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.

...

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.

Math Anxiety: What It Is And How To Defeat It

Let me guess… the question that is currently floating through your brain is as follows: what the heck is “math anxiety?”  While it may sound bizarre and made up, math anxiety is an actual condition that is quite common amongst students.  It is similar to other sorts of anxiety or fear a person might encounter when doing something that is personally terrifying such as public speaking, interacting with strangers, or being around scary animals.  The symbols and the operations can feel overwhelming for some, and that can trigger a subsequent anxiety reaction that completely stifles one’s brain and prevents a person from properly absorbing any material.

The Cause Of Math Anxiety

Math anxiety is a learned reaction.  Students who have negative experiences with math early on tend to have bad emotions and limiting beliefs tied to mathematics. Once these reactions and beliefs are established, students will subconsciously return to those bad feelings whenever mathematics is brought up.  When a student approaches math with low self-confidence, poor emotions, and an overall belief that he/she will be unable to grasp the concepts, the snowball of anxiety builds even more.  The inevitable difficulty with the new concepts reinforces the limiting belief, and the student continues to feel stifled and defeated.

There are several underlying factors that provide excellent fuel for these negative emotions and beliefs to materialize.  These are commonly held misnomers about the field of mathematics.  First and foremost, there is the erroneous notion that math is a confusing, convoluted subject matter that is inherently difficult to grasp. Many people believe that the inability to understand math is normal, and that there are a chosen few that enjoy and understand mathematics (while the rest of the population must simply accept their poor understanding as an unlucky genetic trait).

There are other ridiculous misconceptions that cloud young students’ minds.  For example, there is a distasteful attitude in the U.S. that women are naturally less adept with mathematics than men.  Parents and educators seem to promulgate the idea that below average mathematics skills are par for the course for female students.  This is a toxic and utterly false belief, and the passive acceptance of this attitude furthers this nonsensical notion.  My parents, for example, had a completely different perspective when raising my sister.  My dad encouraged her throughout school and insisted that mathematical comprehension was of the utmost importance.  Moreover, he cemented within her the belief that she could perform at the highest level if she chose to apply herself.  As a result, she went on to earn an 800 on the math portion of the SAT, a 5 on both of her calculus AP exams, and a chemical engineering degree from MIT.  Not too shabby.  Yes, my sister is very bright, but a key component to her success was a proper mentality and a solid inner belief.

Finally, some people have the backwards notion that you are either creative or logical.  If you fall into the former category, math will simply not be part of your repertoire.  This is patently false.  At the end of the day, math is a highly creative endeavor.  It requires a great deal of complex thinking and clever manipulation that is completely creative in nature.  If you look at music production and song writing, an activity that would most certainly be identified as a creative pursuit, there is a great deal of overlap with mathematics.  Music is bound by mathematical rules that allow for all sorts of manipulation within the scope of major and minor scales.  This is akin to variable manipulation in Algebra and Calculus.  It’s funny, but most people presume that an affinity for music comes with a general inability to understand math.  Nothing could be further from the truth.

How To Solve Math Anxiety

Yes, math anxiety is solvable, just like any other potentially debilitating self-limiting belief.  Below are my top four suggestions for tackling this unsightly menace.

