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For a problem where you have a vertical damped spring with an applied force, you have a variety of forces. The basic force equation from Newton's second law is, of course, F=ma or, if we want to put everything in terms of position u, Fnet=mu'', where u'' is the second derivative of position with respect to time (some books use x or y for position instead). This net force is equivalent to a sum of many forces. In this case there is the force of gravity, since the spring is vertical, which is just Fg=mg. There is also the spring force which is given by Hooke's law, Fspring=-kx. In our case, x is the length of the spring, which is the distance the weight brings it down to the starting point, L, plus the position where it may be due to a combination of the other forces, u, so that Fspring=-k(L+u). Also, we have a damping force which counteracts any motion of the spring, and is therefore proportional to velocity, so that its force is Fd=-γu'. The last force we have is an arbitrary applied... read more

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 limitations... read more

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 SKILLS... read more

Hi math students :) When preparing for a mathematics tutoring session, try to have the following things at hand... Textbook (online or e-text) Syllabus, assignment, tips/hints/suggestions, answer sheet/key Class notes Pencils, pens, erasers, paper (graph paper, ruler, protractor) All necessary formulas, laws, tables, constants, etc. Calculator that you will use on tests Do I really need my calculator? I can do most of my work in my head. Having your calculator is just as important as paper and a pencil in most cases. You'll be using it on your test and if you don't know how to input what you want, you won't do very well. Have your tutor teach you about your calculator's functions beforehand. Learn how to check your simple math and how to input exponents, logarithms, or trigonometric functions before your test. Why do I need my book, notes, or answer key? Isn't the tutor supposed to know everything? Yes :), but even the most experienced tutor... read more

If you get stuck doing homework problems often, have a hard time doing your classwork, or sometimes you just can't follow your lecture notes try going to Wolfram Alpha. Wolfram Alpha is a computational knowledge engine that is designed to handle mathematical problems and computation, and scientific problems. It has its limitations but it is a really awesome tool that gives a lot of detail when you need it. Try it out for yourself.

It is no surprise that students lose some of their edge for education over the summer. After all the saying goes, "if you don't use it, you lose it." Summer is a great time to prepare students for the next school year. Tutoring can provide a means to not only stop the loss but also allow students to gain valuable skills for the next year. Imagine the edge your student could have in next years' math or science class if he or she had summer sessions with a certified teacher familiar with the state board curriculum and requirements? Summer is also a great time to prepare for standardized tests. SAT, PSAT, ACT or ASVAB. All of these tests provide information about a student's future potential. Students who are better prepared will score better and be given greater opportunities. That is why the test-prep industry is such a huge market. If you don't believe me, just stroll down that aisle of your local bookstore. However, as helpful as these self-help books can be, how... read more

The reality is that the student may be “in over their head” and no amount of effort will get a satisfactory result. Or maybe the student does not have the time to overly focus on one course over the others even for a short time to recover from a failing grade. This is a difficult and even emotional decision but should at least be momentarily considered. Is this class a necessity? Is there the ability to drop it? If you feel recovery is possible or if there is no other open option then on to the Recovery Plan. Though I am calling this a recovery plan – this is also a “B+ to an A+” or C to a B+" plan! Strategic Thoughts 1) Understand how the final grade is arrived at in detail as this impacts strategy especially if one part is overly emphasized. Usually the “battle” is between homework and exams. Exams are usually the predominant part of the grade - so rally around the next exam, midterm or final. You need 7-14 days for this Mock Test plan below. If homework plays a predominant role,... read more

It's important to plan ahead - "get ahead of the game" whether planning for SAT/ACT or planning for this coming Fall, 2012. Most parents and students wait till they get an "unexpected bad grade" - then REACT. A tutor can help things turnaround at that point - but what about your other classes - do you ignore those to catch up? This is not a good situation. Pressure packed. If this happens to be the semester they are preparing and taking the SAT or ACT, or they have to prepare to take an AP exam - even more pressure. I am thinking primarily in terms of math/science. If your student can start a tough math or science course in the fall having already mastered several key fundamentals of that course, it will give them confidence, relieve stress, and move them to a higher level of understanding. Also plan ahead carefully in class selection. You want a strong high school resume, but not at the expense of a significant drop in grades. My own daughter took statistics... read more

When teachers allow you cheat sheets for math tests, in addition to writing down formulas, I recommend writing out examples of problems you don't easily remember the steps to. Whatever you think you'll have trouble recalling during the test, write it down. Sometimes the examples you write down are very similar to questions on the test, which will significantly help you recreate the answers. Also, study your cheat sheet. Do not fill it out and then not review it. If you don't know where to find the information you wrote (quickly during the test), then it's useless to you. Know your sheet!

Hello all you bloggers out there, Permit me to introduce myself. My name is Lorton and I am a graduate of Brooklyn College where I did my masters degree in math education. Prior to this I had completed my bachelors degree at the University of the West Indies in Jamaica, the island and not Jamaica Queens. "Yea man, Jamaica... no problem man." I specialize in math but if anyone of you bloggers wants to learn some Jamaican lingo, you need to talk to me, just joking. Anyway I also did a diploma in education at Mico Teacher's College (also in Jamaica) where I won the Best Math Student Award in 1991. I am currently teaching at a college in New York City.

