Monthly Archives: June 2007

Problem-Based Learning Environments

I’m convinced kids will play with numbers and many other math concepts if you can just trick them into it.

I was astonished one morning this year to see one of my most reluctant learners approach another student, just before the tardy bell, and begin a little interactive “number trick” with him: “Pick any number between 1 and 10.  Add 2.  Multiply by 5…..”  He had a new toy to share, and he wanted to share it for several reasons:

  1. It amused him, and he thought it would amuse his classmate.
  2. Nobody was making him.

I felt like the worst teacher in the world when I interrupted their math discussion and asked them to take their seats so we could begin math class.

I know one day of intrinsically motivated math discussion, properly guided, is worth two weeks of painful lecture.  So, how can we trick them?

My proposed Problem-Based Learning Environment is a video game.  Students have missions.  To accomplish their missions, they must use the right mix of problem-solving, arithmetic, and familiar common-sense decision-making.

Problems appear as missions, plausible, and surprising, like some kind of weekly rescue-team/detective TV show.  (See “Numbers” on CBS on Fridays.)  There are always more missions, with a revolving core group of characters (good and bad) to interact with, and their content is of course based on the student’s level of proficiency in prior concepts.

The game is current and hip – not funky like a six-year-old educational game.  It has modern graphics and sounds, along with slightly edgy themes.  There might even be some threatening aliens to avoid, to provide a sense of urgency.

To help students accomplish missions, there is a set of tools: formulas, algorithms, identification challenges.  All of these are integrated within the game premise and are only named once mastered.  Once introduced and explored, these tools can (and will) be reused in later missions.

I’m extremely excited about the Algebra 1 concepts covered cleverly in the online games by Tabula Digita (see and  Students accomplish missions set on a coordinate plane – disguised as an alien landscape – and are even occasionally asked for “coordinates” of their location.  (It doesn’t sound like math this time.  It sounds like science fiction!)  This software is very similar too the ideal software I’ve described here.


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).