Conrad Wolfram has a good sound-bite: We need students to be first-rate problem solvers, not third rate computers. One problem — political and social — seems to be that it easier to train and measure computation than it is to teach and measure critical thinking. This is not a new problem, and anecdotally, it seems that the only thing that makes a real difference is an inspiring teacher or mentor. I think that a lot of people hate math because they encountered an anti-mentor in their early education. Once that path is set, it is very hard to change.

]]>I agree entirely that this kind of thinking should be developed much earlier. Particularly as we have ubiquitous devices that do arithmetic and other basic computational mathematics for us, whereas no device built is capable of good mathematical thinking – an ability of real importance it today’s worlds.

]]>Total enrollment: 58,300 (a meaningless figure)

Total active at some time: 44,141 (includes the many who never intended to do more than dabble)

Total active in final week: 4,961 (the “real class,” those taking the full course *as a course*)

Total that completed the course (more than minimal or “passive activity”): 3,900

Total submitting Final Exam: 978

Number of students receiving a SoA: 3,167

Number of students awarded a SoA with Distinction: 676

I think that your course is about the best that can be done for a MOOC. The pedagogy and technology is designed to help the student at every step. Judging by some comments in the forums, a sizable fraction of students who had not seen this material before have learned the basics of mathematical thinking. Whether this is sufficient is an open question.

Judging from what I have read, learning the rudiments of mathematical thinking (or just logical, rational, evidence based thinking) should be taught from a very early age, and not left for the transition from high school to college. Doing so would certainly help people to understand what mathematics *really* is, rather than the present misunderstanding. It would also change the way education is viewed, from memorizing ‘received wisdom’ to learning how to think critically about anything — plus a set of critical ‘data’, which includes history, science, arts and literature.

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