Math Reflections

11 Feb

Clearly, children today are brighter than I.  A fourth grade student asked for my help with the following problem:

A certain rectangle has an area of 30 square inches.  The perimeter of the rectangle is 34 inches.  How long are the sides of the rectangle?

Admittedly, I am not the brightest crayon in the box.  I still possess some recollections of my years in public school.  Math was not a friend.  I recall struggling with math throughout my twelve years in school.  It seemed to take forever to grasp the basic principles: adding, subtraction, multiplication, division both long and short, fractions, decimals, and units of measurement.  Weren’t the first eight years spent in grasping these concepts?  Don’t you have to understand the concepts before applying them to the most dreaded problems of all – story problems?

I admit to some degree of functional fixedness regarding math.  In third grade, Mrs. Shoop would write problems on the board such as

Multiplication Addition

I hoped for the 8 times 8 problem.  Multiplication I could handle; addition was always difficult.  God understood my challenge and arranged for me to get the addition problem.  While other students were rapidly writing the answer to their assigned problems, I struggled with 8 plus 8 is 16 plus 8 is … 24 plus 8 is … 32 plus 8 is … 40 ….  Each pause got longer.  Eventually I would be the last student at the board.  My effort would have ended at 49 plus 8 because my nerves would have gotten the better of me and throw in an addition factor other than 8 simply to exhaust my limited supply of confidence.  Mrs. Shoop would then point out that these are exactly the same problems whereupon self-confidence would be reduced to zero.

I now recognize that from the beginning there has been an element of algebra in all problems.  The unknown, the answer, was always sought.  However, a formal introduction arrived in Mr. Robert McVey’s ninth grade algebra class.  Mr. McVey described what math can do for us and provided plenty of examples and help in understanding this subject.  One unknown; two unknowns; polynomials; slope; graphs; quadratic equations; factoring; inequities; and, most importantly, how to interpret story problems and set up the equation all became known with Mr. McVey’s guidance.  I won’t say it became easy, but I, at least, had some idea of how to address basic math problems.  (He frankly scared me with tales of going to the meat market to get butcher paper in order to do math problems in college.)

The fourth grader’s problem wasn’t the type of problem I had to deal with until Mr. McVey’s algebra class in high school.  I plugged my data into the formulas for area of a rectangle (area = length x width) and perimeter of a rectangle (perimeter = two times the length + two times the width).  I isolated one of the unknowns (l = [34 – 2w]/2 or l = 17 – w) and substituted that into the formula. As I began to solve for “w” it became apparent that “w” was going to be squared.  As Gomer Pyle would say, “Surprise … surprise … surprise” (Gomer Pyle: USMC, 1964-1969). Fourth graders handle quadratic equations!

Clearly, fourth graders today are brighter today than I.

References

Ruben, A. (Creator) & Nabors, J. (Actor). (1964-1969). In Leonard, S. & Ruben, A. (Executive Producers), Gomer Pyle: U.S.M.C. [Television Series] Culver City, CA: Desilu Studios.

 

 

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