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.

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 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!

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.

No commentary necessary.

This past weekend Sergey Sarkisov, several parents, and I traveled with the Alabama ARML teams (plural because once again Alabama has two full teams) to the Georgia site to compete in the American Regions Mathematics League.  A great time was had by all not only during the competition itself, but in numerous card games and ultimate frisbee contests (I came back a little sore).

I am very happy to report that the Alabama team’s score rose more than that of any other team in the nation.  Last year Alabama surely had the youngest team with 6 middle schoolers and only 9 high school students including just 2 seniors.  That team outscored 40% of the 120 other competing teams at the 2010 ARML contest.  This year the team was a bit older and more experienced, though still perhaps the youngest competing top team with 4 middle school students and only 3 seniors.  Alabama scored 77 points more than last year and outscored 65% of the 132 other competing teams.  An excellent showing for a still very young team.

The good: The team improved a great deal during the Power Round.  While scores on this round were higher nation-wide, perhaps no other team improved by 19 points in this 50 point round.  The relay scores were also good with Alabama finishing 10th in the nation — the highest finish during any round.  Also, the Alabama B team scored 21/50 during the Power Round which is great for a team of mostly middle school students.  Senior Owen Scott and junior Jerry Hsu found themselves in the Tie Breaker after scoring 8/10 during the Individual Round.  From what I gather this is the equivalent of scoring in the 95th to 99th percentile overall among individuals — very impressive considering the level of competition.

The bad: The team solved 5/10 during the Team Round for a total of 25/50 points.  This team was certainly capable of a better performance during the Team Round, so there is substantial room for improvement.

The fortunate: Organizing and grading the Power Round was much easier this year due to the nature of the problem.  Instead of feeling exhausted after the process I was able to enjoy watching the end of the competition — particularly the Super Relay where Alabama nearly pulled off first prize (had the answer, not simplified *sigh*) and won second prize (a large pile of candy that got passed around the bus).

Only 3 of the 30 Alabama students were seniors and it is likely that we’ll have several more of the state’s math superstars compete with us who couldn’t make it this year.

Thanks to Sergey Sarkisov and the several parents who volunteered their time to help with the team and support Alabama ARML.