Oped | Pre-Calculus IS on the SAT and students need it by 11th grade

An Opinion by Carolyn Simpson, SVSD School Board Director

You hear it everywhere: most kids will need some college. You hear it from President Obama and from our state’s Washington Student Achievement Council. More importantly, you hear it from the vast majority of students themselves when asked: do you want to go to college?   

As a parent and as a school board member, I want to share my opinion about math paths and preparing students to have college and career options upon high school graduation. Specifically, I will focus on the benefits of Pre-Calculus by junior year (which means Algebra by 8^th grade) for students who are capable, and the potential impact on SAT scores.

You will read below that Pre-Calculus is on the newly redesigned SAT.  You will learn that:

• The College Board said that Pre-Calculus is on the new SAT,
• The College Board said that the old test went up to Algebra 2 and the new test goes beyond Algebra 2,
• The College Board said they made a decision to add Pre-Calculus during the re-design process, and
• The Test Specifications for the Redesigned SAT include many of the topics in the Pre-Calculus textbook table of contents.

The SAT in general

Most students who are contemplating college will take the SAT (and/or ACT) sometime between late March and early June of their 11^th grade, and many will take it a second time (to try to improve their score) in the same period or at the beginning of 12^th grade before completing college applications due in the fall. 

The SAT and ACT are tests used by colleges in their admission practices. Scores not only are considered as part of admissions decisions, but also influence whether students can earn merit-based financial aid, which can be a make-or-break determinant in the decision to attend college.  Although there has been much reported recently about adding social and emotional measurements in the college admission process, most colleges still use and still plan to use the SAT and/or ACT in the long list of admissions decision criteria.

Recently (debut in March 2016), the College Board redesigned the SAT to more directly focus on “college and career readiness and success and rigorous instructional practice.”  In the Math Section, the “Test Specifications for the Redesigned SAT” states:

“The overall aim of the SAT Math test is to assess fluency with, understanding of, and ability to apply the mathematical concepts, skills, and practices that are most strongly prerequisite for and useful across a range of college majors and careers . . . The SAT Math test will reward a much stronger command of fewer, more important topics.  To succeed on the redesigned SAT, students will need to exhibit command of mathematical practices, fluency with mathematical procedures and conceptual understanding of mathematical ideas.  In keeping with the evidence, the exam will also provide opportunities for richer applied problems.”

Is Pre-Calculus on the New 2016 SAT?

There has been some confusion if Pre-Calculus topics are on the re-designed SAT – and was even recently discussed at the April 14th school board meeting.  This question is relevant  in the Snoqualmie Valley School District because district’s new math pathways impact the number of students who can access Algebra during middle school – AND without Algebra by 8^th grade, a student cannot reach Pre-Calculus by 11^th grade (SAT test time) without doubling up during high school, as illustrated here:

Although many news reports and tutoring centers report that Pre-Calculus topics are on the redesigned SAT, this is not spelled out clearly on the College Board’s website.  In the very detailed “Test Specifications for the Redesigned SAT,” the section “Detailed Description of the Content and Skills Measured by the SAT Math Test” lays out topic contents and descriptions, but it does not lay it out by high school math course, making this difficult to ascertain.

To ascertain whether Pre-Calculus is on the re-designed SAT, two approaches were taken: 1) phone calls were made to the College Board; 2) the “Test specifications” were compared to the contents of the SVSD Algebra 2 and Pre-Calculus textbooks.

What the College Board says

In early April, an SVSD parent phoned the College Board (administrates the SAT) and spoke with a supervisor, and asked, “Does the new SAT have Pre-Calculus questions on it.”  The supervisor responded, “In the Passport to Advanced Math section of the new SAT, there are Pre-Calc questions.”  When asked, “Did it only go up to Algebra 2 in the old SAT?” the response was “Yes.” When asked, “Does it go beyond Algebra 2 in the new SAT?” the response was “Yes.”

On 4/21/2016, I called the High School Counselor hotline at the College Board. After explaining that I was a school board director, and not a high school counselor, I added that I am very interested in ensuring that our courses are aligned to prepare our students to do their best on the new SAT by spring of their junior year.  I asked, “Does the newly redesigned SAT have Pre-Calculus questions on it?”  The response was, “Yes, I can tell you that there are Pre-Calc questions on the new SAT.”  The College Board “agent” (who gave me permission to quote him) went on to add, “During the redesign process, there was talk and decisions were made to put Pre-Calc in there.”

The new 2016 SAT Contents vs. Alg 2 and Pre-Calculus Textbooks

I went even further so that I could understand better.  I took the SAT Test Specifications and compared them to the SVSD’s Algebra 2 and Pre-Calculus textbooks.  I discovered that there is a lot of commonality between these two courses, and I can see how there is some confusion. Manu Pre-Calculus topics are first introduced during Algebra 2, BUT the use of the topics is re-iterated and greatly expanded in Pre-Calculus.   (I almost compare it to learning a language and answering the question “Is Spanish 1 covered in Spanish 2” and how the answer is yes, but there is more fluency and more conceptual understanding that is developed during Spanish 2.)

A few examples: In Algebra 2, trigonometric ratios and functions are introduced toward the end in Chapter 9. But, in Pre-Calculus, they are used throughout and combined with other topics. The concepts of Unit Circle, radians, arcs, and degrees are introduced in Algebra 2, and greatly expanded, including using trigonometric ratios and functions in Pre-Calculus.

