You're sitting in Geometry class staring at a monstrosity of lines when the following question comes out of your teacher's mouth in a language closely resembling Greek:
Line segment AB is parallel to line segment CD. Line segment EF is perpendicular to line segment CD. Line segment GH intersects both line segments AB and CD at points M and N, respectively. Solve for angles x, y, and z.
"Gesundheit," you reply. Your teacher looks you in the eye. Before you can go on to suggest some excellent throat lozenges, your teacher says, "Please come to the board and solve this problem for the class."
You take a deep breath and walk toward the board. Everything you just learned about angles rushes through your mind. "Complimentary angles add to ninety. Supplementary angles add to one-eighty..." your thoughts race as you grab the blue marker. The marker remains hovering above the board. "I... I don't know where to start," you stammer.
"What do you remember about opposite angles?" your teacher hints. You stare back at her and realize how dry your mouth has gotten when you reply, "Angles across intersecting lines are equal?"
"That's right!" she says and draws the following picture on the board:
"There's a relationship you missed," your teacher replies while picking up the green marker, "Let's redraw what we were given using the relationships described in the problem."
"Now what do you see?" she asks.
"Angle y equals forty," you say, starting to feel less flustered.
"Exactly!" your teacher explains, "We knew that line segments AB and CD were parallel. That means if they are intersected by the same line you can relate the angles. Now, let me show you something else using Angle Addition." She grabs a purple marker and writes quantities in some of the blank spaces.
You immediately see it. "Angle z equals twenty!" you exclaim.
"Can you explain it to the class?" your teacher asks.
"Well, angle y is opposite of angle z and the given angle. So you could write it like this," you say while you write the following equation: 40 = z + 20. "Solving for z, we find that z equals twenty degrees."
"Perfect!" your teacher smiles. "Just one unknown left."
On a roll you say, "Since line segment AB is a straight line we know that these top angles have to equal one-eighty. They are supplementary angles." You write on the board:
"So angle x is sixty degrees!" you say triumphantly.
"Well done!" says your teacher. "Class, do you see how redrawing the problem helps prevent yourself getting overwhelmed by a flurry of lines?"
"Does this only work for opposite angles?" a classmate asks.
"No, you can use this on any question. Check this out."
The class is buzzing. You smile because looking at all of those lines made you dizzy.
"Looking at the whole problem can sometimes distract you from the simple relationships," your teacher explains. "Try working through tonight's homework problems using this method. You may have to draw a few different simplifications before you find one that works, but don't give up! After enough practice you won't need to draw the simplifications, but they start to jump out at you."
So you're working hard on your physics homework and you go to check your answers. You notice the answer key has your same answer... But with the opposite sign. What's the deal with that? Gravity is always negative, isn't it? Positive gravity? Why?! How?! Well young physics student, you are forgetting a very important physics rule: always define your coordinate system!
Huh? What's that?
The coordinate system defines the cardinal directions of your problem. They are typically labelled as x, y, and z with the direction of the arrow indicating the positive direction. In your math courses you pretty much always see it like this:
However, in physics you are free to define the directions in anyway you see fit. This means you can define your coordinate system in such a way that the signs and numbers are simple. So you might end up with a coordinate systems like this:
Okay, but what does this have to do with positive gravity? Let's look at an example!
You are standing on a cliff and kick a ball off of it. It free falls for 8 seconds. How far has the ball fallen?
Some textbooks have a negative sign in front of the gravity term and make you memorize that it is for a specific coordinate system and that gravity is always positive, yada yada yada. I find it much easier to pay attention to your coordinate system and keep all the terms in the formula positive. Your numbers will work themselves out and makes you think about what's going on.
Good luck on the rest of your homework!
It is not unusual to be hyper focused on athletics in this country. We start children in competitive leagues at younger and younger ages. We buy them the latest equipment. We drive hours for them to play in tournaments for exposure to college recruiters. We enroll them in camps to learn from some of the best coaches. All of this isn't necessarily a bad thing. I played a lot of sports growing up and started playing softball competitively at thirteen. It taught me discipline, teamwork, sportsmanship, and countless other life lessons. That's why parents help their children get deeply involved in sports. Unfortunately, effort in school work doesn't always get the same level of attention. This is more of an accidental reality than a well-thought-out decision. Sports are an easy way for parent's to be involved in their children's lives. Pop culture capitalizes on the entertainment value, making sports an accessible form of entertainment the whole family can enjoy. We need to re-adjust our thinking so that sports and education are valued in a similar way.
My husband loves playing baseball. His dad is not very good at catch, but that never stopped them from playing together. His dad's lack of throwing abilities did not hinder my husband's ability, but it also didn't help him become better. That's why his dad paid for my husband to play in a league. There was a patient and knowledgable coach that taught the kids the rules of baseball and ran drills to improve their skills. A "tutor" is an educational "coach." They are proficient in the subject and work with your child to grasp the concept.
