12

I struggled with this as a new lecturer, and I found a few ways to manage the process of using a big blackboard: Observe people lecturing When I first started lecturing, I visited the lectures of other staff to see how they did it. I realised that when I was a student I had seen many lectures, but I had never thought about the actions of the lecturers at ...


8

I have students present (in classes ranging from grades 7 to 12) and use the following rubric. It is not original, and googling various snippets suggests to me that it has been pieced together from several different sources. Perhaps modifying this could yield something useful (note, e.g., that I have the students present in groups — so if you are having them ...


8

Over the years I have tried multiple tools including commercial and free, gui-based, script-based and LaTeX-based, vector, raster and 3D renderers. For the last three years I've mostly used Inkscape (official website, Wikipedia entry), which I strongly recommend. Advantages: easy to use, enough effects, free, versatile. Disadvantages: not as streamlined as ...


7

There are different kinds of 'learning types'. Some people learn best by listening and talking, some people learn best by understanding the material with the help of pictures, and some learn best by writing things down. The 'classical method' of presenting formulas, proofs and theorems by writing them down gives the students the time to write it down ...


5

Sound effects! I substituted once for a friend in her ODE class. A week later I met her in the Department's lounge and she complained with a smile in her face that I had ruined her class because the students wanted the "bloop" professor back. My task had been to illustrate exponential growth, which I did with reference to a bacterium in a Petri dish. After ...


5

(1) I am shocked that no one has mentioned the so-called Monty Hall problem/paradox. :) (2) The point that "probability" does not directly describe "randomness", e.g., although the sequence of heads-tails HHHHHHHHHH seems "unlikely/not-random", it has the same probability ($2^{-10}$) as "random-seeming" sequences such as HHTHTTTHHT. (3) "The other ...


5

I think the main thing to remember, regardless of which method you choose, is that you are the most important part of the presentation. You could spend hours/days/weeks/months preparing the best slides ever, but if the delivery is no good, then it will all be for nothing. Slides can certainly be an important accessory, but they should only ever be there to ...


5

I do not know of any article or study that "proves" that multiple intelligences exist for math (or for what is worth, any other subject). Such a study will be difficult to design and its results will just show some causation between teaching and learning methods, rather than something physiological within the brain. On top of that, research in math education ...


5

I'm fond of asymptote, but it is not geared towards geometric diagrams. For me it is important that it integrates well with LaTeX (uses the same fonts, even complete math formulas). I use it more for general drawing. Take a look at the gallery, there are several geometric diagrams.


5

I use Adobe Illustrator, but my school has a license so I don't have to purchase it myself. It is extremely versatile, but there is a learning curve. One can paste drawings and images created by other software into Illustrator, and then control many aspects in Illustrator before exporting into PDF or JPEG or whatever format is best for you. Here is one ...


5

Regarding this part of the question: Perhaps someone who uses GeoGebra can provide insight into how to best format GeoGebra so that the drawings fit well into Word documents. There are two distinct issues you might be having, and I am not sure which one is your main problem. When you export the Geogebra diagram to a picture (either via the clipboard or ...


5

We run a weekly seminar at my university where undergrads give math talks to other undergrads. To encourage people to give talks we collected a list of suggested topics which may be useful to you -- https://uwseminars.com/potential-topics/ EDIT: As suggested by Joel, I'll add a few of my favourite ones from the list (there are 83 topics now, but the number ...


5

When teaching complex numbers I used one colour for imaginary parts of the numbers and another for the real parts. More generally, whenever you have a clearly distinguishable object, you might to assign it a colour. If a sequence of functions is approaching a limit, you might make the limit blue. The sequence might be red. A few points to keep in mind: Be ...


4

I can only offer my personal opinion on the matter, having witnessed both formats as a student. I think that the material you use should be designed for the specific use you want them for. Slides are great for talks, presentations and to supplement lectures. They are usually designed in a way that you can see all the important things at a glance. Unwieldy ...