  1. Seek To Understand The Concepts Behind The Formulas – most students who struggle with math attempt to memorize formulas and then apply them in a highly mechanical manner.  While this approach might yield favorable results for easier problems, it falters when it comes to more difficult permutations.  Instead of simply sticking to rote memorization, students should seek to understand the principles behind the formulas.  For example, it is one thing recognize that a variable can be isolated by adding and subtracting variables and constants, but it is something entirely different to understand the concept that equations are like little seesaws that remain stable so long as you affect both sides equally.  Doing something to one side will throw it off balance and topple it, but carefully modifying both sides of the equation proportionately allows one to manipulate the whole thing while preserving its integrity and message.  Once this concept is firm in a student's mind, the application of the rules becomes much easier and more enjoyable.
  2. Eradicate Self-Limiting Beliefs – if someone feel anxious when he/she sits down to tackle a math problem, it’s likely because he/she thinks that math greatness is unattainable.  Take my word for it… this is a false belief. But students can’t just take my word for it; they need to actually internally accept the idea that they are capable of performing well in math.  One awesome method (that some might denounce as hokey) is to adopt a math related mantra.  A mantra is a positive saying that is to be repeated in one’s head or out loud.  For example, a sample mantra could be “I am awesome at math,” or “I can understand anything.”  A student should choose one that resonates with him/her, and then repeat it several times when he/she begins a math assignment, starts an exam, or experiences any trouble working through math problems.  The cool thing about mantras is that people can actually rewire their brains and extract their self-limiting beliefs with enough practice.
  3. Get Extra Help – for those who feel stifled by mathematics, asking questions in class can create more anxiety and stress.  Because struggling students often refrain from digging deeper in class, their progress and confidence are further hampered.  If this is the case, the best solution is to get outside help.  Working with a tutor or a teacher outside of the classroom creates a pressure free environment for the student to ask questions and have concepts explained in a carefully tailored manner.  If the classroom setting is not working, a helping hand can slide everything neatly into place. Then, once the student’s confidence is bolstered and he/she begins to feel comfortable, the extra help can eventually be removed.
  4. Perform Practice Problems Before An Exam – the biggest mistake I see young students make is that they don’t do practice problems before an exam.  What is their preferred method of studying?  They review the textbook and look over their notes the night before a big test.  While that is a highly effective method of studying for most classes, this will not cut it for math.  Not at all.  Instead, students must develop a habit of doing a number of practice problems before an exam.  This will not only uncover any problem areas and weaknesses, but it will serve to firm up concepts in a remarkable way.  When it comes to math, only practice makes perfect.

SAT Prep - How To Boost Your Math Score

So you just took a practice test and you’re devastated by your results.  You thought you would net more points, but lo and behold, your score is painfully below your expectations.  Your math score is especially poor, but you’ve never been good at math.  What is a good plan of action?  Let the math score linger at a subpar level while focusing all of your energy on the verbal portion, right?  Wrong.

First of all, even if you’ve historically done poorly in math, you can easily turn that around with a few months of devoted practice.  Second, math is the area where you can see the most marked transformation as far as testing abilities.  You can certainly improve your score in the verbal section, but the base of knowledge for both the writing and reading sections is far broader.  The English language is highly complex, and it takes most of us a great many years before we learn and understand all the intricacies.

Math, in comparison, is much simpler.  The rules and terms are significantly fewer in number, and trying to learn and apply the concepts in a short time period is much more realistic than memorizing a bunch of vocabulary words and mastering the breadth of grammatical nuances in existence.  Don’t get me wrong, you need to focus on the verbal section too, but my point is that you shouldn’t write off the math portion as a lost cause.  In fact, math is the area where you should double down on your study time.  You will be amazed at what you can achieve if you prepare in the right manner.  So how do you go about breaking your personal math barrier?  Here’s how.

