An intellectual arms race of sorts was started during the '77 - '78 academic year. Kindergarten and first grade, the '75 - '76 and '76 - '77 school years had plenty of very beautiful and some troubling memories. But, second grade was exceptionally special. The class was apparently team taught; because, the teacher who sit among our class in our Spring photo was not the one who was in front of the class most days. It is thought that a number of student teachers who were completing their baccalaureates in Elementary Education taught on a rotating schedule.
One day, the teacher for the day was teaching us our multiplication tables. She would raise a flashcard and then call upon a student. Some of the students did not know the answers. Although, this young lion had remembered the 20 by 20 multiplication table. That we had reviewed over the last couple of weeks. One boy within the class was rather anti-social for his age. And, when the teacher called upon this young lion, he answered correctly, and the blond-headed boy called him "stupid" rather boldly, loudly, and proudly.
This insult began an intellectual arms race of sorts. Because, the young lion started answering each question before his classmates could. It is somewhat overwhelming when one is the only Minority among a sea of White faces, including the authority figure among the crowd. And, although not recalled, the Palomino Hills experience was nestled among his subconsciousness. So, he could stand up or cower in silence and be crushed.
This reinforced a love for numbers and mathematics. And, he became rather quick with his coss routines, basic arithmetic. Which were already quite strong. Seeing that, he had spent numerous hours playing "scientific researcher" and enjoying "recreational mathematics". When, he would think of novel and original ways in which numbers might be added, subtracted, multiplied, and divided. That was fun for him.
The student teachers recognized his ability for solving the mathematical problems which he was given. And, he was quick with it. One of the instructors, Ms. Blacksmith, would take the young lion aside, give him problems on which he could work, and measure his abilities. One day, she gave him addition problems that involved numbers between 1000 and 9999. She would read off each pair of numbers for the problem. And, by the time that she had completed reading the second one, he had formed the answer in his mind. Which he would blurt out rapidly. She looked stunned. She completed four of five problems. After each, she said, "That's right!?" with a shocked look on her face. Then, she asked, "How do you do that?!?". At which, he should have said, "It is an ancient African secret!"; however, he did not and told the truth. He said that he held the four digits of the first number in his head. And, as she read the second off, he quickly added in "reverse" order from the highest order digit correcting the last column sum for any needed carry. so, he had the answer as soon as she finished reading the second number. One can quite easily hold between five and nine objects (numbers) in his short-term memory at one time.
Our mathematics class was modular, and we could progress at our own pace. After completing a set of lessons and assessments. We were given a quiz with ten simple questions. They minimum required score for progress given the other students was seven out of ten. For the young lion, it was nine out of ten; because, he had progressed much further and faster than the other students in class. The other students were quite pleased with this rule. Seeing that, they felt that they were getting "special treatment". In fact, they were done a disservice by being given a lax and lesser standard for success. Seven out of ten was a high "D" based upon the grading scale. And, nine out of ten represented "mastery" being a "B+/A-". Even with that extra high standard, he excelled. So well, Ms. Blacksmith denied him an opportunity at working on the next module on certain occasions giving him an "eight out of ten". When, he knew he had a perfect paper, But, he did not complain. He just did what was asked of him and recompleted the module testing once again. She never held him back more than once on any given module. Truth be told, repeating the work was great practice.
It goes without saying that life is not easy when one outpaces his peers. The students were not especially nice for starters. Most were not interested in associating with him before he showed any great mathematical abilities. It only grew worse when he excelled beyond the rate of his classmates.
Some of the children were discovering profanity, and they called him some choice names. Mostly, they simply insulted and threatened him by calling him a "nigger". One day, while he was playing on the playground by himself. A blond-headed boy came over and said, "Shake my hand!". Simply obliging the lad, he reached for his hand. A sudden shock occurred. Then, the boy became incredibly verbally aggressive screaming, "Nigger! Nigger! Nigger! ...". Overwhelmed, the young lion balled up his right fist and struck his shoulder. So, the boy would move away from him.
Seemingly, everyday on the playground, these taunts grew worse. The young lion threw more punches. At which, the instructor was called. She had been told already by the young lion that some of the children were insulting him and calling him a "nigger"; however, she said that she did not hear anything. And, she would not intervene stopping the verbal abuse. So, the young lion took the only action that would alleviate it for a while.
Blamed for defending himself, he had a few interviews with the school principal, Mrs. Bea. She was a wonderful lady of short stature with a short beehive hairdo. Which was a carryover from earlier years in America. They were still worn by some women during the mid-70s. It is believed that she was a Hebrew. And seemingly, she commiserated and sympathized with the young lion some. She said that she had a grandson in the apartments where he lived and that he should play with him. Which he did at later times. Yet, the situation at school did not change.
