Why?Explaining the New SAT Mathematics Sections

"Why am I learning this math? I'm never going to use it in the real world –– it's useless!" 

We've heard that before. Students have been uttering some variant of the above for a very long time. On the one hand, hearing it is frustrating: educators know that utility is far from the only point of a well-rounded education, and that the problem solving skills that come from working on more obscure mathematics have value in their own right. On the other hand, this protestation brings forth a key issue: while the typical American student is exposed to a wide breadth of mathematics–-–including geometry, trigonometry, and higher-level algebra–––it's likely that this student is not going into enough depth with readily applicable subjects in mathematics. Indeed, all educators at Method Test Prep regularly work with students who, despite having gone through introductory courses in algebra and geometry, consistently struggle with basic and essential concepts like proportional reasoning, conversions, ratio relationships, linear graphing, and data interpretation. To many post-secondary educators, it seems that the reasoning behind mathematics has taken a back seat to rote memorization and procedure. This trend has negative consequences for student success in college and in the workforce, and is a major driver behind the College Board's decision to revamp the mathematics section on the SAT.

Major Change 1: Structure 

The current SAT features three math sections, detailed in the following table. 

Section

  # Questions  

  Duration  

  Calculator?  

  Long MC

       20

 25 min

      Yes

  Short MC

       16

 20 min

      Yes

MC + Grid-in

       18

 25 min

      Yes

Current SAT Math Section Structure: MC = Multiple Choice; Grid-in = Student-Produced Response

 Students are presented with a mix of arithmetic, geometry, algebra 1, and basic algebra 2 concepts in each of the sections. Each question has an equal point value, and there is a –1/4 point penalty for incorrect answers.

On the new SAT, these three sections will be condensed into two, only one of which will allow students to use calculators:

Section

  #Questions  

Duration  

  Calculator  

Calculator

       37

 55 min

     Yes

   MC

       30

 

 

   Grid-in

        7

 

 

No-Calculator

       20

 25 min

     No

   MC

       15

 

 

   Grid-in

        5

 

 

New SAT Math Section Structure: MC = Multiple Choice; Grid-in = Student-Produced Response

 On the new exam, students will be tested in four key areas, presented here in order of frequency: "Heart of Algebra", in which students will work with formulas, equations, systems of equations, and inequalities; "Problem Solving and Data Analysis", for which students must work with percents, ratios, proportions, units, graphical relationships, and data analysis; "Advanced Math", in which students will rearrange equations and expressions, and work with algebra 2-type quadratic equations; and "Additional Topics", in which students will solve problems in geometry and trigonometry. For about one-third of the questions, students will not be able to use a calculator. Worth mentioning: after citing that having a fifth option available on multiple choice questions did not aid, and often hurt, the validity of the questions it presented, the College Board has decided that there will now be only four answer choices (as compared to the current five) on the new test, and no penalty for wrong answers. Also notable: whereas each question on the current SAT is worth the same value regardless of difficulty level or question type, the new SAT mathematics section features differential point values. While most questions will still be worth a single raw point, grid-ins can be worth up to four times the value of multiple choice questions. This means that students will have to be strategic about the questions to which they dedicate their time.

Major Change 2: Content 

In efforts to make the SAT more relevant to post-secondary admissions committees and workforce expectations, the College Board has changed the makeup of the mathematics section content considerably. Whereas the current SAT features an approximately even mix of algebra, geometry, and number/operations questions and does not test concepts in trigonometry, the new SAT content will emphasize topics that, through research into post-secondary and career readiness, the College Board has recognized as having "great relevance and utility for college and career work." The New SAT Math Section

The "Heart of Algebra" content area will constitute a little over one-third of the questions on the exam, reflecting the relative importance of manipulating expressions and equations and "fluency" in algebraic operations in equation- and graph-based contexts. In particular, there will be a much greater emphasis on systems of equations and function models

About one-quarter of the questions will be "Problem Solving and Data Analysis" questions, which will require students to demonstrate their proficiency in graph and chart interpretation. A move toward this question type reflects the acknowledgment that today's real-world content is presented in media-rich formats: the correct interpretation of everything from magazine articles to technical writings is predicated on one's ability to understand qualitative and quantitative information presented in figures ranging from graphs to tables to pie charts. 

"Advanced" and "additional topics" will account for the remainder of the questions on the new SAT math sections. These categories include more specialized mathematics, including quadratic, cubic, and rational expressions, trigonometric functions, and geometric calculations. Some of these concepts are not tested on the current SAT, and the frequencies of the ones that are will be changing significantly. The reduction in the number of geometry questions is perhaps the most noticeable change––whereas the current SAT tests geometry very frequently, geometry-based questions will make up less than 10 percent of the new SAT's math content. The geometry that does appear will be applied to real-world scenarios.

Major Change 3: Style and Approach

Problem solving is the crux of mathematics. It's the skill that develops in students who become proficient in secondary-level mathematics. The current SAT, however, falls short in measuring students' abilities to perform multi-step reasoning towards a solution. According to the College Board, new multi-part question types will address this issue by presenting problems that require students to consider multiple applications within the same context. These "Extended Thinking" questions will involve real-world calculations like currency conversion, proportional thinking, and percentage-based reasoning. While there are sometimes (but rarely) two or three questions that pertain to a single scenario on the current SAT's math section, the new SAT will feature a single multi-part question worth four points on each administration of the exam. This is consistent with the move towards new question types that test mathematics in practical scenarios. 

In introducing meatier questions, the College Board seeks to stress understanding over procedure. This will be good news for students who have a very solid understanding of the math they learn in school, and bad news for students who make it through their mathematics classes by learning to apply formulas on autopilot. On some of the new problems they'll be seeing, students will need to understand the implications of the information they're given, especially when some of that detail is unnecessary for answering smaller parts of larger questions. 

The New SAT Math SectionThe "No-Calculator" section is another major stylistic change, hearkening back to the early 1990s when students were not allowed to use calculators on the SAT. While this might scare students into thinking they must brush up and their multiplication tables and learn to be speedy mental calculators, it will be more important for them to understand the real nature of things like fractions and decimals, along with the operations used to manipulate them. The College Board's idea in limiting calculator use to one of the two mathematics sections is that for some types of math, calculators should not be used as a crutch, and indeed may actually act as a hindrance to thinking and understanding. 

Summary

The mathematics section of the SAT is changing in big ways. Whereas the current SAT rewards memorization of key procedures, the new test is designed to push students to think; Though all mathematics does boil down to a series of prescribed steps, it's the putting-those-steps-together rationale that, according to the College Board, is the foundation of its new mathematics questions. While the sample question set released by the College Board suggests that many questions will still be prone to formulaic, predictable routes to solutions, it does feature many more context-rich problems that will encourage something more than "plug and chug" mathematics.

And now for the big picture. In the first post of this series, I discussed the competition between the ACT and the College Board as a driver behind the development of the new SAT. The fact of the matter: though it does occasionally require more developed mathematical reasoning, the current ACT's mathematics section is based on procedural regurgitation even more than the current SAT's mathematics section. Will the College Board's emphasis on "real" math (i.e., math that requires thoughtful analysis in context) be so appealing to colleges as to convince admissions offices to value the SAT more highly? This, I believe, is the bet the College Board is placing. Most students will dread the conceptual challenges posed by the new SAT, but if admissions committees see this sort of exam as a more valuable predictor of college success, applicants may have no choice but to bear it.

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