A “math dollar” is a documentary reward for students.  In 1994 when I was taking my education courses I observed Mr. Arriaga’s class at Oak Park River Forest High School, who used something like this.  I’ve made some changes to the basic idea and found that it works for me as well.

Math dollars usually get given out on days when I’m doing interactive lecture.  You know the drill:  you’re asking questions of the class and getting no response, and you know they could answer if they wanted to.  I preface my questions with, “For a dollar, what is 2x+7?” (or whatever), or “Judy, for a dollar, tell me what is 2x+7?”  It becomes especially important to call on all students fairly with this system, or they’ll let you know!  I generally hand out the dollar immediately when a student answers the question correctly.  Mr. Arriaga assigned a student to be “banker” for the day and record the debts, and held payday every now and then -- perhaps that works more smoothly.

What are math dollars good for?  For the sake of fairness it’s important to let students know at the beginning of the term what options they will have for using their math dollars.  You can do things like offer to drop the lowest quiz score at the end of the quarter for $20, or the lowest test score for $30.  Perhaps you would sell some privilege.  Mr. Arriaga’s students used math dollars for restroom passes or to raise test scores at the end of marking periods.

But what I have done most is to sell extra credit points by silent auctions, an auction ending every two weeks, with about one extra credit point per student in the class.  The advantage of selling points by auction is that the supply remains limited to an amount I consider reasonable, no matter how many dollars I give out.  So by supply and demand, the more dollars I give out, the less each one is worth. ;-)

The mechanics of the auction are easy.  On the bulletin board I post a sheet.  Each line of the sheet records the students’ bids on one extra credit point.  If a student wants to bid one dollar, she writes her initials in the first column (which is headed $1).  If she wants to bid $2 (presumably because someone else bid $1), she initials the second column.  The bidding rarely goes beyond $3 or $4, until the last auction of the semester.  Students tend to hoard their wealth until time for grades, which is of course a bad strategy.  At the top of the auction sheet is printed the date on which the auction will end -- generally a Friday.  The following Monday, I call students for their money and record their points.  Simplicity!

Once the basic idea is in place, math dollars become useful for many things.  One of the first things I thought of was to improve the quality of the document itself.  In their current incarnation, each of my math dollars shows the face of a mathematician on one side and has a short description of the mathematician’s life on the other.  This way I’m imparting a little math history, without actually taking class time for it.  And the students do seem to collect them like baseball cards -- when I give one out they comment on whether they like “that one” or not.

At the small private school where I taught last year we didn’t have substitute teachers who came from outside; each teacher was responsible for subbing for others during their free periods when needed.  This meant that you couldn’t count on a sub’s knowing any math, and had to devise worksheets in advance that could be used at any point in the course as an emergency measure.  I came up with a simple math history matching worksheet, using information they had on the math dollars.  The beauty of this was that probably no student would have all the answers on her own dollars, so they would have to help each other.  Too bad I couldn’t see how it worked out ...  Almost everyone had almost all the answers correct, which is what I expected.  Perhaps in the future I could make it more competitive, by declaring that the group with the highest score would get some incentive -- so that the groups would have to trade answers one-for-one, and pay close attention to what they were doing.

Math dollars also become perfect incentives for class games, such as Concentration, or students working problems competitively at the board.

Questions, corrections, comments:  Send me e-mail at  markthom@flash.net