The pervasiveness of math

It is a sincere, meaningful, inquisitive, observant, pragmatic, and unbelievably common question that every math teacher will hear ad nauseum: “when are we ever going to use this in real life?” When kids or adults ask this very simple question, I embrace it.  I strive to be transparent about everything I teach, and as much as I love math, I recognize that certain careers and specific life trajectories do not involve the many pieces of math that we learn during our education.  That being said, math is truly enmeshed in most of life pursuits, more so than any other subject matter.  So, if your questions about the applications of math have been rebuffed, I encourage you to grab a small glass of milk and prepare yourself for a laconic essay on the applications of math.  If you would rather watch a four minute video on the topic, click the video below.

At the store

The wheels of commerce grind forward each and every day in stores across the globe.  Whenever you make a purchase for groceries, clothes, light fixtures, cameras, pajamas, or coffee, the basic principles of math are being used to manage and monitor cash flows. Every purchase requires a modicum of understanding of how budgets work and the affordability of items. While short-term decisions such as buying groceries may only require knowing how to count, add, subtract, and manipulate decimals, larger purchases of items like cars and homes requires knowledge of interest rates, amortization charts, and mortgage payments. A thorough understanding of these principles can help you save you a substantial amount of cash when you need to make such heavy purchases.

In nature and art

1, 1, 2, 3, 5, 8, 13 and so on ad infinitum.  Can you predict the next number in this infinite sequence?  For you math savvy folks who instantly pictured the number “21,” bravo. This famous series of numbers is called the Fibonacci Sequence.  Each successive number is calculated by adding the previous two numbers. While it is fun to attempt to decode this slightly mysterious pattern of enumeration, it is a profound arrangement of digits to say the least. This sequence is found in spades throughout nature. Objects like pineapples, sunflowers, nautilus shells, and pine cones (to name a few) all contain patterns that follow this lovely blueprint. The geometric concept of symmetry, which is the property an object possesses when a line can divide it into two mirror images, is a central component of the attraction equation.  Sometimes we look at something and consider it beautiful, while other times we find it unappealing. Why? Despite our belief that this is a subjective judgment based on personal preference alone, scientists and mathematicians alike have found a mathematical principle behind these judgments: symmetry. Symmetrical objects appear more attractive to us and draw our eyes towards them. Leonardo Da Vinci’s Vitruvian Man is an emblem of the perfect symmetry exemplified in the human body, a succinct explanation for why we as humans are drawn to one another.

In the Kitchen

Every cooking recipe involves whole numbers and fractions. Ingredients are always measured in particular units, and those units are then broken down into wholes and parts.  It is common to add a ½ tbsp of sugar, 2 cups of milk, a ¼ tbsp of butter, and 3 tsp of salt to whatever confection that floats your boat.  But to make that special dish taste truly delicious, you must measure those ratios and proportions correctly.  If you plan to work as a professional chef, the onus may one day be on you to perform conversion calculations in your head between gallons and liters, grams and ounces, or celsius and fahrenheit.

On the Road

Whenever you’re on the road, you must consider the rate of fuel consumption and the time it will take to get from Point A to Point B. When attempting to travel conscientiously, knowing your miles-per-gallon when fueling up ensures that you will make it to your destination without extra and unnecessary stops at a cost-efficient price point. Furthermore, calculations are constantly being made, either by you or a third party application, with regards to the time it will take you to drive to a particular destination. You must factor traffic, construction, and a variety of other components to be sure that you will be on time. Whether you use Google Maps, Apple Maps, Waze, or some other application, each must analyze several thousand routes, consider estimated driving time, and factor in general traffic trends as well as real-time data from users. These GPS technologies must perform calculations on the fly so that they can present alternate routes in an instant to get you to your final destination on time. Needless to say, none of this GPS awesomeness would be possible without math.


Three reasons why music matters for academic excellence

 

The importance of music programs in schools has been debated across the globe for decades. As budgets are trimmed and school music programs are cut, there is an ever-increasing need to answer the looming question: does music education matter? I believe that the answer is, unequivocally, yes.

From a personal standpoint, music immersion has had a massive impact on my life.  My introduction to music began when I chose to play the coronet at the age of 9.  After falling in love with the coronet, I then began playing the piano at age 11, strumming the guitar at age 18, and producing multi-track compositions on Pro Tools at the age of 21.  Creating and playing music opened a new dimension in my life that enabled the satisfaction of a creative side that I barely knew existed. It not only made it possible for me to explore a brand new interest, but it ended up having unbounded relevance to what I do now. Because my parents allowed me to develop such a deep love for music composition, I am able to blend that skill set into all of my education related video content today. While some may have considered my love of music composition a potential waste of time and distraction from more relevant pursuits, I am happy to report that it is one component of my tool set that never seems to relent with respect to offering utility.  For parents who are contemplating whether or not to introduce their children to music, my advice is to let them give it a shot. If they don’t enjoy it, so be it, but if it ends being a fit, there are a plethora of amazing reasons to nurture the love of music.

