I'm so glad my GMAT student improved upon his score!! He's in for BIG things... Now, I'm looking for college students to tutor! I want to see even more successes this year!! There is is a reason the student-to-teacher ratio was small in ancient times. IT WORKS!!! :)
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I am a University of Utah mathematics major and I love the word FREE. (cheap is good too) I don't have a lot of money so any Free resources to help me study are worth it to me. Since I know a lot about mathematics that is what I will be posting here. The key to Mathematics is Learning, Practicing, Learning, Practicing, and sometimes it goes in the opposite order: Practicing, Learning, Practicing, Learning. But either way a good resource to me has a bit of both: they teach you how and why you do something and they make you do it as well. A really good resource will teach you how and why, make you try it, and then will show you why you got it wrong and what you should have done, and then make you do more problems of the same type. So then, without further ado, here are the resources: Paul's online notes (type it in google it will be one of the first to pop up) http://tutorial.math.lamar.edu/ his notes are free, come with worked out problems, solved... read more
I've started brushing up on Calculus. I studied Calculus in high school and took two semesters in college, bu that was forty years ago. It's really interesting how persponal memories pack themselves in along with Diffrential Equations and Integrals.
Fun Related Rates / Optimization Question: Smallest Surface Area of a Square and Circle Cut From a Single Piece of Rope
Hello everyone, One of my Calculus students had an interesting Related Rates problem that I had to go home and think about for a while in order to figure out. The problem was set up as such: A 25 inch piece of rope needs to be cut into 2 pieces to form a square and a circle. How should the rope be cut so that the combined surface area of the circle and square is as small as possible? Here's what we'll need to do: 1. We will have to form equations that relate the length of the perimeter and circumference to the combined surface area. 2. We will then differentiate to create an equation with the derivative of the surface area with respect to lengths of rope. 3. Wherever this derivative equals 0 there will be a maxima or minima, and so we will set the derivative = to 0 and determine which critical points are minima. Let's start by looking at the problem conceptually... read more
You can find some really good resources for math test prep in the used bookstores in a college town. Some examples that I like are: (1) Humongous Book of ______________ Problems (fill in the blank with your math topic); (2) the REA Problem Solvers series; and (3) the Schaum's Outlines. If you don't live near a college town it might be worth a Saturday trip just to buy books. Alternately, all of these are available (used) through the Amazon Marketplace sellers at really low prices. You should preview each title of these book series that you might be considering to be sure you like the authors style. Each one is different. You may like one series' treatment of Pre-Calc but prefer a different series for Calculus. So how do you use these books ? They are an alternate resource for explanations of basic concepts and problem solving techniques. You should use them as 'hint mills' and sources of problems to make up your own practice exams. Sometimes you will... read more
You'd think that, "If I'm paying for tutoring, he should be answering MY questions. Not the other way around." While I can sympathize with the general sentiment, I'd say,"you're way off base there!" I think that the tutor/teacher/coach should never ask the student directly,"Do you understand __________ ?" Not knowing the subject matter, how would the student know/evaluate/determine if they understood or not ? Generally they can't, that's why the need a tutor. Rather than ask about specific content, directly, I ask questions to determine if the student understands the material and how the pieces fit together. Sometimes that's five or six questions. Here's my general GAME PLAN: Find out where they are. Tell them, show them, then see what they heard and saw. When your tutor's asking you questions, he/she is probably working the same kind of plan. You can help them help you by always providing the syllabus for your class, with some graded tests and... read more
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
Another assignment meant another stressful evening. I was 12 weeks into AP Calculus and I was so worried I wasn't going to be able to understand the class. So far I had completed the assignments, but I never felt I understood what I was doing. Our assignment was on rates of change. Hours went by and I was still trying to figure out the problem. How do I even start? It was like a door opened and light flooded in. I knew how to do it! I wrote my steps down, checked the answer in the back of the book, and there it was. My answer matched! It was one of those moments when your confidence soars. It seems silly now that I got so excited about solving that one problem, but I consider that moment a defining moment when I knew I could be good at math. The rest of the year was still challenging, but I felt like I knew how to get better at solving math problems: do as many problems as I could from the book until you understand the steps perfectly. That's what... read more
I have many students tell me that they are afraid to ask a stupid question in class. I tell them that there are NO stupid questions, only stupid mistakes because you didn't ask the question! Too many smart students in Calculus think that by asking a question they will appear weak. What most students don't know is that probably there are many other students with the same question in their head that they are afraid to ask! The look of relief on other students' faces when some else asks a question is amazing. Another thing smart students have a problem with is writing down each step. Newsflash: by the time you get to Calculus you can no longer do the problems in your head. Calculus problems generally are difficult because it is not just a matter of memorizing a formula and applying it. In Calculus you are expected to extrapolate the knowledge you have learned to problems you have never seen before. This is scary for most students. However once you start to... read more
