How Watching Football Can Make You Better at Math

The other week my cousin posted on her Facebook page, "It's official we're switching from a man-to-man to a zone defense."  I saw the post and joyously commented congratulating them on their news.  Earlier that same day, my wife saw that same post and thought nothing of it.

I arrived home later that night and asked my wife if she had heard the exciting news.  Not knowing what I was talking about, I explained to her the nuances of the man-to-man and zone defenses in sports.  She then understood the news, my cousin was having her third child!

In my tutoring session the other day, I was reviewing an algebra test that my stuent had recently gotten back from his teacher.  The area that my student struggled with revolved around definitions.  I understood his problem, most of the time definitions in math textbooks are written in a language only a mathematician would understand.

Much like football lingo for my wife, these definitions meant nothing in the words of the textbook.   You need to think of the definitions in your own words and context.  For example, one of the definitions he got wrong referred to the associative property of equations.  We went back to the textbook and it said some garbage like,

"The grouping of the numbers to be added does not affect the sum. For example: (2 + 3) + 4 = 2 + (3 + 4). In general, this becomes (a ∗ b) ∗ c = a∗ (b ∗ c). This property is shared by most binary operations, but not subtraction or division or octonion multiplication"

Whoa, what in the world does that mean?

So we talked about it and came up with a definition that made sense to him.  He said if I had two bowls of fruit with four pieces of fruit in total.  It doesn't matter if I put an apple and orange, and a banana and pineapple in each bowl.  Or that I put an apple and pineapple, and an orange and banana in each bowl.  At the end of the day I still have one apple, one orange, one banana, and one pineapple.  I thought that was great.

Math isn't just about memorizing definitions and rules.  To understand something you must use the words, pictures, sounds, really anything that make sense to you.

You Should Never Get Inequalities Wrong

When doing graphs of inequalities, do you have trouble deciding whether to shade above or below the line?

Let me tell you something, you should never get the answer wrong.

These are so easy to check.  All you need to do is plug in the coordinates (0,0) into the equation for the x variable and the y variable.  This will help you with your shading.

If you plug in (0,0) into the equation and it works, then you know that (0,0) should be in the shaded portion.

If not, then it will be in the unshaded portion.

You will be right 100% of the time.

Units of What?

Units are so important in math because they are important in real life.  Does the answer to that problem equal 200 dollars or 200 cows?
Label your answers with units.

When Getting the Right Answer Isn't Right

It is always exciting to meet new students.  Oftentimes, the students are nervous about meeting me and to be honest, a lot of times I'm nervous about meeting them.  I always hope that our personalities click and we can get over any hurdles that seem too difficult to overcome.

The first lesson that I always start my sessions with involves form over substance.  I learned a while ago that getting the right answer is not always the right answer.

Showing your work is the key to unlocking the door of success in math.  Every time you do a problem you need to follow these steps:

1. Write down the problem.  Not part of the problem, but the whole problem.  This is always where you start.
2. Simplify the problem and each time you do write the simplified problem again.  This is where most people take short cuts in their heads.
3. Once you have the problem simplified as much as possible, circle, star, underline, or whatever you feel like doing to show this is your answer.
4. The final step is to check your work.  Do the problem again from the beginning and see if you get the same answer.  Test equations to see if they hold true.

Follow these steps and don't deviate, because sometimes the right answer isn't about being right, it's about how you get there.

You Struggle With Math Because of Your Approach

When you prepare for your algebra course, what is your approach?
With many of my students, questions that they have in algebra are not from lack of understanding of the concepts.
The frustrations that build are due to a lack of a good approach. The first change that I always have my students make is to write down every single step of a problem. Often we think that we can do parts of math problems in our heads.
While oftentimes we may be able to do problems in our head, many times we miss details that completely change the answer.
I hope this simple tip helps you in your course.

The Genius of Audacity

Seize this very minute; what you can do, or dream you can, begin it; Boldness has genius, power and magic in it. - Johann Wolfgang Von Goethe
This week in one of my tutoring sessions, I asked my student how often he raises his hand and answers questions in his math class. He responded to me and said, "There is one boy in my class who knows everything about math and he answers all of the questions." I was a little bothered by this because this boy really knows his stuff and he is being shoved out by another obviously bright student.
I remember those days of being afraid to participate for fear of being ridiculed for being wrong. Even as an adult, those thoughts and fears still creep into my mind from time to time. But when it happens I remind myself how people with a low tolerance for risk, whose behavior is guided by fear, have a low propensity for success.
Raise your hand, ask questions, be wrong, shine bright and be bold.

