StudyBlog

“But when are we ACTUALLY going to use this?!”  As a tutor, I must hear that question at least once a week.  At some point, every student wonders why he or she is forced to study math.  They question the point of learning the esoteric topics our math classes have to offer.  The Pythagorean Theorem, Geometric Proofs, Trigonometry, and Integral Calculus – just to name a few – all raise the question, “Why should I bother with all this?”  As educators, our response usually wavers somewhere between feeble justification (“You’ll need math to… uh… you know… when you’re trying to figure out how much to tip your waiter… and stuff like that.”) and dismissal of the question altogether (“Stop wasting time and just do your work!”).  Clearly, even educators are not completely clear about why we study math.

Most of what we learn in math class – for that matter, most of what we learn in all our classes – is completely useless in real life. Take a moment to let that sink in.  The tutor – whose very livelihood depends on the importance on education – says that at least 90% of what we learned in school will never get utilized.  It’s true.  When was the last time you needed to know the exact time a train leaving Boston would pass into a train leaving Chicago?  When was the last time your were required to recite the names of the US Presidents in chronological order?  Or provide a detailed explanation of photosynthesis? Except for basic arithmetic, fractions, percents and proportions, the mathematics we learn in school has no place in real life.

What’s the point of spending so much time in a classroom if we’re never going to use any of what we learn there? The truth is that school isn’t just about learning reading, writing and ‘rithmetic.  Beyond the joy of learning for it’s own sake, the most important function of school, and therefore an educator’s biggest responsibility, is to train student’s minds.  We don’t study math to know how to determine the volume of a cone or the median age of the students in our classroom.  We study math to train our brain in logical thought and problem solving. Mathematical thought is purely logical thought; so mastering math is about mastering organized, rational thinking. Learning to count, memorizing multiplication tables, solving geometric proofs, and all the other tasks given to us by our math teachers coach our brains in how to follow a problem from its conception through it’s solution.  Math teaches us that even though we won’t always be able to see our way through an entire problem, we can still start with what we know, and go from there – and that this challenge can be rewarding, even fun.  I often compare approaching a difficult math problem to solving a jigsaw puzzle with many pieces.  What fun would the jigsaw puzzle be if, from the time we spilled the pieces out of the box, we automatically knew exactly where all the pieces should go?  What would be the fun in watching a mystery on TV if we knew whodunit from the very beginning?

So when do we use math in “real life”?   Yes, we use math to figure out how much to tip a waiter, to estimate the discount we’ll receive when buying that sweater on sale, to compute the mileage we get in our car, to figure out how to make a half recipe of cupcakes.  But we also use our math brain to figure out how to fit those last two suitcases into a car trunk that already has too much stuff in it.  We use logic (and therefore math) to figure out the best route to take home from work, given the traffic conditions.  Indeed, a training in math helps us every time we use our brains to solve a problem.

As AP Exam time grows nearer, I get quite a few calls from parents looking for help with preparing their son or daughter for the big test day.   Whether the student is preparing for Calculus, Physics, US History, or any of the 30 Advanced Placement subjects,  my first suggestion is always the same: Flashcards – good ol’ fashioned paper ones.  The truth is that whether you are a High School Senior getting ready for your AP Chemistry exam or a kindergartener learning the alphabet, flashcards are fun, economical and very effective.
There are all kinds of pre-made flash cards you can buy – for vocabulary, multiplication tables, ISEE preparation, anything you can imagine.  But honestly, you’re best bet is to make them yourself.  It’s cheaper, and the process of making the flashcards is a major part of the benefit from using them.  Even as you write out the cards, before you even have started “studying”, your brain is learning the material.  Keep the info on your flashcards “bite-sized” – never put more that a short sentence, or two on each. That way each card is easily understood with little more than a glance.
I always encourage students to be artistic when making flashcards.  Pictures can be drawn or taped onto the cards.  You can use different colored cards or pens.  You can even include sayings, poems or puns to help you remember.  Personalizing your flashcards will help each card to stand out, while making the learning process more fun and creative.
Once the cards are made, there are countless different ways to use them.  You can test yourself, or have someone else test you.  You can spread the cards out on the floor and pick them up as you master the information on each. You can mix all of your cards together, or separate the cards into categories and study one category at a time.  You can get together with your classmates, divide up the cards between you, and teach your pile to the rest of the group. The more ways you can find to use the cards, the better you will learn the information on them.
One of the great things about flashcards is their size.  A stack of 50 or so will fit into your pocket, and can go anywhere you do.  Anytime you have a spare minute, you can pull them out to review a few concepts.
The best thing about flashcards is that they will tell you exactly what you know, and exactly what you need to study. If you are sure of a concept, you can put the card aside.  If you don’t know the answer on the back within a few seconds, look over the card and put it back in the mix.  That way, you can reinforce the knowledge later.  As you get better and better, you can watch your pile of “known” cards grow, and easily measure your success.

Success in any area is found in the mastery of its most basic skills and concepts. Every NBA all-star had to learn to dribble a basketball perfectly. Every concert violinist playing in Carnegie Hall had to learn the proper way to hold a violin bow. The same is true for our school subjects. When we start with a new student, the first issue we scrutinize is basics. In English, that may be vocabulary or indentifying nouns, verbs and adjectives. In music, this could be a knowledge of scales or even the proper way to hold the instrument. Nowhere are the basics more important than in mathematics.
For example, when a student is having trouble grasping a concept like finding the roots of a quadratic equation (I’m sure you ALL remember how to do that, right?), I first look to the concepts of basic multiplication tables, and then an understanding of factors and multiples before trying to teach the more complex skill. If the student has mastered the basic concepts, I’ll know within a matter of minutes, and we can move on from there. But if they haven’t yet mastered the basics, then learning the more complex skill will become much harder to manage.
The key here lies in understanding the problem-solving process. Complex concepts are made up of smaller, simpler concepts (which are in-turn made up of even simpler ones). If a student is having trouble with one of these fundamental skills, it presents a stumbling block each time they need to use it in a larger context. Whether the student is using the skill incorrectly or simply has a moment of uncertainty or hesitation as they go through the process, this leads to more mistakes. More mistakes mean more uncertainty, which leads to more mistakes. Gone unchecked, this is the sort of thing that frustrates a student and, without the benefit of a little perspective, makes them feel that they are “just no good” at math. On the other hand, a student with a solid foundation in the basics is more comfortable with new and unfamiliar concepts. They are less likely to make mistakes. They trust that they can rely on their fundamental knowledge when they reach a place in a problem where they are unsure how to continue.
Will this solve every problem? Certainly not. But it’s a crucial first step in getting any child back on track in school. Time spent on the basics is always time well spent.

The StudyShop Blog is up and running! This blog is a place for students and parents alike to find the tools they need for a more successful education. It is a forum to ask questions and find answers. Here you’ll find practical advice and observation, based on years of educational experience and an enthusiastic commitment to children’s vital social and mental development. Welcome!