Eventually, a psychologist from the public school system was called. She spake with the young lion in Mrs. Bea's office. She claimed that no one else had heard anyone use any racial slurs. And, he was insistent upon speaking truth; however, she said that "Those sweet little children would not do such a thing!" And then, she said, "You are hearing things. You are a schizophrenic." At which, the young lion retorted, "I am not a 'skits-so-frantic'." At that age, he could read rather well, use a dictionary, and understand quite well his father's college textbooks. His father, dear old dad, had a post-baccalaureate of social work from the Warren Brown School of Social Work at Washington University in Saint Louis. Which is considered one of the best schools in the world for such. He had done some readings in social psychology. Which, considering the state of modern mankind, should most likely be called "psychosociology". Because, only in a "crazy world" and an even "crazier country" would any God-fearing adult deal with a child the way in which she did. She next said that the you lion was "acting out". As if, he was the one misbehaving. That phrase is an abbreviated form of "acting out his frustrations". And, his frustrations arose from the needless abuses and barriers with which he dealt. While, he sought a "pro-social" goal. Any psychologist and sociologist will tell you that by the textbook this always yields a "anti-social" response. Hence, the punches that had been landed. When, the instructor and authority figure did not provide him will the "equal protections" that she provided the other children. Our classroom was a microcosm and reflection of what was, is, and will be happening in America. Until, it fades away from the face of the earth and history. The remnant of remaining African descendants of the system of "chattel" slavery stemming from the late-1400s on these soils are basically unwanted. In the eyes of many, they have served their purpose and should be permanently discarded.
Although, the young lion believed in what he knew of the Civil Rights Movement. He did not believe that his daily activities should include holding up that banner. He was just seven, sought simplicity in life, and just enjoyed living and playing. He did not feel that each day in grammar school should be a protest march of sorts. He was not in Little Rock, and this was not Central High School. This was Thomas Alva Edison elementary, and it was a year after the Bicentennial.
Long story short, he asked if he could attend Kellom Elementary. It was a small school which had a Family Service of the Midlands build as annex, the Logan Fontenelle Multipurpose Center. It was near the heart of the African American community in a school system which only started its desegregation program during the mid-70s. It was the place where his father worked as the Director, the primary custodian and principal, overseeing its daily operations. He could ride with his father everyday leaving home at 8:00 A.M. and returning at 5:00 P.M. When, school ended at 3:00 P.M. He could spend time in the small public library. Which also adjoined the school and community center. That "special transfer" was never granted. Seeing that, the student teachers and other members of the public school system were studying his abilities. And, they would not that "little gem" get away; because, he would openly share his secrets of his successful academic techniques, and they planned on using him. So, they might better the abilities of the White youth and strengthen their community.
That psychologists name will never be forgotten. It was Evilyn Baker. And, she was definitely "evil". And, she was seen much later in life during a major fiasco that arose during his twenties. During that time, she continued with her racially charged assessment of his academic abilities plus his social and emotional functioning.
Ironically, the agents of the public school system asked him if he wanted a "special transfer". So, he could play basketball at the number one program in the state during his freshman year of secondary school. The coach who approached him felt that he would make an outstanding small power forward at just over seventy-five inches in height.
The special sessions of measurement continued for much of second grade; often, he would be placed in a empty classroom with a educational professional who would proctor examinations and intelligence quotient measurements. He was told that she scored well enough on the test which measured intelligence that he could join Mensa. Which is a fraternal organization that only accepts members of society who are beyond ninety-eight percent of the population based upon those assessments of intellectual function. When that became known, he was despised by much of the rest of his classmates. And, his parents, being from the Old South, where a child should know his place; think, reason, and act like a child; plus be seen and not heard: they were not all that thrilled. So, he might be compared with other students. Some of them were taken aside and given the same test. How they faired is unknown. The examinations seemed rather simple and straightforward.
During that year, apparently our parents received a letter telling them that the student must rotate classes during the day. One room would be a homeroom, one room would be for mathematics, one would be for art, one would be for science, one would be for the core subjects, and so one. No one told him. So, he sat in his homeroom all days somewhat oblivious as the student groups changed. Seeing that, he was the tallest child in class. He should have realized that something was wrong. When, some of the girls were taller than him. He was so focused on the subject matter that was taught. It seemingly never registered. Plus, he was never in a room that had a lunch break. So, he went all day without eating. His mother noticed that he was famished when he got home and asked why he was so hungry eating a double portion meal during his evening snack. He simply said that he did not have lunch. Interestingly enough, one would think that he was missing important second grade lessons that would prevent him from graduating and entering third grade the next year. However, the LORD had placed him by time and chance in the core room. So, he sat in core classes for the second, third, fourth, fifth, and sixth grades. It so happens that the public schools have a policy for minimum graduation requirements for elementary school. It required that a student have at least one class in each core subject from every grade level. He had already completed Kindergarten and first grade.
