Episode #125 of the Stack Overflow podcast is here. We talk Tilde Club and mechanical keyboards. Listen now
20

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 ...


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 ...


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 ...


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 (...


7

A few years back I followed a distance master degree in maths at UPMC (Université Pierre et Marie Curie, in Paris). At the time the university sent course documents and exercices by post every week, solutions to exercices had to be sent back, and students had to be physically present for the final exams. Subscription was cheap (a few hundreds euros I think). ...


7

I started strongly encouraging my students to participate in math.SE about a year ago. Excluding this year it was all with third year students taking group theory and/or complex analysis. This year I'm also teaching discrete maths to first year students. What I notice is that those students who take the few hours to climb the learning curve for properly ...


7

Almost 20 years ago, I faced a similar issue in the course of designing some on-line calculus exercises... For me, it turned out to be simplest to use a Monte-Carlo idea, namely, to evaluate both expressions at a "random" set of locations, and test for agreement within some not-too-tight bound. Yes, some necessity of tolerating invalid inputs and such, but ...


6

Khan Academy has been very helpful as a supplement to my instruction in the classroom, especially for developmental students in higher education. I agree it can be confusing for students at times, as some topics are hard to find, but I occasionally set up a Khan Academy shell for my classes (especially over the Summer when my courses are online) to help ...


6

There aren't many choices that hit all the bullet points you listed, but there are some approximations that are quite good: Piazza (mentioned in another answer) is good. I've used it several times for classes. It does handle LaTeX very well. However, it's a threaded discussion board and not chat software -- i.e. it does not do things in real time (unless ...


6

There's Abstract Algebra: Theory and Applications by Judson and Beezer. It doesn't get to Grobner bases but does cover the standard material (and some non-standard stuff, too). It has Sage code and exercises throughout. I will also add that it includes chapters on coding theory, cryptography and lattices and boolean algebras, all of interest to people in ...


5

This won't help the OP for the summer of 2017, but let me put this here for future readers of this site: Michigan Virtual High School is (as I write these words) developing its own online Algebra 2 curriculum. The curriculum, which is expected launch in September 2017, consists of two separate half-courses (Algebra 2A and Algebra 2B) which can be taken ...


5

Here's a quick and dirty implementation: http://nilock.github.io/MathSnips/MultQuiz/MultQuiz.html edit: This was a bit of a seat-of-pants stream-of-consciousness hack job, so the flexibility of the platform going forward is not great. Usage should be mostly self-explanatory, but I'll mention that the system is biased against questions involving 0 and 1 (...


5

I would be pessimistic. An open-ended approach works well in the liberal arts and social sciences -- such as the course on video game culture -- where there are a fairly small core group of skills (reading critically, researching, analysis, writing and commentary) that can be applied broadly to a large number of subject areas, and practiced in a spiraling ...


5

The folks at Art of Problem Solving have what you need. It's not cheap ($559), but they work with many students like you, and are highly recommended. I think you will find it worth what it costs, if you can afford that. (And if not, ask them for a scholarship. I don't know if they'd do it or not...)


5

One of my students recommended using https://piazza.com/ for my classes. Basically, it gives you a way of holding online office hours and harnesses some of the utility of the stack exchange model without being public. I haven't personally used it, but, I think it might do pretty much everything you want and then some. Check it out.


4

Consider Khan Academy: they offer high-quality ad-free math videos and exercises in English, Spanish, Portuguese, French, Turkish, and Norwegian. (The content is more limited in non-english languages.) For negative numbers, start here: Negative Numbers and Absolute Value For scientific notation, start here: Scientific Notation It may interest the teachers ...


4

The Florida Virtual School offers high school level classes in all subjects, including Algebra 2, and is very well regarded. They're considered a school district within the Florida school system so I would expect a course from them to be considered acceptable by another public or private high school. If you don't live in Florida, you can still take classes ...


4

My institute is using this system: http://www.math.rwth-aachen.de/~OKUSON/ While it takes some time to understand how to use it - and it is sometimes a little annoying, as it was written by Mathematicians who needed something for their exercises, not by Computer Scientists aiming to sell a perfect product - it can do what you want and it is free and open ...


4

WeBWorK of course 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 math courses and some advanced courses. Supported courses include ...


4

If the goal of the first bullet point is to practice multiplying single-digit integers, then I have a site for that specific skill: http://www.automatic-algebra.org/timestables.htm That site also has basic-level drills for operations on negatives, order-of-operations, etc., but not your other bullet points.


3

I'm going to explain how I think of the category-theoretic definition of products. Unfortunately, this viewpoint won't lead directly to the usual universal property but rather to an equivalent formulation in terms of morphisms into products. I hope that it can still be of some use even if you'd rather go directly to the universal property. In most of the ...


3

Here is my intuition: First, each object can be used to encode some information which is accessible through morphisms. For example, take the $\mathbf{Set}$ category and two objects $A = \{0\}$, $B = \{1, 2\}$. Now you can encode one bit of information by picking one of the morphisms $f_1(0) = 1$ or $f_2(0) = 2$. Now, suppose that we could assign to each ...


3

I don't know about the online part, but Discovering the Art of Mathematics definitely has some ideas that are low-level (non-major, even) but yet stumble upon very interesting things indeed. I'm sure they'd be interested in discussing an appropriate online pedagogy. The AIBL would be a good resource. To be sure, one doesn't have to be a strict '...


3

The Open University offers distance learning and has undergraduate and postgraduate programmes in mathematics. Unfortunately, I do not know anything beyond this about it, but the linked to pages should lead to all kind of information. For your first question of severe limitations, I would say, no, mathematics is rather well-suited for this, as there is no ...


3

At my institution, some profs use Adobe Connect. Here is a Johns Hopkins University link explaining its use for online office hours, and here is a similar link from University of Washington. I have experimented with it, but not used it in a course myself. (I use piazza in all my classes, but not for live online office hours.) I doubt Adobe Connect satisfies ...


3

The only advice I can give is from my own experience: I've studied 3 of their MSc modules, at a rate of one per year whilst working full time. It's a shame their undergraduate courses are now so expensive as some would be ideal (re)preparation for the MSc. It's useful/important to know that the "routes" they describe are just suggestions: you can study any ...


3

Why not use Google Hangouts? It enables screen sharing both ways - effectively turning your screen into a blackboard. As others pointed out there's probably no free and yet good site/app that aligns with what you propose. However, functionality-wise hangouts would suffice. Having a dedicated website would certainly help in creating a good tutor community. ...


3

It's an imperfect correlation. The best athletes are not always the best coaches. Sometimes those who struggled to perform can teach better than the star athletes that did it all naturally. The how language affects definitions and triangle square nitpicking scares me. And the "Russell group". And the academic eduction versus practical education slant. ...


Only top voted, non community-wiki answers of a minimum length are eligible