1. Music develops and refines interpersonal skills

Music classes teach students valuable skills that can be applied outside of the music room. One critical feature of the study of music is the obligation to perform.  Whether it’s a piano recital, an orchestral performance, or an open mic debut, music participation requires a student to eventually stand up in front of an audience and perform.  While this can be a terrifying and difficult experience, it is essential for growth and development.  Students must deal with stage fright and learn how to cope with performance anxiety. Adults who neglect to address this fear at an early age can suffer crippling anxiety that can make it difficult to pursue careers that require regular public speaking.  

Another major benefit of music participation is that students get the opportunity to become a part of a positive organization. Joining a string quartet, orchestra, or rock band can give students an unparalleled opportunity to meet new people that share similar interests. This opportunity for interaction can strengthen a child’s social skills by providing a solid environment for the development of social bonds.  

2. Exposure to music helps children achieve success in academia

Several studies have been conducted regarding the positive relationship between music and academics. A Harvard study revealed that music training in children results in long-term enhancements of visual-spatial, verbal, and mathematical performance. Specifically, math and reading are improved by the processes of (1) learning rhythms and (2) decoding the notes and symbols in sheet music. Another study conducted by the College Board showed that students with music training produced scores that were higher than non-music students by over 60 points on the verbal section and 43 points on the math section. Even if music instruction stops, studies reveal that early music exposure will have a lasting and positive effect on the adult brain. Interestingly, adult musicians with age-related hearing loss can detect speech in noise more accurately than a non-musicians without hearing loss because music training has made their brains more adept at processing sound.

3. Brain activity is heightened via music immersion

Playing a piece of music requires the use of the auditory, visual, motor, and emotional centers of the brain. According to Dr. Norman Weinberger, research professor of neurobiology and behavior at the University of California at Irvine, brain scans show that there is more activity in the brain during a musical performance than there is during most other activities. This increased activity helps to shape the brain itself. The most pronounced enhancements in brain structure are visible in those who began music education early in childhood.


Academics and athletics: a confluence of positivity

During primary school and beyond, students often gravitate towards others who share similar passions and interests.  While finding individuals with shared passions is a terrific way to form strong friendships, there seems to be an assumed bifurcation that forms arbitrary lines based on the love of sports. Those with athletic proclivities seem to join together, while academically centered children form their own social circles. It seems so black and white, as if you must choose one or the other. But that is simply not the case. There is no reason why a straight-A student cannot be a dedicated and successful athlete. It is absolutely possible to excel at both sports and academics, and attempting to do so will bring students great balance and mental focus.

The pervasive benefits of athletics

First and foremost, playing sports in school helps students deal with the stresses of the school day. After a long day, it is difficult for a child to immediately jump into homework. As a result, many students will try and relax temporarily by playing video games or watching television. While these mini mental vacations provide some much needed down time, they are not the healthiest options when done on a regular basis. Sports, on the other hand, provide students with positive a way to refresh their minds from the long school day in a manner that is healthy and enjoyable. Physical activity does not only bolster cardiovascular health, but it can drop cortisol levels, reducing feelings of stress and anxiety. Furthermore, students can learn valuable life skills from sports, such as time management, mental fortitude, discipline, dedication, and camaraderie.

Another educational element of sports is learning how to lose. No one can win all the time, no matter how skilled or athletic a person is.  Accordingly, athletes must quickly get used to the fact that losing is part and parcel of the process. When framed the right way, students can recognize that failure is in fact something positive.  For example, if a basketball player ends up turning the ball over a number of times during a game, he knows what he needs to work on in practice: dribbling fundamentals. A game time failure in this area shines light on a deficiency and shows precisely what needs to be remedied.  There is no amount of self-analysis and introspection that can equate the amount of value that can be gleaned from a real-time failure.  

The same type of learning lessons are ripe for the plucking in the academic arena. Whenever a student does poorly on an assignment or test, it is a golden opportunity to grow.  I regularly see students bemoan a poor performance, considering it an indication of their inadequacy.  Instead, it is simply sign showing what needs to be strengthened.  Students can workout their brains and habits the same way an athlete can ameliorate certain athletic abilities through practice.  When a student makes a mistake, he can critique his study habits and try to see what needs improvement.

Sports also teach athletes how to deal with disappointment despite excellent preparation. In swimming, for example, a hundredth of a second can determine whether or not a swimmer qualifies for state level competition. At the regionals meet, there are many swimmers who come extremely close to qualifying, but end up falling short because of tiny fragment of time. These swimmers recognize that they are excellent athletes with amazing track records despite losing a race.  While this type of an outcome may be hard to swallow, it forces students to disconnect a poor performance from their self-concept. Translation: failure at something does not change the way they view themselves.  They learn to appreciate the process of preparation.  Instead of having an outcome based viewpoint, they train their minds to focus on the positive externalities of athletic competition.  As such, most swimmers learn to handle disappointment very well, both in the pool as well as the classroom. Student-athletes realize that a poor grade on an assignment does not reflect who they are as a person.

