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I taught gifted elementary students for over 25 years and feel my 4th-6th grade students benefited greatly from using Khan Academy with some direction from me. The first time I used Khan Academy was with my sixth graders who were having trouble understanding why the distributive property was true. I showed them the Khan Academy's video on the topic so ...


18

I don't want to argue about if one should still teach integration techniques or not (could be a good separate question) but ask under the premise that it is meaningful to learn integration techniques and that homework has to be done: How should you design homework today to let students learn integration techniques? One answer is trust, but verify. For ...


15

I've created roughly 40 videos for an online course and a flipped course in biology, so I've got some experience making videos. I researched the maker of your videos, and he deliberately does NOT reveal his process. So I don't know if this is his method, but I'm comfortable that this would produce something very similar. Supplies: Computer (I use a ...


14

For undergraduate level, Gnu Octave is probably what you want. It is open source, cross-platform, and syntax-compatible with MATLAB. It's very useful for 2D and 3D plotting and for numeric linear algebra, and it's a tool that will be beneficial for students to know. Also, GeoGebra is excellent plotting software, and has recently added 3D graphing support. ...


13

In terms of free software, a large portion of the available choices are based on a Gnuplot backend; I however would probably not recommend directly using Gnuplot. Instead, your choices are mostly between the various front ends. In terms of the front end, depending on what your students are familiar with and are willing to learn, there are many options. ...


12

First of all, I try to be honest with my students by telling them directly and explicitly about the existence of such integration machines (It is silly of me assuming that they don't know that!). Then, I add, but we don't integrate for the sake of integration. For us, it is a practice of problem solving in which we need to choose the right techniques from ...


10

I've made roughly 900 videos in Norwegian, in the same style as Khan Academy over at http://udl.no - Check out the videos and see if it's what you're looking for. I use SmoothDraw3 to draw into. I use a Wacom tablet to draw on. Most Wacoms are affordable, and surprisingly good quality. I've had the same one for over 3 years, and not a single thing has ...


10

You might want to look into Geogebra. The current beta version (Geogebra 5 Beta) has a 3D mode and allows you to create 3D plots of a function of the form f(x,y) and a graphical interface for rotating, zooming, etc. It is also open-source, free, and cross-platform.


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Mathematica has impressive graphics capabilities. Here is an example taken from an expert's answer at Mathematica StackExchange (Vitaliy Kaurov): For more examples, see the many Wolfram Demonstrations.


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There are many such programs, but I highly recommend WeBWorK. The founders received the American Mathematical Society award for impact on teaching math in 2016, it is used at hundreds of institutions (primarily in the United States, but I believe not exclusively at all) and is open source. You can (I think still) pay for hosting or set it up locally, which ...


9

If you type a function into a Google search, you get a pretty nice graph. In order to get interactive 3d graphics, you will need a WebGL enabled browser (with WebGL actually enabled, of course). Try these for starters: y=sin(x)/x z=-x^2+y^2


9

Here are some tools that can be used for creating high quality Maths video lessons: Hardware Computer with tablet, or just a tablet computer (e.g. Microsoft Surface Pro 3). External microphone of a reasonably high quality. I use the Blue Yeti which seems to be a good compromise between quality and price. Previously I used a Logitech Headset which I found ...


9

For several years I taught I course (which no longer exists) making heavy use of Maple. All the material is at http://neil-strickland.staff.shef.ac.uk/courses/MAS100/. Obviously technical details would change if you wanted to use Mathematica instead, but the general approach might still be useful.


9

There are a number of resources I like out there. I tend to use a variety of different sites for different needs -- I don't think there is one that "does it all" but here are some of my favorites. Most of them are pretty random, though the first few below that have lots of customization options tend to make very usable worksheets, and for some applications ...


9

Gnuplot is widely used in academia. It can plot in 2D and 3D, both analytical functions and numerical data. While the command line interface might be a little intimidating at first, you can use it as simple as plot sin(x) or plot 'data.txt'. All the options to finetune the looks can be accessed through the GUI if you don't remember the name of something and ...


