Schooled

Parents are very concerned with their children’s education, attending parent-teacher conferences and analyzing grades in order to gauge their child’s progress. They claim that they’re acting in the best interest of their offspring, but their chief aim is receiving favorable report cards. For most parents it doesn’t matter whether their child understands long division, World War I or proper semicolon use; they simply want their child to get good grades so they can enroll in a reputable university and earn more good grades.

But are grades really a trustworthy measurement of understanding? As we’ve already discussed, testing in schools often more accurately measures memorization and study tactics than authentic comprehension. Also, we know that students are often graded on knowledge and abilities that have little or nothing to do with the subject of study. For example, it is common for students to be asked to draw pictures, record and edit video, give presentations and create posters in classes such as English and social studies. These tasks are often explained as an avenue for artistic students to succeed in classes that aren’t artistic in nature. In other words, we want students with a poor understanding of the subject matter to do well. In addition, we also know that our education system does little to prepare young people for adult life, namely raising a family.

So what if we actually wanted to measure, with some objectivity, the quality of the education a child is receiving? In order to properly assess the situation, we must look at both the efficiency and the effectiveness of our educational system, for we must consider both the resources and time spent educating students as well as the results of that education if we are to determine the success of our schools. Let’s being by examining educational efficiency.

There are about 195 school days every year, with students spending about 6 hours of each day in class. This regimen echoes 12 times, allowing each student about 15,000 hours of education by the time they graduate. However, this number doesn’t account for time spent studying, doing homework or participating in any extra-curricular activities. As for the funding, the total projected education expenditures in the United States for the 2012-2013 school year is $571 billion. With about 50 million primary and secondary students enrolled nationwide, the annual cost per student works out to approximately $11,500. Now let’s examine the fruit of this expense.

American College Testing exams are designed to measure comprehension of English, reading, math and science in an attempt to determine the level of preparation for post-secondary education. Recent scores indicate that only 1 in 4 high school graduates are prepared for college in all four areas. These findings are corroborated in a study produced by the Alliance for Excellent Education, which revealed that 1 in 3 young adults are unprepared for life after high school. The study asked employers of recent graduates to rate them in certain areas. Around 80% of employers observed deficiencies in communication, work ethic, critical thinking and basic writing skills.

This apparent lack of effective education could even translate into a national security issue, according to the United States Secretary of Education. Today, nearly 25% of young people are unable to pass the U.S. Army entrance exam, which asks basic science, reading and math questions such as, “If 2 plus x equals 4, what is the value of x?”

So after 15,000 hours at school and $150,000 spent, we should expect high school graduates to be flexing some mental agility and confounding their elders with the volumes of knowledge they retain, but as we’ve seen, this isn’t the case. The failure of this educational model becomes even more stark when contrasted with an alternative to traditional education: homeschooling.

Studies have repeatedly confirmed that children taught at home outperform their publicly educated peers on standardized tests. They are also spared from many temptations and adversities that public school students encounter, resulting in reduced teen pregnancies, drug and alcohol abuse and bullying. A common criticism of homeschooling is that children are sheltered from society, leading to deficiencies in communication and social awkwardness. These assertions have no legitimate foundation, since studies show that homeschooled students are significantly more likely to vote, involve themselves in the community and identify themselves as happy. Besides, if parents were really concerned that their children would miss out on the social aspects of public education, they could simply reject and berate their children throughout the day.

So homeschooling is clearly more effective than traditional public education, but how efficient is it in terms of the time and resources invested? The average cost of homeschooling is about $500 per year, which is about 4.3% of the cost of public education. Homeschooled students also put in less time, usually requiring only 3 to 5 hours per day, or around 67% of the time a public student will take.

Homeschooling is clearly far more effective and efficient than public education, revealing just how unsuccessful our schools have become. For if a facility with a library, gymnasium, classrooms, computers, educated teachers and administration, special needs services and counselling can be outperformed by a concerned parent with a textbook, then our approach to education is seriously dysfunctional.

If instead of spending $60 per day to send our child to public school, we were to homeschool them and put the difference in a savings plan, our child would graduate with a better education, a happier life and about $190,000 in the bank.

Gradient

Whether motivated by a biological imperative or the need to vicariously atone for their own deficiencies, parents pursue the success of their children with fanaticism. And since we all know that education is the foundation for happiness and wealth, it is often the center of parental focus. Even after secondary graduation, the importance of education is stressed by parents as well as left-wing radicals bent on brainwashing young minds.

