Update on the new SAT: Math

Part III of our series on the Redesigned SAT, this post clarifies how the Math section is changing on the upcoming Redesigned SAT. For a broad picture of general changes to the test, see Part I here.

When the College Board released test specification documents on the Redesigned SAT last Spring, most test prep professionals were stunned at the difficulty level of the proposed Math section. It seemed that a fundamental characteristic of current SAT Math – that the most difficult problems retained use of basic math topics like percents and ratios – had been jettisoned in favor of a new type of difficulty, namely, extended algebraic manipulation of advanced concepts encountered only in precalculus.

The most recent Redesigned SAT curriculum release, a full-length PSAT/NMSQT, confirmed this basic impression, even if it “backed down” from the degree of difficulty implied by the 2014 release (as some of my test prep colleagues have argued elsewhere). In addition to this top-level shift, there are two features of the Redesigned SAT’s Math section that warrant scrutiny:

1. A content shift to include more advanced math topics and feature more word problems with real-world contexts.
2. An additional, no-calculator section to force students to demonstrate in-depth understanding of algebraic principles.

I’ll take these each in turn, elucidating with concrete examples.

 

A major new component of the Redesigned SAT’s Math section – and one that might intimidate test-takers – is an emphasis on real-life modeling with math. This emphasis aligns the new SAT closely with the Common Core.

The College Board’s new take on SAT Math represents both a shift of emphasis (from arithmetic and geometry to algebra) as well as an expansion of topics. See the table below for a comparison of content area distribution.

Current SAT Redesigned SAT
Number and Operations 20-25% Heart of Algebra
(equations, inequalities, systems)
33%
Algebra and Functions 35-40% Problem Solving and Data Analysis
(statistics, ratios, percentages)
29%
Geometry and Measurement 25-30% Passport to Advanced Math
(quadratic equations and polynomials)
28%
Data Analysis, Statistics, and Probability 10-15% Additional Topics in Math
(geometry and trigonometry)
10%

Since it’s not clearly discernible from these confusing new titles what precisely they involve, we’ve added examples beneath each. It’s helpful to note that geometry (incl. trigonometry) is relegated to the “Additional Topics in Math” category, comprising merely 10% of the new SAT Math test – a significant departure from the current SAT. In fact, we recorded only two (2) of 48 problems on the Redesigned PSAT/NMSQT that tested concepts two-dimensional, plane geometry. This is a marked departure from the current SAT, in which plane geometry comprises approximately one-third of the test.

In addition to this recalibration of content area, the Redesigned SAT will introduce problems concerning a range of new concepts. Here’s a complete list of topics that the new SAT will assess, taken from the 211-page test specification document (new topics in bold):

  • basic algebraic equations and inequalities (may involve exponents, radicals, and absolute value)
  • linear equations
  • functions and their graphs
  • arithmetic on polynomials
  • mean, median, and mode
  • percentages, ratios, and proportions
  • unit conversions
  • range and standard deviation of data
  • interpreting scatter plots
  • linear vs. exponential growth
  • frequency
  • conditional probability
  • evaluating text and graphics
  • justifying conclusions and evaluating data collection methods
  • coordinate geometry
  • lines and angles
  • radian measure
  • area and perimeter of triangles and quadrilaterals
  • area and circumference of circles
  • sector area and arc length
  • chords
  • equations of circles
  • trigonometric functions applied to right triangles and complementary angles
  • trigonometric functions with radian measure

If you’re wondering what the upshot of all this is for College Board, it has to do with the ability to assess students’ readiness to analyze, interpret, and manipulate quantitative information relevant to “real-life contexts” as well as to a variety of scientific subdisciplines. Take this example of a data analysis problem set, derived from the field of astronomy:

Redesigned PSAT Math: Sample Data Analysis Problem

This change is only one way in which the new SAT counters the ACT’s Science section, which never asks students to compute anything so sophisticated (after all, students aren’t allowed to use a calculator on the ACT Science section) but nevertheless gauges their abilities to interpret graphs of a complexity level on par with college coursework. In fact, the College Board has pledged to take its assessment of “real learning for real life” (a Common Core rallying cry) even one step further: the new SAT score report will include “cross-test” metrics to assess a student’s fitness to reason in specific disciplines, such as science or history/social studies. The only info we currently have on these subscores as they pertain to SAT Math is that roughly eight (8) questions will have a science component and another eight (8) will have a history/social studies component.

When all is said and done, the sort of students who will excel at the new SAT Math will be those who are able to see the world mathematically and model real-world situations with algebra. Ultimately, it’s this real-life facility that the College Board hopes to promote and evaluate with this new emphasis on application of mathematical principles.

 

The new SAT Math also prioritizes fluency and comprehension in mathematical reasoning, which it does via descriptive, procedural answers and a no-calculator section.

