First of all, thanks for putting so much hard work into this course. Being a maths teacher (with a maths PhD) I signed up for your course not with the intention of completing any coursework, but in order to check out the material before recommending next year’s course to some of my very talented high school students.

One of the reasons I find the MOOC developments so exciting is that I used to live (and teach) in East Africa, where there are so many talented students who never had the opportunity of good schooling or good university courses. To have courses like yours available to everyone, is just… amazing.

While I’m commenting, I just want to thank you for something else as well – when I started my undergraduate studies in engineering, I found your book (The Joy of Sets) in the library, and it was one of those things that made me love mathematics, and eventually switch to pure maths.

I saw another instructor in a stats course make the point that the heterogeneity of the massive number of students turned out to be a big advantage, because the least prepared students, far from holding everyone back, would ask question that provoked discussion that cut out a lot of presumption built in to the lessons and forced people to get at the heart of the concepts.

I’m currently a student at Georgetown University in D.C. and also a student of yours in Coursera.

My High School math experience was abysmal, and when I took Calculus during my Freshman at GU, I lacked the necessary skills to succeed in the course. I’ve only begun your Intro class, but I’m excited with what I ve seen so far.

I think there’s defnitely has got to be some change in the education system. I wish I knew what that was because I’d save my nephews and niece a whole heap of trouble.

Another great benefit of giving MOOCs, is we can use the feedback from collective intelligence to improve that we do. Truly, the “wisdom of the crowd” at work.

Thanks for commenting.

In the end, I ended up going to graduate school for economics and worked at Texaco doing computer liaison work. After leaving industry to become a mom, I have taught high school math as a substitute, and I tutor.

Math economics did not mean we took math-economics classes. When I got to graduate school to study economics, the calculus was intimidating, even to me with a math background. When I wrote to my former economics professor and told him they should make calculus a requirement for an economics major (not math/economics) because of all the calculus in economics, he wrote back saying very few of their students pursued graduate work. That was not the answer I wanted to hear.

Perhaps with MOOCs I can attempt some of these higher level classes that I managed to avoid.

This is my third MOOC class and I must say that I appreciate your presence in the forums. It is clear to me that you are committed to making yourself available to us.

Your point that anyone who gets a grade of 90 or more probably should not be taking the course is well taken. I was taking the course mostly to see what a well-run MOOC is like. I was first exposed to formal logic in high school when I read Whitehead and Russell’s Principia, which had just come out in paperback to *56. My teachers were of no help here — I was told to sit in the back of class in Geometry so the other students could get a chance. (I invented a geometry during class — won a science fair.)

I would say that I succeeded in maths despite my education. I wish that I had a professor like you (or Gilbert Strang, etc.) when I was studying maths. Now, with the internet, I can, and other students can.

One problem with maths education as I see it is that the curriculum for high school and especially college maths has been designed by people like me, most of whom assume that the easy stuff is ‘intuitively obvious’. Personally, I have a hard time working on maths in a social context after decades of doing the work alone. One other problem is that K-8 maths is usually taught by people who either do not understand maths or hate it. (That was my experience in the 1950s and early 1960s, and I see no evidence things have changed.)

I think that MOOCs are here to stay, in some form. I would also like to see more choices, so that people with different learning styles can find something that works.

I am a very amateur flute player. One thing that has happened over the last 50 years or so is that the standards of performance has risen. Students in high school learn pieces that used to be held until graduate school, for example. What is shocking is that the same thing has not happened in maths, science, or even writing. Of course, the reason that standards have risen for instrumental performance is that only those who are motivated continue beyond the early stages of learning an instrument. The vast majority of people who start an instrument in grade 4 drop out by grade 6.

With maths, unmotivated students cannot drop the subject, so a way must be found to make it possible for them to learn anyway. The other side of the coin is that motivated students are often held back because the educational system wants to move people in lock-step. (When I was in high school, ‘smart’ students were tracked, but that did not help much, and I don’t think it is done as much any more.)

I think that the best thing that can come out of education reform is a diversification of teaching methods and ways to deliver the experience. For that to happen, the old idea of what education is simply has to change.