Finally, one of the best and most obvious learning lessons that regular participation in sports provides is how to balance a packed schedule.  When students have an academically challenging course load and a heavy practice schedule, there is little time that can be wasted. Students must carefully evaluate their daily schedules and find a way to accommodate both athletics and academics. Interestingly enough, it seems students with extremely busy schedules end up studying more and doing better in school than their counterparts.  According to Angela Lumpkin, a professor of health, sport, and exercise sciences at the University of Kansas, “the lessons learned in athletics, combined with the knowledge that they must do well in school to participate, improves students’ persistence and chances for success.”

Is there an optimal sport?

Parents often want to know the best sport to cultivate good habits, social skills, and strong time management abilities so that they can encourage their children accordingly.  To me, however, directing a child towards a preselected sport is the wrong approach.  I believe that sports, like most endeavors in life, should be pursued out of love.  Sport are meant to be fun, and if athletic participation is borne out of obligation, then a child will be unable to develop intrinsic motivation.  This will likely diminish any chances of long-term athletic commitment, making the entire endeavor less fruitful.  Whether a child wants to play golf, tennis, basketball, badminton, or ping pong, I encourage parents to simply be supportive.  As my favorite saying goes, “follow your bliss.”  


Five Tips To Keep Young Students Attentive And Engaged

Working with high school students is very straightforward. Kids in their mid to late teens are often focused and self-motivated to learn and perform. They are thinking about college and beyond, and usually have some goals in mind that they would like to achieve. Young children, however, are not as determined to plow through hours of mathematical tutelage as their older counterparts. They are substantially more disconnected from the real world and career ambitions. What usually occupies their minds on a regular basis is playing sports with their friends, video games, and sleepovers. In a word, their lives are primarily centered around “having fun.” And that’s a beautiful thing. In fact, I do what I do on a daily basis because I love having fun. It just so happens that my version of fun is teaching math.

Because younger children are carefree, unencumbered by concerns of college admissions and career goals, it can be a challenge to command their attention. But after working with countless fourth, fifth, and sixth graders in both group and one-on-one settings, I have developed an understanding of how to engage these young minds. Not only do my students work with me at a stellar pace, but they are excited for our sessions. They actually look forward to learning about math! And to be honest, I wouldn’t want it any other way. I have fun when I teach, and I want my students to feel the same way.

The secret to my tutoring success is that I bring more to the table than math education. I don’t look at my sessions as standard lessons; they are multifaceted interactions. They are play-dates, discussions, comedy shows, pep talks, and explanations all rolled into one. Because I’ve been able to successfully implement these components into my lessons, I’ve received rave reviews from both my students and their respective parents. Now, a great deal of this magic formula comes naturally to me. My personality and general nature inclines me to take on this varied role. I like talking and having fun with my students. As such, in order to pass on advice to other teachers, I had to sit down and think critically about precisely what I have been doing that works so well. After a bit of reflection, I have boiled down my formula to the following five tips:

  1. Always Maintain A High Level Positivity – when working with kids, never let your positive attitude wane. It doesn’t matter if you’ve had a rough week or got no sleep the night before. When you walk in those doors, it’s game time. You must put on a super happy and positive face. If you’re not positive, your kids will follow your example. This basic tenet is derived from our understanding of mirror neurons. Mirror neurons are the pieces of our brain that make us yawn from other yawns, frown when we encounter third party sadness, and smile when we are around jovial individuals. Essentially, people often mimic the mood and body language of those around them. If you are hunched over and overtly depressed, your kids will mirror that vibe. If, however, you smile and stay super positive throughout the lesson, your students will be much more likely to remain happy and eager to learn.
  2. Keep Energy Levels At A Maximum – think about tutoring kids as part education, part entertainment. If your lesson begins to drag, your students will rest their heads on their hands and gradually zone out. Not an ideal mind frame for optimal knowledge absorption. Your goal should be to keep your kids active and engaged. Instead of allowing yourself to drift into a monotonous tone, speak with power and inflection. Use hand gestures whenever possible. If you keep your energy levels high, your kids will be energized as well.
  3. Show Excitement For The Subject – when you sit down to teach children, you are asking them to give you their undivided attention. This whole process is much easier if your students are actually excited about the subject matter. The first step in engendering excitement is showing your own enthusiasm. After all, if you’re not thrilled to be going through math problems, how can you expect your students to be? Get excited and broadcast it.
  4. Intersperse The Lesson With Fun Conversations – for kids who are 9 through 11 years old, you need to keep the session lively. You can certainly accomplish a great deal of this with a positive attitude, loads of energy, and a healthy dose of enthusiasm. But those components alone will not carry the day. You need to connect with your kids. Accordingly, you need to take inventory of their interests. As the lesson rolls forward, take the time to bring up their topics of interest and engage them in a fun and interesting conversation. It will break up the lesson and rein in students who are potentially dozing off in the middle of the lesson. For example, some of my students share my interests in science, particularly astronomy.   For them, I always make sure to mention any cool documentaries I have seen recently, and routinely ask about the latest fun facts that they have learned.
  5. Joke Around – everybody likes to have fun. One of the most common ways that people bond and have fun is by joking around. Inject your lessons with jokes and humor whenever possible. Not only will this bring life into the session, but it will help forge the bond between you and your students. Once they see you as more than just a tutor, you will truly be able to make a solid impact on their education.

