Please excuse the exceedingly pretentious title of this post.  This post is a continuation of my recent articles Who Gets to Fall in Love? and Mu Alpha Theta, FAMAT, and Regional Math Competitions.

I recently started working out again.  Just before I moved to Alabama I started running, and I’ve been running off and on for four years now.  Maybe 60% on and 40% off due to a work schedule that sometimes gets intense.  During some of that time I’ve lifted weights also, and I’m stronger for it, though I’ve improved my cardiovascular condition moreso than my physique.  Until recently.

A friend of mine, Kirez Reynolds, runs a CrossFit center in Arizona.  Seeing his blog posts about CrossFit finally motivated me to bend my routines closer to the CrossFit methodology.  I’m not working out in the true CrossFit style yet, but I’ve been gradually conforming the style of my workouts toward the CrossFit conditioning method.

CrossFit just works.  There is hardly anyone left in the fitness world who doubts it, unless they’re selling their own thing.  The oversimplified inspiration behind the CrossFit philosophy is that (1) gymnasts learn new sports and athletic activities more quickly than other athletes, (2) power lifters are able to apply strength to a wider variety of practical tasks, and (3) sprinters actually do build exceptional endurance along with their skills in speed bursts.  The gymnasts have incredibly tough core muscles, flexibility, and muscle control.  The power lifters are less concerned than body builders about the look of their body, and more concerned about applying force, hence the practicality.  The sprinter handles extreme intensity centered around a solid core and is able to handle the moderate fatigue imposed by endurance activities with relative ease.  This is why middle and long distance runners still train by running quarter mile sprints.

CrossFit is a workout that focuses on the strengths of all these kinds of athletes, training a kind of super-athlete.  And it doesn’t take all day.  The CrossFit Workouts of the Day (WODs) are intense, but relatively brief.  Perhaps 15 minutes of training per day, three out of four days (that’s less than an hour and a half per week) is enough to make incredible strides.  The WODs are demanding like sprinting, requiring total body functionality (nearly always centered around the core) like gymnastics, and require power like lifting (parts of the WODs involving lifting or analogs).

Put simply, CrossFit is a revolutionary workout.  And it works for tangible reasons.

Years ago I used Bruce Lee’s book, the Tao of Jeet Kune Do, to create an exercise routine for myself that helped me lose 34 pounds in a year and built so much muscle that I could do pushups with Amanda on my back and 30 pullups at a time (don’t I wish I’d stayed in that shape…).  Looking back, it was clear that the way I went about the exercises in that book was very similar to CrossFit.  Though the real reason I bring up Lee’s book is that the philosophy of Jeet Kune Do is similar to that of CrossFit. Jeet Kune Do is not a single martial art.  It is the philosophy of taking what is practical from all martial arts to train the most effective possible martial artists much in the same way CrossFit draws from the most successful aspects of all schools of athletic training.

It is nothing short of awesome that the practical science of physical fitness has come this far.

So, why not apply this to math?

Or, more broadly, mental training?

The simple answer is that it’s harder to change the educational system because it is larger, more centralized, highly bureaucratic, and exceedingly self-important.

The answer answer is, “why the heck not?”

As MIST Academy has evolved, I’ve designed class curriculum and activities to be intense and based on the most effective educational methods I’ve studied and put into practice on my own.  As a result, the students in our program find themselves able to accomplish more in essentially every academic discipline.  They aren’t memorizing facts of decaying value.  They’re building a mental core around which they can apply mental kung fu.  They learn to sprint (think quickly and accurately), gymnastics (the flexibility to look at problems from a variety of angles), and power (the ability to erect their own mathematical concepts and models).  Forgive these imperfect analogies.