Hello again everyone! After a solid summer of tutoring I'm ready for...more tutoring! Calling all potential clients - my schedule is filling up fast and anyone who wants to lock down a slot better let me know ASAP! Here's what's new with me : I'm happy to report that I just got engaged to my girlfriend! Woohoo! It's a shame that she lives in Canada and that it'll be a long engagement, but no worries and hooray for commitment! I'm going to grad school around the 19th of September. This is going to take a LOT of my time and severely limit my driving time and so I might have to turn down some students or curtail my availability as necessary. Sadly, my studies are going to take precedence these days, but fortunately for you all, the classes will make me a better teacher! With grad school comes the Army ROTC program and I'm finally going to begin taking the necessary steps to becoming an Army officer. I look forward to the journey, despite the hardship it's going to put... read more

I assign my students homework to be completed before our next session. The homework is usually specific and focuses on filling any gaps in their knowledge I discover during the previous session(s). I verify the gap is gone by thorough questioning and testing. By doing this, I help my students develop confidence, competence, and mastery of the subject so they may avoid a "train wreck" later on when they take a test in school or use the material at work. Filling in knowledge gaps as they are discovered is an effective way to achieve these goals, but this is not the secret to learning mathematics. There are some teaching techniques that work better for some people than others but, in my opinion, mathematics is best learned through regular and frequent practice and experience. Math skills are perishable and improve through cumulative study; i.e., build math strength through effective mental workouts.  If there is a "secret" to learning math, that's it!

Mathematics is the only language shared by all human beings regardless of culture, religion, or gender. Pi is still approximately 3.14159... regardless of what country you are in. Adding up the cost of a basket full of groceries involves the same math process regardless of whether the total is expressed in dollars, rubles, or yen. With this universal language, all of us, no matter what our unit of exchange, are likely to arrive at math results the same way. Very few people, if any, are literate in all the world's tongues—English, Chinese, Arabic, Bengali, and so on. But virtually all of us possess the ability to be "literate" in the shared language of math. This math literacy is called numeracy, and it is this shared language of numbers that connects us with people across continents and through time. With this language we can explain the mysteries of the universe or the secrets of DNA. We can understand the forces of planetary motion, discover cures for catastrophic... read more

Gentle Student, If you're anything like me, at times you've wished for an easy way to work math problems and get the answer in the back of the book.Of course, you probably tried just copying the book's answers on to your homework paper only to have that "unreasonable" teacher of yours refuse to give you credit for all those answers!... something about not showing enough work. Well, you're in luck! I've taken a couple of math concepts from the internet,combined and refined them into a technique will take answer you have, no matter how wrong or bogus, and "transmogrify" it into the answer in the back using simple algebra which you can use to show full work. I call this technique The Correct Answer Algorithm (it's so simple it needs a really complicated name to make it sound sophisticated enough to impress your teacher.) So here it is... the algorithm which will in short order transmogrify your answer into the answer in the back of the book: X = Ff... read more

Ken B, who tutors mathematics, chemistry, physics, computers, and computer programming, both high school and college, and who works in the Houston and surrounding areas has just passed his 700th tutoring hour with WyzAnt. Ken has the exceptional gift to make it very clear so that when you finish you session(s) with him, that you thoroughly understand how to do the work on your own without his help.

Ken B. in Houston, Texas - known as the "Best Little Tutor In Texas" has surpassed another WyzAnt tutoring milestone by going over the 600th tutoring hour for WyzAnt. All subjects in mathematics and science, high school or college, are done by Ken except biology and biochemistry. Ken has now worked with many many students to help them work on their own and be able to do well on homework, basic studies, tests, and special projects. So, if you are in need of someone in Houston and the surrounding areas who can do all levels of mathematics, plus chemistry, physics, computers, and computer programming, Ken is the one to contact.

For most people, solving a problem or a question is not difficult if they have a model to follow and the correct data to plug into the model. Take one of the most basic functions, paying for something at a cash register. If the cashier tells you the Happy Meal costs (with tax) $4.23, and you hand the cashier a $10.00 bill, I suspect that most cashiers will give and most people will expect their $5.77 in change. Oh, you can confuse people and make the problem more difficult (7 dimes, a nickel and two pennies, rather than 3 quarters and two pennies), but these are just "tricks." This works, because for the vast majority of people, this is an "ordinary" occurrence something we've either done or witnessed hundreds of times, and we can intuitively extend our addition and subtraction rules to a new problem. Unfortunately, most classroom topics are taught like the math example above using clear, intuitive, and easily understood examples, but tested using confusing... read more

Richard Feynman once said: "The problem of how to deduce new things from old, and how to solve problems, is really very difficult to teach, and I don't really know how to do it. I don't know how to tell you something that will transform you from a person who can't analyze new situations or solve problems, to a person who can. In the case of mathematics, I can transform you from somebody who can't differentiate to somebody who can, by giving you all the rules. But in the case of the physics, I can't transform you from somebody who can't to somebody who can, so I don't know what to do." This humble and frank assessment came from a man widely regarded as a fantastic teacher. It came in a review lecture available in "Feynman's Tips on Physics" (Feynman, Gottlieb, & Leighton; Pearson-Addison-Wesley; 2006), a supplement to "The Feynman Lectures on Physics", one of the most fascinatingly thorough digests of undergraduate physics. However, Feynman was... read more

Ken B in Houston, Texas, better known as "The Best Little Tutor In Texas" has just surpassed the 500th hour of tutoring for WyzAnt. For any subject or combination of subjects dealing with mathematics, chemistry, physics, computers, and computer programming, he is the one-man-source. His diversified expertise and ability to simplify complex subject for students makes him a par-excellent source for student's studies.

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