SAT Prep - Tackling Tough Math Questions

Nailing an 800 on the math portion of the SAT can be a tricky feat, even if you are steadfastly familiar with all of the requisite formulas and rules. A difficult problem can overwhelm even the most prepared individual come test day. Time constraints, test surroundings, and the overall weight of the exam can unnerve the most grounded students.

So what do you do when panic strikes and your mind draws a blank? How do you re-center yourself and charge forward with ferocity and confidence? What you do is this: write everything down from the problem. This is the most important part of the problem solving process. As you peruse the question, write down the pertinent data and establish relationships by setting up equations. This exercise will help you see solutions that were previously difficult to decipher.

As you work on practice tests and sample problems, you must work diligently to form a solid habit of writing down important bits of information as you plow through the SAT math section. To give you an example of what it means to “write everything down from the problem,” I will explore the following three math questions in great detail. These in-depth explanations will give you an idea of what should be going through your brain every time you see a math problem. With practice, these thoughts and processes will manifest faster and faster until solving problems in this fashion becomes a reflexive response.


  1. The average of 4 different integers is 75. If the largest integer is 90, what is the least possible value of the smallest integer?

  a. 1

  b. 19

  c. 29

  d. 30

  e. 33


Right off the bat, the problem states that we have four different integers. We can begin the problem by creating variables to represent the four integers:

W     X       Y       Z

We also know that the average of the integers is 75. This means that we can set up another equation based on this relationship:

(W + X + Y + Z)/4 = 75

Isolating the variables, we get:

W + X + Y + Z = 300

We also know that the largest integer is 90. So:

W + X + Y + 90 = 300

The question then asks “what is the least possible value of the smallest integer?” This detail is a bit tricky to interpret, but we can reason this out fairly quickly. To get the smallest possible number, what needs to be true about the other two integers? They need to be as large as possible. Since 90 is the highest value for the integers, it makes sense to assign the other two variables to 90, right?

Not so fast. If we read the question carefully, it says that there are “four different integers.” This restricts us from using 90 for the other two values. Instead, we must use 89 and 88. We now have an equation to represent the four integers (where W = the smallest integer):

W + 88 + 89 + 90 = 300

Solving algebraically, we get:

W + 267 = 300

W = 33

Therefore, the final answer is e.


  1. Solution X is 10 percent alcohol by volume, and solution Y is 30 percent alcohol by volume. How many milliliters of solution Y must be added to 200 milliliters of solution X to create a solution that is 25 percent alcohol by volume?

  a. 250/3

  b. 500/3

  c. 400

  d. 480

  e. 600


Let’s start writing down the relevant information:

.1X = AX

.3Y = AY

The above equations denote the amount of alcohol given a certain number of milliliters of solution (where AX = alcohol for X, AY = alcohol for Y, X = milliliters of solution X, and Y = milliliters of solution Y). The next part of the question asks how many milliliters of Y must be added to 200 milliliters of X to create a solution that is 25% alcohol? To answer this, we can represent the facts as an equation:

.3Y + .1X = .25(X + Y)

Once again, we have a two variable equation. Translation: we cannot solve it. But, we have a value for X: 200. So, plugging in 200 for X, we get the equation down to one variable:

.3(Y) + .1(200) = .25(Y + 200)

Perfect. Solving for Y algebraically, we get:

.3Y + 20 = .25Y + 50

.3Y - .25Y = 50 – 20

.05Y = 30

Y = 600

Therefore, the answer is e.


  1. On a certain multiple-choice test, 9 points are awarded for each correct answer, and 7 points are deducted for each incorrect or unanswered question. Sally received a total score of 0 points on the test. If the test has fewer than 30 questions, how many questions are on the test?

  a. Cannot be determined

  b. 16

  c. 19

  d. 21

  e. 24


The first step is to write down what we know and assign variables:

+9 points = correct (X)

-7 points = incorrect (Y)

Sally scored a total of 0 points

We can set up an equation with this information:

9X – 7Y = 0

Since we have two variables, this is not a solvable problem. Unfortunately, we do not have another relationship that we can reference to simplify this further. What can we do in this situation? When all else fails, try to isolate the variables:

9X = 7Y

X/Y = 7/9

What this tells you is that the ratio of questions answered correctly and incorrectly must be 7 correct (X) to 9 incorrect (Y). This is very useful information. According to this ratio, the number of questions on the test must be some multiple of 16 (so that the 7 to 9 ratio can be preserved). For example, 7 right and 9 wrong would work, as would 14 right and 18 wrong.

Now comes the critical piece of information: the total number of questions must be less than 30. With this helpful tidbit, the only possibly choice is 16 questions.

Therefore, the answer is b.


How Many Practice SATs Should You Take?

Practice is the key to SAT mastery. No matter what preparatory course you take, what tutor you hire, or what study guides you purchase, all of your resources are for naught if you don’t devote significant time and effort towards practice exams.