An old math team classmate recently sent me this article, which explains many things including how this approach works empirically when forged into culture:

Now some things will happen with a piano in every classroom. The children will love to play around with it, and a “chopstick culture” is likely to develop. This is “piano by bricolage. Some will be encouraged by parents to take lessons, and a few rare children will decide to take matters into their own hands and find ways to learn the real thing without any official support. Other kinds of technologies, such as recordings, support the notion of “music appreciation.” It seems to turn most away from listening, but a few exceptions may be drawn closer. The problem is that “music appreciation” is like the “appreciation” of “science” or “math” or “computers,” it isn’t the same as actually learning music, science, math, or computing!

But 50 years ago, I had the experience of growing up in a community that desired “real music for all,” and found a way to make it work. It was a little town in New England that only had 200 students in the high school, yet had a tradition of having a full band, orchestra and chorus. This required that almost every child become a fluent musician. The secret is that every child starts off as a musician in their heart and each has a voice to sing with. They taught us to sing all the intervals and sight-read single parts in first grade. In second grade we sang two parts. In third grade we sang four parts and started to chose instruments. Talent was not a factor, though of course it did show up. This was something everyone did, and everyone enjoyed. I did not find out that this was unusual until I moved away. An important sidelight is that there was a piano in every classroom and all the teachers could play a little, though I am sure that at least one of the teachers was not very musical. What seemed to make it work was that the community had an excellent musical specialist for the elementary grades who visited each classroom several times a week. I remember that one teacher didn’t like my phrasing in a song and tried to change it, but the specialist did like it and encouraged me to see if I could phrase the rest of the song that way.

The central point to this story is not so much that most of the children became fluent musicians by the time they got to high school–they did and had done so for generations–but that as far as I can tell, almost all still love and make music as adults (including me).

We can find this “create an embedded environment and support classroom teachers with visiting experts” strategy in a number of schools today. The Open Charter School of Los Angeles has succeeded in setting up a “design culture” in their third grade classrooms that embeds the children in a year-long exciting and difficult adventure in the large-scale design of cities. The most successful elementary school science program I know of is in all of the Pasadena elementary schools and is organized along the same lines. It was developed by Jim Bowers and Jerry Pines, two Caltech scientists, and the key is not just an excellent set of curriculum ideas and approaches, but that the classroom teachers have to gain some real fluency, and there is important scaffolding and quality control by expert circuit riders from the district.

To say it again, children start off loving to learn, and most can learn anything the culture throws at them. But they are best at learning ideas that seem to be an integral part of the surrounding culture. Having a parent or teacher that encourages them to study math and science is not even close to having one that lives math and science (or seems to). This is the strongest pedagogical strategy I have encountered over more than 25 years of working with children. Technologies–such as books, musical instruments, pen and paper, bats and balls–can help, but they are clearly not enough to get kids over the critical hurdles all by themselves. On the other hand, literacy, music, art, dance, and sports can all flourish with little or no supporting technologies at all–supporting adults are all that are needed.

As the culture has changed among the students in our program — as the day-to-day philosophy of the approach we take has been accepted widely among participants, a new culture has emerged.  Students see understanding as more important than short term success, and they appreciate working in intervals of intense preparation because they see themselves learning more and far exceeding their classroom peers at school.

As an analogy, MAO/FAMAT, and local competitions are essentially like sprinting.  That’s cool.  Learning to sprint is a reasonable part of the educational process.  The problems with this one-dominant-activity approach lie in the lack of mental gymnastics (AMC/ARML/Mandelbrot/AIME/Vi Hart/Math Circles) and power lifting (Power Round & Contest/USAMTS/Olympiads/Proof Writing more broadly/Math Circles).  Why build in a niche culture — a monoculture?  Why train every student only to sprint?  How many pure sprinters do we need in the world?

Not as many as we need intellectual Bruce Lees.

May this article be received as respectful and constructive criticism.  It would not be an exaggeration to say that I’ve altered the course of mine and my wife’s lives in order to contribute to mathematics education in the Southeast.  This topic is very dear to me.  I grew up in a violent atmosphere using math team as my healthy escape from the nearly constant presence of drugs and drug dealers in my home and bedroom.  Math team may literally have saved my life and given me a path to college on a full scholarship, and jobs thereafter.

