I just finished uploading the first batch of Gliya curriculum to a forum post.  We’ll eventually make nice webpages to guide students through the curriculum, but for now this is over 100 pages of free curriculum that students worldwide can use to learn from.

In particular, much of this curriculum should be helpful to students studying for the AMC 8 exam and MATHCOUNTS.  It does not include the harder concepts and problems tested at state or national MATHCOUNTS, but it should be accessible to a wide swath of students — both contest problem solvers and otherwise.

This curriculum is currently in what I would call “semi-polished” form.  That’s fine with us because it’s best to be practical and help students learn now than to be perfectionist and wait months or years until its in its highest quality form.

We’ll gradually release thousands of pages of curriculum at many levels over the next year or two, and continue to polish our work, adding additional features to the site along the way.

It’s been a while since I blogged.  I’ve been busy developing a new company, Gliya, devoted to creating free educational resources for students worldwide.  We are starting with mathematics (as is my primary interest as an educator), but we plan to spread out to additional subject matter when we’re ready.

The current incarnation of the Gliya website will be short-lived.  It will evolve with some new resources over the next few months, but will change into something radically different next year.  Our goal is to leverage internet technology in targeted ways to make education easier to achieve, more enjoyable, and more accessible to students worldwide.

Our first free resource is the Gliya Network forums where I (and others) will be helping math students not only at MIST Academy, but others who join the forums as well.  Elementary, middle, and high school students are welcome to join as well as all others curious about elementary mathematics or math competitions.  We encourage parents to join as well.  See you there.

I haven’t decided for certain if I never plan to blog here again, but since the inception of Google Plus, I’ve found it to be an easier forum for writing.  I can write everything in one place — both private messages to friends about going out for dinner as well as messages to students about how to approach mathematics.  I get to pick and choose the audience for each post.

My blog-like posts will be made public.  If you want to find me on the web writing more consistently, get a Google Plus account and add me.  My gmail address is crawford.mathew@gmail.com.  I’m interested in reading your thoughts as well!

Seen today on my Google+ feed:

“Even failed experiments and theories teach valuable lessons.”

Not entirely disconnected, here is an email I recently received from Jason Knapp of Ohio:

For what’s it worth - I have a great amount of respect and admiration for what you’re doing, and what you have achieved with your Academy. My son loves your Number Theory book - it’s his favorite out of the AoPs set.

[anecdote for your classroom]

I have a mathematics background, and I direct research for a small biotech company. I’m honestly dismayed by the ever increasing difficulty of finding people with good problem solving skills - from finding interns to hiring PhD level scientists. I have actually recommended some of the AoPs books to some of our interns (kids working on their masters - smart, but poorly trained). Not because they need to know power-of-a-point or sum-of-cubes, but because the process of solving those types of problems is remarkably the same as that used to solve *real* problems: getting organized, searching for patterns, thinking of a simpler problem, changing your point-of-view, etc …

There certainly are some reasons why grades are beneficial, but I think that their total weight is not sufficient to justify the great costs.  I would say that the main reason that we grade is since we really are not in the business of providing an education but rather in the business of providing degrees.  To award a meaningful degree you need to grade.  To deliver a meaningful education you do not.  I know that I shouldn’t complain since the degree-awarding business (aka higher education system) is really a great one to be in, but I do wish that someone would design an education-delivery one.

To read the whole article, click here.  I’m always glad to see professors evaluating this problem.  To me the answer seems clear: divorce the process of education from the proceedings of degree/credential granting.  My hope is that at least some of my career is spent encouraging this change.  I happily spend far less than 50% (perhaps 5%) of my time grading.  We give no formal grades (though we do share some test score information during the evaluation process at MIST — when it’s useful).

A year ago I wrote two of the topic tests for this year’s Mu Alpha Theta National Convention.  Students are given one hour to work on 30 problems during these tests.  I spent time considering how I might write such tests, and I came up with the following philosophy:

*There should be problems for every interested student at the competition to work on.
*There should be problems that challenge every student to think in new ways with tools they already understand.
*Students should be interested enough in the problems themselves to want to read the solution manual (at least parts) and they should learn from reading it.
*It should be unlikely that more than a scarce few students finish more than 25 problems.
*The easier problems should take the best students very little time so that the top students can quickly move through at least half of the test.

I felt the last principle to be highly important because one hour is not a lot of time and 30 is a large number of problems.  I wanted the most motivated students to have a different competition experience where they tried to solve 6 or 8 or 10 of the 15 harder problems and there was plenty of diversity among the challenges to make places between the students highly meaningful.  I also wanted students with singular expertise to be able to earn their teams more points as opposed to writing a test with a low ceiling for perfection where many schools might earn maximum points and places are determined more by errors than solutions.  To me this is a positive definition of specialization and that seems to be what the topics tests are all about.

Here are the tests that I wrote:
* Alpha Sequences and Series (key and solution guide)
* Open Combinatorics (key and solution guide)

It’s not clear to me if they were ever edited between the time I wrote them and the time the competition was held because I never received feedback.  So it may be that the competition tests looked different.

I’d never heard of PEMDAS until recently.  Actually, it’s probably more true that I’d heard of it and let it go in one ear and out the other.  For some strange reason I’ve had three conversations about it and read about it several more times just recently.  This is at least a partial summary of my thoughts about PEMDAS.

Just teach math.  The concepts.  If you need to rely too much on gadgetry, that’s a good sign that the message isn’t being received clearly.

Two very bright guys I met while I lived in Southern California will soon host a television show on the History Channel called Invention USA in which they interview modern inventors and discuss their amazing inventions.  These invention experts are Garrett Lisi, sometimes known as “the surfer dude physicist” and Reichart Von Wolfsheild, perhaps best known as producer of the famous Goldfish Aquarium screen saver used at least partially to highlight the advent of modern computer/TV screen technology.

I suspect with good reason that the show will be very good.  While I only met Reichart once very briefly, he has a big personality and strikes me as an entertaining guy.  Garrett has become well known for his Theory of Everything — long sought after in physics — is a very comfortable public speaker.  Unfortunately I’ve been unsuccessful in finding a debut date for the show, so stay tuned.

No commentary necessary.

This is one of the best (most fun) things I’ve ever found on the web.  And it was purely by accident.