9

One possibility is to use GeoGebra. I use it for making any geometrical drawings I need, especially if I want to show them in public. It can be used via text, too, but I've only used it via the graphic interface. One benefit is that even in text mode this is WYSIWYG so you don't have to compile to see what you'll get.


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If you use LaTeX to prepare your documents, there are many packages that automatically randomize the order of choices in multiple-choice questions. One recently updated package is esami. (This documentation is dated July 27, 2016.) Its official description is: The package allows to write various type of exercises (multiple choiche questions with ...


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 ...


8

A free tool for Linux and Windows is gnuplot. This same graphical interface can be used from within Octave (as in mkasberg's answer), which is also free. I haven't used it in a while, so I don't recall the difficulty of use. It does have a set of tutorials available for download. Sage is also available on Linux and Windows. It is a python based program. The ...


8

For already TeXed documents, I have generally attached them to threads in the discussion forum. As an example, I did this with a proof sketch of the Cantor-Bernstein-Schroeder Theorem using a .docx attachment. (Indeed, one of the prospective teachers in the class gave a chocolate-worthy answer!) More generally, I find that the discussion forum through ...


8

If you are familiar with Python coding, you can easily use matplotlib to get quite good outputs. The library's website has some demos. This also is a pretty good/easy way to produce animations, if you can generate the frames from an algorithm. I threw together this animation with about 150 lines of actual code (not counting comments and blank lines). ...


8

Not formally an answer (so if you have one, do not let this prevent you to post it), but I think challenging the implicit assumption that it would be good to have your kid use any such software deserves more than a comment. First, I remember that several studies failed to prove any improvement on teaching math using computer technologies. This lets me ...


8

In my view, Khan Academy should be used as one would (ideally) use a textbook: To provide students with an overview of the material and algorithmic drills so the teacher has more free time to discuss the nuances. I think Khan Academy is brilliant if used in this way. I personally learned to handle basic probability thanks to Sal's explanations. The trouble (...


8

I do this kind of thing using SageMath every time I teach it. In this case, there are even pre-made interactive things for this. Here is one for the midpoint rule Here is one for various rules You can even embed them in webpages, use them in the Sage cell server (try it!), as well as in notebooks locally or online. Note: Geogebra should also be able to ...


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 ...


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I'm not sure how software would be helpful here. To make a problem of this form, you need to: Choose any center point $M$. Choose two orthogonal vectors $\textbf{v}$ and $\textbf{w}$ of the same length. Compute $M + \textbf{v}$ and $M+\textbf{w}$. Find two other points on the line through $M+\textbf{v}$ and $M+\textbf{w}$. The volume will end up being $\...


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I've used iPython with matplotlib. It has a basic mode which mimics matlab, but it has facilities to make many kinds of graphs/diagrams easier. It does not have full 3D, just 2.5D, which is limiting for nicely shaded 3D graphics, but fine for most graphs and diagrams. It would be perfect for creating your final animation graph. As it is programatic, it is ...


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There are indeed several LaTeX packages available for this. I have only experience with one - TikZ. The best impression of what it can do is probably the corresponding Texample page. If you want to learn it, at least the introductory chapters of the manual coming along with the package are rather good. While looking them up I noticed that there's also a ...


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I think you only need to have this knowledge if you are teaching a unit or significant part of the course, using a CAS. This is probably a small minority of courses.* In that case, what makes sense is whatever CAS you will be expecting the kids to use (I recommend picking one specific one). The one I know is Maple, but I'm sure the others are fine too. ...


6

Have you considered the online homework system WeBWorK? From the MAA's WeBWorK site: WeBWorK is an open-source online homework system for math and sciences courses. WeBWorK is supported by the MAA and the NSF and comes with a National Problem Library (NPL) of over 20,000 homework problems. Problems in the NPL target most lower division undergraduate ...


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