Start Writing

We all have that one friend who says, "I had the idea for eBay. If only I had acted on it, I'd be a billionaire!" That logic is pathetic and delusional. Having the idea for eBay has nothing to do with actually creating eBay. What you do is what matters, not what you think or say or plan.
Stanley Kubrick gave this advice to aspiring filmmakers: "Get hold of a camera and some film and make a movie of any kind at all." Kubrick knew that when you're new at something, you need to start creating. The most important thing is to begin. So grab your pencil, put it to the paper, and start writing.

Go To Sleep

Forgoing sleep is a bad idea. Sure, you get those extra hours of studying or writing right now, but you pay in spades later: You destroy your creativity, morale, and attitude.
Once in a while, you can pull an all-nighter if you fully understand the consequences. Just don't make it a habit. If it becomes a constant, the costs start to mount:
Stubbornness: When you're really tired, it always seems easier to plow down whatever bad path you happen to be on instead of reconsidering the route. The finish line is a constant mirage and you wind up walking in the desert way too long.
Lack of creativity: Creativity is one of the first things to go when you lose sleep. What distinguishes people who are ten times more effective than the norm is not that they work ten times as hard; it's that they use their creativity to come up with solutions that require one-tenth of the effort. Without sleep, you stop coming up with those one-tenth solutions.
Diminished morale: When your brain isn't firing on all cylinders, it loves to feed on less demanding tasks. Like checking your e-mail/Facebook/Twitter accounts, making meaningless lists, or aimlessly paging through your textbooks. When you're tired, you lose motivation to attack the big problems.
Irritability: Your ability to remain patient and tolerant is severely reduced when you're tired. If you encounter someone who's acting like a fool, there's a good chance that person is suffering from sleep deprivation. Frustration is the enemy of anyone who is having difficulty studying for a course.
These are just some of the costs you incur when not getting enough sleep. Yet some people still develop a masochistic sense of honor about sleep deprivation. They even brag about how tired they are. Don't be impressed. It'll come back to bite them in the butt.

Don't Copy

Sometimes copying can be part of the learning process, like when you see an art student replicating a painting in a museum or a drummer playing along to John Bonham's solo on Led Zeppelin's "Moby Dick". When you're a student, this sort of imitation can be a helpful tool on the path to discovering your own voice.
Unfortunately, copying is usually more nefarious. Maybe it's because of the copy-and-paste world we live in these days. It's too easy to steal someone's words, images, or thoughts instantly. And that means it's tempting to take shortcuts in your education by being a copycat.
That's a formula for failure, though. The problem with this sort of copying is it skips understanding--and understanding is how you grow. You have to understand why something works or why something is the way it is. When you just copy and paste, you miss that. You just repurpose the last layer instead of understanding all the layers underneath.
If you're a copycat, you can never keep up. You're always in a passive position. You never lead; you always follow. You give birth to something that's already behind the times--just a knockoff, an inferior version of the original. That's no way to live.
How do you know if you're copying someone? If someone else is doing the bulk of the work, you're copying. Be influenced, but don't steal.

Focus

Watch chef Gordon Ramsay's Kitchen Nightmares and you'll see a pattern. The menus at failing restaurants offer too many dishes. The owners think making every dish under the sun will broaden the appeal of the restaurant. Instead it makes for crappy food (and creates inventory headaches).
That's why Ramsay's first step is nearly always to trim the menu, usually from thirty-plus dishes to around ten. Think about that. Improving the current menu doesn't come first. Trimming it down comes first. Then he polishes what's left.
When studying for exam or preparing for a difficult course, the natural inclination is to throw more at the problem. More time, more books, more study guides. All that ends up doing is making the problem more daunting. The right way to go is the opposite direction: Cut back.
So do less. Your coursework won't suffer nearly as much as you fear. In fact, there's a good change it'll end up even better. You'll be forced to figure out the concepts that truly matter.