I love finding out how the world works, and sharing that joy with other people has become one of my passions. (Yes, the same classes that currently induce stress can eventually become sources of joy with some help and effort in the right direction.) My students' ages and abilities range from 7 years old and behind in first grade math, to 21 and taking upper-division college physics, to 60 and taking a professional development course as an employee in the oil & gas industry. Most of my teac... [more]
On Wyzant, I've tutored Algebra 1 for more than twenty hours, and all my ratings have been five stars. Algebra 1 might lead all subjects in the number of times students ask, "When will I use this in real life?" One answer is "almost every other math class you ever take from this point on." Here are some more. Nurses use it to determine how much medicine to give, based on your body weight. History students use it with census records to determine when people moved from the country to the city. When cooking, you can use it to figure out how full to make the measuring cup when doubling the recipe and you don't have the right sized cup.
High schools usually offer this course after Geometry and call it Algebra II or Advanced Algebra. Colleges call it College Algebra. *The best way to make this subject easy and enjoyable is to master algebra 1 first.* In algebra 1, you learn that the graph of y = x^2 looks like a U (a parabola); in algebra 2, you learn how to move that parabola up and down, how to shift it left and right, how to stretch or compress it, and maybe even how to rotate it. In algebra 1, you learn how to solve for x in an equation; in algebra 2, you learn how to solve for both x and y in systems of two equations. In algebra 1, you learn how to factor x^2 + 5x +6 into (x + 2)*(x + 3); in algebra 2, you learn how to divide x^2 + 5x + 6 by (x + 4), even though the result is a fraction.
I got a 5, the highest score, on the AP United States History exam. History classes often assign tons of reading, and it can be hard to keep up. Also, some students are often afraid of writing essays, while others fear multiple-choice tests; high school history offers both. The good news is that, in my experience: 1) In social studies (like history), the big picture is more important than the details. If you have to read fast, it's okay to miss a few details. Focus on the trends. 2) History essays don't need to be fancy, like writing assignments in English class. Answer the question, tell the reader which facts support your opinion, and explain how the facts support your opinion. No fancy language needed!
I tutor calculus all the time, and business calc occasionally. Most colleges split this series into four courses over one and a half to two years. Here's my rundown of each course. Calc 1: derivatives. You already know how to get the slope of a line; this course teaches you how to get the instantaneous slope of a curve like a parabola, whose slope is always changing. The most important concept you should know for Calc 1 is the limit. What's the limit as x approaches infinity of (5x + 3)/(6x - 1)? Calc 2: integrals. You already know how to find the area under the graph of the line y = 2x + 3 between 0 and 1; just draw the graph, shade in the trapezoid, and use geometry. This course teaches you how to get the area under curved graphs. The most important things to know for Calc 2 are 1) the derivatives of basic functions, i.e. the derivative of tan x is sec^2 x, and 2) the rules from Calc 1 like the chain rule, product rule, etc. Calc 3: a mix of topics that's different at different schools, but always includes series. You already can guess the sum 1 + 1/2 + 1/4 + 1/8 + 1/16 + ... where each term is half of the previous one. This course teaches you how to find the sum of other series, like 1 - 1/2 + 1/3 - 1/4 + 1/5 - 1/6 + ... The most important skill to master is more linguistic than mathematical: be able to convert between summation notation and regular, long form sums. Calc 4: again, different schools include different topics, but this always includes vector analysis. The most important skill here isn't to be able to *draw* a vector or a 3D graph; it's to be able to interpret drawings of vectors or 3D graph, and to "ballpark" approximately what the answer should be. Do two vectors look like they're perpendicular? If so, their dot product should be zero.
One of the best things about tutoring is helping students who think they hate physical science not only succeed in chemistry on their way to nursing school, but also make connections in the real world they never knew were there. Who knew that the body heat you give off during exercise (metabolism) can be thought of as low-grade fire (combustion)? Who knew that you can unclog your drains and spot-clean clothes with cooking ingredients like baking soda and vinegar? Most students who struggle in General Chemistry 1 do so not because any one skill is beyond their ability, but because you need to use widely varying skills at once. GChem requires you to know the difference between an electron and a molecule, AND to master scientific notation and algebra, AND to learn how many orbitals are in each energy level, AND to master the art of balancing reactions, AND ... My approach is to start by asking really easy questions and get one step harder each time. Eventually, we'll expose where you're getting stuck, and fix your weaknesses one at a time. By learning one thing at a time, chemistry is nothing to be afraid of.
My favorite way to learn vocab (that works often but not always) is by learning several words at once that all have the same root. Let's take the word "excise." What does the "cise" part mean? cut. We all know that scissors cut. So do incisors (the sharp teeth in front). When a surgeon cuts a patient's flesh, we call that cut an incision. So what does it mean for a director to excise a scene for a movie? It means to cut it out. (ex mean out; think "exit.") Excise has another definition; it can mean a type of tax. In this case, it has nothing to do with cutting; it's related instead to the word "assess." When "excise" the tax became a word in English, it so happened that there was already another word with the same spelling and pronunciation. In summary, adding up the pieces of the word isn't foolproof, but it's often helpful.
