MATHCOUNTS and the Monk

I had the opportunity to be a proctor at the Dallas Chapter of TSPE sponsored MATHCOUNTS at Southern Methodist University yesterday.  Two important observations.  The first, the event has become almost gender equal - - the same number of boy competitors as girls.  I suspect this is also a national trend.  The second observation - - the engineering volunteers that support this event at SMU were also gender equal.

The engineering community is wise to support programs such as the Future City Competition and MATHCOUNTS.  These are worthy programs that start middle school age students down the path of engineering.  But engineering also needs to move beyond this age group to an older audience - - the high school student.  One alternative would be to support and staff open source organization such as TechShop.  Give future engineers an alternative to the theory, the textbook, the classroom, the calculator - - give them tools, workbenches, and design projects.  Give them a hands on experience in product development.  Give them potential customers.  Give them an opportunity to think like an engineer.

 

Engineering can also help students with visual thinking and the visual components of engineering and design - - skills such as storytelling, storyboarding, diagramming, sketching, and low-fidelity prototyping.  Too often engineering starts kids down the analytical and ignores the visual.  Consider the following simple problem and learning tool:

 

"One morning, exactly at sunrise, a Buddhist monk began to climb a tall mountain.  The monk ascended the mountain path at varying rates of speed, stopping at many times along the way to rest.  He reached the summit shortly before the sunset.

 

After a few days of meditation, he began his journey back along the same path, starting at sunrise and again walking at variable speeds with many pauses along the way, and reaching the base shortly before sunset.  His average speed descending was greater than his average climbing speed.

 

Prove that there is a single spot along the path the monk will occupy on both trips precisely the same time of day."

 

The MATHCOUNTS student and most engineers would attempt to solve this problem the traditional engineering and math way.  You would try and develop a non-linear function for  both the ascent and the descent.  After some calculus, you might have the proof.  A math solution to the monk problem is problematic - - mathematics is traditionally a linguistic representation, it makes use of sequential reasoning, and it is usually less an intuitive representation.

 

The proof is easily seen as a simple graph - - Height on the Y-axis and Time on the X-axis.  One line for up and one line for down - - cross at the same place and time.