Sports doesn't stop with your YMCA league. High performance athletes seek a wide variety of help to step up their game. There are sports psychologists, physiotherapists, personal trainers, and nutritionists that assist the coach in shaping the athlete. Why do we expect school to be the be-all-end-all for our child's education? If an athlete has a prayer in making it big, they need a support system that helps them hone each aspect of their game. Think of a tutor as a necessary part of your child's support team. The teacher's do there best to educate your child, but there are a lot of children in the room. For some students they go too fast, for others they go too slow. That's where a tutor can go at the pace specifically needed for your child.
Professional athletes are not the only people that make a lot of money. Athletics are not the only form of scholarships. There are more high-paying careers and academic scholarships than there are positions on a professional sports team. Anyone with a child has worried about the costs of college tuition. In-state tuition at Kansas State University is estimated at just over $20,000 per year . That's $80,000 for a four year degree. Considering a university degree is a near necessity in today's job market, this potential $80,000 bill isn't outside of your horizon. But, you could get one year nearly paid for simply by having an ACT score of 30 and GPA of 3.6 . Not a bad return on investment if you spent $1000 on tutoring and got a $14,000 scholarship in return - and that's for a scholarship given simply by being eligible when you apply to university. Think of the others that have academic requirements that you apply for on the side.
It is easy to justify costs for our children's sports. It's an easy way for parents to spend time with their children. Popular culture idolizes athletes and often reports on their successes. Don't forget that education can be just as valuable to your child's growth and well-being. Similar to when you reach out to a coach to teach a sports-related skill, you may want to reach out to a tutor to help with their academic skills.
 "Tuition and Costs." Kansas State University, 29 Jul. 2016. Web. 12 Sept. 2016.
 "Scholarships." Kansas State University, 01 Sept. 2016. Web. 12 Sept. 2016.
"When life gives you lemons, make lemonade." We've heard this saying often. Some obstacles in life cannot be changed. Instead, you have to make the best of the situation. This is great advice, as long as the obstacle you face is truly unchangeable/unavoidable. Sometimes, we throw up our own roadblocks. These self-made roadblocks are built on a foundation of self-doubt and fear of failure. It gives us something to blame when we don't succeed. Don't waste your time building roadblocks, instead focus that effort on succeeding at what you are afraid of doing.
To tear down your self-made roadblock you need to figure out why you built it in the first place. Doubt fuels our insecurities and validates our excuses. Doubt plays a feedback loop of "you can't do that, so don't even try." In tenth grade, my math teacher (Mrs. R) went out on maternity leave. In Canada, maternity leave lasts a year. I had Mrs. R for math since seventh grade. I knew how she taught, how she tested, and with her math was easy. That all changed with the substitute (Mr. M). He didn't simplify the material like Mrs. R. She made it so easy to understand, why did he have to make it so difficult? Both the grades of my classmates and myself started to fall. I thought, "Why even try? It's obvious I'm having trouble because of him. He needs to change." I threw my hands up and blamed Mr. M for my problem. I started building a wall.
It was after yet another test and my grades slipping even lower, that I finally realized Mr. M wasn't going anywhere. I needed to change if I really wanted to get a good grade. That realization broke my cycle of blame and put the responsibility back on myself. After all, is it Mr. M's fault if I never tried to understand it for myself? No. He was at a different level than me and I wasn't trying to join him. Instead, I sat down and built a wall around myself, refusing to risk climbing to the next level and falling.
I started bringing my textbooks home - something I only did to complete homework problems. I read the chapters he covered. I re-wrote the notes and added my own thoughts based on what I had read in the textbook. The next test came back and... It was the grades I got with Mrs. R! It was well worth the effort. I started to really enjoy Mr. M's teaching. He pushed me to a deeper understanding and ultimately a deeper love of the learning process. It was the first time something in class didn't come easily. It was the first time I had to earn it - and it felt good.
After years of reflection, I realized I bogged myself down in believing that someone "naturally smart" should never struggle with a concept. That meant I was stupid, right? Not exactly. It meant I was pushing myself beyond what was comfortable. But, if I worked on building a bridge rather than building a wall, eventually I would cross the chasm and learn something new. This would lead to new land to discover and more chasms to cross. Learning was an adventure!
We all encounter that concept that stretches us further than we have ever been before. For some that's in elementary school, or high school, or even college! But eventually it happens. You come across something that you don't intuitively understand and your normal effort isn't enough to figure it out. Instead of building a wall, be thankful for an opportunity to push yourself and get to a new level of understanding. You will love the view!