How I Learned to Stop Worrying and Love New SAT Math

This January, we released Applerouth’s Guide to the New SAT—an overhaul to our SAT curriculum that reflects the recent changes to the test. This book release marked the culmination of a year spent dissecting practice tests, categorizing questions, and crafting a pedagogy to help our tutors and students gain mastery over the new SAT. Now, standing on the other side of all that research, we find ourselves uniquely positioned to help introduce the new test on the block to the rest of the neighborhood.

Throughout the year, we plan to do just that: provide you with in-depth reflections on each section of the New SAT from our perspectives as the Applerouth book writers. Now, whether due to Stockholm Syndrome or genuine enthusiasm (it’s too soon to say), we have actually become true believers of this new math section everyone’s been talking about. So let’s start there - new SAT math. What is it, how is it different, and why should we stop being so scared of it?

Writing a New Curriculum

When the College Board first announced its plans to overhaul the SAT, we predicted that market pressure would push the test closer to its increasingly popular rival, the ACT. Those predictions were confirmed with the first preview of the test, with one glaring exception: while the grammar and reading sections looked suspiciously similar to the ACT, the new math section was something entirely new. Indeed, despite already having hundreds of pages of math instruction for ACT and SAT topics, we decided that we’d need to write this new math curriculum from scratch. We commandeered one of our conference rooms and set to work, cutting out test problems, taping them to the wall, and rearranging them in carefully labeled groups as if on the verge of unmasking some grand conspiracy. Chaos was quickly replaced by order, and we emerged with a few hundred pages and a solid appreciation for the redesigned SAT. In particular, we were impressed with its ability to effectively test, for the first time, what we called math “fluency”: that is, a student’s understanding of how different math concepts connect and reinforce one another.

Illustrating Math Fluency

To illustrate what we mean, let’s take a quick look at examples of four question types on the new SAT that, together, make up almost a third of all math questions. Each type tests the same, basic skill—manipulating linear equations—from a slightly different angle. As we’ll see, this has big implications for both teachers and students.

Basic Algebra

One of the most common question types, particularly on the No-Calculator section, is the Basic Algebra problem. These straightforward questions test your ability to manipulate a linear equation in a balanced fashion. These are the classic “solve for x” problems:

To solve such problems, students need to have a basic flexibility with algebra: identify a goal (e.g., “solve for x”) and make intentional, balanced changes to each side in order to achieve that goal.

Now, let’s hop on over to the Calculator section of the test to see how this same skill can be tested with a slight twist.

Applied Algebra

On the calculator section, students will run into a related question type that we call Applied Algebra, or “Alphabet Soup” if we’re feeling particularly charming. These questions feature a paragraph describing a given physics equation (or something equally intimidating), but their bark is far worse than their bite.

This question may look tough at first glance… but it’s not! If you glance at the answers you’ll notice that the problem is just giving an equation (PV = nRT) and asking students to “solve for T.” The skill required to solve this problem is the exact same as for Basic Algebra: rearrange an equation to reach a goal. The only real difference is that, this time, the equation comes with a backstory.

These first two problem types test a student’s flexibility with thinking about linear equations; the next type deepens the stretch.

Equation of a Line

Equation of a Line questions require students to understand the context behind an equation in the familiar slope-intercept form (y = mx + b). For example:

Students are expected to know that the “m” in "y = mx + b" represents the slope of a line and that “b” represents the y-intercept of a line. Students often must then use that understanding to (once again) manipulate the equation to reach a goal. But whereas the science behind Applied Algebra problems was largely irrelevant, the graphing context actually matters here!

That leads us to one last question type where the focus is almost entirely on understanding the real-world context behind a linear equation.

Modeling

“Modeling” problems directly test how an equation can be used to represent, or “model”, a given context. These questions give a real-world context that is relatively straightforward and ask students to create an equation that models it:

Or they may ask students to interpret the meaning of one piece of the equation:

Either way, modeling questions reward students who have an understanding of algebra as a language with meaning rather than as a series of rules to memorize. By focusing on a single skill from different angles, from the highly mechanical Basic Algebra problems to the highly conceptual Modeling problems, these four question types effectively test a student’s fluency with linear equations. As we’ll see, this is great news for students and teachers alike.

The Benefit for Students

When the College Board’s president, David Coleman, announced the redesigned SAT, he predicted that the new test’s emphasis on fluency over “tricks” would make tutoring less important and less effective. After living, breathing, and teaching the new test for a year, we’ve found the exact opposite to be true.

Math “fluency” - the understanding of how different topics covered in school connect with one another - is precisely what a good math exam should test. It is the very thing that many struggling students feel they are lacking when they claim to be “just bad at math.” These students often use hard work and memorization to tackle each new topic, yet are haunted by the sense they are missing something that connects each year of math education to the next. This is a frustrating, demoralizing feeling that may take root as early as middle school and follow students into their college and adult years. It can cause students to write off entire career paths as “not for them.” And yet, it doesn’t have to be that way: targeted tutoring can help those students fill in the gaps and catch up with their peers.

Unfortunately, the old SAT, with its “grab-bag” style of testing many different concepts in isolation, created some incentives that proved counterproductive. Math skills were often tested in a single context with predictable language and little overlap with other concepts. As a result, the quickest path to improving a student’s score was often to teach the test rather than the concept (e.g., “When you see a wordy algebra problem, just try plugging in numbers.”). In short, it was often best to work around the gaps in students’ knowledge rather than work to fill those gaps.

Which at last brings us to the reason behind our Stockholm Syndrome: why, after spending the better part of a year studying it, we feel this new test is good for parents, students, and teachers alike. By combining concepts and testing fewer skills from more angles, the redesigned SAT effectively rewards students who demonstrate math fluency, not SAT familiarity. As a result, the shortest path to success for tutors of the new SAT is not to teach the test, but to teach the math. When a student masters the Basic Algebra chapter of the new curriculum, they are laying the groundwork for the more conceptual Modeling questions to come. When they practice Applied Algebra, they are reinforcing their skills on all three question types. And all throughout, they are forging the connections between concepts that may have eluded them for years in school. In this way, the smart redesign of SAT Math has made the benefits of test prep more relevant, more durable, and more impactful in students’ lives.