Some provocative thoughts crossed my mind the other day that might, possibly, be worth exploring for the sake of primary and secondary public education in America. I suppose that the memories of my childhood learning experiences will always play a part in the way I perceive the solutions to basic and advanced mathematical, logical, and scientific inquiries generally found in life, which are generally posed as solvable problems in an educational application. The way I learned to explore, intuit, deduce (or induce), and solve simple math and logic problems, which were the same methodologies for solving other, subsequent, more convoluted problems, was the way my mother learned to do so under the direction of a master teacher in a one room schoolhouse eight miles south of the City of Chandler in East Texas. This master teacher, a future U.S. Senator, insisted that all of his students learn the rudiments of number operations in order to logically solve math and conceptual problems systematically and intuitively. This particular teacher required daily class recitation and memorization of rudimentary conceptual and numerical facts, and required his students to stand and orally deliver.
In her equivalent of the fifth grade, my mom, Dessie, was given the task, at the age of 10, of solving the following math problem, which was basic to the agrarian requisites of a rural farming community in 1920. Some current educators and educational philosophers might say that what was basic to mathematical problem solving in 1920 is hardly applicable in a modern technological classroom of 21st Century fifth graders, but I totally disagree. The problem she was given went like this:
A farmer sold his crop for $100. After deducting 4/5’s of the amount for seed and fertilizer, what percent of the total amount was his net profit?
If the typical 21st Century American fifth grader, ending his fifth year, were given this very basic problem to solve in class with only a pencil and a clean sheet of paper (with no calculator) on his, or her, desk, would that random student, graduating into the sixth grade, be capable of solving it? Well, I have my doubts. Why? My mother taught me the multiplication tables (through the 12s) and fractions at home before I was eight years old, and she had only a sixth grade education. She made learning fun for me. Today, in the 21st Century world, very, very few high school and college educated parents spend time at home in the evenings, or on weekends, helping their children learn basic math, and most (75 percent) of all seventh graders in the public schools don’t know their multiplication tables by heart by the end of the seventh year of public education. That’s because pocket calculators have replaced rote mathematical leaning in the classroom, and multiple choice testing of young minds has replaced the requirement for paper and pencil calculations where students must show their step-by-step processes in computational solution.
In order to solve the above problem, the student must be able to understand fractions and divide numbers. The intuitive student, who understands how to multiply and divide, will say to himself, or herself, that 4/5’s of 100 is equal to $100 x 4/5, which equals $100 x 4 divided by 5, which equals $400/5, which equals $80. Now, the student looks again at the problem and says to himself, or herself, that the calculated $80 is the amount of money spent by the farmer for the seed and fertilizer. So, $100 – $80 equals $20 dollars, or the farmer’s net profit. Now, the student may solve the problem after determining that the net profit, $20, is a certain percentage of $100. So the student creates a basic equation, Percent = $20 divided by $100, or 20 Percent. As far as intuiting percentage, the 1922 fifth grader who understood fractions was logically capable of seeing that 100 percent of $100 is $100, so, logically, 10 percent of $100 is $10 and 20 percent of $100 is $20, and so on, for fractions and percentages go hand-in-hand.
A famed math and physics tutor, who was very successful over 25 years in helping high school and college students, who didn’t learn their fundamental number operations in elementary school, stated that the reason most 21st Century students in junior high, high school, junior college, and in universities have difficulty with basic and advanced algebra is simply because they cannot factor numbers; and not being able to factor comes from not knowing how to basically multiply and divide whole numbers and fractions. This is a poor statement for the validity of current public school education. Moreover, extending this criticism, I doubt very seriously if, even, two-out-of-ten random 21st Century American eighth graders could correctly solve the foregoing problem, solved by a typical 1920 fifth grader left alone with only pencil, paper, and his, or her, mind.
Going back to the old 1920 one-room schoolhouse approach to teaching might be just what the doctor ordered to heal the ailing public school systems. With master teachers who regard memorization, oral recitation, and comprehension of fundamental number and logic facts as vitally important in a student’s education, and caring parents who regularly spend time at home with their elementary school children, assisting them in learning the multiplication tables and how to add, subtract, multiply, and divide numbers, such a beneficial step back in time would be a breath of fresh air in a stale 21st Century America that calls systematic student regression and federal intervention into independent state education progress. Such a shameful, stagnate place, where public school children are not expected by society to properly develop and use their God-given reasoning faculties to intuitively solve mathematical and conceptual problems they will regularly encounter throughout life as adults, seems to be the America in which we now reside.