A lot of students from Palos Verdes and Peninsula High School come into our Redondo office despising math, and I don’t blame them. Mathematics is a tough subject that takes a lot of time to understand, and students often try to get by by memorizing the rules, proofs, and theorems without ever perceiving how they work. After all, it’s a nasty subject that I’ll never really need. Who cares about the directrix of a parabola? When do I need to know how to calculate the area of a n-sided polygon? What’s the point of being able to do basic arithmetic in my head? I can just use my iPhone calculator to get the answer, or Google search it. That’s good enough.

It’s tough to argue against these points, but I believe that putting your best foot forward when tackling math builds a solid foundation, not only in regards to academics but to life as well. If a child is willing to put in the time to genuinely understand how trigonometric identities work, they’ll be more likely to work for things in life, whether it be a job, sport, or relationship in the future. If a student understands that they need to address their poor grades in math head-on instead of ignoring it, they won’t run when life gets tough. On the other hand, if that student resorts to taking short cuts in math or gives up after trying only once, they’re likely to throw their hands up in the air whenever they face adversity. Just like there are no short cuts to becoming a great Sea King or Panther athlete, there are no short cuts in academics, especially math.

So please, help your child develop good life habits by spending some extra time one or two nights a week helping them with their math. Make sure they show their work and don’t just guess the answer. Ask them questions to see how well they really grasp the material. Tell them, “Good job!” or “Nice work!” when they’re trying their best. Teach them the joy of hard work. As a math tutor, there are no secrets to help these students. I help them first understand the basics and then build on those basics. I teach them how to systematically analyze a problem and try various approaches instead of looking in the back of the book for the answer. I encourage them to ask questions when they don’t understand something. These are all good habits that people need to succeed in life, and mathematics is a great place for children to start developing them.

With the increasing amount of accessible technology and decreasing amount of human attention spans, people get bored easily. Nintendo DS’s, Kindles, and iPads are meant to serve people with an immediate means of pocket-size entertainment. But what some people forget is the simplicity of those things we use every day: our words. The challenge of a cross word puzzle is usually more intriguing than mindlessly staring at a solitaire screen and the reward of a completed puzzle is oh so blissful. This particular brand of brain teaser is not only great for killing time while waiting for your parents to pick you up from practice, but also conducive to a learning environment, such as the Study Hut. You see, crossword puzzles require a certain out-of-the-box mindset to be solved. This is helpful to students who are preparing to take standardized tests, such as the SAT or ACT. These standardized tests, at their core, are not about testing intelligence. Rather, they test students on whether they can adapt to a certain style of thinking and deductive reasoning in order to answer their specific questions.

For the crossword novice, the Los Angeles Times or USA Today crosswords are the best because they allow the user to see when they are correct or incorrect. Also, the Los Angles Times crossword puzzles start with their easiest puzzles on Monday and get progressively more difficult through Sunday. This is a great way to spend down time because it increases mental acuity and also builds a stronger vocabulary, another reason why it would improve standardized testing scores.

Here is an example from a Monday clue in the LA Times: “One quarter of M” (3 letters.)

For this clue, the puzzle draws upon your knowledge to recognize this as a math problem and to solve using Roman numerals. Since “M” is 1,000. One quarter of that is 250. C = 100 and L = 50. The correct answer is: CCL.

Here is an example from a Sunday clue in the LA Times: “It might have a nut at each end.” (5 letters.)

If you’ve done enough crosswords, you can figure out that they don’t mean the kind of nuts that you eat. Drawing on homonyms for nut, another type of nut might be the tool used with bolts. Since it is 1 more letter than bolt, the answer is “Ubolt.”

The mentality employed by crossword puzzles makes one think outside of the box, using verbal puns, pop culture knowledge, mathematics, history, and anything else we use our brains for. Being able to adapt to this thinking style is a sure way to keep your brain sharp, acute, and ever ready for the perfect riddle!

Luv,
Whitney

Many people think math is really boring. This is because, for the most part, teachers are lame and don’t make the material interesting. There is a lot of cool and weird mathematics out there that kids unfortunately are not exposed to. Here are a couple of interesting mathematical oddities that will hopefully spark some interest in math:

You want to find the sum of the infinite series 1-1+1-1+1-1+1-… This pattern repeats forever. At first glance, you would likely say (1-1)+(1-1)+(1-1)+… = 0+0+0+0+… and conclude the sum is 0. At second glance you may say the 1+(-1+1) +(-1+1) +(-1+1) +(-1+1) = 1+0+0+0+0+… = 1. Turns out both of these are wrong and the sum turns out to be ½. Here is why:

Let’s call the sum of the series S, whatever it may be. So, S = 1-1+1-1+1-1+1-…

Now, look at 1-S. We get 1-S = 1- [1-1+1-1+1-1+1-…] = 1-1+1-1+1-1+1-… = S. This is the same as our original series. We just showed that 1-S = S which means that 1=2S or that S=1/2. Pretty crazy that you can add 1 and -1 infinitely many times to get ½.

Here is another cool little proof why 1=2:

Let a =b. Then a2 = ab.

So, a2+ a2 = a2+ab or 2a2 = a2+ab.

Now, Subtract 2ab from both sides of the equation. Doing so, we get:

2a2 -2ab= a2+ab-2ab

So, 2a2 -2ab= a2-ab

Now, we factor out a 2 from the left side of the equation which leave us with:

2(a2+ab) = a2+ab

Divide both sides by a2+ab leaves us with:

2=1.

Take a close look though. While everything seems to be right, we all know 2 does not equal 1. Can you find the erroneous step? If not, come to the Study Hut and we can show you what’s up.