My mastery of grammar is what got me a position as copy editor of my high school newspaper. In college, a couple of linguistics classes gave me experience switching between standard grammar and the non-standard colloquial grammars used by certain age groups, races, residents of geographical areas, and subcultures. These days, when I teach ACT and SAT prep, we go over what you might call "everyday grammar" and "textbook grammar."
Some people think of geometry as that subject that high schoolers take about their sophomore year, after algebra I. But most people will agree that Sesame Street teaches geometry with each segment about rectangles and circles. It turns out that other geometry courses are so advanced, they aren't taught until graduate school. At the high school level, generations of students remember having to write proof after proof. Proving stuff is important, but I had a student once who needed help in a different area. She could follow all the logic, but had no idea how big a 50 degree angle was because nobody had given her a protractor to play with. So we made our own protractor with pencil and paper. Once she was able to see things for herself, her assignments got way easier.
My favorite subject of all, and the one I tutor most often, is physics. The way I see it, there are three types of skills involved in doing physics. 1) conceptual skill: what basic principles are involved here? Write a few sentences in English, qualitatively explaining what you expect to happen. Explain the situation to Grandma, or someone who is smart but has never taken physics. 2) analytical skill: break the problem into steps. What will you do first? What will you do second? Will you set two things equal to each other? 3) mathematical skill: can you solve for x in the bottom of a fraction? Do you remember unit conversions from chemistry? How do you convert from meters to centimeters? If you're in college, your instructor will probably focus on skill 2. If you're lacking in skill 1 or 3, you might not ever get help in class or discussion. So expect me to focus on a different area from what your professor or teacher focuses on. Also, I like to begin with a super simple problem that only tests skill 1. Once you get that right, we'll add one complication at a time until we reach the original HW problem.
Prealgebra is often taken by middle school students. You know who else takes it? Highly paid oil & gas employees. Their companies include it as part of a course in drilling or well-logging or something similar. Lack of competence in prealgebra can prevent a roughneck from being promoted. Let's suppose the topic is percents. There are several ways to doing percents, and I'm okay with any method that words for an individual student. When in doubt, break up percent into "per" and "cent": 20 percent means 20 out of 100, or 1 out of 5.
Colleges call it precalculus. High schools often call it math analysis. It includes trigonometry, and overlaps with algebra III. You're expected to take this either in your senior year of high school or at the beginning of college, depending on where you live. If I had one piece of advice for precalc students, it would be: at least master the easy cases. If you can't remember laws of logarithms, at least memorize that the (base 10) log of 1 = 0, the log of 10 = 1, the log of 100 = 2, the log of 1000 = 3, etc. Then, you can check a rule: log 10 + log 100 = 1 + 2 and log (10 * 100) = log 1000 = 3, so it appears that (log a) + (log b) = log (a*b).
Do you plan on taking AP Physics or college freshman physics? If so, I would say that the math topic that's most likely to cause trouble is trigonometry. For this level of physics, you'll be using little to no calculus, and you can usually get around the trickier parts of algebra. But you have got to know sines and cosines in order to split a vector into components. In high school, trigonometry is usually included in a course titled Math Analysis or Precalculus. Colleges might do the same or might offer a full course titled Trigonometry. Either way, I like to think of trig as the closest we get to "Geometry II." My secrets to success in trig are as follows. If you can do these, you're well on your way to mastering the subject. 1) Learn the triangle inequality inside and out. 2) Memorize the Pythagorean theorem and SOH-CAH-TOA. 3) Draw from scratch a 45-45-90 triangle (an isosceles right triangle) by cutting a square in half diagonally. Label the length of each side and the measure of each angle. Compute the sine, cosine, and tangent of each angle except the right angle. 4) Draw from scratch a 30-60-90 triangle by cutting an equilateral triangle in half. Label the length of each side and the measure of each angle. Compute the sine, cosine, and tangent of each angle except the right angle.
Astronomy courses are taught from two perspectives. The first is geared toward the general public and focuses on where to find stuff in the sky: phases of the moon, declination of the sun, the rising and setting of constellations and planets, and how to find the North Star. I enjoyed earning the Astronomy merit badge as a Boy Scout. Now that I'm an adult, I use the sun, moon, and stars to find my way in unfamiliar territory all the time. When I'm out camping, I can use the phase and location of the Moon to estimate what time it is without looking at a clock, just like you know it's getting late in the day when the Sun is low in the west. The second type of astronomy course is taught by a college's Department of Physics and Astronomy, and is treated as a branch of physics. My degree in Physics included a handful of upper division courses in astronomy and cosmology.
