From a message I received today from a friend:

Hey, I wanted to pass this tidbit your way- my son’s kindergarten teacher- who does an excellent job, in our opinion- revealed confidentially to my wife that she sometimes allows some of her students to retake standardized tests if she feels they didn’t do as well as they could have.

Obviously this is something she and we are keeping quiet, because she is an excellent and devoted teacher, and if this is what it takes for her to stay afloat, we see it as more an indictment of the system than of her character.

I just posted the first blog post at the Reengineering Education blog.

The other day I read this article about math performance in Rhode Island. Ignoring most of the rest of the article, I focused on the problem given from the standardized test, and percentage of the students who got it right/wrong.  The problem calls for students to recognize the need to multiply a quarter of a mile by 3, then convert the total distance to feet.  Here’s what I found interesting: 69% got the answer wrong, and while the author doesn’t explicitly say that 31% understood how to get the right answer, they make no effort to explain what this means.  I don’t really fault the author for that, but there is an important point to be made.

It’s interesting to note that one of the three incorrect answers is less than 1/4 of a mile, one is equal to 1/4 of a mile, and one is greater than a whole mile.

Suppose we begin with the naive assumption that a student who takes a guess at the answer gets it correct 25% of the time.  I would hope this percentage would be higher given that an educated case, which seems more than plausible, would have a better chance of success.  Then again, a partially informed educated guess might lead to a certainty of an incorrect answer.  Still, suppose 100 students take the test, and n understand the problem and answer is correctly, while the other 100 – n guess randomly.  Our expectation is that 1/4 of the guesses are correct, meaning the number of students who bubble the correct answer is

n + (100 – n)/4 = (3/4)n + 25

When this total is 31 (as in 31% get the answer correct), that means that n = 8.

Let’s reflect on this observation.  Only 8% of Rhode Island high school juniors can recognize and compute 3 times 1/4 times 5280.  Granted, there is some context involved, but the context is simple and ordinary.  I doubt that many students can do the math who can’t comprehend the problem.

Maybe there is some variance and perhaps my naive modeling assumptions aren’t perfect, but I doubt that the number of students who truly solved the problem is particularly close to 31%.  Maybe 10% or even 15%, but not 31%.  Then again, haven’t a substantial fraction of the lowest performing students dropped out by the point this test is administered?

The article states that there is an epidemic in education, but if this problem and performance are at all indicative (it’s just one data point, but…), then math education is broken far beyond what most people imagine.  There must be entire schools where a single-digit percentage of the students can demonstrate a correct solution.

may be that recognizing solutions that work seems almost impossible for most people.  Education is such an ordinary part of everyday life that whatever biases we have get automatically applied to our views on education.  For this reason, it’s far harder to have a productive conversation about education.

We just added a 2012 AMC 10 B Solution Guide to the growing list of AMC contest resources at Gliya.

Results from the 2011 AMC 8 are now public, and we are very pleased to see so many current and recent MIST Academy students among the award winners.  These awards represent strong efforts by an awesome group of students, though you might not realize how hard they work if you saw them having fun in class!

MIST Academy Award Winners on the AMC 8 by years:

2008: 8
2009: 17
2010: 16
2011: 30

I suspect this recent jump represents a jump in the number of students who have been with us since an early age, exploring a wider variety of mathematical topics to a deeper level.

I spent all of yesterday writing up a 2012 AMC 10 A Solution Guide, and I’ll hopefully complete a 2012 AMC 12 A Solution Guide this evening, though I have class and potentially a basketball game to attend tonight.  If time permits, I plan to make this a regular writing effort.  Most of the solutions can be sorted into our other lesson documents.

I’m debating whether or not to do the same with each new MATHCOUNTS, AIME, and AMC 8 exam.  These exams have solution guides, but they usually aren’t written in a way that captures the mind of the broadest audience, and that’s my goal.

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!