The SAT also covers Data Analytics, Statistics, and Probability in both the math and reading/writing sections.  From reading the Test Specifications, these topics are so prevalent in the new SAT because of their use in college and careers. SVSD students get some exposure to these topics at the end of the Algebra 1 and at the very end of the Algebra 2 (if the class finishes the book, see below). Again, these topics are covered in much more depth in Pre-Calculus.

To be even more specific, here is a partial list of topics which appear on both the SAT Test Specifications  and in the Table of Contents of the Pre-Calculus textbook   :

• Linear Equations in Two Variables
• Functions – Quadratic, Rational, Polynomial, and Trigonometric
• Two Variable Linear Systems
• Right Angle Trigonometry
• Complex numbers
• Radian and Degree Measure
• Probability

This explains that students who take Pre-Calculus by junior year will be better prepared for the SAT because of the in-depth coverage of many of these topics.    

For students who are in Algebra 2 as juniors, they are not only missing the in-depth coverage of content in Pre-Calculus, but there is also a timing issue for even the introduction of some important math concepts. These Algebra 2 juniors may not even be introduced to major components of the SAT prior to taking the test. The entire chapters covering trigonometric ratios and functions and data analysis, statistics, and probability are at the end of the Algebra 2 book.  These students may not have the benefit of learning these chapters prior to taking the test in the spring of their junior year, even if the class finishes the book. 

[At the April 14th school board meeting, it was also stated that the SVSD Algebra 2 classes have not been completing the textbook, although they hope to be able to cover more in the future. Parents need to be aware of this so they can plan with their students accordingly to prepare for the SAT.]

The New 2016 SAT’s focus on fluency and conceptual understanding of math

It seems clear throughout the explanation of the redesigned SAT, that there is strong evidence of the benefits of more in-depth use of many Pre-Calculus math concepts –  rather than the introduction of the topics in Algebra 2. 

The word “fluency” is used 17 times in the math section of the Test Specifications document.  The phrase “conceptual understanding” is used 7 times.  They are usually used together.  It states in one of those cases “the redesigned SAT assesses fluency with mathematical procedures and conceptual understanding with equal intensity.”

It also states:

“Applications on the redesigned SAT’s Math Test require students to demonstrate the ability to analyze a situation, determine the essential elements required to solve the problem, represent the problem mathematically, and carry out a solution.  These applications often also require linking topics within the mathematics domain (e.g. functions and statistics) and across disciplines (e.g., math and science).  Learning to model and problem solve is enhanced when students use the same mathematics (e.g., linear equations) to solve problems in different contexts (e.g., science, social studies, or careers).”    And, it states, “The redesigned SAT’s Math Test requires students to apply their mathematics knowledge, skills, and understandings in challenging, authentic context. . . . Students taking the Math Test will encounter a range of disciplines and will be asked to address real-world problems . . . and demonstrate a capacity for sustained reasoning over the multiple steps required to answer many of the questions on the exam.  In these ways, the Math Test also rewards and incentivizes valuable work in the classroom.”

Conclusion:  Yes, Pre-Calculus is on the New 2016 SAT

So, is Pre-Calculus on the SAT?  Indeed it is, and so is Algebra 2.  And, the impact of Pre-Calculus influencing success on the SAT isn’t new. Even before the redesign, having Pre-Calculus by junior year was linked to higher SAT scores (there are probably other reasons as well).  

In 2015, before the redesign of the test, the College Board’s Total Group Profile Report provides data showing  students who had Pre-Calculus or higher by their junior year (presumed from Calculus by senior year) had a 36% higher score on average than students whose highest math course in high school was Algebra 2 and a 20% higher score than students whose senior year class was Pre-Calculus, shown here:

My opinion

As a parent and as a school board member, I think families need to know that students will have a much better chance to be prepared for success on the math portion (and parts of the reading and writing portion) of the SAT if they have Pre-Calculus by 11^th grade.  Although my opinion is based upon the many benefits of this math path, today I focus mostly on the information about Pre-Calculus on the SAT.  I was particularly influenced by:

• The list of topics between the Pre-Calculus textbook which coincide with SAT Test Specifications,
• The SAT’s overwhelming focus on fluency and conceptual understanding of these topics,
• The influence on SAT achievement by having Pre-Calculus prior to taking the test.

Because of the SAT’s use in the college admissions process and its use in merit based financial aid decisions, I encourage all students who are interested in college (and who can be capable in these courses) to take Algebra in 8^th grade and Pre-Calculus by 11^th grade. 

For those who may need or prefer a slower or a different math path but still want college as an option, it is important for parents and teachers to develop supports and interventions to help them do their best on the SAT in light of some of the timing and depth issues discussed here.

[1] SAT Comparison Grid, Old SAT v. New SAT https://www.c2educate.com/test-prep/new-sat-test/; New SAT: Helping your Child Prepare http://washingtonparent.com/articles/1601/1601-new-sat.php;  Washington Post: Is SAT Angst Easing Off?  https://www.washingtonpost.com/local/education/is-sat-angst-easing-off-here-are-some-tips-for-dispelling-pre-test-terror/2015/09/06/5c1dc126-5297-11e5-8c19-0b6825aa4a3a_story.html