  1. Master Mental Math – yes, I’m aware that you can use a calculator on the SAT, but quick arithmetic skills will drastically augment your ability to succeed.  Why?  Because the SAT is administered under a serious time constraint.  You will have 50 minutes to complete 44 multiple-choice questions and 20 minutes to complete 10 grid-in questions.  That’s not a lot of time.  Having to refer to your calculator for basic arithmetic will unnecessarily impede your ability to race through the exam.  Lack of quickness can spell disaster even if you are very familiar and comfortable with all of the concepts.
  2. Memorize The Formulas And Rules Covered On The Exam – the SAT covers a finite universe of math.  The core topics are as follows: (1) numbers and operations; (2) algebra and functions; (3) geometry and measurement; and (4) data analysis, statistics, and probability.  The College Board provides candidates with a test prep book that reviews all of the pertinent concepts under these categories.  You can go to your local library, check out the College Board’s Official SAT Study Guide, and review these concepts for free.  If you give yourself ample time to prepare, you can easily master all of the basic principals.  This will ensure that you are at least capable of nailing each and every math problem.
  3. Take A Prep Course – there is a very small percentage of people that can annihilate standardized tests without a prep course.  Accordingly, I recommend that all students enroll in some course.  The strategies and methods of each course are certainly helpful, but the key benefit is having a structured study plan.  It is essential that you develop a rhythmic study routine that does not linger or falter.  You need to review math concepts and go over practice problems in unison.  Now, precisely which prep course you choose can vary depending on your budget, time constraint, and your current testing abilities.  You should certainly shop around, from recognized names to private entities, to see which company or tutor is right for you.
  4. Practice, Practice, Practice – there are loads of practice tests available for sale.  You can purchase them at a bookstore or use the repository of practice exams at your chosen test prep company.  Most tutoring and prep courses will have you take approximately three or four exams as part of the standard class, but I encourage you to take many, many more.  When I prepared for the SAT, I took 15 practice tests.  What’s the benefit of taking so many practice exams?  There are several.  First, the SAT is standardized. This means that from year to year, while the precise material varies, the core subjects and concepts are constant.  Translation: the more questions you see, the fewer curve balls can be thrown at you.  With enough practice, you can familiarize yourself with the entire universe of possible question types. This will not only improve your test taking abilities, but it will bolster your confidence come test day.  Second, practice problems make you exercise your brain in a critical manner.  It’s one thing to know a concept, but it’s another thing to put that concept into use.  The more practice you get, the more comfortable you will be with the concepts, and the more speed you will have when chugging through the math section.  Finally, practicing thoroughly will expose your weak spots.  You may think you know the entirety of the subject matter, but the practice tests will weed out your areas of uncertainty.  I recommend that students take at least 10 practice exams.
  5. Study Over The Summer – most kids wait until the school year to start preparing for the SAT.  I highly recommend you get a jumpstart over the summer. High school curriculums are tough enough as they are, but adding on a rigorous study routine is a sure fire recipe for disaster.  You will likely have to sacrifice either your schoolwork or your SAT preparation, neither of which is a good option.  So, if you want to be ahead of the curve, sign up for a program that spans the summer and put in a solid effort.  Take as many practice tests as you can, go over as much material as possible, and ask your tutors for the maximum amount of help.

Tailoring Math Education To Different Learning Styles

Math can be a puzzling and often frustrating subject for students.  Some pupils seem to effortlessly pluck A+’s from the heavens, while others grind away to earn average grades at best.  Why the discrepancy?  Are some brains simply predisposed to math success, while others are hopelessly misaligned?  Of course not.  If I believed that, I wouldn’t be teaching math.  So what’s the deal?  Why the blaring gap in math performance?  One key factor is learning styles.  Despite what your folks might say, people learn in different ways.  Some students naturally thrive in standard Prussian style classroom settings; others, however, only truly soar in different environments that are better tailored to their particular strengths.  If a student is struggling in math at school, it could be because the standard curriculum is not in sync with his/her learning style.  This article will (1) run through the seven learning styles, (2) explain how to identify where students fit on the learning style spectrum, and (3) advise how to optimize math education accordingly.

Social/Interpersonal

Social learners prefer to learn in groups surrounded by other people.  They are often charged up by the presence of their classmates, and usually derive energy from social interactions.  They are the prototypical extroverts.

Telltale Signs Of A Social Learner

  1. They are known for possessing a wide network of friends and associates
  2. They feel excitement and energy when around other people (i.e. extroverted)
  3. They are particularly adept at negotiating and resolving conflicts

Suggestions For Math Education

While learning math in a group setting can be difficult for many, folks who thrive in social environments are best served when surrounded by their peers.  Working in teams to complete homework assignments and prep for exams can often charge the energy levels of a social learner.   Moreover, creating a supportive network of caring classmates can help nurture an interpersonal child struggling to improve his/her grades.

Solitary/Intrapersonal

Solitary learners thrive in isolation.  They often do their best when working alone and using self-study.  Reading books can be an especially effective learning vehicle for these individuals.

Telltale Signs Of A Solitary Learner

  1. They prefer solitary activities
  2. They spend a great deal of time reflecting introspectively
  3. They recharge their energy levels while alone (i.e. introverted)

Suggestions For Math Education

Solitary learners are usually folks that thrive in our modern education system. Their characteristics set them up nicely to achieve high marks in standard academia.  But, however, to help an intrapersonal learner soar even higher, it is important to recognize that these students are designed to work alone and in isolation.  So, finding a spot free of disturbances is often the first step to maximizing their abilities.  In addition, it is useful to simply recognize that the majority of information they learn will usually be absorbed at home while studying (as opposed to in class during the lecture).

