answer it. So you need to be asking questions consistently through the course. The next point I'd like to make is that it will take time for the ...

33

The think-pair-share technique is an oldie but a goodie: Pose a question Give students 1 minute to quietly think of and write down their answer (if you have a computer/projector setup you can use an onscreen timer to enforce the "1 minute" frame) Give students 2 minutes to exchange / compare solutions with a neighbor Ask for volunteers to share results with ...

31

Every time I add a new technological object to my classroom, I increase the chances that my class does not happen that day. Imagine if you could only make copies for your students in class in front of your students, but the copies came out very quickly. This would be extremely stressful, because when you brought a quiz to class, there would be a small ...

29

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; ...

28

Safety: When a wrong answer is given, if you can figure out what would have made it right, you help the student feel safer. Teacher: 2*3 is...? Student: 5 Teacher: oh, I bet you're thinking about 2+3. In calculus, teacher: integral of sinx? Student: cosx. Teacher: If I were asking the derivative, you'd be exactly right. What's the derivative of your answers?...

24

Here's what I've found, based on my own clicker use for the last 5-6 years and by doing clicker workshops: Cost. Clickers (and their software BYOD variants) cost money and many profs don't want to ask students to buy Yet Another Item for class when textbooks are so expensive already. Also, many IT departments don't want the hassle of managing fleets of ...

24

Wikipedia always has some great animations, often by User:LucasVB or User:Cmglee. A few Fourier transform–related ones: Approximating a square wave with a Fourier transform (more of these for other functions here: sawtooth, triangle, partial cubic) Fourier transform time and frequency domains Continuous Fourier transform of rect and sinc functions

22

Once upon a time I was one of those brighter students. Two things helped. One was the opportunity to help other people. I got started tutoring mathematics when people would come to me for help with their homework, and I learned that the effort to explain a concept helped me understand it better. A couple of times, I found that I didn't understand a ...

17

There are a lot of good answers already. That said, we have just scratched the surface. Shifting the environment of math classrooms from one in which students attempt (usually only semi-successfully) to passively absorb, to one in which students actually think, is a profound project and I think our profession is only partly underway with it. I would like to ...

16

Only a small percentage of lecturers use these tools despite claims from their manufacturers that they improve learning dramatically. Maybe people who actually use these tools have a different opinion on their effectiveness to that of people trying to sell these tools? I'm a part of the network support team in a college, I don't deal directly with ...

15

When presenting some example, I like to let them cast votes on the correct answer (e.g. for choosing methods of integration, or for the question how many solutions a given linear system has, after reducing it to row echelon form). I offer them 3 possible answers (sometimes including "Who doesn't want to vote on this?"). This gives me a quick way to see how ...

15

I think it turns out that "perfect" numbers do not interact much with other parts of number theory. Some of these very old, elementary, very ad-hoc definitions of special classes of integers have proven (and will prove) to interact interestingly with other ideas, but some seem not to. It's not easy for a beginner to guess the significance or subtlety of one ...

14

I know a lot of people use slides to teach, but I cannot imagine doing so myself. Here's why: Slides are boring. It's vital to good teaching to keep the students interested in what's happening, and one of the best ways to do this is to keep things spontaneous. Slides kill spontaneity. Slides are one-way. They are entirely about the professor conveying ...

14

A year after this question was asked, the bloom is definitely off the MOOC rose. The primary finding is that the majority of people who finish one already possess a prior bachelor's degree; offering one to say, at-risk or remedial students has been a failure over and over again. Some links that you should consider: Recent overview of the field, "The MOOC ...

13

Disclaimer: I teach at university, it is much different than teaching younger students (e.g. I wouldn't really know how to handle them well). The approach that works best for me is to force them to answer and to do it so frequently as to make it natural for them to ask questions, while, at the same time, letting them know it's alright to make mistakes. To ...

13

As in other answers and comments: while in gigantic "classes" one might hope to either get meaningful responses, or do quick polling/quizzing via in-real-time responses, ... techno-glitches make it impossible to depend on these, in the first place. The potential plus that feedback can be anonymous, allowing perhaps more sincere response than otherwise, ...

12

First of all I would highly recommend Derek Bruff's definitive book on this subject. There are more good ideas in that book than any one faculty member can expect to implement. If there's anything I do with clickers in the classroom that works, it's probably appropriated from Derek in some way. That said, here are three ways I use clickers on a regular ...

12

I've found it more natural, and more helpful for the students, to arrange the out-of-class work around the learning objectives you have for your instructional units rather than the number of pages in a book. There's not always a natural linear relationship between page numbers and concepts -- sometimes a concept that takes a couple of pages takes twice as ...

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 ...

11

Differentiation is one of the hardest parts of teaching, for sure. One thing that has helped me a lot is reframing my questions so that they are more "open." For instance, instead of asking my students to factor a quadratic, I'll ask them "Say that I've got $x^2 + bx + 9$. What can $b$ be if this expression is factorable?" What's great ...

11

Slides are great... if you know how to use them correctly. Some advantages: It works without blackboard (e.g. at a conference, or unprepared lecture room, sometimes even a pale wall will do if at some unusual venue). You can present pretty pictures (and animations) that would take ages to draw (or would be plain impossible). It helps to organize the class ...

11

I've used clickers and helped other faculty with clickers for over 10 years. I'm at a very large, very research-oriented public university. Here are the reasons I've seen for why research faculty don't use clickers when they teach: They team-teach, which means all instructors have to agree to use them They teach only 5 weeks a year, and have to re-learn the ...

11

I think I would personally dispute the claim that this "went viral". I didn't see any people in my social networks talking about this problem until well after the media started reporting that "Everybody is talking about this problem!" Even now I don't see anybody talking about the problem; they are only talking about the coverage of the problem. Having ...

11

I second Adam. Keep it with strong with examples if you can. There is a mathoverflow answer with a ton of group theory examples. You might want to force them to practice doing more "rote" exercises that often come in an intro abstract algebra book to help gather examples. Also it should be mentioned that not all CS students have a strong background with ...

11

One of the charms of graph theory is that people of all ages often enjoy learning graph theory ideas and tools. One place one can read about these ideas is in the book called For All Practical Purposes (I am a co-author) which has gone through 10 editions. The book was designed for college liberal arts students who might have almost no proficiency with ...

10

I would suggest a distinction: A MOOC really should be massive, that means some 1000 participants or even more. In this case your problems will be about server capacity and technical things. The work like answering questions will then be done by the community (like in this forum). This, however, always requires some people to be online in your forum. Blended ...

10

One advantage of slides (I don't use PowerPoint, I use Beamer) is that it is a memory prompt that keeps me on track and in order. However, like many people I use a combination: I might have a definition on the slide and do examples at the board. That helps me keep to a pace they can follow and also helps me avoid being just a slide reader.

9

In teaching calculus, I like to have something like 5% of the course grade be based on "Participation". On the first day of class, when going through the syllabus, I go over what I mean by 'participating' (it includes, for example, asking questions as opposed to only answering any questions I happen to pose to the class, coming to office hours, etc.) and in ...

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