...are probably the two most common things I hear from students who come to me because they are struggling with geometry. While I will admit that there are quite a few theorems and it can take a bit of practice to get really good at proofs, a solid understanding of geometry provides us with so much more than the knowledge required a good grade in a required math class. Specifically, we interact with the world around us through our understanding of space and the shapes, curves and voids that make it up. Geometry helps us to develop our visual-spatial abilities, thereby providing the means to a richer, more complete perception of our surroundings. Put another way, this is math finally put into a familiar context.
"I just don’t get proofs!” & “Why do I have to memorize all of these theorems?”
It is a common misconception that an aptitude for geometry (and math in general) lies solely in the more logical, linear-thinking left hemisphere of the brain, thereby placing the more right-brained, lateral-thinkers at an intrinsic disadvantage. This couldn’t be farther from the truth. Throughout history, the greatest mathematical minds (Newton, Einstein, and Da Vinci, just to name a few) were the ones who were good at engaging both sides of their brains, which is precisely what geometry teaches us to do. We all may learn a little differently from one another, but the ability take in and synthesize visual information is hardwired into each and every one of us – the key is finding the approach that helps you, as an individual, get there. It is my job to help you find this approach and is something that, after 15 years of working with students privately, I become quite good at. So! If inscribed angles and contrapositives aren’t making sense, don’t fret. Know that you do, in fact, possess the intelligence to do well in geometry and clarity, though it may not seem so at the time, is right at your fingertips! I can show you.
Algebra I and II
Algebra, frequently referred to as “the gatekeeper subject”, is one of the most important math classes you will ever take for a variety of reasons. As your first introduction to higher-level math, algebra helps to build mathematical intuition and problem solving skills that are critical for professions both inside and outside the hard sciences. Algebra is used by architects, accountants, graphic designers, doctors and engineers and, accordingly, is a core requirement in many college degree programs.
Unfortunately, algebra is also a subject that many people find foreign and confusing at first. A bad experience in a challenging math class can leave a bad taste, which all too often discourages people from continuing on with higher-level mathematics. Personally, I have felt like this more than once in the many years I have studied mathematics. I like to use the analogy that learning algebra is a bit like learning a foreign language – clear as mud when upon your first introduction but, with guidance and practice, soon becomes second nature. Having struggled with the subject myself, I have become something of an expert at spotting mistakes of all shapes and sizes (precisely because I have made most of them myself!) and I use this knowledge to help my students understand their errors and learn from them. One of my favorite experiences as a teacher is when I see one of my students experience their first “Eureka!” moment and I know things are finally starting to make sense. It is one of the greatest rewards of my job and a huge part of why I chose to be a teacher in the first place.
No other field of math is as much a part of our culture and history as calculus. Yes, really! From the motion and forces that trace the paths of planets and stars to Pythagoras’ eponymous theorem and Maxwell’s seminal work on electricity and magnetism, calculus lies at the very heart of these advancements and discoveries. Have you ever wondered why the 360 degrees that make up a circle seems so close to the 365 days that make up or a year or where the all of those geometric formulae and trigonometric identities come from? How about natural logarithms or enigma of compounding interest rates? And for that matter, how about any situation in which you have ever tried to solve for x? Would you believe me if I told you that every single bit of this falls out of calculus as naturally as apples fall from apple trees…?
…and while were on the subject, did you know that Sir Isaac Newtown actually created calculus to describe the laws of physics? While the bit about getting beaned by an apple is probably just legend, the formalization of the derivative and integral was truly revolutionary. These two simple concepts recast the vast majority of real-world problems as those that could now be simplified and solved exactly, providing scientists and mathematicians with a means to examine, thread by thread, the complicated tapestry of the known universe. Kind of crazy how all of this stuff is connected, eh?
Beyond the thrill of understanding that calculus actually has a purpose other than that of an academic torture device, our mastery of it also has some rather serious implications. Calculus has proven essential to the survival of the human race insofar as it has helped us to develop climate and population growth models, predict and control the spread of disease, and manage periods of extreme financial and economic upset. It may be surprising to learn how deeply embedded calculus is within the fields of social, physics and biological science. Knowing this is the first step towards understanding that the world is not simply the sum several independent ideas, concepts and objects buzzing along through the space between the stars, but something much more integrated and beautiful; a complex organism tied together by the elegant framework of calculus.