Many students go into statistics expecting to hate it, and prove themselves right when they don't understand z-scores and t-tests. My advice? Master mean (average) and standard deviation first. Let's look at two samples. Sample A: 16, 18, 22, 24. What's the mean? About how far from the mean would you say a typical member of this sample is? What's the standard deviation? Sample B: 6, 8, 32, 34. How does the mean compare to the mean before? About how far from the mean would you say a typical member of this more spread out sample is? What's the new standard deviation? If you can answer these, you'll have a much easier time learning the topics taught later in the course.
Geography has been one of my favorite subjects from second grade through college, plus outside of school. Like most people, I focused on physical geography when I was younger, and got into human geography when I was older. This subject is unusual in that most people don't take a class called "geography" -- they learn bits and pieces of it in their other classes, like science, social studies, history, and foreign language.
One of my favorite classes in college was an upper division class called Writing in the Physical Sciences, where I made scientific topics approachable to lay audiences. In grad school, a professor said he "wondered where you learned to write so engagingly." If you need to dissect the motifs Shakespeare uses in Macbeth, hire another tutor. The thing I can help with is writing clearly, without grammar mistakes.
Future college students often ask "should I take the ACT or the SAT?" The mathematics on the SAT is less advanced than ACT math: you will not be asked anything from precalculus or trigonometry on the SAT. The tradeoff is that questions on the SAT can have trickier wording. For example, the SAT might give you an equation like x^2 + 6x + 9 = 49, and then ask for the positive value of 3x. If you don't read carefully, you'll get x = 4 and pick the answer choice that says 4. But the right answer is 12, because 3x = 12. (Yes, another solution to the equation is x = -10 which would make 3x = -30, but we were asked for a positive value.)
I got a perfect score on the GRE Quantitative section, scored one notch below perfect on the essays, and scored well above average in the Verbal section. Here's my advice for each section. Quant: review all the math you've forgotten through high school geometry, beginning with the most basic arithmetic. If the GRE gives you letters, pick some numbers. Substitute your numbers into the problem to give yourself a concrete example. Verbal: learn your vocab. Pay particular attention to *seldom-used definitions of common words.* What does catholic mean, besides the religion? What does flag mean, besides the colored piece of cloth? What does nice mean, besides pleasant personality? Writing: Before the test, look at some essay prompts. Spend some time coming up with examples that can be used for several prompts. During the test, make your essay long. It's better to get your examples and reasoning on the paper than leave some ideas unwritten because you were too busy micromanaging your transitions.
When my high school began publishing a newspaper, I was asked to be the copy editor -- the guy who proofreads everyone else's articles and corrects any errors in spelling, grammar, word choice, style, etc. Nowadays, I teach test prep, and standardized tests love to give you grammatical mistakes to fix. The ACT English test is basically a proofreading test. I have lots of practice at reading papers and finding the sorts of errors that are easy to fix: small ones that deal with language usage and mechanics rather than with content or tone.
My experience with GED prep consists mainly of the math section. We'll attempt a practice problem or two, and it'll usually become clear where the gaps are in the student's math knowledge. Usually, it's something we've all seen before, like adding fractions or simplifying square roots. My preference is to teach the math itself, in isolation. Once the student feels better about the math itself, *then* we'll apply it to actual GED questions.
The term "physical science" means any natural science that doesn't deal with living things; it includes astronomy, physics, chemistry, practically all of engineering, and earth sciences like geology and meteorology. My college coursework includes classes in all the above subjects except geology. Junior high schools and high schools offer classes in Physical Science, usually aimed at 7th and 9th graders. These classes cover the very basics of what you will learn years later in those other, more specialized courses. For me, physical science is an opportunity to help students who think they hate science find out that 1) science doesn't have to be hard, and 2) the world is a pretty cool thing to learn about.
After tutoring ASVAB students for over fourteen hours so far, my impression is that the raw skills needed to do well on the ASVAB aren't much different from the basic skills used on the ACT and SAT: vocabulary, literacy, arithmetic, some algebra, and the ability to organize information in a word problem. The military is looking for general knowledge more than specialized knowledge. (Specialized knowledge would be something like your score on the Mechanical Aptitude test. This skill can be learned more quickly than mathematics or language.) In other words: even if you don't plan on going to college because you're enlisting instead, you still need to learn the material in your English and math classes. The armed forces consider them important, so you must as well. Students often tell me "I'm good at ____, I just am bad at taking tests" or "I don't understand the way the ASVAB asks questions, but I know the material." In most cases, the student underestimates just how much he or she has forgotten, or doesn't completely understand, about the material itself.
