Math Education:Formulating the Problem

Math educator, Dan Meyer  (video) has argued that today’s math students have a profound impatience with irresolution.  That is, many math students employ a ‘plug and play’ approach to solving math problems, one where the formula is obvious, only the particulars have changed, and they can simply plug in the numbers for an obvious solution.  Meyer uses a number of textbook examples demonstrating that each word problem is essentially the same – a perfectly formulated problem that requires only the application of the formula for resolution. 

Building on Einstein’s observation that, “…the formulation of a problem is often more essential than its solution, which may be merely a matter of mathematical or experimental skill,” Meyer has taken a much different approach with his math students.   Meyer’s approach is much more conversational  and focuses on the formulation of the problem, an approach, in Meyer’s words, in which ‘math serves the conversation’ – not the other way around. 

Here’s a typical textbook problem:

A water tank is in the form of a regular octagonal prism.  The base octagon has side length of 11.9 cm.  The lateral edge of the water tank is 36cm

a.What is the surface area of the base?

b. What is the volume of the water tank?

c. If you pour water into the tank at a rate of 1.8 oz/sec, how long will it take to fill the tank?

Here’s the same problem as Meyer would formulate it:

Here’s a water tank.  How long would it take to fill the tank

Meyer’s students then set about on a conversational and discovery process, processes in which they determine the proper way to formulate the problem and then discover the sorts of formulas that would help them solve that specific problem. 

Meyer is a passionate and thought-provoking educator.  Be sure to take a look at the entire video for a window into how his passion is serving math students.

By the way, if you haven’t checked out the site TED before, do yourself a favor and take a look.  TED compiles short, thought-provoking lectures (none longer than 20 minutes) on a wide range of topics from thought and industry leaders from around the world.  And all of the content is free.  Enjoy.

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