A-List’s in-house math expert, Gary Surman double-majored in Mathematics and Physics at SUNY Geneseo and earned his Masters with honors in Mathematics from the University of Colorado. In addition to his extensive experience tutoring all levels of math (including at the university level), ELA, physics, and chemistry, Gary also analyzes standardized tests, writes curriculum, and trains tutors and teachers. He has conducted particle & nuclear physics research at the Lawrence Livermore National Laboratory in California and has a special affinity for the number 137.
There’s so much buzz going on about the new SAT Math and how different it is from the old SAT and ACT. You’re a math quiz – what’s your take on the new test?
SAT Math has always been more intimidating and convoluted than difficult, and the new SAT certainly continues in that tradition. The main focus is on Algebra, which means that our main Math techniques, Plug In and Backsolve, are still essential! However, there are some skills that weren’t really all that important on the old SAT but will be critical on the new SAT, mostly due to the fact that the 20-question non-calculator section will force you to work by hand. That means you’ll need to practice solving equations, evaluating expressions, and manipulating algebraic expressions by hand, not to mention working through Arithmetic problems, particularly involving – cue the scary music – fractions. Get used to it!
Another important aspect of new SAT Math is that it conforms much more directly with Common Core Math, which is a mixed blessing. If you are familiar and comfortable with Common Core Math concepts, then much of these Math sections will be pretty straightforward for you; on the other hand, if you’ve never studied Common Core, then you’ll have to make sure to work though the available practice material so you can get comfortable with the questions they ask and the way they present information.
You’ll also see a lot more data analysis in the second Math section, in which you are allowed a calculator. That may seem like a big advantage, but many of these questions will revolve around simple understanding or estimation, so your calculator may not be useful – in fact, relying on that device could again lead to trouble. Remember that you’re the one with the brain, so you’re the one that has to do the thinking! Your calculator is just that – a device that performs calculations. It does not explain Math concepts to you!
Overall, the Math sections on the new SAT initially look very difficult; I admit that my first thought when working through the first PSAT they released was that many students would struggle with this new format. However, the more I’ve looked over the practice tests that have been released and really worked through the problems, the more confidence I have that this will truly be a manageable test – students with a strong understanding of Math will likely find this new test a bit easier than the old, and those who struggle more will have many opportunities to use Math techniques to simplify the more difficult questions. As has always been the case, preparing for this test is about learning what they’ll ask and how they want you to solve the problems.
What advice do you have for juniors who are on their final stretch and hoping to take their last tests in June? Any special things they should do to prepare?
With about a month left before the June tests, there isn’t any time to waste! If you want to be ready, you’ll need to work on preparing every day, whether that means working through practice questions and sections, reading through your preparatory materials such as the Book of Knowledge, or reviewing questions that you’ve had trouble with in the past. What you do to prepare, though, is not really as important as how you do it!
Many students think that the best way to prepare at this point is just to burn through question after question, trying to answer as many as you can before the next test. However, in doing this, they make a critical mistake: their focus is entirely on what the right answer is. But wait, isn’t that the entire point, to find the right answer? Well, not when you’re practicing. When it comes down to it, whether or not you get a question right when practicing at home is irrelevant – if you get it right, that doesn’t count as credit toward the test you’re going to take in June, and if you get it wrong, nobody from the College Board or ACT, Inc. will be there to take note so you can be punished later. What really matters is that you can get the right answers when you sit for the test in June, not when you’re in your living room tomorrow night.
In order to ensure that you can do that, you should focus not on what the right answer is but on how you got it or why it’s right – it’s the “how” and “why” that are most important! Once you answer a practice question, you’re pretty much guaranteed never to see that exact question ever again, but the method you used to answer it will be used again and again and again, all throughout the test.
When working on grammar questions, make sure you know what grammar rule is being violated and why the right answer fixes that error. When working on Math questions, make sure you think hard about how you’re getting the answer and show all your work (seriously, every single step! Again, get used to it!). When answering a Reading question, make sure you can find the supporting evidence for the correct answer in the passage – there’s always a reason why the right answer is right and the wrong answers are wrong! It’s your job to find those reasons. If you’re taking the ACT, you’ll need to practice Science effectively. Most of the points students lose on Science come from careless error or misreading questions, charts, or graphs, so don’t give yourself a chance to mess up! Underline all the key terms in each question: know which table, figure, experiment, or viewpoint they’re pointing you to and know exactly what to look for when you get there. Don’t be afraid to write all over the test! Circle your answers in the tables given! Use the edge of your answer sheet as a straightedge in order to read graphs more effectively! Draw lines and circle the axes labels! PAY ATTENTION!
One last point about Science: one of the major reasons why students struggle with this section is that it is last! By the time you get to this section, you’ve done tons of reading and math, and your brain will be exhausted. You need to be ready for this! If you always work on Science sections when you’re awake and motivated, then you’re not going to be prepared for how drained and fed up with the test you’ll be when you get to Science on test day. So, work on Science passages when you’re tired! Get up an extra half-hour early and do a science section before school! Just got home from a terrible day full of tests at school? Perfect time to work through a Science section! Completely exhausted and about to go to bed? Wait, do a Science section first! Get used to trying to focus on these charts and graphs when it’s the last thing your brain wants to do.
My last bit of advice for this month is to try to focus on a few key skills that will get you lots of points. You’re not going to learn all the rules of grammar in a month; you won’t be able to review every math concept you’ll see on the test; one month is not long enough to transform into the consummate reader. If you try to do too much, you won’t accomplish anything. Instead, focus on one or two topics in grammar that have been chronic issues. Review Plug In and Backsolve and focus on using them in practice. Focus on getting Main Ideas in Reading, or maybe on Anticipation or timing instead. Mastering a few important skills will get you many more points than being somewhat familiar with a wide breadth of skills.
Every good mathematician has a favorite number – what’s yours?
This is a question that hits near to my heart as both a Mathematician and Physicist. My favorite number is 137, and the reason is most likely far more involved than you’d expect; I’ll try to explain without getting too deep into physical concepts.
The number 137, or more precisely 1/137, is called the fine-structure constant. I first learned about this constant when studying atomic structures; when deriving the radius of an atom, we combine several different fundamental physical constants, including the charge of an electron, the speed of light, pi, and two other constants called the permittivity of free space and Planck’s constant. Don’t worry about what these are! What I find so amazing is that many of these constants are irrational numbers – that is, they are never-ending, never-repeating decimals that cannot be written as a fraction – and they all have different units, like speed measured in meters per second and charge measured in Coulombs.
However, when combined into the fine-structure constant, something truly astonishing happens: not only do these irrational numbers combine into the rational value 1/137, which is amazing on its own, but all the units cancel out, and we’re left with a pure number! This is so extraordinary because that means this constant does not depend on our measurement units whatsoever, so that if there is another intelligent civilization out there that also managed to figure out the radius of an atom, they will get exactly the same constant! Their units for length, mass, and time may be different, but this number will be exactly the same.
For me, this is a conundrum that represents how incredibly mysterious our universe is and how much more there is for us to understand. Why 1/137? What significance does this pure number have, and why does a number so neat and tidy (as opposed to a number like pi) come up repeatedly when we try to understand how this universe works? Many physicists have devoted their lives to trying to answer these questions with no success. For me, 137 is a numerical representation of the mystery of our fantastic universe.