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.

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.

At The Hut, we know that all students learn differently and come to tutoring with unique expectations. For those high achieving high school students who are immersed in Advanced Placement courses, SAT practice, and extracurricular activities, time management is key.

Junior and senior year of high school are the most academically demanding years of the four. This is the time when students are mastering those tough classes (AP Euro, Bio, US, Chem, Spanish…) and special skills (soccer, music, community service…) that will make them competitive at the university of their choice. With little sleep and less free time during the day, what these teens need is a schedule.

Mira Costa junior Danny came to The Study Hut in need of a little planning. With a full schedule of electives and extracurriculars, Danny had no trouble learning the material; he just needed to find the time to do it. During tutoring sessions, Danny and I spent time organizing his schedule for the week – ensuring that he would have time to do the activities he loves as well as the focused studying that he needs to ace information-dense AP Biology. With a realistic amount of time blocked out every day for biology review, and the creation of specific goals for the completion of assignments, Danny’s test scores immediately improved. With the continued use of these organization techniques, as well as weekly concept review at The Study Hut, Danny’s grades are steadily improving. By the time of the AP Biology exam, he had drastically improved his grade in the class and his ability to retain large amounts of information.

One hour of one-on-one tutoring for high school students is not only an excellent way to clarify difficult concepts, it is also a way to keep busy students on track all week long. Short-term study techniques will prepare a student for an upcoming test, but organization and planning skills with a long-term focus are the key to improving a student’s ability to learn information, retain information, and succeed in the analytic-based learning that is in their future. The commitment to a regular schedule allows students to anticipate assignments and plan their schedules accordingly. This reduces stress, which in turn makes test-taking less of an ordeal. Less panic means better decisions and higher scores. Period.

If a student can stick to a study plan and stop relying on last-minute cramming, they are guaranteed to see positive results. And a little more sleep never hurts either…