Since returning to Alabama I’ve done a lot of thinking about math team in the region.  In particular, I’ve felt a little like the local math tournament paradigm and the closely associated Mu Alpha Theta competitions have devolved.  By that I mean specifically that they are less effective – far less effective – in contributing to the overall education of students than they once were.  This is not a criticism of the activity of math team as a whole, but a critique of the specific format that has come to dominate the local culture of math team.

The contests of which I’m speaking revolve primarily around one hour tests with 25 to 30 multiple choice problems.  This format likely developed because the tests are easily graded in a short period of time, and there were no initial drawbacks.  Where I grew up, 25 problems became standard probably because of the easy scoring system in which four points per problem results in the round perfect score of 100.

The style of these tests varies considerably.  Some test writers create curriculum-based tests that could double as final exams in challenging honors math classes.  Experienced math contest problem solvers can tell you that these are the easier competition tests.  Some test writers create tests that include problems outside of standard curriculum.  Favorite additional topics include areas of discrete math (combinatorics, number theory, graph theory) and an expanded geometry curriculum that typically makes use of a fuller pallet of synthetic geometry.

There are other styles of exams, sometimes called Olympiads, in which students submit written solutions to problems.  Obviously time becomes a limiting factor, so Olympiad contests often involve just a few problems, perhaps three to six in most cases.  Olympiad problems involve an even wider range of mathematical disciplines due to the limitations inherent in multiple choice examinations, but the real difference is that Olympiad problems are traditionally designed to test the inventiveness of the competitors.

This isn’t to say that 25-30 problem multiple choice exams lack the potential to encourage and test ingenuity.  But when a student has 120 to 144 seconds to work each problem, most students find themselves pressed for time just to bang through computations while working the bulk of the exam.

When such tests were new and rare, they must have been magnificent inspirations to students.  Even the best students likely learned new techniques while working the harder problems on every test.  Exactly what they couldn’t get in school, they got from math competitions.  It wasn’t all that hard to achieve this goal: 20 problems ranging from ordinary to advanced curriculum, maybe with some discrete math thrown in, and 5 problems that require novel thinking.  Truly brilliant students might have solved 19 of the 20 more ordinary problems and 2 or 3 of the novel problems, won an award for an exceptional performance, and gone home thinking about the problems they didn’t solve, uncovering new methods for additional hours or even days.

What may be easy to achieve once can difficult or impossible to achieve many times.  After a while the best and most prepared students had seen hundreds or thousands of problems.  No longer did those 5 “novel” problems separate top competitors precisely because few of them were really novel.  An arms race among a few top schools and individuals began.  Tests were written in the same style.  But now maybe one of those problems was still novel, but the rest were previously analyzed, dissected, and categorized.

This arms race was initially good, and one of my best experiences as a math student was to be part of it.  When I solved a problem that was new to me, I taught the technique, strategy, or observation used to the rest of the math team students.  This was much of how Vestavia came to dominate math competitions in the Southeast – we explored, researched, and shared.  Eventually most of the students on math team new most of the ideas behind problems once considered to be uniquely interesting.

It’s also the reason many schools gave up.  Less than half as many schools now compete in the Alabama Statewide Mathematics Contest.  Many teachers feel that the contests just showcase “tricks”, so they quit all of them.

Those teachers are both right and wrong. 

To make the tests harder, those 5 novel problems expanded to 10, then 15, then all of them.  Not always, but sometimes.  If you didn’t attend a school that taught all those tricks during math team class, you had to be quite an amazing genius to even win an award.  Two schools in Alabama – Vestavia and Grissom – soaked up the vast bulk of individual awards in Alabama for more than two full decades.  Only recently has a little bit of competition creeped in from Hoover, ASFA, Bob Jones, Spain Park, and other schools.  At Vestavia the tricks would be so obscure at times that the award winners began to appear to be an exclusive group of “insiders”.

