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# Christmas Present!!

Hi All!   In the spirit of giving, starting on 11/29/2013,  I will be offering a few brainteasers/ trivia questions where the first 3 people to email me the correct answer will receive a free, one hour, tutoring session in any subject that I offer tutoring for (via the online platform)!  That's right free!  Get your thinking hats on everyone!   Merry Christmas!!  Andrew L. Profile

# Interesting problem from a section on Trigonometric Identities

I was working with a student today, and as we worked through the section in his book dealing with Trigonometric Identities and Pythagorean Identities, we stumbled across a problem that gave us a bit of trouble. The solution is not so complicated, but it sure had us stumped earlier.   The problem was presented as such:       Factor and simplify the following using Trigonometric and Pythagorean Identities:   sec3(x) - sec2(x) - sec(x) + 1       We tried a couple of different approaches, such as factoring sec(x) from each term:   sec(x) * [ sec2(x) - sec(x) - 1 + 1/sec(x) ]   and factoring sec2(x) from each term:   sec2(x) * [ sec(x) - 1 - 1/sec(x) + 1/sec2(x) ]   We followed these approaches through a few steps, but nothing we were attempting led to the solution. After doing some reading online, I found that the solution required a simple approach that I had overlooked.   Instead of attempting... read more

# Mathematical Journeys: What's a Radian?

Buckle up readers, it's Trig time! Trigonometry can be scary to many students, and in my opinion, a lot of that is because one of the most confusing concepts in trigonometry occurs right at the very beginning, in the form of the Unit Circle and Radians. Let's start at the beginning. Give yourself a circle with a radius of 1.  Now center that circle on the origin of a coordinate plane, so that the line of the circle itself passes through the points (1,0) (0,1) (-1,0) and (0, -1). Got that? Now, this circle is referred to as the Unit Circle, because the radius is one unit and it is therefore easier for us to do various manipulations and calculations with it. Now choose any point on the circle (we'll call the coordinates of that point (x,y)), draw the radius to it (which will still be a length of 1), and drop a line back perpendicular to one of the axes. Do that and you'll have a right triangle with the radius as the hypotenuse,... read more

# Intuitive Trigonometry

I was very fortunate to have been taking electronics at the same time I was learning high school trigonometry.  Like most folks, I was never good at abstract math, but being able to see physical demonstrations of math principles was a huge help. One of the real "bears" for most math students is the concept of the imaginary number...and yet it's crucial to working with all alternating current electrical and electronics problems. When I teach electronics, I have students ranging from postgraduate math majors to middle school students who want to take a few shop classes before high school.  (Nice thing about working at a technical arts extension of the local University!) I introduce practical trigonometry without even using the term, using nothing more than a straightedge, some graph paper, and a protractor.  I avoid trig tables entirely UNTIL they understand how to manipulate the Pythagorean theorem inside out and upside down. I then demonstrate how the Imaginary Number... read more

I was a fairly typical young person and, like my peers, counted down the days until summer. My mother was a math professor, so I never stopped doing math during the summer, but felt like other parts of my brain became a little mushy in the summer. Come September, it was difficult to get back into the swing of writing papers and studying history and memorizing diagrams. I was out of practice and lost my routine. As an adult, I have almost continually taken classes, because I enjoy learning and find that from class to class, I need to maintain a routine, i.e. a study area and a time of day that I complete my assignments. I have also found that reviewing material a week or two before the course begins helps me to start the class with more confidence and competence. I am a big believer in confidence fueling success and I wonder if younger students practiced assignments in the week or two prior to return to school, if that confidence would help the transition to the school year... read more

# Week 3 and I had a Breakthrough with the same Earth Science Student for Algebra I

I was excited on Tuesday, July 16th, 2013. This was my third meeting with this student and I finally had a breakthrough with him. On the first meeting it was clear that he saw Algebra I almost as a foreign language. I began with one of the test packet, and had him do 10 questions and reviewed the questions he had done wrong. So this continued for a while, and of course sometimes he would say that he understood, but it was clear that he did not. Anyway, after reviewing the entire packet I began a teach and learn session, in which I picked a variety of topics and had him practice various equations. After which I gave him a quiz. He failed the quiz miserably, so of course he still did not understand. Anyway, I gave him another packet for homework. When I saw the student again, I reviewed with him, but still not much improvement, but at least he tried. I did the teach and learn session again, of which some of the questions were from the previous session, and I gave him... read more