4

I personally use IPE to draw diagrams for insertion into TeX documents. Some benefits about it that I like: It is free. It generates .pdf outputs, easily inserted into TeX files or usable/viewable on their own. It renders LaTeX text so you can label parts of diagrams easily. The "grid snap" feature is great; quoting from the site linked above: "It is easy ...


4

Almost any chapter of this wonderful book could serve as a seminar topic. Each chapter is pretty much self-contained. Matoušek, Jiří. Thirty-three miniatures: Mathematical and Algorithmic applications of Linear Algebra. Vol. 53. American Mathematical Soc., 2010. (AMS link.)          


4

Not aware of any software but here's a simple hack to achieve what you want: Go to codecogs equation editor. Write your LaTeX equation. Copy the url generated (it will be exported as swf). In import dialog box in Prezi, enter the url Voila! Someone has written a detailed blog post about it here.


3

This is not a direct answer to your interesting question, but rather just one instance where I found it useful to use sound to convey aspects of an algorithm's operation. The algorithm walks through the space of polygonizations of a point set, and I used the polygon perimeter to control the pitch of a "Crystal" MIDI instrument.         &...


3

Google Docs has a very convenient "Create drawing" option that has mist of the core functionality of Illustrator or Inkscape and requires no software download. I've used it for several papers and Wikipedia articles. As a total amateur, I find it easy to make lame drawings like this in 10 minutes: Or this in 20 minutes:


3

Here are three books I have used in various ways for such a course, focused on mathematics history. Journey Through Genius - lower level in some ways but easy to supplement for any background Mathematical Expeditions Mathematical Masterpieces Any book by Eli Maor is also definitely game. Again, supplementing for higher levels - but there is a surprising ...


3

Personally I would discuss Graph theory, in a diverse and conceptual way with a few deeper dives. Students of that level should be familiar of weighted graphs, have an intuition for the size of functions (which could be leveraged in a discussion of travelling salesman, big O notation, how quickly networks can grow, Ramsey Theory R(3,3), chromatic polynomials,...


3

How about a talk on the continuum hypothesis (CH) and related topics? It's a fascinating subject and can be tailored for basically any level depending on how detailed you get. Full disclosure, I'm biased because I gave such a talk aimed at MS students and upper-level undergrads on this topic almost 9 years ago. And I think this meets all four of your ...


3

I've discussed this several times with other education researchers and it does not seem easy. A learning style (or maybe thinking style) should scarcely depend on the knowledge someone has or specifities of a task or topic. It should rather be a personal preference. As such, it is very hard to describe. If you choose a geomtrical way to learn - is it due to ...


3

I am happy to share my Beamer slides, available through each course webpage at my homepage. The courses that have slides are: Combinatorics: A course in enumeration, including simple counting, combinatorial proofs, bijective combinatorics, and generating functions. The page also has information about the structure of the course project involving individual ...


3

Last semester I purchased lots of different colors, and used them liberally. I could not be as disciplined and as careful as Tommi Brander's impressive control. But certainly distinct parts of geometric drawings, labels of vertices and labels of edges, any objects of distinct categories, were easy choices for different colors. Some of my students took notes ...


3

How about drawing a straight line, then fixing a point above that line that is not directly above the middle, and take this as the third vertex? This way, the two upper sides will not have the same length; and the chance that one of them has the same length as the straight line you drew at random is very low. edit: Looking at Thales theorem might help to ...


3

ADVICE: When you have a question about a speech, you should give us more information to help you. Especially how long is the speech (it affects how much intro you do). But also the audience. And even how important this is to you and how long you will spend preparing it. It helps us help you and may help you strategize also. ANSWER: I would start with ...


3

I think the bug can actually be a feature. Kids need work on the "muscles" of computation. It's not like this is the only setting where doing long calculations is needed (can be the norm in physics and engineering problems.) Look at all the questions here about the frustration of dealing with kids that can't perform algebra. It can be good to look at ...


2

First: I'm not aware of any research on this sort of thing. Neither is specifically designed to create opportunities for students to think mathematically, so I doubt there is a significant math ed basis (or interest) for looking into this. My guess is that a lot of the use of one or the other technology will come down to preference and convenience. As far ...


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