Knocking out a healthy load of practice tests is particularly important for standardized exams. Why? Because standardization means that the test makers (a.k.a. the College Board) are bound by an obligatory adherence to consistency. As such, from year to year, while the precise questions vary, the core subjects and concepts are constant. Moreover, the style of questions is uniform. Translation: the more questions you see, the fewer curve balls can be hurled your way. With enough practice, you can familiarize yourself with the majority of possible question types, which will (1) improve your test taking abilities and (2) bolster your confidence come test day.

Another reason why practice tests are so important is that they are excellent learning tools. It’s one thing to know a concept, but it’s another thing entirely to put that concept into use. The more practice you get, the more comfortable you will be with the material. Additionally, if you are diligent with your post-practice test review of missed questions, you can effectively fill in knowledge gaps in a very targeted and efficient manner.

Point made: practice tests are extremely important. But how many should you take? What is the magic number to achieve SAT stardom?

Stop. Hold up. Before you read any further, recognize that results can vary wildly depending on education level, familiarity with the tested concepts, and overall test taking abilities. There might be some standardized test wunderkinds who can nail down stellar scores with little to no practice. Alternatively, some students may need to rack up a hefty number of practice tests before their scores begin to climb. So, this is a highly nuanced question. But if I were pressed to give general advice without a proper consultation or additional information, I would err on the side of excess. Basically, I would suggest taking as many as humanly possible.

Now, if you insist on pinning me down for a precise number, here it is: 15. That’s right, 15 practices tests is my minimum number. I took 15 practice SATs when I was a high school student, and if you plan right, you can do it too. And I didn’t take 15 tests while watching TV and eating ice cream. Nope. Instead, I replicated exam center conditions each and every time I sat down to take a test. Plus, I graded each one promptly and read through the answer explanations for all of my missed questions.

I've read a number of test prep sites that recommend taking four or five practice SATs during the course of preparation.  If you are sincerely shooting for excellence, this simply will not do you justice.  The reason why 15 is such a powerful and practical number is because it is around this point where you truly hit your stride.  I can't precisely explain why, I can only tell you that I've witnessed it over and over again.  The tipping point generally occurs for students somewhere around the ninth or tenth test.  It is at this mark of progress that students begin to feel at ease with the test format.  After this point is reached, the remaining tests firm up any lingering weak spots and forge a stable and confident mindset.  It simply works.

If you have additional time to prepare for the SAT, I would push for even more practice tests. Say, for example, that you’re studying over the summer. In that case, I recommend squeezing in 25-30 exams. That’s approximately one every three days.

If you want to practice like a champion but don’t know where to locate the practice tests, there is an abundance of resources that can provide you with the requisite material. Below are four study guides that contain high quality practice SATs.

  1.  The Official SAT Study Guide – this book comes with an overview of each subject along with 10 full-length practice tests. These are the best tests you will find because they are authentic SAT exams.
  2.  Gruber’s Complete SAT Guide – this guide has five full-length tests along with strategies and key vocabulary words.
  3.  11 Practice Tests For The SAT – this book has a lot of practice problems that are really good representations of what you will find on the real test. It actually only contains 10 SATs (as one of the 11 practice tests is a PSAT).
  4.  Barron’s SAT – this book comes packed with a high quality diagnostic plus five full-length SATs.

The Habit Of Reading: Why It's Important And How To Develop It

Of all the important academic exercises, none are as critical to your success as routine reading. Throughout your education, teachers will assign mounds of textbook reading in social studies, English, the sciences, and beyond. While it is imperative that you take your assignments seriously and blast through your requisite reading, that is simply the bare minimum. Your eventual goal should be to read as a pastime. Reading shouldn’t solely be an activity guided by obligation, but one prompted by an organic desire.

You all know what it’s like to be driven by desire. It’s all encompassing, automatic, and thoughtless. For example, some of you likely possess a powerful sweet tooth, causing you to gravitate towards cookies and chocolates whenever there is an opportunity to indulge. Others are might be fans of video games, eager to squeeze in playtime whenever and wherever possible. The interesting thing about these activities is that you don’t need to actively tell yourself to play video games or eat chocolate; your body naturally pushes you towards those activities. These subconscious desires and urges to perform certain activities or routines are what are known as “habits.”

Habit Formation

Habits can come in two broad categories: good habits and bad habits. A few examples of good habits are (1) regular exercise routines, (2) diligent homework completion, and (3) well oiled cleaning rituals. Bad habits are things like (1) biting your nails, (2) eating junk food on a regular basis, (3) and playing four hours of video games per day. Habits, both good and bad, are formed the same exact way: via a feedback loop. It works like this: when you try an activity, it will either cause you pleasure or pain. Your brain then links that activity with the particular feedback.