# The Summer Session has just begun and I had a Break-through with a few Students!

The Summer session has just begun. The stress has already begun to set in, but this week I had a break through with a few of the students. So this is my second week with a student who I am tutoring for both Algebra I and Earth Science. So far he seems stronger in Earth Science but still needs much practice, before I can be very confident about his ability to pass the Regents exam in August. After the first session of Algebra, I walked away thinking about how am I going to get him ready by August 13th. I recommended an additional session to the parents, but so far they have said no. I did several practice examples, and made the second session mainly a teaching and learning session. Then I ended the session with a quiz, but he failed :(. So when I had to meet him again for Earth Science, my mind was swirling as to how I can help him, and will I at least be successful with this subject. When I checked the homework, there was a slight improvement but not enough to celebrate.... read more

# 96 Percent For Global History Regents Exam!

Hello Miss Gil, I received a 96% in Global History. I was so excited to hear these words from my student! At first she did not want to be tutored. Her father dropped her off at the Library. So I told her that if she did the practice test, and did well, she would never have to see me again. Well, she scored a 58%, and there were so many events and topics that she did not know. We scheduled 3 additional three hour sessions. By the last session, her essays had improved and her overall score was an 83%. I told her that I believe that she can score as much as a 95% on the Regents Exam. She laughed and said "Yeah right". Well she scored a 96% and I am very proud of her.

# Be Like Water...

Humans have a tremendous capacity to learn and adapt. However, we consistently build barriers that hinder our natural ability to change and grow. Many people, regardless of age, perceive themselves as not being talented enough to excel at math and science. They view math and science as the realms in which only scientists, engineers, mathematicians, and geniuses truly soar. Nothing could be further than the truth. Sure, possessing a natural affinity towards these subjects helps. Yet, a supposed lack of talent does not prevent you from learning. The path may be more arduous. The journey may be longer. Nevertheless, you possess within you the fire to endure. Willpower, dedication, self belief, and an open mind can compensate for any lack of ability. Bruce Lee was a legendary martial artist, actor, and philosopher who continues to inspire millions with the sheer intensity which he pursued his endeavors. Frail, sickly, and small as a child, Bruce Lee overcame many physical... read more

# Summer Tutoring

SUMMER OPPORTUNITIES Now that students, teachers, parents and tutors have had a chance to catch their breath from final exams, it's time to make use of the weeks we have before school starts back. Consider all that could be accomplished in the next few weeks: Areas of math that students NEVER REALLY GRASPED could be fully explained. This could be elementary skills like adding fractions, middle school topics like systems of equations, or high school areas like sequences and series. Students could have a TREMENDOUS HEAD STARTon topics that will be covered in the first few weeks of school. Imagine your son or daughter being able to raise their hand to answer a question in the first week of school because they had worked several problems just like the ones that the teacher is demonstrating. ENORMOUS PROGRESS could be made in the area of preparation for the standardized tests (PSAT, SAT, ACT and more) that are so important to getting into a great college. STUDY... read more

# That Sinking Feeling - "Top Performance"

A wise man once told me: "You can continue to beat your head against that rock, but you will not chip the rock, your head (on the other hand) will be deformed." I guess I should have seen it coming, my being summarily fired from a tutoring job - The parent (in this case the mother) demanding extra "busy-work" for her son between sessions, the lack of discipline, on the student's part (especially his inability to do homework or speak to his subject teacher) and his continual lack of attention during sessions. The call came, "You are not coming here anymore, Billy Ben (not his real name) ONLY got an 81 on his Geometry test. We want top performance, 95 or better, YOU failed." Did I tell you that this student, previous to my seeing him, was working on a solid average of 40? So, it was over. Had I failed? I'm not so sure. First, I didn't take HIS test, and second, knowing the student as I did, I actually thought that an 81 was pretty good and we might have saved the semester after... read more