Learning tricks also obscures “real math” from talented and passionate students who need exposure to it.  I’ll come back to this.  But suffice it to say that the teachers who avoid local competitions do have a point.

But those teachers are wrong for primarily two reasons: those tricks are really just novel problems to the top students seeing them for the first time.  The tests can perhaps be great again if we can get all the great teachers discussing ways to improve them.  Second, to judge all competitions the same way reduces options for talented students, and those options are valuable.  Nobody can tell me the AMC exams are a bunch of tricks.  They are extremely well crafted in that they require only simple tools and deep thinking.  I can only hope I can start recruiting ARML students from some of these schools, but it’s hard to get past the wall of enmity toward the competition system.  Clearly there are students at some of these schools capable of deep thinking.

But how much deep thinking happens at local contests that have evolved to favor the student who can speedily churn through both well drilled curricular problems and a few problems requiring now-standard tricks.  How much of that one hour is spent on reading, computation, jumping through trick hoops, and other going through the motions?  Might each student spend a whole ten minutes…thinking?

Bogus!

As many good things do, the local tests evolved past their prime.  At least for now.

Yet many schools build their math team programs around these contests.  Memorizing fact sheets and drilling students to perfection so that they read, compute, and jump through trick hoops the best.  To win trophies and the all coveted Best in Show award.

As if no cost is sacrificed.

As I’ve said before, what these students miss dwarfs what they get out of that kind of process.  In retrospect it doesn’t surprise me that I got more email supporting that post than anything I’ve written in my life (aside from textbooks and AoPS courses).

Kids have finite time.  Here’s where I get critical of MAO and FAMAT in particular.  Going to tournament after tournament, formula chugging and speed computing leaves little time to sit down and spend the hour or two necessary to learn about something unique, fascinating, and highly useful like the Problem of Josephus, or any of hundreds of other topics that will never appear on a MAO or FAMAT test.  At least, not beyond a simple computation (“blah, blah, which of 12 people will be the survivor?”).

Outside of the Southeast, it’s well understood that MAO is impenetrable exactly because nobody is interested in penetrating it.  Grandmasters don’t play speed chess.  They play chess.  It’s a different discipline.  It’s a different game.

Around the rest of the country, there are just one to three opportunities a year to compete in a local tournament held at a school.  Yet the top math students stay constantly busy.  There are great talks on interesting topics, and cool activities at math circles.  Summer programs of all variety dot the landscape.  The AMC exams, and subsequent AIME and USAMO exams are taken more seriously.  The Mandelbrot exam entertains a lot of students.  The top students participate in the USAMTS.  It’s time intensive, but it’s much better preparation for the USAMO than any multiple choice exam I’ve seen with the possible exception of local Olympiads like those in the Bay Area and San Diego.  For the top 10 or so students per grade in state like Florida and Alabama, the USAMTS can do more to foster real math education than all the local tournaments combined.  The ARML contests are also taken much more seriously outside of the Southeast.  Wow, that’s so much awesome math going on with only a few of the 25ish problem multiple choice exams.

Instead of 50 minutes of formula chugging and jumping through hoops, the vast bulk of time is spent thinking.  Exploring.  Unraveling new ideas.  Learning to invent.  Learning to discover.  Time is the currency and its poorly spent on plug and chug activities beyond a basic investment.

Which philosophy prevails?  Nobody is saying that the 25-30 problem multiple choice test has no merit.  But after breakfast, lunch, and dinner it gets old and uninspiring with diminishing marginal returns.

One time during my career in education I received a letter from a student at AAST in New Jersey, himself a USAMO qualifier and MOsP participant, lamenting burnout.  I’ve received a couple of such letters from students in Alabama, and around a dozen from Florida.  No others.  My guess is that no more than 10%, and probably closer to 2% of students I’ve known were from Florida.

