Tuesday, March 08, 2011

Puzzling Learning

Numeric puzzles are a great way to challenge students to Think Critically.

Some students see puzzles are an excercie in futility because they attack them from the perspective of plug in numbers at random, hoping eventually that the right pairing of numbers will magically fall into place and the puzzle will be solved. Usually, it is a race between frustration, their eraser and luck.
Some students however use sytematice processes to whittle down possible choices until and answer is found.
Still other students search for the logic behind the solution.  It is the understanding that all activities with numbers from puzzles to algebra to calculus have a defined pattern of logic and sequence that provides a path for success rather than a brick wall of frustration.
Therefore, I ask students not only to solve the puzzle, but to explain the pattern or logic behind the solution.
Two verey simple examples of puzzles that I use are a 15 Magic Square and and 8 Circle Pattern

In order to solve this puzzle students must understand that the combination of numbers need to be of patterns of 5 + 10 = 15.  Therefore the numer 5 must go in the middle and be surrounded with the proper pairings of numbers with a sum of 10: 1 + 9 = 10, 2 + 8 = 10, 3 + 7 = 10, 4 + 6 = 10.  Next students must understand that the number 9 must not be placed in the corner because there would need to be three cominbations of 6 in order to reach a sum of 15.  This means 9 must be in a side square opposite the 1.  The 8 and 6 then need to be paired with the 1.  This then pairs the 2 opposite the 8 and the 4 opposite the 6.  That leaves the final two spaces for the 3 and 7.  Once students understand the pairing pattern the rest of the numbers fall in to place.

In the Eight Circle pattern above the same logical processing makes the puzzle very easy to solve.
Students must first understand that the numbers 1 and 8 need to be separated from only one number. The 1 must be away from the 2 and the 8 needs to avoid the 7.  Therefore, the 1 and 8 need to go in the center circles which contact six numbers each.  In turn the 2 must be placed in the center row opposite the 1 and the 7 likewise opposite the 8.  Once these first four numbers are set, it is very easy to arrange the other numbers.  The 3 must be distanced from the 2 and the 6 apart from the 7 and so on. 

Each of these puzzles should be solved in less than 5 minutes, when students approach the solution from a logical process of looking for the patterns involved with the numbers.

Challenge students to think beyond the answer, and pursue the purpose for the answer.

  Brain: an apparatus with which
         we think we think.                                    
-Ambrose Bierce-


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