Category Archives: ESEC602

Would You Try Harder to Memorize the Slope Formula If Your Life Depended On It?

“A bio-digital virus has been released on a remote island and threatens to infect the world’s eco-system and destroy mankind. As Kep, Commander of a special ops team sent to secure the island, you must locate four weather stations.”

What teen-ager could resist such a backstory?  The world built around this premise is DimensionM, a first-person, 3-D video game similar to the hugely popular Quake and Doom.  As in those games, you run over alien landscapes and shoot at bad guys, who in this case are cephalopod-like creatures that hover in the air.  Even more current than those classics, DimensionM features eerie, post-modern graphic design, from its 70% transparent control panels to its hazy mists and dingy machinery.

Unlike standard first-person shooters, however, DimensionM, developed and produced by Tabula Digita, Inc., in New York, has an agenda, revealed when you continue reading the backstory:  “[You are] given an ordered pair and shown [your] location in a coordinate system….”

Disguised as useless fun, DimensionM is actually an educational game.  It was designed from the ground up by educators with the latest research, built for serious use by classroom teachers.  Students play the game by taking on missions, moving over and interacting with a Cartesian landscape of axes and coordinates.  Occasional transmissions from headquarters require you to report your location, forcing students to live in the coordinate plane.  And sometimes you even die in the coordinate plane, when your special bio-suit disappears and you crumple to the ground.  Who would have expected such risks in an educational game?  Hence the tag line: “Learn Math or Die Trying”

Will students work on an educational game which is transparently educational?  That’s what Mexican academics Gabriel Lopez-Morteo and Gilberto López counted on when they developed their “electronic collaborative learning environment.”  The system is a portal comprising “portlets” (portal elements), their word for open-source objects such as Jabber (chat rooms and instant messaging) and email clients; a collection of these, along with custom math objects (called “Interactive Instructors of Recreational Mathematics”), is available for the individual to install and customize on his or her own page.  The inventors of this system have tested it and reported their results, which they claim (the data actually look ambiguous to me) support their belief that “this approach has the potential to promote the mathematics learning process, basically on its motivational aspects.”

Is this overkill?  What about using the classic “help Mario find his way to the secret treasure” approach, where the story is minimal but accessible through its commonness?  Creative simulations such as SimCalc Math Worlds provide involvement with little commitment. Math Worlds uses a fish-vs.-fisherman story  to explore the difficult concepts of slope and rates, in the context of functions.  Students drag objects on a coordinate plane to change the story’s parameters, and then click the Start button to see how their fish behave.  Although the story isn’t fully fleshed out – are the fish trying to avoid the fisherman’s hook?  is the fisherman even aware of the fish? – the interface is flexible and invites experimentation.

One of the most creative uses of technology to study math is one built for the student with musical intelligence.  The Harmonic Series Rhythm Player, developed by the Center for Technology and Teacher Education, University of Virginia, is part of a suite of math-oriented simulations that allows users to set up rhythms and polyrhythms by choosing numbers from a variety of series (Fibonacci, odd numbers, natural numbers, …) and hear them played on a simulated xylophone.  Each rhythm is assigned a different pitch, allowing the listener to easily distinguish the overlaid patterns.  If you want to hear quarter notes with eight notes laid on top, choose 8 and 16 and click Play.  (The buttons below 5 do not produce sounds reliably.)  To add triplets to this, choose the 12 button.  You can easily explore such difficult combinations as 17 against 8 with this program.  Although there are a few bugs in this Flash program, there is plenty of valuable opportunity too.

When they’re motivated (end of week, end of year, winter break), kids will fight for every classroom point.  Wouldn’t it be an obvious good idea to turn this into a game?  Especially in a math class, you can make the crucial concepts of ratios and fractions personal.  This is only possible if there is near-instantaneous feedback on their grades.  I’ve been working toward shorter latency on grade feedback, with the (probably distant, probably dependent on handheld technology, at least for the teacer) goal being direct display of the day’s results along with the current overall semester score on the LCD.  Students are happy to share their lives on My Space, and they willingly share their rankings in various online games, so wouldn’t it be natural for them to compare each other’s scores in an algebra class?  Possibly not.  The students who are naturally competitive or at the top of the class would be happy to compete, but students who have a bad test day or miss a week of school for illness might not be comfortable having their status exposed publicly.  Maybe only the assessments that are primarily based on effort – worksheets and other classwork, for example – would be exposed like this, and only with a well thought-out and fair make-up policy.  In fact, it might be fair and productive to extend this game out beyond the classroom so that students could “play” at home or at the school library – earning points for successfully completing exercises.