I received a somewhat similar email yesterday from Patrick Lu, whom I’ve never met:

I’m a friend of Eli Ross and he showed me your article, Who Gets to Fall in Love? It’s a great piece; it sums up what is wrong with MAO perfectly. I completely agree with this paragraph in particular: “What the students learn in the process pales in comparison to what they miss…”

It’s a curious case when the top MAO competitors are average to below average in contests that require even the tiniest bit of creativity and problem solving. People that are #1 in the state at their respective subjects get 0′s at ARML, don’t even qualify for AIME. And that is the biggest issue with MAO: students are trained to be robots. Program the robot to recognize certain question types and then input question, output answer. There is no creative thinking, no ability to solve problems that haven’t been encountered before. Now, this isn’t true of all MAO students, but it is for the majority. 

For me, I never excelled at MAO. I was always good — occasionally placing top 10 — but never a top competitor. I didn’t have the passion for it, it was much too repetitive and boring. I was even about to quit the competitive math scene as it didn’t suit me. Luckily for me, Eli invited me to ARML in 2009 (good thing they were short of members). Everyone expected me to be one of the lower scoring members based on my average performances at MAO. They were taken completely by surprise when I was one of the highest scorers from Florida. This was my introduction to “real math”; I only wish it came much sooner. I fell in love with math because of ARML 2009. I went on to qualify for AIME the next year and even beat Eli on the AMC 12B. I went from a kid that was about to drop math competitively to a kid that qualified for AIME, and more importantly loved math. Finding a beautiful solution to a very tricky problem is one of the best feelings in the world. 

MAO is a major problem for Florida math; kids like me get lost in the repetitiveness and boringness of tests and other kids turn into MAO machines, losing and hindering the development of their ability to problem solve. Much of MAO can be summed up by one test: 2008 Nationals Proofs. IMO team member Delong Meng got 10th place on this test; now how does something like that happen? Eli’s told me his plan for a future AMC style math contest in Florida; hopefully that will work out and move Florida math one step in the right direction.

Cheers,

Patrick Lu

I think Patrick is an outlier.  Guys like Eli found value in MAO, but they didn’t want to it be all that they did all the time.  But Patrick makes the point: greater diversity is necessary to reach more students.  In particular, it’s the students who really love math who are often left behind.

Fortunately there may be nice ways to fix the problem:

