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Mathematics

Satisfactory Essays
Mathematics

At the recent annual meeting of the Psychology of Mathematics Education--North America Chapter, held in Florida, Bob and I were playing Frisbee on the beach. The lure of the surf soon led us into thigh deep water where waves added to the fun we were having with the wind. We were throwing parallel to the shore but the waves were coming in at an angle so that a breaking wave first hit Bob before hitting me a few seconds later. Verbal communication was difficult due to the noise of the surf, so thumbs-up or down, applause, head-nodding or shaking, along with smiles or frowns took its place. Soon a game had evolved and the use of the signs mentioned above became structured.

Entering Paul's Umwelt

The waves are high and strong making it challenging to catch the Frisbee unless it is thrown accurately. But the waves are also high enough to make it interesting to try to throw the Frisbee such that it just clears a wave as its crest passes the halfway point between Bob and me. Shake the water off, wait...wait...throw! Alright! A thumbs-up from Bob. He's right I got really close that time--but I bet I can cut it closer--just have to get a feel for the timing--aim a tad lower. OK, here comes his throw. Oops! Too high--Arrgghhh-splutter...YES--got it! Big complimentary smile from Bob. Actually it's fun when he misses high because then I get to jump for it just as a wave crashes into me. OK, my turn, wait...wait...remember-low...now! Perfection--that one skimmed the crest of the wave!!

Entering Bob's Umwelt

The waves are high and strong enough to make it challenging to catch the Frisbee unless it is thrown accurately. Uh-Oh...another low throw...Arrgghhh-splutter--yes! Hangs on for the touchdown. Big smile and thumbs up from Paul. Hmmpf! Does he really enjoy making it so hard for me to catch it? He always seems to time it so that a wave crashes on me just as the Frisbee arrives. OK, back to him...have to clear the waves...wait for the calm between the waves...now! Yes! Right on target and high enough for an easy catch--not too high like last time. Hmmm...no response from Paul--doesn't he appreciate my accuracy?

Umwelts in Collusion

While walking back to the hotel we discussed our "game".

Bob: You sure had a knack for timing your throws!

Paul: It was challenging to see how close to the water I could throw it and have it still get to you.
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