Verbal/Linguistic

Verbal learners, as the name suggests, prefer learning with words in both speech and writing.  These types of minds soak up knowledge through various mediums centered around language.  Words naturally resonate with these folks.

Telltale Signs Of A Verbal Learner

  1. They have a natural affinity for words when reading, writing, listening, and speaking
  2. They have an uncanny ability to recall definitions and spellings of words
  3. They enjoy creative writing such as poetry

Suggestions For Math Education

For these folks, I recommend sitting down with a teacher or tutor after class to hear in depth explanations.  While the material may not sink in during chalkboard lectures, verbal learners will be more likely to pick up math lessons that are conveyed in plain English.  Words, after all, are their bread and butter when learning.  They should steer clear of relying too heavily on symbols and drawings.  Instead, they should seek word-based explanations, either written or oral, from a teacher.

Logical/Mathematical

Logical learners do their best when employing logic and reasoning.  They are effective problem solvers and typically succeed with task-based learning.  These minds often do well with standard math education.

Telltale Signs Of A Logical Learner

  1. They enjoy asking questions and finding solutions
  2. They are often preoccupied with puzzles and other logic based games
  3. They have a knack for mathematics and other variable based subjects

Suggestions For Math Education

Since logical minded people often enjoy games and puzzles, it makes sense to frame math problems in the same mantle.  Now, I have always felt that math assignments are inherently similar to logic games or puzzles, and are naturally fun for folks who like these types of challenges.  But, for the logical brains out there that still find it hard to enjoy their math homework, I recommend searching out math-based games.  One decent website for such games is http://www.coolmath-games.com.  In addition, I suggest employing rules during study time to make practice problems feel more like a game.  For example, adding time constraints can make the practice problems feel more like a game.  Additionally, keeping track of percentages and trying to beat out old scores is another way to make the process more fun.

Visual/Spatial

Visual learners are specially built to use pictures and spatial tools.  They learn well when lesson plans incorporate photos, videos, visual maps, and other pictorial based instructions.

Telltale Signs Of A Visual Learner

  1. They visualize problems clearly in their minds
  2. They tend to learn better from pictures and movies than word based mediums
  3. They are naturally drawn to activities that involve visual design

Suggestions For Math Education

For the mind that learns with pictures and images, I suggest infusing math education with loads of drawings related to each concept.  They should be encouraged to draw out diagrams and use visual cues to ease memorization of various operations and theorems.  In addition, they should color code their notes and study materials.  This will help their visual brains organize and assimilate various pieces of information.

Aural/Musical

Aural learners are best equipped to understand and store information absorbed via sound and music.  Their ears are particularly adept at deconstructing and parsing heavy mixes of tones.  They will often do better with books on tape versus printed versions.

Telltale Signs Of An Aural Learner

  1. They deeply enjoy listening to and making music
  2. They have a natural understanding of music and its various elements
  3. They tend to connect emotional experiences with various sounds and songs

Suggestions For Math Education

Many aural learners enjoy listening to music.  I suggest that they play pleasant music in the background while learning mathematics.  This will evoke positive emotions and stir up a bit of energy while working.  Just make sure that the music is not overly distracting or played too loud.  In addition, musical minded people should try to organize formulas and operations into musical patterns or rhymes.  For example, coming up with a rhyme or melody to remember the quadratic equation would be more effective than simply attempting to remember the visual image of the formula.  Finally, when reviewing notes and examples from the textbook, they should read aloud so as to stimulate their aural memory.

Physical/Kinesthetic

Physical learners learn best by touch and movement.  A lot of superb athletes tend to fall into this category as physical processes and activities seem to sync well with their learning and memorizing capabilities.

Telltale Signs Of A Physical Learner

  1. They enjoy physical activities such as dance or athletics
  2. They spend a great deal of time being active and physically engaged
  3. They like to express themselves using a wide range of physical gestures

Suggestions For Math Education

For physical learners, devising a specially tailored strategy to approach math is a little trickier, but still doable.  Since these types tend to learn best when active, it is important for them to stay in motion while studying.  This could involve squeezing a stress ball while working, or simply taking a break every 20 or 30 minutes to walk around the room.  Hands on models are terrific as well when applicable.  If there is a tangible learning device that the student can actually touch and interact with, all the better.