Once the activity and pleasurable feedback are linked, your brain has formed a habit. But you don’t start engaging in that activity non-stop as soon as the relationship is formed; what then prompts the activity is what is called a “cue.” A cue is any sensory input that reminds your brain of the embedded activity. For example, a cue for junk food might be the smell of a candy bar or the sighting of a candy wrapper. Once you receive the right cue, your brain will create a response based on the associated feeling. If pleasure was associated with this activity, your brain will generate a craving or desire to partake. That craving is the feeling you get when you really want to eat a chocolate bar. In sum, the basic cycle is “cue -> action -> reward.”

The Benefits Of Regular Reading

So why have I gone through the trouble of explaining the mechanism behind habit formation? Because the goal of any ambitious young person should be to create a soundly ingrained habit of reading. Why? The benefits of reading are innumerable. First, regular reading is the surest way to boost your vocabulary. Reading different words in various contexts multiple times is the best way to learn their meanings and correct usage. Over a lengthy period of time, this method of learning words is far superior to rote memorization because it is more likely to engage the visual parts of your brain.

Second, reading will naturally bolster your writing ability. At the end of the day, learning to write is a very complex process. The English language has numerous idiosyncrasies and bizarre rules that are very difficult to master. But with enough reading, you will be able to learn these rules and nuances by osmosis. You will naturally develop a feel for what looks right. You will subconsciously know that a comma is out of place or that a period needs to be deployed to break up a lengthy sentence.

Finally, reading will massively boost your ability to… well, read. Reading is the fastest way for any person to absorb new information. That is why it is a staple of all educational disciplines. Most people speak at approximately 100-125 words per minute, whereas the average reading speed is around 300 words per minute. That’s nearly three times more information via reading than listening to a lecture. Until scientists invent a way to upload information directly into our brains, reading is the optimal delivery vehicle for knowledge. The more you read, the faster and more efficient you will become.

How To Build A Habit Of Reading

Point made: reading is really important. But how exactly do you build in this habit of routine reading? Here’s how.

My first piece of advice is this: “follow your bliss.” This philosophically charged phrase was coined by Joseph Campbell, a famed scholar with an unbridled passion for the humanities. It’s simple, elegant, and spot on advice for all walks of life. In essence, it is a straightforward directive to do what warms your heart and makes you happy. Translation: if you like science fiction, read science fiction. If you like fashion, read about fashion. Simply take inventory of your passions and choose books accordingly. This will make reading fun, and when things are fun, you tend do them more frequently.

My second piece of advice is to create a reward system in order to forge a strong habit. Remember the “cue -> activity -> reward” progression? The idea is to take advantage of this mechanism and use it to build a positive habit. It’s all about inserting the right rewards for the right activities over and over until the habit has been formed. For example, every time you read for 30 minutes straight, give yourself a quick reward. This could be a brief intermission to play a favorite video game on your iPhone, or a few bites of your favorite food. The idea is to associate a reward with the activity of reading.

Once you put the reward in place, the cue (which is anything that makes you think about reading) will eventually trigger a craving to read. Once this habit is hardwired into your brain, you will naturally want to read in your spare time. It won’t be a task that you will have to force upon yourself; instead, you will do it of your own volition. If you can reach this point, you will be well on your way to achieving academic excellence.


Preventing Silly Mistakes On The SAT And ACT

The “silly mistake” is quite possibly the most mischievous and irksome of the math demons.  It is a sly beast that lurks in the deepest recesses of your mind, emerging only periodically to sully your scores in a most disturbing way.  Because of its crafty nature, it is able to lull you into the false belief that your thorough understanding of mathematic concepts will keep you safe from its clutches.  But, as I’m sure you know, “silly mistakes” afflict even the most soundly prepared students.

What exactly constitutes a “silly mistake?”  Here are some common examples for standardized tests:

  • Misreading the question (or failing to read the entire instructions)
  • Filling in the wrong bubble on your answer sheet
  • Making a slight arithmetic error
  • Incorrectly copying down the original problem
  • Turning a negative number into a positive number (or vice versa)

I don’t care who you are, what your educational background is, or where you go to school… you have been a victim of “silly mistakes” at one time or another.  The whole fiasco probably went down like this: you whizzed through an exam with utter confidence, only to receive a shocking and confusing grade. Why?  Because you missed several questions that you were sure you had answered correctly.  You glossed over some inane details that ended up costing you a slew of points despite your clear understanding of the concepts.

When it comes to standardized tests like the ACT and SAT, silly mistakes are just as costly as any deep conceptual misconstruing.  Accordingly, it is imperative that you devote substantial resources to ensure that these mistakes are weeded out.

At the end of the day, extricating these little demons comes down to a few core principles and strategies. Here are five quick tips on how to tackle these nuisances once and for all.

