ACT ▌SAT ▌Math SAT I+II subject tests ▌PSAT
ISEE ▌SSHAT ▌SSAT ▌NY state tests ▌Regents
ERB ▌Hunter exam ▌Matholympiad ▌Math Kangaroo ▌AMC
I have 20 years of experience tutoring for the exams above. I have worked with many renown test prep institutions in the NYC area and was trained extensively in their methods. Over time I have come up with a few essential approaches of my own that I have found nowhere else. Here is a quick summary.
I do not use any complicated methods or material. In my opinion there is really only one manner in which to proceed: give students the test sections in order to reveal their strengths and weaknesses . Then very carefully go over the mistakes they make and address the issues that arise. In math this may mean going over certain (often very basic) concepts that are causing problems. In the English sections this could lead to a review of the basic grammar rules needed for the exam or looking at texts such as Mark Twain to remind students to read in-between the lines (see below). Once these basic mistakes have been identified and eliminated, advanced students need to understand exactly what it is the exams are looking for and why they are still losing those last few points.
Depending on how the student is scoring in these practice sections and how far away the test date is, sections can/should at first be completed without time pressure. In the month before the exam, at the latest, time pressure must be added to the mix. As I like to say, first you get the train on the tracks and then you add fuel to speed up, not the other way around.
There is also a multitude of basic facts about the exams that both parents and students need to understand that are surprisingly not common knowledge. These include:
- The real, striking difference between the ACT and the SAT. Do not simply go with what your high-school recommends.
- How to maneuver the extra time situation-an essential hack if there ever was one!
- Good practice material is hard to find, even the best material available is flawed. Do not use bad materials, it can be tragic! Tutoring services have tests on their websites that are too hard in order to scare students into taking lessons. Theses tests often have questions on topics such as matrices or quadratics that aren’t even on the actual SAT or ISEE tests at all! The actual exams themselves, on the other hand, are pristine. This is very important for students to understand.
Test prep can be roughly divided into 3 different approaches depending on type of student.
Of course, most students fall somewhere in-between these extremes, but by and large the main issue to be addressed with each student is one of the three.
A common in-between case would be a student that actually does understand algebra but is not 100% confident in their current algebra skills because they have been heavily relying on memorization in school. This student might just need to brush up, stop trying to memorize and thereby regain confidence.
I will briefly address each of these three categories.
To be perfectly honest I did not believe in test prep for myself back in high-school. I thought all a gifted candidate had to do is familiarize themselves with the test, work hard, and the smarts will do the rest. What else could it be, right? I did do well on the SAT, 1540 out of 1600. It was good enough for UC Berkley and a scholarship from the University of Chicago. However, the truth is I could easily have scored 1580 or perhaps even 1600 with the correct advice! These students can profit from professional coaching just to eek out those last few decisive points. This is accomplished by fully understanding the nature of each exam’s questions.
“You cannot memorize for the math sections of the standardized exams” is definitely a true statement. On the other hand, if you understand what the math sections are looking for on a higher level it can be a game changer. There are, surprisingly, concepts to be “memorized”. I call these concepts the cliches of mathematics. These are ideas that you should be familiar with if you are seriously interested in pursuing anything to do with science or mathematics. There are 3 or 4 of these cliches per math topic, making for a total of around 30 ideas. These concepts, if identified and thought about beforehand, will help talented students breeze through the math sections of the standardized exams and save an amazing amount of time, giving the desired edge. Just one common example of such a cliche is: what happens to the area/volume of a shape (any shape!) when its dimensions are doubled? The answer is certainly not doubled! The area is increased by a factor of 4=2×2, and the volume by a factor of 8=2x2x2! If you look closely, there really is at least one question about this idea on almost every SAT in one form or another. The standardized tests are written by actual scientists (or at least aspiring ones), not school teachers. Without fail, the math questions, in one form or another, always return to these same fundamental principles!
When I first started tutoring the reading comprehension sections, there were sometimes one or two answers where I didn’t understand the explanations given in the official books. I found it hard to decide between the last two answer choices remaining after eliminating the obviously incorrect ones. Even talented students are often left confused by a few of these per reading comprehension section. One very specific insight changed this for me. The tests are not asking the student to demonstrate poetic prowess, to be a great writer or bend language in any way. This in conjunction with the fact that the instructions say “choose the best answer” not “choose the correct answer” leads to an especially tricky situation. We will naturally try to reinterpret an incorrect answer when none of the choices are satisfactory. By bending the language ever so slightly, we make an unfavorable choice seem like the correct answer. The best answer, however, can be a completely non-satisfactory choice. The best answer is often something you would never consider to be the correct answer. Since no one likes choosing an answer they really don’t agree with, this reinterpretation of incorrect choices is a great temptation! Ever since I fully grasped the extent of this particular twist I have consistently had perfect scores in the reading comprehension sections. Talented students may think this sounds obvious but, because they are not consciously looking for it, will often make precisely this subtle mistake.
And this I have found to be the key, even for these top scorers. Understanding exactly what the questions are looking for, what particular knowledge and skill it is they demand, goes a surprisingly long way to improving exam results for all students-even the very smart ones!
II. test taking is an art
Of course, these finer points are only useful once the student is scoring in the upper ranges.
First, all the usual tactics and tricks, standard to all prep courses, must be addressed. These are: timing, working backwards, plugging in answer choices, guessing, skipping questions, how to use the calculator correctly, bubbling in the answers correctly, avoiding silly mistakes by writing down your work, only reading the question stems (not the answer choices) before going back to the text (reading comprehension), sometimes reading the answer choices before the question (long ACT math questions!), how fast to read the different sections (ACT Science) and much more.
Basic test anxiety will definitely be helped by learning these methods but consistent practice and feeling confident in ones abilities is undoubtedly the best remedy.