The second important distinctive of the new SAT Math test is its priority on fluency and deep comprehension of algebra and computation. The test specification document outlines two areas that drive this emphasis: “procedural skill and fluency” and “conceptual understanding.” SAT test writers have then worked to engineer problems that deliver on these directives.

One way to assess these skills is to ask students to interpret variables (“what is the meaning of 3 in the equation above?”) and model equations (“what expression could be used to determine how much the babysitter earned?”). These questions will be multiple-choice rather than grid-in, and answer sets will involve some reading – thus verbally articulating the principles underlying the math involved and thereby demonstrating comprehension. It’s no longer sufficient simply to solve without knowing how or why the math inherent in the problem works.

Here’s an example from the calculator portion of the new PSAT/NMSQT:
Redesigned PSAT Math: Sample Procedural Fluency Problem

What’s important about these new problems is that the tried-and-true test prep tactics like plugging in numbers or backsolving – tactics Stanley Kaplan built the test prep industry on (and which old guard companies like Kaplan and Princeton Review still rely on to this day) – will be rendered useless. In other words, students will need to actually enrich their understanding of the components of expressions, equations, inequalities, as well as graphical representations of all three. This feat will require a new kind of test preparation, accordingly: one in which students are taught to think mathematically rather than monkey a handful of test-taking tricks over and over.

Another component of procedural fluency and conceptual understanding problems that bears consideration is the test’s attempt to force students to decide when to use a piece of info or tool (like a calculator) and when not to do so. What the test specification document says about the no-calculator section is particularly telling:

The redesigned SAT’s Math Test will contain two portions: one in which the student may use a calculator and another in which the student may not. The no-calculator portion allows the redesigned SAT to assess fluencies valued by postsecondary instructors and includes conceptual questions for which a calculator will not be helpful. Meanwhile, the calculator portion gives insight into students’ capacity to use appropriate tools strategically. The calculator is a tool that students must use (or not use) judiciously.

The calculator portion of the test will include more complex modeling and reasoning questions to allow students to make computations more efficiently. However, this portion will also include questions in which the calculator could be a deterrent to expedience, thus assessing appropriate use of tools. For these types of questions, students who make use of structure or their ability to reason will reach the solution more rapidly than students who get bogged down using a calculator.

When we worked through the new PSAT/NMSQT Math sections, we observed that while the old SAT maxim that “there are a variety of pathways to the right answer” holds true, there are some pathways that are clearly more expedient than others – and choosing the most efficient way to solve is likely what College Board has in mind above. A thorough understanding of the conceptual backing of formulae and processes, as well as heightened number sense (ability to make judgments of outcomes of operations based on properties of numbers) on the no-calculator section, will be important assets on the SAT of the future.

I’d like to conclude with another representative example, this time from an entirely new problem type, the “Extended Thinking” problem set:
Redesigned SAT Math: Sample Extended Thinking Problem

While not the hardest SAT Math problem in the College Board releases, this one definitely illustrates the sort of creative problem-solving and algebraic manipulation students will need to perform – as well as the difficulty of having to work with little to no feedback from an answer set. Lastly, in my opinion Part 2 represents a scenario in which keeping your calculator in your hand (from Part 1, presumably, wherein it’s essential) might prevent you from reasoning out the problem algebraically, which is the only way to be sure without wasting loads of time. (See here for College Board’s answer and explanation.)

EPILOGUE

So what sorts of students should look forward to the new SAT? Those with robust foundations in mathematics – not necessarily those with As in higher-level math coursework, but those who have done their due diligence through the years of ensuring a thorough comprehension and facility with algebra. (Also, those who are willing to begin the difficult but important work of thoroughly understanding it now!)

On an encouraging note, one of the important distinctions between SAT and ACT, their different approaches to pacing and time constraints, seems heightened by the new PSAT release. Consider this: the ACT gives one (1) minute per Math question, but the new PSAT/NMSQT indicates that students will have 70 minutes to complete 47 problems. That’s 89 seconds per item, or about 1.5x what the ACT allows.

Perhaps most importantly, it seems the SAT is beginning to shift away from its broadly inductive approach to math and toward a more deductive understanding (again, á la ACT). On the one hand, this might mean less options for students to choose from; but it might also simply mean that students need to reassess their strengths and challenges, given the new landscape of testing in 2016. It’s almost certainly true that some who would have previously done well on the current version of the SAT will now do better on ACT, and students who we would have coached toward ACT might in fact excel in Redesigned SAT Math.

If you’re interested in discussing which test is ideal for you, contact us to schedule a free consultation. For more college prep tips and techniques, follow us on Twitter and Facebook, or subscribe to our newsletter.

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