Friday, April 26, 2013

Braid groups for nine year olds

Homeschooling my daughter in math has been a very interesting experience so far. As a mathematician, I try to re-imagine the topics in our curriculum with the goal of introducing deeper concepts as soon as I can.

Recently thanks to Allen Knutson, on Google+, I found out about a great video series by Ester Dalvit on braids and knots. My daughter has made it though about half of it, which already covers quite a lot of mathematical concepts (especially from a nine-year old's perspective). So I am trying to use it as a springboard to do some algebraic concepts that most K-12 students never see, like noncommutative groups.

So far I've just made a worksheet on braids along with a reference sheet, which went over pretty well today. I'm not sure how much farther I should push it now.

Friday, April 5, 2013

MOOCs - the hype and the pleasant reality

MOOCs - massive online open courses - are all the rage right now, and many people are wondering what their eventual impact will be.  For example, an opinon piece in the New York Times quotes someone as saying that students might be told to "take the following online courses over the summer or over a certain period, and then, when you’re done, you will come to campus and that’s when our job will begin.”

I don't think that's going to happen to a great extent.  Before explaining why, I'd like to make it clear that I am a big fan of MOOCs.  I've signed up for many courses on Coursera, EdX, and Udacity over the last two years, and learned a lot.  I use some of them to supplement my homeschooling, and I plan on incorporating some of their material into courses I teach.  I wish there had been MOOCs when I was in middle school and high school - I'm certain I would have eaten them up.

But the current hype can be pretty unrealistic.  Its interesting to compare the expectations of MOOCs to a very similar phenomenon of 100 years ago, the correspondence course.  Here's the beginning of an article in the journal Science (volume 24 from the year 1906):

There was tremendous interest in the general population in correspondence courses.  Here are some enrollment numbers for one group of correspondence schools (I'm sure there were many others in addition):

Consider that the population of the United States was about a quarter of what it is now, so this is comparable to enrolling a total of almost 4 million people today.  Its not hard to imagine that people thought this would radically change the nature of higher education.

There are many things that make colleges and universities attractive and useful and important to students that are not easily captured by a correspondence course or MOOC.  To be fair, the social and collaborative aspects of MOOCs make them far superior to a correspondence course.  But even for the limited goal of learning a well-defined list of concepts and skills, I think the shared commitment of physically showing up to class is psychologically crucial for most people and it will continue to be so. 

Tuesday, April 2, 2013

More math worksheets for the adventurous

These are still a work in progress, but here is another collection of worksheets I made for my daughter as part of her homeschooling in mathematics.

These include the ones I posted about previously.

I am planning on polishing up the complete collection once I stop making them for the year, sometime in June.  One thing that is missing is acknowledgements - I have taken many ideas from many sources, such as Fawn Nguyen, Dan Meyer, Kate Nowak, Alfred Posamentier, and many others including state math tests and standards from around the country.