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…

One-on-one tutoring has many advantages over group tutoring. One-on-one tutoring is more focused and versatile than group tutoring. With group tutoring, tutors focus on more general concepts. They often have to teach material some of the students already understand. Its hard for the tutor to explain the concepts in a way each student can understand. With one-on-one tutoring, the tutor can develop a study plan to strengthen the students’ weaknesses . If the student is having trouble understanding a concept, the tutor can spend more time explaining the concept in a way that the student can understand. The tutor also helps to build an infrastructure for studying at home that best suits the student own preferences for learning. Students can also get help with more than one subject with one-on-one tutoring. If they have and a math and a chemistry test the next day, but feel strongly on about math, they can quickly go through the math concepts that aren’t understood and spend the rest of the time focusing on chemistry.

One on one tutoring keeps students focused and engaged in the lesson, allowing the students to use their time more efficiently. When in groups, many kids are overly self-conscious of what their peers think. They do not ask as many question and they do not engage in the conversation for the fear of feeling stupid or being laughed at. As many teachers would contest, students are also more likely to get distracted by their friends and engage in side conversations. One-on-one tutoring cuts out these distractions, giving students more bang for their buck.

Another benefit of one-on-one tutoring is that each student can choose a tutor that best suits his or her liking. The session is a lot more enjoyable and more can be accomplished if the if the student likes the person who is tutoring him/her. The students will stay more focused on their work rather than how much they dislike the tutor.