1. Dimenxian Algebra. Tabula Digita, Inc., New York (2007).

2. Lopez-Morteo, G., and López, G. (2004). Computer support for learning mathematics: A learning environment based on recreational learning objects. Computers & Education, 48(4), 618-641

3. SimCalc Math Worlds, University of Massachusetts Dartmouth (2005).

4. The Harmonic Series Rhythm Player, Center for Technology and Teacher Education, Charlottesville, VA (2005).


Review: “Computer support for learning mathematics: A learning environment based on recreational learning objects”

In this era of ubiquitous Internet access, cell phones, PDAs and other digital technologies, today’s teachers face a time-honored dilemma: students who won’t think in school and who avoid homework will spend all their free time on something recreational yet mentally challenging, especially Massively Multi-Player Online Role-Playing Games (MMORPGs). If we could only find an activity which motivated the kids to work as hard on learning as they do on playing!

The authors of the paper “Computer support for learning mathematics: A learning environment based on recreational learning objects” may be on to something. They describe an “electronic collaborative learning environment” and report on its power to motivate high-school math students.

The environment Lopez-Morteo and Gilberto López have built is essentially a portal populated by “portlets” (portal elements), their word for open-source objects such as Jabber (chat rooms and instant messaging) and email clients. In addition to these familiar objects, there are math objects called “Interactive Instructors of Recreational Mathematics” (IIRM). These include games, simulations and other applications, designed to encourage student involvement through problem solving.

Students log into the system and can customize the appearance and contents of their environments – exactly as users of MySpace or other social networking sites might. The authors describe a specific math object, a memory game built in Java called “ArithMem.”

Having established a full-featured environment, the authors tested its ability to motivate math students. Groups of students logged onto the system, watched a lesson presented by the teacher, and then used the interactive elements of the system (programs, spreadsheets, animations) freely. Students then filled out a survey about their attitudes toward mathematics.

Although the authors seemed satisfied with the results, I did not see any convincing statistical evidence that the environment served its primary goal: to motivate students to learn math. Rather than overwhelming evidence collected in the survey, the authors provided opinion and a few weak statistics to support this claim, along with anecdotes to back it up. Nevertheless, I would probably use such a system if I had access to a computer lab for a year and a set of classes with which to try it.


1. Lopez-Morteo, G., and López, G. (2004). Computer support for learning mathematics: A learning environment based on recreational learning objects. Computers & Education, 48(4), 618-641.

Review: “A Brief History of American K-12 Mathematics Education in the 20th Century”

As related in detail by David Klein, the history of mathematics standards in the United States is the story of a pendulum swinging back and forth for the last hundred years.  The priority – placed at various locations along the spectrum of practical skills vs. intellectualism – has shifted repeatedly since 1925, when William Heard Kilpatrick argued for discovery learning and utilitarianism in his book Foundations of Method.

Klein traces the ebb and flow of “progressive” education in its various forms since Kilpatrick (who considered mathematics “harmful rather than helpful to the kind of thinking necessary for ordinary living”).  The Life Adjustment Movement of the 1940s advocated a paternalistic approach to education, actively avoiding stigmatization of the majority of secondary-school students who were intellectually incapable of algebra and beyond.  After dormancy during the Sputnik and New Math eras, progressivism emerged again in the 1970s as the Open Education Movement, in which children were free to choose what they wanted to learn and what they didn’t.  (Hint: most of them preferred making Jello and cookies to studying math.)

Klein uses the repeated failures of the various progressive movements as the backdrop for the growth of national math standards, inspired by An Agenda for Action (published by  the National Council of Teachers of Mathematics in 1980) and by A Nation at Risk (written by a commission appointed by the U.S. Secretary of Education).  The combined effect of these two documents was that the public collectively woke up to the sorry state of math education and began supporting the development of standards.  In the wake of this attention, National Council of Teachers of Mathematics (NCTM)  developed several standards-like documents – which Klein describes as instruments for promoting NCTM’s agenda,  characterized by Klein as pro-calculator and anti-calculus.

Against the anti-intellectual tide of the NCTM pressure, California and other states adopted rigorous standards in the 1990s.  Still, various localities (for example the LAUSD and El Paso schools) worked with NCTM-aligned programs, some homegrown and others developed by textbook publishers such as McDougal Littell.

Klein pits the National Council of Teachers of Mathematics against organized groups of informed parents and university mathematicians, who were concerned about the documented poor results of public math education in the 1990s.  It’s a fascinating and complicated story, with no obvious villain and enough ineptitude and corruption to go around.

1. Klein, D. (2005). A Brief History of American K-12 Mathematics Education in the 20th Century. In Royer, J.M. (Ed.), Mathematical Cognition. Information Age Publishing, Charlotte, NC.