Social Aspects of Mathematics
Abstract Thinking
As we consider the economic and political partitioning that plagues our country, one must ask themselves, “What has happened to our inherent understanding of honesty and truth?” Where should these normative values have been learned?Social
I often tell my students that Mathematics is The Almighty’s gift to humanity for understanding His Creation. Well, you can imagine the stares that I get. “But, I hate Math! Math makes no sense to me!” And some parents are worse. I tell them that their son or daughter needs to spend more time on math assignments and they proudly announce to me, “Well I didn’t like math either!” From this reply I guess that I am supposed to infer, “Don’t expect too much help from me!” Using this experience as a point of departure, I thought that a discussion of a very basic aspect of Mathematics and how it influences our lives, would be appropriate.
Basic Math Facts
In elementary school, youngsters learn their multiplication tables: 4 times 5 equals 20; 9 times 7 equals 63, for example. When I was a young scholar, students had to commit these basic multiplication facts to memory — I am not sure whether or not that is a present day requirement. Nevertheless students should next be exposed to verbal problems that employ these basic facts. I have found that many youngsters do not like word problems. They argue that they are unable to determine which mathematical operation to perform. “What should I do — add, subtract, multiply or divide?” However developing problem solving skills is an important aspect of the learning.
Sharief had five bags of marbles. Each bag had 8 marbles. How many marbles did Sharief have in total? Using verbal problems, students come to realize that it is not necessary to empty all five bags of marbles and count them one at a time. A solution to this problem is achievable simply by applying previously learned basic facts. Beginning with basic facts and then learning to transfer this knowledge to other situations is a very important mathematical concept known as abstract thinking.
As youngsters mature, they apply previously learned internalized knowledge — basic facts — to new situations. For example, Sharief may have to solve the following problem: ”How many doses of vaccine can I transport to Nevada if I have 5 trucks each of which can carry 7,500 vials of medicine?”
Sharief does not need to count each vial one-by-one to determine the total. He has learned to trust his basic internalized knowledge and consequently there are 37,500 vials of vaccine. He has learned and internalized basic multiplication principles and is able to transfer this knowledge and logically predict outcomes based upon his prior experiences.
Abstract thinking as adults
As Sharief interacts with others in his circle from youth through adulthood, he gradually internalized Divinely inspired basic facts dictating acceptable moral and ethical behavior, also. He learned that honesty yields positive results while being caught in a lie results in disapproval or punishment. He learned that family and community responsibility are more precious than selfishness and greed. Concern for others and positive interactions built his self-esteem through positive family and community experiences while greed and selfishness led to social disapproval, isolation and avoidance. He learned that others treat him respectfully when he responds in kind. Sharief’s socioeconomic circumstances may expose him to challenges in these areas of vital human interaction. But these experiences, over time, help him to discern appropriate behavior in his relationship with others.
Elevating these basic ideas to divine
Just as Sharief was able to transfer basic multiplication facts to his daily employment challenges, so too, he must learn to apply abstractly any divinely inspired moral and ethical behavior in his daily human interactions. As he approaches the autumn of his life, he will look back and see, through his own experiences, the times in which he was able to transfer ideas abstractly to a variety of situations resulting in favorable outcomes.
With normal maturity comes a desire for peace in one’s life and Sharief will recognize that this desirable condition can only be achieved when divinely inspired, moral and ethical principles are abstractly applied to all human activities.
So, appreciating the concept of abstract thinking learned through Mathematics, when applied to family and community personal interactions, can lead to a more rewarding life: and, hopefully “The Big Lie” will not find fertile soil soil in which to grow.