So how do we know whether or not a student is succeeding in school? The answer is by simply looking at the student’s grades. What isn’t so simple is the method by which those grades are calculated, interpreted and transcribed.

The basic concept of grading is that teachers award their students a score for each of their assignments and exams. Then, using the student’s combined scores, a grade is assigned. This grade determines the student’s level of achievement in the class and dictates whether they are passing or failing. Although nearly all institutions assign grades in this way, their interpretation of a student’s performance will vary significantly. In some countries, students are graded on a 1 to 20 scale, some simply use 1 to 5, while others assign letters.

In many parts of the world, most predominantly America and Western Europe, a student’s score is expressed as a percentage representing the ratio of correct answers to problems given. For example, a student who answered 24 questions correctly out of 31 is given a score of 77. Now everything up to this point has made sense, but we’re about to make a bumpy trek into the world of letter grades.

In an attempt to more clearly communicate the level of achievement, many nations have adopted some form of alphabetized ranking derived from the percentage score. In these systems, the letter A indicates the highest grade, while E or F represent the lowest. Here are some different interpretations of the letter grade system:

United States Ireland Singapore Pakistan Jordan
A 90-100 A 85-100 A1 75-100 A1 90-100 A 60-100
B 80-89 B 70-84 A2 70-74 A 70-90 B+ 55-59
C 70-79 C 55-69 B3 65-69 B 60-70 B 50-54
D 60-69 D 40-54 B4 60-64 C 50-60 C+ 43-49
F 0-59 E 25-39 C5 55-59 D 40-50 C 35-42
F 0-24 C6 50-54 E 33-40 F 0-34
NG 0 D7 45-49
E8 40-44
F9 0-40

As we can see, there is great variety even among nations that use letter grades. To complicate things further, many districts consider letter grades too vague, so plus and minus suffixes are used to add complexity to a system designed to be simple. Here’s how it works in most American schools:

United States
A 90-100 A+ 98-100
A 93-97
A- 90-92
B 80-89 B+ 87-89
B 83-86
B- 80-82
C 70-79 C+ 77-79
C 73-76
C- 70-72
D 60-69 D+ 67-69
D 60-66
F 0-59 F 0-59

Now we would expect that such a finely-tuned system would satisfy all concerned parties, but this isn’t the case. Because employers and post-secondary institutions often wish to know the overall average grade of a student during a semester or program, an entirely new system was devised: the grade point average (GPA).

Grade points are awarded based on either the student’s final letter grade or percentage score achieved in a class. Most institutions use a system in which students are awarded between 0 and 4 points per course. Institutions that use use percentages to calculate grade points do is in a number of ways, and the most common is to simply divide the percentage score by 100 and multiply the product by 4.

Institutions that determine grade points using letter grades will simply translate an A as 4 points, B as 3 points, C as 2 points, D as 1 point and an F as 0 points. However, letter grade suffixes allow a student to be awarded more than 4 grade points for a single course. In many schools, the plus or minus suffix simply adds or subtracts 0.3 or 0.33 to the grade point value.

Standard 4 Point System 4 Point System with Suffixes
A 90-100 3.5-4.0 A+ 98-100 4.3
A 93-97 4.0
A- 90-92 3.7
B 80-89 2.5-3.49 B+ 87-89 3.3
B 83-86 3.0
B- 80-82 2.7
C 70-79 1.5-2.49 C+ 77-79 2.3
C 73-76 2.0
C- 70-72 1.7
D 60-69 1.0-1.49 D+ 67-69 1.3
D 60-66 1.0
F 0-59 0.0-0.99 F 0-59 0.0

The grade point average is then calculated by adding together a student’s grade points and dividing by the number of courses taken during that time. Sometimes grade points also incorporate the credit value of courses by multiplying each course GPA by its credit value, then dividing by the total credit value of courses taken.

So to recapitulate, here’s how grades are calculated:

  1. Assignments and exams are graded with a score, usually a ratio of correctness (24/31).
  2. The ratio is expressed as a percentage (77%).
  3. The percentage is converted to a letter grade, sometimes with a suffix (C+).
  4. A combination of percentage, letter grade and course credit value is translated into grade points (2.3).
  5. The grade points are divided by the number and/or value of courses taken, resulting in the grade point average.

Now if you begin to feel an intense and crushing feeling of terror at the concept, don’t be alarmed. That indicates only that you are still sane. For in the same way that the measurement of fuel consumption and time have been corrupted by counterintuitive expressions and unnecessary calculation, grading also suffers from superfluous complexity.