Many undergrads and grad students in business and psychology have to calculate probabilities based off of z scores -- standard deviations above the mean. They do this by referring to a series of tables in the back of their textbook. My senior year of college, I took a math class in probability where we learned how to generate that table from scratch. One of my favorite things about probability is how it can surprise people who think that something is obviously false, but it's true. For example, let's imagine that twenty-four random people are in a room together. Do two of those people share the same birthday? Probably yes. More than half of the time, you can find a pair of people out of a sample of 24 who share the same birthday.
I suppose now's the time to mention that I was my city's spelling bee champion in my youth. My approach to learning spelling is, when possible, to relate new words to words I know. Let's suppose someone's having trouble remembering there vs. their vs. they're. What are some words that are related to "there"? You might think of here, where, everywhere, nowhere, etc. If you're using the word "there" but could substitute "here" or "where" in the sentence, you want the world that's spelled similarly.
I've taught and tutored ACT prep to about 150 students. First, a personal story. In school, I always had trouble finishing reading assignments on time. This was partly because I didn't know what was important and what I could skim over. It wasn't until 12th grade that a college admissions officer told me, "You don't read a novel the same way you read a science textbook. It's okay to skim sometimes." What's important in this section? Whatever they ask questions on. This means you don't need to read the whole passage to get a lot of questions right. Start by looking at the questions -- they'll tell you which parts of the passage are important. (This is also good advice for science or social studies reading. Look at the homework questions -- if the author bothers to ask a lot of questions on inflation, consider inflation the important part!)
I've taught and tutored ACT prep to about 150 students. Unlike Reading, English is mostly a proofreading test. The few general questions are things like "what should the author do here?" In this section, details are more important than the big picture. The grammar tested on the English section isn't advanced or controversial: you'll need to know the difference between its and it's, but won't have to choose between "James's birthday" and "James' birthday." Master the basics and you'll do well.
I've taught and tutored ACT prep to about 150 students. The good news is that it's not as tricky as the SAT; expect ACT math questions to be relatively direct. It's true that the Math section does have a few questions on advanced topics (but NO calculus). However, most of the difficult questions aren't hard because you haven't reached that math class yet. So, what makes a question hard? Possibilities include 1) it's a word problem with lots of information to keep track of, 2) it asks about hypothetical values rather than giving you numbers, and 3) it disguises easy math in an unfamiliar scenario. The key to improving your math score isn't learning trigonometry; it's learning through about algebra 1 and *avoiding mistakes on questions you're able to do.*
I've taught and tutored ACT prep to about 150 students. All the test prep geniuses say you don't need to know much science for the ACT Science section, only basic stuff like "males are XY and females are XX." (True for mammals, but not birds.) They say it's really about reading numbers off of figures and following patterns. While technically this is true, my experience tells me that if you're familiar with the scientific topic in the passage, it will be super easy to read the tables and figures. If you've never seen the topic before, the same passage will be almost impossibly hard. The ACT doesn't require you to know science facts, but it's easier to learn *some* science first than to try to make sense of a Science passage on a topic you know nothing about.
Of all the subjects in the world, I would say the most important subject to learn in this country is English as a Foreign Language, combined with learning to read. Number two is arithmetic, also called elementary math. I often see high school seniors, or adults, who are embarrassed by their inability to do math problems they learned in elementary school. (The elementary school students I've tutored have not been embarrassed because they're not expected to know it yet, so they're often quicker to say "I don't get it." This makes my job easier.) There's no need to be ashamed -- it's been many years since you've done division with someone looking over your shoulder, and many people never received good instruction in the first place; they were just told to memorize a process and not given any number sense. When I tutor arithmetic, I start by having the person estimate the answer -- 105 - 88 is "one hundred something - eighty something. 10 - 8 = 2, 100 - 80 = 20, so the answer should be around twenty." Then we'll go over a few different ways of getting the answer, and you can use whichever method you like best.
This is one of the first subjects in which kids can stump their parents, and that makes it fun for all involved! This early on, the concepts themselves usually aren't too hard. When a student doesn't understand something, it usually works if I 1) explain it using different words, or 2) let the student see it with his or her own eyes.
I have taught both MCAT Physics and MCAT General Chemistry courses for a total of about four hundred hours to hundreds of classroom students. That's not counting more than a dozen 1-on-1 tutoring students. Student evaluation excerpts can be found in the Free Response section. In addition, I am familiar with the CARS (Verbal) section and the organic chemistry tested on the exam. I don't normally teach these subjects, but I have completed all the reading, lectures, and homework that an MCAT prep student would, and can answer many questions about them.
I have tutored several students in chemical engineering classes at the University of Oklahoma. The courses I've previously tutored focus on fluid mechanics (for example, Bernoulli's equation) or physical chemistry (for example, the first law of thermodynamics). What I bring to the table is a solid understanding of the underlying mathematics and physical science. I can help you master the concepts from physics, general chemistry, and calculus your instructor assumes you already knew on the first day of class.