So, yeah. Calculus is pretty neat and you should totally study it. And I’m just a phone call or email away if need any help along the way.
Physics is my favorite subject to teach, and that’s not just because it’s my area of expertise. I love teaching physics because I think it is, by far, the coolest and most versatile subject I have ever encountered. I think physics is interesting (and you should too!) because it helps us understand how the world around us works, from baseballs, airplanes and garlic presses to the cell phone in your pocket; from the muscles in your arms and legs, the rhythm of your breath to the nerve cells in your brain; from earthquakes, tornadoes and hurricanes to quarks, black holes and supernovas. Physics is the language with which this universe we live in converses with us.
But let’s not stop there…
Physics is useful. Physics provides the quantitative skills to analyze data, solve real-world problems and is used each and every day by scientists, engineers, doctors, economists and professionals in countless other fields you might not immediately associate with a hard science. Physics is also the basis for most modern technology - there would be no WiFi, iPads or GPS devices to help navigate you to the nearest gas station without it. Physics also opens doors to career options. A solid understanding of physics is essential to do well on college entrance exams such as the MCAT. You can’t become a doctor or pursue a career in technology without physics.
Finally, physics is also challenging, and that’s not necessarily a bad thing. Taking a class in physics teaches you how to think about and approach problems in ways you never have before. Unlike other classes you will take that involve rote memorization, you can usually write everything you’ve learned over the semester in a physics class on the back of an index card, and that is because physics is as much as about learning as it is about doing. Physics will teach you how to apply a small, basic set of tools to a truly limitless pool of problems. It would be a lie to say that it is anything short of mental gymnastics, but the benefits of its mastery are far reaching and well worth the effort. I assure you this is true whether physics is a stepping-stone to a career as scientist or if your dream is to write the next Nobel Prize winning novel and you never take another science class again. In pushing its boundaries, it will be forever opened to beauty and elegance of the world in which you live, in all respects.
Standardized Test Preparation
"College entrance exams DO NOT test what you know – they test what you can come up with in the allotted time. Full stop."
When I first prepared for the SAT waaaay back in the dark ages I learned what is (I think, at least) the single most important truth about standardized exams.
This doesn't mean that I think they’re terrible tests – quite the opposite actually, because their use in projecting how well a student may do in college requires that they be exceptionally well written. Standardization means that they have a very specific and well-defined scope and, because of this, test writers can only create questions that conform to this particular standard. For example, you will never see an advanced calculus problem on the ACT or SAT because it would be beyond the scope of what the exam was created to evaluate. Put simply, test writers have to abide by strict rules to ensure a fair and level playing field for the thousands of students who take these exams every year and it is precisely this fact that makes test-taking strategy so important. When I prep my students for an upcoming exam, my approach involves equal parts of the following:
- Review: I provide a thorough overview of the material you will be tested on. If your algebra is a little rusty or you never really got your head around reading scientific graphs, have no fear! I am here to teach you everything you need to know in a simple and concise manner.
- Strategy: I integrate the most effective test-taking strategies into our lessons to help you move through the test quickly and solve problems accurately. You will also learn process-of-elimination, ball-parking techniques and guessing strategies to help you effectively answer questions you either are not sure of or flat out don’t know the answer to.
- Timed Drills: This is the final piece of the puzzle and is intended to prepare you to answer questions under the time constraints imposed by the actual exam. We have all had experiences where we have made mistakes we would not have otherwise made because we felt rushed or under pressure. By practicing problems under conditions mimicking those of the actual exam, you will gain essential confidence in your own knowledge, learn how to pace yourself, and become more comfortable dealing with problems you may not immediately know how to solve.
The idea is to adopt a holistic approach to your preparation so that you not only know how to the solve the problems, but that you know how to take the test; you will achieve your highest score when you master both of these things!
I provide test preparation services for the following standardized exams:
- AP Calculus AB & BC
- AP Physics