  1. Read Each Question Prompt Carefully - the most common source of errors is the misreading of test questions.  When time constraints are a factor, you will likely be racing the clock, pushing your reading pace to its limits.  While speedy reading is important, you must figure out where to draw the line between speed and accuracy.  My advice is to read each question prompt slowly and carefully before jumping to the answers.  If time warrants, I would take two passes through the prompt.  The more certain you are of the actual contents of the question, the far less likely you will be to make a mistake.
  2. Write Clearly And Neatly  - As you work through problems on the mathematics section, you will be writing down notes and equations as you make your calculations.  If you tend to write in a jumbled fashion, you will be setting yourself up for disaster.  You need things to flow clearly and neatly from step to step so that you are able to properly decipher the right answer.  A few tips for writing clearly are to (a) always write in straight lines, (b) progress downwards as you move forward with your work, (c) use clear handwriting, and (d) don’t write too small.  The most important factor to developing a solid habit of writing clearly and neatly is to practice.  As such, make the extra effort to keep your daily homework neat and organized.
  3. Master Time Management – as time begins to run out, you are more likely to make mistakes. Why?  Because your speed will increase along with your anxiety, making you much more error prone.  To counteract this natural tendency, make sure that your time management skills have been properly honed.  The only way to accomplish that is to include many timed practice exams before the actual test.  During the timed practice exams, keep an eye on where you are and how much time is left. The SAT math section, for example, has 54 questions that must be completed in 70 minutes.  As you are going through the test, you can see how many problems you have finished at the 17.5-minute mark.  Then, at the halfway mark, you can check your progress again.  Keep in mind that you should ideally be more than halfway through the math section at 35 minutes because the math questions increase in difficulty as you move forward.
  4. Verify The Question Number In Your Test Booklet Before Filling In Your Answer Sheet – there is nothing more frustrating than getting a question wrong because of a misplaced answer.  But the solution to this problem is quite simple.  All you need to do is get in the habit of verifying the question number each and every time.  Most kids get accustomed to deriving and answer and then filling in the next empty row of bubbles on the answer sheet.  That method can get you into trouble if you inadvertently skip a question.  To be safe, always verify the question number. 
  5. Practice, Practice, Practice – the more exams you take, the less likely you will be to misread or miscalculate something.  Every error on a practice test is a terrific learning opportunity.  Those mistakes will be etched in your brain as constant reminders of what not to do in the future.  The more of these practice tests that you rack up, the less likely you are to make mistakes on the real exam.  Moreover, getting in substantial practice will calm your nerves come test day.  Less anxiety = better overall performance.

ACT Prep - The Friday Before Test Day

For those of you taking the ACT in the next couple days, your fastidious and dedicated preparation routine is coming to an end. Whether you studied five hours a day for three months, two hours a day for one month, or merely crammed the last week and a half, it doesn’t matter anymore. All of that is immaterial now. Close your eyes, take a deep breath, and exhale. Release any lingering rumination about what you could have done, should have done, or might have altered within your study routine. Let. It. Go. It’s nearly game time, and the only thing left for you to do is get yourself ready for the big test.

Over the years, I’ve worked with a number of students preparing for both the SAT and the ACT. For some reason, I routinely encounter students possessed by the urge to study relentlessly the day before the test. This is NOT advisable for a number of reasons. First and foremost, the likelihood that you will absorb anything of value that close to the test day is slim to none. Second, cramming the day before will likely shake your confidence. You will be hypersensitive and overly critical; therefore, any mistakes or unfamiliar material might send you into a tailspin.

Third, your brain, like every muscle in your body, needs to rest.  A vigorous workout of practice problems will impede its ability to function at a high caliber come test day. Finally, studying the night before can make it difficult to fall asleep. If you are not well rested, you will be shooting yourself in the foot before the test even begins.

To make sure that you give yourself the best chance possible for success, I have prepared a chronologically ordered “to do” list for those of you who are about to take the ACT. I wish you all the best of luck.

Friday before the exam

4 PM – Review the following checklist to ensure that you are completely ready for the test

  • Photo ID – ensure that you have a valid photo ID
  • Admission ticket – print out your admission ticket
  • Three #2 pencils and erasers – you will need backups in case one or two break
  • Calculator with fresh batteries
  • Watch – make sure that it is an approved device that does not make any noise
  • Test center location – look up the location of the test center as well as the entrance on test day
  • Set your alarm

5 PM - Exercise

If you like to play basketball, go shoot some hoops with your friends. If soccer is your thing, then kick a ball around for an hour. A solid workout will boost your serotonin levels and reduce your stress. It will kick up your metabolism while tiring out your body, ensuring that you are able to get a solid night’s rest.

6 PM – Eat a healthy but filling dinner

Nutritionists recommend eating lean meats (such as fish or chicken) along with a healthy portion of green vegetables the night before an exam.  Personally, I like eating a sesame based fish stir-fry with broccoli, bean sprouts, mushrooms, and onions.

7 PM – Do something fun and relaxing

If you love to read, curl up with your favorite book. If you are a cinephile, I recommend watching a great movie. A quick word of caution: don’t dive into something new or overly exciting. An intriguing movie or captivating novel could potentially spike your adrenaline making it harder for you to fall asleep. Choose something that you are already familiar with.

9 PM – Go to sleep

Enough said.

Saturday, ACT test day

6-7 AM – Breakfast

Depending on the length of your commute, you should wake up early enough to have a nice and relaxing breakfast. Nutritionists recommend a combination of eggs, oatmeal, and fresh fruit. You should try to avoid overly sweet items or caffeinated beverages as they can cause drastic energy swings, potentially leaving you susceptible to a mid-test crash. If, however, you are accustomed to always taking exams after a cup of coffee, I recommend that you stick to your test taking routine.