• Let the students opt out.  A lot of the students feel like MAO and FAMAT is “all or none” and that they must spend more time on it than they believe is reasonable in order to satisfy their teachers, on whom they depend for a good recommendation.  Any time a system of educating children comes down to implicit blackmail, something needs changing.
• Fewer problems and less computation.  It’s killing the more creative students.  Not to mention that it’s repulsive to many other math team programs.  The MAO rank and file has been too insular to recognize that this is one of the primary reasons they have trouble recruiting new blood, so they remain a largely regional minor league.
• Fewer superficial tricks.  The primary difference between a trick and a method is that the trick is drill-taught and expected.  It shifts the balance away from the students who spend their time learning to think deeply, exploring and inventing as they go.  But you can’t run through a 30 problem sprint unless there are tricks to help, so the 30 problem format may need to die.
• Fewer tournaments.  It is rumored that the royal counter tallied 491 tournaments in Florida last year.  Google currently has a data center fact-checking that claim and documenting all the problems.  How many students don’t get tired of it?  Yeah, I met that kid too.Diversity works for a reason.  Have the kids branch out and compete in Purple Comet, HMMT online, and ARML Power/Local.  Or other events.  There is so much going on.  And it’s more educational because it doesn’t all look the same.
• Less politics.  Despite what MAO coaches would like to think, many people around the country heard about bizarre rule changes mid-competition that resulted in national championships changing hands during the 90s (A math competition?  Really?).  Yes, this is part of the creativity problem.  Yes, it is.  It forces the Southeast into a bubble of weirdness through which few individuals pass.  Nobody on either side of the bubble knows much about the species on the other side.  We’re on the side that’s falling behind.  Yes, we are.  Not to mention that I see kids all over the country working together, but in the Southeast I see often bitter rivalries and kids hiding their formula sheets from one another.  Those who fail to learn how to network and collaborate simply fail. (Yes, this is an exaggerated criticism, but it’s important like oxygen.  The kids who find a way above the bubble are heaving for air.)
• Less dependence on standard curriculum.  The standard math curriculum is a baffling American failure.  Despite the in-your-face relevance of discrete math, we’re stuck in the same arithmetic-algebra-geometry-trig-calculus track.  MAO/FAMAT does a little of this, but it remains at a level that promotes drill-to-kill.  I hate sermons, but to the extent that there are teachers afraid to learn a little more math to teach kids during math team practice, we need to preach just a little.  Okay, fine, friendly conversations are also acceptable.
• Change the standards.  A hard working honors student expects to get 90 percent or more on exams.  What’s 90?  It’s inefficient.  It wastes enormous amounts of time.  People learn the most when they’re working at their own level – when they’re challenged, and the challenge never ends.  Instead of focusing on how many problems the students get right, focus on how many of them are talking about that one cool problem after the test (a different cool problem for each student if the test is really nice).  It takes a lot of creativity to engage and challenge students at their own level – more than it does to write 25-30 stock math team problems.  Reduce the number of tournaments and problems and it gets easier.  How about three tournaments a year with,
  * 5 easy problems based in curriculum.  The typical A Honors student can get 3 or 4 of them.
  * 5 easy-medium problems in expanded curriculum.  The typical A Honors student can get 1 to 4 of them.
  * 5 medium level problems.  The award winners begin to distinguish themselves here.
  * 5 hard problems.  The champions distinguish themselves here.So what if most students get fewer than half the problems?  That’s the way it happens on most of the national contests: AMC exams, AIME, ARML, USAMO, USAMTS.  The goal isn’t 90 percent.  The goal is for each student to spend as much time thinking and learning as possible.  And maybe have some to take home.  Personally, I love a great restaurant where I have enough left to take some home.  Perfect scores should be rare or extremely rare.  Students will be happy to solve just 3 to 7 problems if they learn something cool along the way.  That’s exactly what happens at ARML – kids go and solve 2 or 3 really hard problems in a whole weekend and walk away inspired and better educated.  Did I mention inspired?
• Do anything else possible to change the incentive from, “Work 500 problems at this level until you don’t have to think” to, simply, “Think.  Learn.  Learn to think.  Laugh, smile, and do all of that some more.”

I’m tired now and don’t have the energy to be edit (I don’t look forward to picking through my mistakes in the morning), be more thorough (I’m sure I missed a lot), or better organize at the moment.  So for now, this is it.  I hope these thoughts and suggestions have some positive impact on math team in the Southeast or elsewhere.

Addendum: Oh yeah, and kill the trivia questions.  When you get a talented student hooked who learns all the techniques and curriculum, and solves 29 out of 30 problems on a contest, missing only the trivia problem, and winds up 4th place instead of 1st, he isn’t pleased.  In fact, he might hate it.  He might feel cheated out of a Saturday and all the time he spent working *math* leading up to the competition only to have his superior talent and hard work fall short because he didn’t memorize which mathematician did exactly what.  He might even write me a letter about the experience, searching for some validation.  I might even spend an hour on the phone with his mother, listening like an unpaid therapist as she pulls her hair out.

Okay, fine, we can have competitions with trivia.  But asking the kids to take them seriously will lead to more problems than it will do good.  And if you don’t think so, I have a few phone numbers of parents I’d like you to speak with.  Just to get a grip on the psychology of truly unrewarded hard work.  I currently live in fear of phone calls with Florida area codes.

Addendum: I fixed a typo and changed a sentence to avoid grammatical ambiguity.  I may continue to edit on this level.

I love competition.  It’s not clear that life could evolve to such interesting heights without it.  We work and we work.  But we reach to great heights not to work more.  We reach to the level that we desire for the sake of love.

