I have a good friend, Eric, who is a math professor and respected teacher. (He was one of a half dozen primary contributors to a National Science Foundation textbook project in the 90’s.) He’s been aware of my family’s work with the game EQUATIONS for decades. In a talk several years ago about our online programming project, he made a very candid and insightful observation.
It went something like this:
“Well, the math teaching profession in America spent several decades creating lists of objectives with drill and practice exercises to reinforce them …and that didn’t seem to work. So, then we tried creative and relevant story problems as the basis for curriculum and that has had limited success… and there you still are with that wonderful game with all this NAKED MATH and kids loving it… maybe the world is finally ready for that!”
“Oh, my God” I said, “NAKED MATH – we should have used that name instead of Online EQUATIONS!” We both shared a laugh, but the thought stuck with me.
What is it about this game based on Resource Allocation math problems that is so much more interesting and effective than traditional methods?
It certainly has something to do with the rich environment. When you consider all the Solutions that can be built equal to a numerical Goal by choosing among twenty-four single-digit numerals and operations, the number of potential Solutions usually runs into the hundreds – with everything from simple arithmetic to complex relations between algebraic operations in play. In fact, any time a mathematical operation appears in the game, you cannot exclude absolutely anything someone might do with it – and in relation to all the other operations available as well. So, yes, it is amazingly rich.
And within this incredibly rich environment, it’s the players’ knowledge and insight that determines the complexity of what actually gets applied in the game. This is a blessing and self-regulating factor, but it also leaves a tantalizing sense that in every match, players only touch part of the mysterious whole of the system they are exploring.
The intensity of problem solving in every minute of EQUATIONS is only approached by something like the SAT test or similar ordeal. Yet, matching wits in EQUATIONS is a blast and kids will voluntarily do it for hours. Try getting that kind of response by offering them a handy five-page list of story problems to slog through… oh, goody.
And EQUATIONS has all the elements that make classic games great: the bluffing of poker combined with the strategic planning and counter-moves of chess. All of this unfolds as the end game crystallizes from the multi-faceted potential present at the start down to a few elegant Solutions in the final challenge.
When one adds in systems for balanced competition with tournament structures that reward players at all ability levels simultaneously, the whole effect in a classroom is absolutely electric.
It is this systemic whole that is not created by traditional instruction. Efforts at objectification will never develop wholistic appreciation of mathematical systems. Fred Goodman, esteemed professor at the University of Michigan (and one of my dad’s closest colleagues), often used the example of the futility of objectification for learning something like how to ride a bicycle. You could identify and analyze each muscle, tendon and ligament involved in bike riding. You could develop a series of drills that maximally exercise each one of those individual components. But such an approach would have no value whatsoever in actually learning to ride a bike. Why? Because we all know the wholistic integration of velocity, balance and “feel” that learning to ride a bike involves. After mastering that integrated experience, THEN doing all those exercises might make you into Lance Armstrong – but it is not a way to grasp the initial synthesis.
Appreciating the primary system of mathematics – the arithmetic and algebraic operations and their relationships that form the bedrock of K-12 education, is a lot like riding a bike. Breaking it into hundreds of parts disallows appreciation of the systemic whole. Playing EQUATIONS succeeds because that whole potential is present at the start of every match and then proceeds toward specific Solutions as the game unfolds. I think this is the magic of it. How each match starts with the whole of the possible mathematics and then crystallizes down to a specific elegant Solution meeting the constraints created by the alternating player moves. As the minds of players swing back and forth between scanning the potential of the whole and focusing on the specific Solutions, flexibility for handling real-life problems is cultured.
Real-life challenges are always resource allocation problems with many possible approaches. To succeed, it’s always useful to consider: What are the most elegant Solutions? What are the economical ones? Have we missed any economical Solutions in the past? These are the basic decision-making questions EQUATIONS players reflect upon with every move in the game. And this is what makes this game so special and powerful.
So, are you ready for NAKED MATH with kids loving every minute of it? Contact me, it has never been easier than with Online EQUATIONS.
Layman G. (Buzz) Allen 641-919-2466 firstname.lastname@example.org http://gamesforthinkers.org