7:30 AM – Arrive at test center

You are required to arrive at your test center no later than 8:00 am. Should you be arriving at 7:50? Maybe 7:55? No. You do not want to leave anything to chance on test day. Give yourself an adequate cushion so that you will most definitely be on time. Moreover, a tight timeframe will stress you out. This added anxiety is not only emotionally disruptive, but it can lead to an energy crash later in the test day.

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One last piece of advice: do not talk about the exam to anyone during the breaks. Sometimes students are tempted to compare responses in an effort to verify their answers on previous sections. This is a completely counterproductive activity. It can potentially shake your confidence and derail your progress for whatever sections remain.


The Power Of Willpower: Five Tips To Strengthen Your Discipline

Willpower is unique to humanity.  It is the keystone characteristic that is directly responsible for our technological advancement over the last several hundred thousand years.  Willpower can be defined as the capacity to restrain our impulses and resist temptation in order to maximize our long-term success.  It is the expulsion of energy to fight off innate survival based urges to exponentially increase future advantages and benefits.  It is the driving force behind all civilizations, and it is what prods humankind forward to learn and grow.

When we turn down a bite of cheesecake, step away from a mind numbing reality sitcom, or push off a nap to get some work done, the credit goes to willpower.  It is this ghost like aura of control and discipline that we rely on to extend our existence and maximize our accomplishments.  When we watch highly successful individuals exercise routinely, read voraciously, and work tirelessly, we are impressed with their ability to resist instant gratification.  Most of us struggle to hold ourselves back from daily pleasures so as to work on self-improvement.  But how do the chosen few make it happen?  Are they the lucky recipients of steadfast genes, predisposed to adeptly control their yearnings better than the rest of us?

To some extent, yes.  Certain individuals are superiorly calibrated to fight off fleeting desires in the short term.  But, what’s far more important is the revelation by psychologists that willpower is akin to a muscle.   Regardless of how weak one’s innate level of willpower is, it can be trained and strengthened to rival the willpower of those super ambitious and successful folks we all admire.  According to Roy Baumeister, an eminent social psychologist and famed expert on the subject, willpower can be bolstered with great success.  This is an extraordinarily important discovery since willpower, in Baumeister’s opinion, is “the key to success and a happy life.”

For many students who struggle with mathematics, having a sturdy level of willpower is the difference between finishing an assignment and turning in a half-hearted problem set.  It is the difference between spending an extra hour and a half preparing for an exam, or merely skimming a chapter review the night before.  In sum, it is the difference between excellence and mediocrity.

For students who truly enjoy mathematics, there is no war to wage.  Math is fun, and homework will be done thoroughly and completely as a means of gratification.  But for those students who have to fight urges to play video games, watch movies, skateboard, or read novels while trudging through their math homework, willpower is what will save the day.

So how can willpower be developed?  How can students engineer a perfect level of self-control and discipline?  Just like actual muscle fibers, willpower must be exercised in the right away.  Overexertion can be exhausting and counterproductive, whereas just the right amount of use can (1) optimize productivity and (2) augment one’s willpower capacity.  For folks who are interested in bolstering their willpower muscle, here are five quick tips:

  1. Stay fueled up with healthy meals – using willpower has been shown to deplete levels of glucose in the brain.  Since it can often require great effort to stave off temptation, it is recommended that students maintain a healthy and regular diet replete with nutrients.  Healthy meals will give the willpower muscle the fuel it needs to operate at its highest levels.
  2. Maintain a positive attitude – being happy and positive makes individuals far more able to employ their willpower.  When students feel down or depressed, a common reaction is to dive into things that provide instant gratification.  This could be an unhealthy meal, a lengthy break involving television or video games, or a long nap.  Feeling happy and positive makes it much easier to stay on task.
  3. Partake in a healthy number of extracurricular activities – the reason why participating in many activities is beneficial is because it exercises the willpower muscle.  When students have obligations and commitments that cannot be avoided, it trains them to push off their fleeting desires to focus on something in particular.  Enrolling children in piano lessons and karate isn’t to make them professional musicians or seasoned MMA fighters.  The most important aspect of extracurricular involvement is the development of strong willpower, something that will be applicable and useful during school and beyond.
  4. Apply willpower sparingly and gradually – trying to hold back on too many things can spell disaster.  If someone is attempting to stick to homework, avoid fatty foods, stop watching TV, and exercise regularly all at once, he will find it highly challenging.  Why?  Because his willpower will be depleted very quickly.  This means that the end result will likely be failure on all fronts.  Instead of overcommitting, students should pick something in particular to focus on.  Once someone grows accustomed to a single task, that action will have morphed into a habit requiring very little effort to maintain.  At this point, one can then deploy his willpower elsewhere.
  5. Offer rewards each time a task is accomplished – every time a student successfully fights off temptation, he deserves a reward.  Not only will this reinforce positive behavior, but it will help to rest and replenish the willpower muscle.