What is the difference between a student and a teacher? A student, when willing, is an open vessel. Ready to embrace the things given to them, a student will take part in learning. Learning is not only accepting information, but also applying it in a way that will demonstrate that the information is true. If, this said student, cannot apply the information through trial and error, they will dismiss this information as false, or unnecessary. A student needs to experience to fully learn. A teacher, on the other hand, is the supplier. Teachers should have experience in the information they present to be true and believe it to be useful and measurable. Why then, are there teachers still being questioned by the students, about which they are unable to answer? Wouldn’t that mean that teachers are, in essence, still students as well? Let’s dig deep into why there is no difference between a student and a teacher, but only a group of students at different levels experiencing alongside one another that which they can find to be useful and measurable at the moment.

At 13 years old, Breanna walks into a class and is told to sit down and take out her workbook. The class, Math. The “teacher”, Mrs. K. Mrs. K goes on to demonstrate how while we don’t know exact probabilities in some cases, we can estimate them based on past history of events. Breanna thinks, well that leaves no room for change. Change is something Breanna is familiar with. When her mother and father fought everyday and then suddenly filed for divorce, the probability of them going on to fight another day was irrelevant. It had worked the same way, day in and day out for years, but based on experience, they stayed and found new battles for the upcoming days. In recent years, she hears that the probability of divorce is 50%. This is measured on the amount of reported divorces with variables like how old they were when they got married, how quickly they had children, whether they lived together before marriage or not. None of it was based on how frequently they yelled at one another. When Breanna’s parents both remarried and fought equally or similar with their new spouses, to the way they fought with one another, Breanna recognized the impending doom of the marriages and accepted right away that they would fail. But they didn’t. They stayed together. Despite the probability stating that second marriages are MORE likely to fail. So Breanna takes into account that people can change depending on willpower. She knew both parents were proud as well as stubborn so she recognized that their self preservation may be because of a resistance to look “unworthy” or “unlovable” to the other, therefore, tolerating the new battle rather than a flaw in their image. Where was the measurement for the probability in those qualities affecting the outcome?

Breanna spoke up and questioned her instructor. “If we all have calculators and can do fundamental math on them, why are we still being taught how to equate them mentally by hand?” Mrs. K said that the basis of all math is fundamental math and without learning it, one would not be able to apply the concepts of higher levels of math. Breanna did not agree. So she asked as many people as she possibly could the same question until she found an answer online (not the old school encyclopedias we used in previous years, thank you technology) which satisfied her. Dr. Math from the Drexel’s Math Forum, explained that “math is not really about learning probabilities, or fractions, or the use of algebraic equations. It is about learning ‘the art of problem reduction’.” Seeing an issue in front of you, which may be absolutely difficult and challenging, being able to disregard the solution and focus on breaking the problem down, is the essence of what is being taught through mathematical demonstration. Until the problem gets smaller, and smaller, and you’ve been able to find a solution which makes sense, the problem is still a problem. Learning problem solving skills is essential in life. Unfortunately because this concept is not being taught in math classes, or even known by math teachers, the concept is being negated. Fortunately for Breanna’s teacher, another teacher taught her how to research when you are unsure of something, so the next day Breanna was able to share with her adult student that math, in fact, was about learning problem reduction and solving skills, for all problems, not just the ones with numbers and figures.

What we have learned here with Breanna, is that the probability of an outcome is not always fixed dependent upon history if you factor in willpower. And that those who think they know all the answers, sometimes don’t. The probability  of adding a negative to a negative and equaling a negative is fixed, but subtracting a negative from a negative can equal a positive, and always equals less negative. You can just as easily add a positive to a negative, and end up with a positive if the positive is great enough.

Why don’t we recognize and do this in the world? In everyday life? In the way we treat our neighbors and friends, and enemies for that matter? Why don’t we value the proven probability of a negative and a negative equaling a negative? How many mathematicians and scientists need to prove theories for our governments and society to figure it out? How many people does it take for this to change to begin? Well, lets see… there are 7.4 billion people in the world today. Even if all 7.4 people are negative, 7.4-1=7,399,999,999, which is less than 7.4. It starts with just one. It can start with you.

Up until now, I have focused on the negative aspects of things happening around me and in me. I have highlighted their subtracting factors with my own.

From now on, I will focus on the positive. I will be positive in negative situations. I will be encouraging even when times are tough. I will be a small portion of what needs to happen, but without me, it will not, so I will stay positive. I will look toward the light and force myself to find the silver linings.