We should not manipulate systems to suite our interpretation but interpret the expressions of the simplest and most efficient system. In this case, a percentage is the simplest and most efficient expression of a grade, since it is nothing but the numerical representation of the correctness of a score. Letter grades, suffixes, grade points and grade point averages are all derived, directly or indirectly, from the percentage, and they necessitate additional levels of interpretation to understand.

Whether expressed as a B, B+, 3.3 or 3.4, everyone understands that 88% is a pretty good score, so let’s just grade in percentages.

Dice

There is an explanation for everything. Our world is comprised of matter and energy that behaves in predictable ways, allowing us a degree of certainty when imagining hypothetical situations. Yet, despite the massive leaps forward in science, we occasionally find ourselves in the midst of events so absurd, so seemingly unpredictable, that we can only respond with the words, “well, that was random.”

It wasn’t.

Although we may not have been able to predict such scenarios, they weren’t random; they only seemed random because we didn’t know why it occurred. There’s likely a perfectly legitimate explanation for the any situation we find ourselves in, no matter how strange. Before we continue, let us make some important declarations and distinctions about how the universe operates:

  1. Nothing is random, because everything has a cause.
  2. Some things are pseudo-random, having a nearly incomprehensible cause.
  3. Some things only seem random, but actually maintain a comprehensible cause.

Although no occurrence can be truly random, by categorizing all measurable events as either pseudo-random or seemingly random, we may better understand what is meant when something is characterized as random. First, let’s deal with those things that we might consider random, but which are actually just unpredictable.

Random number generation has been used throughout history for many purposes, most notably gambling. By creating devices that use high speeds and complex vectors, such as dice or roulette wheels, we can produce outcomes which cannot be predicted, at least not with the human eye. More recently, we have used computers to generate pseudo-random numbers using algorithms and seed values. Though much more elaborate than physical random number generation, the results are still derived from a concrete source, so they cannot be truly random.

A popular example of perceived randomness, often used to prove some point about the universe, is the idea that an infinite number of monkeys on an infinite number of typewriters will produce the complete works of Shakespeare. The premise being that the typing pattern of monkeys is random and, therefore, it will eventually produce every outcome. This is not true.

Monkeys will never produce the works of Shakespeare, and we don’t need to lock a monkey in a room with a typewriter to find that out. If we were to simply imagine the result of such an experiment, we would likely conclude that the monkey had been hitting keys randomly, but this is not the case. The mind and motions of a monkey are not random, they follow a pattern. Much like the roll of a dice, we might not be able to predict the outcome, but there is most certainly a pattern, and it is most certainly different from the pattern found in Shakespeare. If we were so inclined, we could observe and record the results of monkey typing on a massive scale and eventually produce some algorithm which would describe the most commonly used keys, key combinations and punctuation. For all we know, it’s possible that monkeys might detest pressing the Q key and avoid touching it at all costs, or maybe they would continuously press the Home key in a depressing attempt to communicate their longing for freedom.

Now let’s discuss the second type of event, which includes those things that might seem random, but are actually quite predictable. It is possible that rolling dice might belong in this category, for if we were watch the roll in slow-motion or merely increase the size of the dice, the outcome would be much more predictable. Also, rolling a dice on a smooth surface makes the process less complex and, thus, further from the unattainable state of randomness.

Benford’s law is another example of finding a predictable pattern where we would typically expect randomness. In 1881, Simon Newcomb, a bearded man, observed a peculiar statistical phenomenon. While spending a relaxing evening beside the fire, sipping a glass of wine and thumbing through logarithm books (as all of us do), Newcomb noticed that the pages which contained numbers that started with the number 1 were more worn than other pages. He then analyzed a variety of different data sources and found the same anomaly, but his discovery was largely ignored until it was verified years later by similar examinations of data.

Basically, Benford’s law says that if we examine data from almost any source, we will find a definitive pattern in the value of the first digit of those numbers. The most frequent number is 1, which is found to be the left-most digit in a staggering 30.1% of data values. The frequency of each number decreases as we approach 9, which appears as the first digit a mere 4.6% of the time. Benford’s law can be used to detect tax fraud, since forged numbers contain a more even distribution in first-digit frequency.

Unusual behavior is much easier to predict than a dice roll, for it can often be traced back to previous experiences, trends and habits. In fact, these events are not at all difficult to predict; they are merely unexpected. If we were to attempt to prove the existence of randomness by, for example, saying a random word, the word would be inevitably predictable. The process of choosing that word would merely be a brief expedition into the subconscious – nothing more. After blurting out the unchosen word, one would likely need only to probe recent memory to find its inception.

Go ahead, try to say something random.