Recently a former student of mine emailed me with a couple of questions about a hard problem and a hard concept.  I tried my best to help him with the hard problem in the most general way possible — by pointing toward a good mindset for approaching math, but also discussing how somebody with the right mindset might think about the specific problem.  In chatting about mathematical philosophy, the topic turned to the way his high school math team (and many high school math teams) gets run.  He tells me

Even the math class is geared towards a MAO mindset, memorization without comprehension.
that’s very very odd; why would something like that happen in the first place?

First, I’ll explain what he’s talking about.  Most of the local math competitions around the Southeast, and Mu Alpha Theta (that’s the “MAO”), which runs a national competition at which primarily Southeastern schools compete, focus on a form of testing that promotes speed and accuracy at what might be called “honors curriculum”.  Few if any of the problems require out-of-the-box thinking.  Tests rarely include more than a couple of problems outside of the algebra-geometry-trig-calc curricular track, and those problems are typically standard and trivial to the more talented students.  A test involves 30 problems over the period of an hour.  If a student does not know what to do with a problem immediately or almost immediately, that student very quickly loses out.  The only way to win is to drill drill drill.  To perfection, or as near to it as possible.

That’s nothing close to a complete description of the testing.  Many local competitions here in Alabama have 25 problem tests, but they are mostly the same.

Winning looks good.  And usually for good reasons.  You can bet that any school consistently scoring highly on the AMC exams has an exception teacher (or two or three), an exceptional system, or both.  Most likely both.  It’s hard to consistently have one of the highest school scores in the nation.  Only the school’s three highest scores count in to the team score.  That might include two seniors and a sophomore one year, or it might include a senior, a junior, and a freshman.  The school’s outliers.

Mu Alpha Theta and local competitions are different.  The top four scorers in each grade contribute to the team score.  I think it’s great that there are some competitions run this way.  It rewards schools with a deep pool of well coached talent.  It also means that some students are contributing who are perhaps very talented (high performers, but not outliers on the 4+ standard deviation level like those who make up the top scorers from good schools on the AMC exams).  The problem arises when math team coaches begin teaching to the tests as opposed to using the problems and topics as a simple guide — or even encouraging the testing process to conform to whatever goes on in their classroom along the lines of the talent level the teachers believe they can maintain.

And winning looks good.  Winning coaches certainly get attention and praise.  It may be perfectly justified.  But that attention may promote winning for its own sake.

Several schools have built the math programs at their schools around gaming the competition system.  The students are drilled to the point where they can quickly answer a large number of problems that might show up on any given exam at school.  Quicker, faster, and more accurately.  Go go go!  At the state level, and at the regional level (which is really what Mu Alpha Theta is), that works.  A school can build a program to dominate, or at least be one of the very top schools year in and year out.  But the bar for domination is not particularly high because only a few schools can compete — those with large student populations and an administration that allows the “right kind of program” to be built.

Then the drilling begins, and it never lets up.  Our tribe must win!  That’s what defines a great chief.  Or something like that.

What the students learn in the process pales in comparison to what they miss.  They miss the wider body of mathematical curriculum – the discrete math, problem solving, proof techniques like induction, the deeper hour or even week long explorations into interesting concepts, and the love.  The love!  The art!  The excitement of unraveling connections between ideas, and learning to see math that way.  Of stumbling upon a new theorem!!  Oh, it’s not new?  That’s okay because independent discovery is a breath-taking affirmation of young, passionate creativity!  But…

1. A
2. C
3. C
4. B
5. D
6. E 36
7. A
8. A
9. A
10. D
11. A
12. B
13. B
14. D
15. C

…

The very best performers at anything do drill themselves.  But they don’t do it at the expense of understanding.  They drill themselves to attain a level of performance or efficiency of thought to match their love of the subject.

Drilling students who have not yet glimpsed an understanding is to rob them of some very beautiful things.  First, it’s a piece of their childhood.  Second, it’s the opportunity to fall in love.

Math is a great first love.  A kid could do a lot worse.