I used to do this and I see a lot of students who do this common mistake when studying. Maybe you are working through old homework problems to prepare for an exam in math or physics and you have the solutions in front of you. You get to a certain point and you get stuck, so you check the solution, see what the next action you have to take is, and then continue working through the problem. Eventually you get an answer that may (or may not) be right and check the solution again. If it is, you feel great and move on. If it isn't you compare the work and see what you did wrong and understand the mistake so you move on. All this is a fine way to start studying, but the major mistake is that most students don't go back to that problem and try to do it again. Even if you were able to understand the solution or the mistake you made, you never actually got through the problem completely without aid. So now if you come to this problem on your test, this will be the first time you actually... read more
Naturally, Anything new can be challenging. For example, Calculus, now my favorite math topic, once was something somewhat confusing. How did I master Calculus? By asking people around me to explain it. The trick, at least for me, isn't how you explain it, it's how you define it. When someone finally stated "the change in y with respect to x" I finally understood. It was an immediate understanding of all concepts of calculus. So what my secret? It's learning everyone elses secret until I find one to make mine!
I've heard this sentiment over and over--sometimes from students, and sometimes, I'll admit, in my own head. Last night, I was working on my own math homework, and there was one problem I just couldn't get my head around. I read the book, looked back at my class notes, and even sat down with a tutor for a while, and still, when I tried a new problem of the same type on my own, it just didn't work! "Maybe I'm not as good at math as I thought," I told myself. "Am I REALLY smart enough for bioengineering?" It was hard, but I told myself "YES!" And I kept working. I laid the assigned problems aside and started doing other problems of the same type from the book. I checked my work every time. Each problem took at least ten minutes to solve, and the first three were ALL wrong! I kept going. I got one right, and it made sense! I did another, and it was half right, but there was still a problem. I did another, and it was right! Eventually I had a page... read more
Group tutoring in Calculus (including AP Calculus) is available beginning this week for only $16 per hour. Bring your homework questions which we can review in class. Also, we do selected topics from the book each week. Contact me now so you don't get behind, but start off the semester strong.
Developing a grounded understanding of numbers, and number operations provides the firmest foundation for learning math. Touching, seeing, and manipulating physical objects are perhaps the surest way to accomplish that in the beginning. Developing the practice of drawing pictures to reflect an arithmetic or story problem is the next step and soon becomes a central tool for thinking through a math problem whether represented in math and science, or encountered in life. Finally, talking about, through, and around math, arithmetic, problems, and solutions is equally important to proficiency in math and any other area of education, socialization, and life. It is important to recognize the preferred learning style of each student in order to achieve the best opportunity to that student’s learning and performance. Yet, excellent teaching includes multiple approaches and learning styles on the way to each student’s full facility, proficiency, and confidence. This necessary... 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... read more
As summer approaches this Friday, thoughts turn to fun in the sun, relaxing on the beach, swimming in the surf and the sand between your toes, strolls on the boardwalk, and just enjoying time with friends and family. This summer may be a little different at my beloved Jersey Shore, where many towns and beachside communities have been impacted by the fury of Super Storm Sandy. Much rehabilitation and reconstruction has been done to both homes and hearts, but make no mistake that much work still needs to be initiated and completed. As a tutor, I have been much more aware of the importance of keeping the academic skills of students sharp during the summer months. Studies have indicated that students actually regress academically during the months, with a loss of knowledge previously acquired. I have a ten year old daughter just completing fourth grade, and we always spend time in the summer on Math skills and drills, reading comprehension, and writing. From a business point... read more
Before I go run a marathon, play with my family at the pool, ride a roller coaster, head to the beach, or eat some serious amounts of ice cream, I will look back on the successful school year I have had. I got to tutor over 15 students in Middle School, High School, SAT, and College Math...and even Chemistry! I watched GPAs rise for everybody-some were happy just to pass that College Math course to graduate, others enjoyed their hard earned As that were brought up from the D level. I must say, that things did get crazy with exams at the end of the year, but it all worked out amidst our busy-ness. My tutoring schedule is light for the summer, and I am hoping nobody waits until December exams to contact me! I want things to be done the right way...after all of the swimming, adventure, and ice cream, of course! :) -Becky
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
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
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