To get there in the math sections, real mathematical understanding is absolutely necessary, there is simply no way around it. This quite often involves kicking the tires on some very basic math concepts, even going back to things like the distributive law from 7th grade. This may sound terrifying, but in my experience it is absolutely astounding how quickly most students rebound and improve drastically once the “leaks in their mathematical life raft” have been found and fixed. This is, in my quite extensive experience, surprisingly true of even the most troubled math students!
In the English sections (both reading comprehension and grammar/ vocabulary) there is, in fact, a silver bullet to improve every score whether high or low and really gain confidence dramatically. Most tutoring companies don’t like to mention this simple remedy and most students, alas, don’t follow it-reading! It really takes some coaxing and then it has to be the right material. But getting students to, for example, grasp that Mark Twain’s tongue-in-cheek humor cannot be understood at face value has an immediate effect on their understanding of what it is these exams actually want from them. This kind of realization is often a real eye opener that improves scores substantially.
Grammar rules are often a scary subject for these types of students. They would often prefer not to think about grammar at all, hoping to get by without learning the rules somehow. After all, many have successfully avoided them since 6th grade! The good news is that these exams only require the most basic understanding of grammar. The hardest rule students need to know is when to use a semi-colon. The grammar rules necessary for the standardized exams can be covered in a matter of 30 minutes! Knowing this surprising fact about the exams is often a source of great relief and new found confidence for students worried about the test.
III. to memorize or not to memorize
Regardless what you may have heard or read about standardized exams, there is one indisputable fact. You cannot memorize your way through them. Unfortunately our school system trains kids in exactly that. How often have I had bewildered parents say to me: “But my child has an A in math in school, how can it be possible that his/her math scores are so low on the SAT/ACT/ISEE?” etc. This happens all the time! If this is happening in your household, you are definitely not alone. This is unfortunately quite common.
In school math classes students usually spend the week memorizing a bunch of patterns for the test on Friday. Then all they have to do is guess which pattern to apply to which question. Sadly, the questions are often so badly phrased that thinking about them too much will actually make things harder, and so students learn to memorize rather than think about math. This is the opposite of how these standardized exams work, you must read and understand the questions. Without writing a saga here about why this is so (see school-math), suffice it to say that this is the biggest hurdle for a lot of students when it comes to standardized exams.
This is the toughest of the three cases above. So what to do? After decades of tutoring I have come to a very optimistic conclusion. I truly believe that the vast majority of students are far smarter than our school system gives them credit for. I have always found that if you can remove the blinders, take away the fear and have students look at math with a fresh attitude, as if they had never seen it before, if you can get them to just use their natural common sense again, then miracles will almost always happen! This may sound overly ambitious and, even if it could work, it would take forever, right?
Wrong! As mentioned above, it always astounds me how fast students (or even adults for that matter) will recover from this state of blind guessing if given half a decent explanation of what is going on. They obviously know that they have just been guessing at math. This is like walking blindfolded around a room full of obstacles, randomly bumping into things. Because of this many students have actually been in a subliminal state of silent panic for years when it comes to math. They have been longing to be saved the whole time, to finally understand what it is they are doing. In any case there is no other way. Understanding basic math is the only choice and so a revamping of their entire mathematical understanding is often necessary. The amazing thing is that this is actually possible and manageable, even given a limited time frame of a couple months. I have done it successfully hundreds of times!
The ACT is perhaps the only standardized exam where something close to memorization can succeed. A good part of the ACT questions are pretty standard and do allow for a certain level of pattern recognition and repetition (this is certainly not true of the the SAT.) But even for the ACT basic math must be understood and you will certainly not get a high score this way either, but you may survive.
The distinction between memorizing and understanding is not quite as stark when it comes to the English reading comprehension sections. There is, however, definitely a tendency of many students to simply repeat platitudes and take everything they read at face value as they wait for someone else (the teacher, the textbook) to do the heavy lifting of actual interpretation for them. Here the solution is once again reading. Confronting students with the opening scene of Tom Sawyer by Mark Twain, as mentioned above, has worked wonders for me in this respect. Books are not movies. Students often simply do not have the slightest inkling that they are not reading correctly at all. Often the shock of finding out that half of what is being said in Mark Twain’s books is exactly the opposite of what is meant is enough to wake them up!
The ACT is again a lot easier in this respect than all the other exams (including the 8th grade ISEEE/SSAT/SHSAT). For the most part the ACT will let you get away with a more or less straightforward statement of fact with little nuance to it. But even on the ACT, this approach will only result in an moderate score, as they do have a few demanding questions as well.
Many tutoring agencies will present students with long lists of vocabulary or prefixes and suffixes to memorize. While memorizing vocabulary can be helpful, or at least psychologically comforting for some, it is in truth a rather futile endeavor. The English language has a vocabulary 5-10 times the size of any other language. We have at least 54 words for “hammer” alone. The real solution here again is reading substantive writers that employ a large and versatile vocabulary ( and there are some great ones). It is reading words in context that really anchors them in our minds. This in turn strengths our ability to surmise a word’s meaning through said context which is essential for all of these exams. Reading challenging material is like weightlifting for the English part of our brains. Having a student read good material and explain what is being said immediately boosts scores noticeably.
The extensive prefixes and suffixes lists are really more of a joke than anything else. More than half of the tricky words on these tests do not conform to these rules at all. In fact, more often than not, they are the exact opposite of what would be expected, such is the English language. Of course I am not referring to the very basic cases such as anti-, pre-, dis-, non-, re- but then again most students know these already, if not they can be covered in a matter of minutes.
Of course there are a lot of students that are caught in a memorization pattern when it comes to math, but are quite the opposite when it comes to English- and visa-versa.