I think I have posted this before (the private communication dates from the mid-90s) but it has been some time.  Anecdotes can be great when they represent a widespread (although, thankfully, not universal) problem as this one does; the Locker Problem is a long-standing POW favorite.  It is interesting to point out that this math department faculty member is really quite supportive of the reform movement in mathematics education butů

The Locker Problem

A natural outgrowth of shoddy mathematical preparation is the following from a colleague at another CSU campus.  Notice that this is the honors math class so probably represents the mathematically best prepared teacher in the entire school:
"I have 13 year old twin boys who are in seventh grade.  Generally, they try to stay away from taking the same class, but since there is only one section of Advanced Math in their Junior High School, they ended up in the same class.  Their teacher is considered a very tough and demanding teacher but in my opinion, she represents everything that is wrong in the way we teach mathematics in middle school.   She is an absolute freak about procedural things and things have to be done exactly in one way (whatever she thinks is the right way).   Early in the school year she assigned a POW (problem of the week) that went like this:
There are 30 lockers and 30 kids.  At the start, all lockers are closed.  Then kid #1 goes through and opens every locker; kid #2 closes every other locker, kid #3 reverses the position of every third locker and so on.  The problem asked for the status of each locker after all 30 kids had gone through it.  One of the twins drew a picture (a square for each locker) and then proceeded to work out the problem by sheer brute force (marking the entire sequence of changes in each box).  The other twin observed that the number of times a locker got changed had to do with the number of divisors of the locker number, so that if one could find the number of divisors of an integer one could solve the problem in total generality.  He then illustrated his argument by picking locker #12 and illustrating how and why his general argument works.   For his efforts he got a D, while the first twin got an A.  

This is only the most blatant example of what goes on in that classroom in the guise of mathematics."
In case there remains some doubt as to whether I am misinterpreting his perspective, here is more of his message:
"I know that there are many other people out there who share my strong feelings about the dismal state of mathematics education in this country.  I find it ironical in this country we have more professional mathematics-education people per capita (by far) than any other country in the world.   I always wonder if there is a cause and effect relationship here.   In any case, you are not alone in opposition to a lot of the garbage going on, and I sense more and more a tremendous dissatisfaction with the politically correct movements in mathematics education."
         -------------------------------------------------------------  maybe you talking to you keep waking now

At 09:17 AM 2/15/2013, r!chard tchen wrote:

Coincidentally, the _Mathematics Teacher_ article that the National Council of Teachers of Mathematics (NCTM) has made available for free this month discusses an action research study on teaching strategies used to facilitate problems of the week -- and includes student performance data from the Northwest Educational Assessment (NWEA) and Indiana Algebra 1 exit exam:

Punch Up Algebra with POWs (downloads 2.5M PDF)


Richard Tchen

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