# Mathematical Journeys: The Function Machine

y = f(x) I can't tell you how many times I've had students come to me profoundly confused about their entire math unit, all because their teachers never fully explained this concept. Teachers throw this equation up on the board without discussion as if it explains everything – which it does, but only if you know what it means. So let's discuss! First off, it's important to remember that this is not just an equation; it's an indication of a larger concept. We'll get to that in a minute, but let's start at the beginning. Imagine that I have a little machine which I set on the table in front of you and turn on. You place a number in the slot in the top, and the machine begins to hum and churn. After a few moments, a drawer opens at the bottom and you pull out a different number. You can repeat this with any number you like, any number of times. Now this is a single-purpose machine, which means it has one rule that it uses to transform the starting number into the... read more

# Homeschool Math Support and Accelerated Math Development for Public and Private School Students

I have been working with a few students who are ready to learn math much, MUCH faster than allowed by the traditional classroom model in which math is taught over 6 to 8 years. Based on this experience I believe that many students as young as 4th grade and as old as 8th grade (when starting in the program) can master math in 2 years from simple addition through the first semester of Calculus, with Arithmetic, Algebra 1, Geometry, Algebra 2, Precalculus, Probability, Statistics, and Trigonometry in between. This is significantly faster than the traditional approach and is enabled by a combination of one-on-one teaching and coaching and a variety of media that I assign to students to complete in between our sessions. This is a "leveraged blended learning" approach that makes use of online software, selected games, and selected videos with guided notes that I have created that ensure that students pick up the key points of the videos, and which we discuss later. The result is... read more

# The IMPORTANCE of ALGEBRA!

To My Future and Current Students, I can't stress enough the IMPORTANCE of ALGEBRA! Of all the mathematics I have taken in my lifetime...BELIEVE ME IT'S BEEN A LOT, ALGEBRA is the only course that is WOVEN into every single course. I was lucky enough that my first mathematics teacher in High School (Mr. Large), turned me from a B student into an A student such that I graduated High School with a 4.0 in mathematics. The one piece of advice he gave me that I will share with you is that...I NEED TO CHECK, DOUBLE CHECK AND TRIPLE CHECK ALL OF MY ANSWERS! Algebra is a required course (prerequisite) for many of your other math courses, but most importantly in your High School career it is MANDATORY in order to be successful in Algebra 2. It may seem silly to learn and master Algebra, however, it is an integral part of every math course you will take after that except some geometry courses. Algebra teaches you how to think, be organized and how to prove your answers by checking... read more

# Your Child's Success is My Success

A parent told me recently that her son scored a near 100% on his last test. I was so proud. I feel proud when all my students succeed. The question is what does it mean for a student to be successful. I think it's a mix between the student having more confidence than when I begin working with the student, as well as an increase in the student's grades. Depending on the student and his or her own situation grades may increase immediately and with others it may take a bit of time. I want my students to feel confident about their abilities and also be able to show the world and themselves that they understand what's going on in class. I make a commitment when I take on a student, which is, I will work my hardest to be available and flexible. Your child's success is my success.

# Paul' s online math notes

Greetings, scholars! The first step to success in any endeavor is having the right tools. Keeping tools organized and handy is equally important, but the overwhelming amount of information in most classes causes even the most powerful tools to get lost in the cluttered garage of facts, formulas, and applications. What we need as mathematical scholars is a neat, uncluttered toolbox where key formulas are organized and kept close at hand. Luckily, Paul' s Online Math Notes provides just that! Here is a link: http://tutorial.math.lamar.edu/ The "cheat sheets" on the website below are invaluable resources. I recommend printing them out for quick reference as you practice working problems. You can also use them to make flash cards and commit important formulas to memory. You may find these notes so helpful that you no longer need assistance. If you find that you still want one- on- one instruction, I am accepting new students and will be glad to help.

# Yesterday was a Great Day

What a way to start off the New Year! First I met with a student for US History and Living Environment. She is taking the Regents exams in three weeks. When I first met with her, Cee had a fear of taking exams, and was very nervous. She struggled with understanding both subjects; the Historical Events and dates, as well as the vocabulary words for Biology. Her next struggles were understanding and answering the document based questions for US History and the short responses for LE. Now she answers them much more confidently and accurately, and has even improved in writing her document based and thematic essays for US History. I am so proud of her and is certain that she will pass both Regents exams. Then I met with my grade 4 student for Math, English Language Art and Science. He has gone from scoring 31% to 83% on his practice science exam. He is much more confident with doing Math and ELA assignments. I am so proud of him. Then it was on to my grade 6 Math student. When... read more