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.

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.

Yesterday was a busy Thursday. In fact, every school week there is a busy Thursday, whether you come to Study Hut Tutoring or not. With tests and quizzes, homework and projects, six classes of papers going in and out of the backpack everyday and all your friends jammed into one classroom, the task of managing a workload is impossible. Am I right? Let us take a quick look of how this impossible situation appears when our 8th grader Corey sits down for his tutoring hour. Corey is a very sharp student who is able to breeze through his pre-algebra assignments. He is very capable in other areas too. He is maintaining a strong grade in social studies, however, his grades dont reflect his intelligence.

So what is the matter? What do we do? How can we bump up these “C” grades up if Corey doesn’t need help with the actual subject matter? Lucky for Corey, the Study Hut knows exactly what to do. After speaking with his mom, I know she is frustrated with Corey’s sluggish performance around the house. So now Corey is at Study Hut, sitting down with me. The first thing I do is look at his daily planner. It is a bad sign when the whole thing is blank. The planner is the tool that fosters accountability, so if the planner is blank, Corey isn’t even accountable with himself, let alone with parents, teachers, and his tutor. The next step is manually going through the backpack. This is crucial to set the record straight and explain the reasoning and utility of behind using the daily planner.

After all, why do something if it doesn’t serve a greater purpose, save time, or help in the short term and in the long term. Young students are no different. You would never do a lot of things the right way if there was no direct or indirect benefit. After digging through every subject and organizing the folder, we see that there is a pile of old, completed work that can go into a folder and can be stashed away at home in the closet. The other pile was larger than I would like. This pile had a ton of incomplete work. Our plan from here on out at home everyday and at tutoring is as follows:

1)Write in the planner for every subject, during each class period, every week.

2) take notes each class period, everyday

3) make a list prior to tutoring of what we will be working on at Study Hut, and what will still have to be done at home.

4) Make one study tool (flashcards, outline, study guide, practice test) for each class each week.

5) show all of this to the tutor to remain accountable during bi-weekly tutoring sessions.

These simple tasks will, and have already started to, pull grades up, increase accountability, and lead to domination.