It was determined that as a result of this mishap of classroom location he was only lacking an art credit for his second-grade school year. So, he attended summer school that year and worked on art projects. Which was fine with him; because, he liked school and could attend year-round. If, the school day allowed for ample recess time. It is ironic how this situation appeared. The other children who were in summer school repeating subjects that they had not passed were likely thinking that "That idiot is working on a art class. He is repeating art. He did not pass art. How stupid is he!"
And as, Ms. Blacksmith wrote with a smile. As, she handed him his final grade report. He graduated "summa cum laude"; however, he entered third grade during the next year not the seventh. If, his parents had allowed such. Which they would not. He would have been minced meat for some of those grossly delinquent anti-social teenagers of the mid-70s. It would have been a more "solitary, isolative, and friendless" existence.
It seems that the young lion had a unique perspective on solving problems simply, using elementary and fundamental approaches, and learning from his mistakes and those of others. When, he was in one of the wrong classrooms during second grade. The teacher was describing division on the board. She drew a large circle and said, "This is our pie. We are dividing it in half." And, she drew a border in the circle along the diameter partitioning it and producing a pair of equal portions. Then, she asked the class a simple question in a very informal manner with imprecise language. She said, "If, we have a pie and divide it twice. How many pieces do we have." And, some of the students grew confused. She was simply reviewing what she had done. Which some of the other students understood. One of the girls raised her hand and said, "Would not you have four pieces?" And, the teachers said, "No." seeming somewhat perplexed. The girl's assumption and interpretation of the question was based upon placing a pair of borders in the pie along perpendicular diameters. So, that couple of slices would evenly divide the pie producing four slices. What the instructor meant was, [How many pieces are yielded when one divides the pie in half.] Which is a couple. Mathematics are somewhat informal and sloppy. When, they discuss division in natural language. If, someone divides five by one. They will likely say that they are dividing the number once. Which is untrue; because the quantity of five is left whole.
This was recalled many years later during moments of mathematical recreation. It was realized that division can be viewed as a partitioning or grouping activity which organizes implements. One very important fact that is frequently taught during the early years of mathematics education but gradually forgotten is this, mathematics is the study of manipulating implements. That includes counting, aggregating, decimating, magnifying, partitioning, or grouping them. Which is done by addition, subtraction, multiplication, and division.
It was while watching a television broadcast of a college algebra course where the teacher was teaching from the perspective of implements and the art of balancing equations that one student asked about the disappearance of some of the implements. They had been taught that in an equation the number of implements on one side must much match the quantity on the other side. And, that balance must be maintained throughout the "balancing process" when solving for the variable. The instructor had written an equation of the board like:
(2x/5) + 15 = x + 7
And, he said that the implements on each side must be equal since the statement includes ("=") and the state of this "balance" must be maintained. So if, one adds or subtracts a given number of implements on one side. He must do the same on the other. The same is true with multiplication and division. The same magnification or "demagnification" (grouping) must done on each side.
So, in the equation above, he subtracted (2x/5) and 7 from each side. Which produced:
8 = 3x/5
Then, he had:
(5*8)/3 = x
And, he said that:
x = 13 1/3
With which, most successful students of algebra would agree.
However, one student in his class became puzzled and asked what some might call a "not-so" bright question. But, from a certain perspective, it was incredibly astute.
She said, "Where are the forty (5*8) implements that we had. Where did the go? How did they become 13 1/3?" Truth be told, when we structure an algebraic statement, we are doing so so we might ascertain an answer. In other words, we are asking a question. What is "x"? And, based upon the way in which the expression is drafted, the value of "x" has a particular meaning.
In the equation above, we might be interested in knowing how many groups of 3 we can make from the 40 implements. Which is 13 with a remainder of 1. So, that is 13 1/3. However, we might be instead interested in the fact that we have 40 objects that are grouped somehow. In this case, we might have 13 groups of 3 with 1 left over. Or, we might have 3 groups of 13 with 1 left over. But, we still have 40 implements on the non-variable side of the final equation. Although, they seemingly vanish.
After, this was realized during some recreational mathematics during his twenties. The young lion came up with an alternative and simplistic approach for solving work-rate problems. That did not let the implements "vanish". It seemed novel and original; seeing that, it was developed independently. Yet, similar approaches had been done and taught before. This he uncovered on further investigations. It is something apparently called "semantic arithmetic".
But, it was much like the "quick adding" for four-digit numbers. Although, it had mostly been done before. It was not widely used or commonly taught. In other words, it was not normal. Interestingly enough, he saw a "special" infomercial on an educational program in mathematics. Which increased the typical student's speed in mathematics during the 90s. Ironically, during the programming, the class which was being taught included a singular African American child. And, his performance was a little slower than the rest of the students. Who were all European American. Mostly likely, that was done so sales of the product would soar; because, the typical White American simply eats up such "stereotypes".
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