This seems timely-- Devlin just had a Coursera course go live. Probably not suitable for the youngest kiddos here, but could be a good fit for the 10y+ set.
Intro to Mathematical ThinkingIt looked interesting, so I thought I'd give it a whirl. I'd really like for my DD to take a look at it if it is a good course, as the
ideals espoused in the mission seem positive.
The goal of the course is to help you develop a valuable mental ability – a powerful way of thinking that our ancestors have developed over three thousand years.
Mathematical thinking is not the same as doing mathematics – at least not as mathematics is typically presented in our school system. School math typically focuses on learning procedures to solve highly stereotyped problems. Professional mathematicians think a certain way to solve real problems, problems that can arise from the everyday world, or from science, or from within mathematics itself. The key to success in school math is to learn to think inside-the-box. In contrast, a key feature of mathematical thinking is thinking outside-the-box – a valuable ability in today’s world. This course helps to develop that crucial way of thinking.
The primary audience is first-year students at college or university who are thinking of majoring in mathematics or a mathematically-dependent subject, or high school seniors who have such a college career in mind. If that is you, you will need mathematical thinking to succeed in your major. Because mathematical thinking is a valuable life skill, however, anyone over the age of 17 could benefit from taking the course.
There is fairly extensive coverage of proofs, which makes me pretty pleased.
