Reasoning in the Presence of the

Calculator on the SAT

Good ideas in teaching precalculus and…

Rutgers University

March 16, 2012

Presenters

• Brian O’Reilly• The College Board

boreilly@collegeboard.org

• Robin K. O’Callaghan• The College Board

rocallaghan@collegeboard.org 

SAT UPDATE

Pre-calculus Conference

Rutgers University

March 16, 2012

SAT takers in class of 2011:– 44% were minority

students– 27% reported that English

was not exclusively spoken at home

– 45% intend to be first-generation, college-going students

• The SAT is administered by over 7,000 test centers in more than 170 countries!

Who Took the SAT® This Year?

4

The 2011 cohort was the largest, most diverse group ever!

The 2011 cohort was the largest, most diverse group ever!

SAT® Participation: 20 Year Trend + 59%

Note: SAT participation data for 1990-2006 includes students in each year’s graduating class who took the SAT through March of their senior year. SAT participation data for 2011 includes all students in each year’s graduating class who took the SAT through June of their senior year.

Cohort

SAT® Participation Growing; High School Graduates Declining for Six More Years

0%

1%

2%

3%

4%

5%

6%

2007 2008 2009 2010 2011

% C

hang

e vs

. 200

7 Co

hort

US SAT TakersUS High School

Graduates

CohortSource: 2011 College-Bound Seniors Total Group Report; WICHE (2008)

Average SAT® Math Scores by High School GPA

8

Students earning higher grades in high school earned higher math scores on the SAT.

Students earning higher grades in high school earned higher math scores on the SAT.

Average SAT Math Scores

Aver

age

SAT

Mat

h Sc

ores

High School GPA

Average SAT® Math Scores byAverage High School Math Grades

9

Aver

age

SAT

Mat

h Sc

ores

Average High School Math Grade

Students earning higher math grades in high school earned higher math scores on the SAT.Students earning higher math grades in high school earned higher math scores on the SAT.

Average SAT Math Scores

Average SAT® Math Scores by Years of Math Study in High School

10

Average SAT Math Scores

Students taking more years of math in high school earned higher math scores on the SAT.Students taking more years of math in high

school earned higher math scores on the SAT.

Aver

age

SAT

Mat

h Sc

ores

Years of Math Study in High School

Average SAT® Math Scores by Highest Level Math Course Taken

Aver

age

SAT

Mat

h Sc

ores

Highest Level Math Course Taken

Average SAT Math Scores

Students taking higher level math courses earned higher math scores on the SAT.

Students taking higher level math courses earned higher math scores on the SAT.

Math Subject Tests vs. the SAT® Math Section

12

Math 1 Subject Test

Math 1 Subject Test

Math 2 Subject Test

Math 2 Subject Test

SAT Math Section

SAT Math Section

60 minutes(1 section)

60 minutes(1 section)

70 minutes(3 sections: 20,25,25)

70 minutes(3 sections: 20,25,25)

3 years3 years More than 3 yearsMore than 3 years 3 years3 years

44 multiple choice10 student produced44 multiple choice

10 student produced50 multiple choice50 multiple choice

LengthLength

Years of StudyYears of Study

FormatFormat

Test AttributeTest Attribute

Recommended Course Work

Recommended Course Work

• Two years of algebra • One year of geometry • Two years of algebra • One year of geometry

• Two years of algebra • One year of geometry• Some precalculus /

trigonometry

• Two years of algebra • One year of geometry• Some precalculus /

trigonometry

• Two years of algebra • One year of geometry • Two years of algebra • One year of geometry

What’s AssessedWhat’s

AssessedMath content/subject-area knowledge and

the ability to apply that knowledgeMath content/subject-area knowledge and

the ability to apply that knowledge

Mathematical reasoning,problem solving &

critical thinking

Mathematical reasoning,problem solving &

critical thinking

Mathematics Subject Test Selection

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• Students who have taken trigonometry and/or precalculus and received grades of B (or better) should probably select Math Level 2.

Consider taking the test that covers topics learned most recently (when content is fresh in the student’s mind).

Consider the requirements of the colleges and/or programs in which students are interested.

• Students who are sufficiently prepared to take Math Level 2 but take Level 1 in hopes of receiving a higher score may not do as well as they expect to.

• Students who have taken trigonometry and/or precalculus and received grades of B (or better) should probably select Math Level 2.

Consider taking the test that covers topics learned most recently (when content is fresh in the student’s mind).

Consider the requirements of the colleges and/or programs in which students are interested.

• Students who are sufficiently prepared to take Math Level 2 but take Level 1 in hopes of receiving a higher score may not do as well as they expect to.

Choosing Between the Mathematics Levels 1 & 2 Subject TestsChoosing Between the Mathematics Levels 1 & 2 Subject Tests

SAT Subject Tests™ & AP® – How Do They Compare?

14

• Cover more advanced topics or in greater depth, which is more reflective of a college-level course

• Primarily used for college course credit & placement

• Indication of rigor of courses taken in high school

• Cover more advanced topics or in greater depth, which is more reflective of a college-level course

• Primarily used for college course credit & placement

• Indication of rigor of courses taken in high school

SAT Subject TestsSAT Subject Tests AP ExamsAP Exams

• Assess knowledge of fundamental concepts and the ability to apply that knowledge

• Primarily used for college admissions

• Indication of interest in specific subjects

• Assess knowledge of fundamental concepts and the ability to apply that knowledge

• Primarily used for college admissions

• Indication of interest in specific subjects

High-school-level tests that indicate a student’s readiness to

take college-level courses in specific subject areas

College-level tests that assess a student’s knowledge, skills and

abilities learned in the corresponding AP courses

SAT Subject Tests can also provide students without access to certain AP classes the

opportunity to demonstrate subject-matter achievement.

The Timing of AP® Exams and SAT Subject Tests™ Makes a Difference

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• Timing – SAT Subject Tests provide AP students who have not yet taken the AP Exam an opportunity to demonstrate knowledge and achievement during the admission process.

• Most students do not take any AP math course until their senior year; AP Exams are in May.• Subject Tests in Mathematics are offered six times a year and can be taken by students in

any grade.

• Timing – SAT Subject Tests provide AP students who have not yet taken the AP Exam an opportunity to demonstrate knowledge and achievement during the admission process.

• Most students do not take any AP math course until their senior year; AP Exams are in May.• Subject Tests in Mathematics are offered six times a year and can be taken by students in

any grade.

SAT Now on a School Day

• Two SAT School Day test dates in 2011-12 in selected districts and states.

• Administering the test on a school day eliminates barriers of

transportationfamily work obligations

that may hinder weekend testing, helping to get even more students on the road to college.

Increasing Access: State Initiatives, Fee Waivers

States providing/paying for SAT• Maine administers May SAT to all public school juniors• Texas pays SAT fees for any junior for any test date• Delaware administers school-day SAT to all juniors, as will Idaho

Fee Waivers• More than just the waiver of test fees — low-income students get

access to a set of tools that help them realize their college dreams.• Over 350,000 low-income students (21% of all SAT-takers) in the

class of 2011 benefitted from SAT Fee Waiver Services, a 77% increase since 2007

• Over $37 million in SAT fees and services provided to students in grades 9 – 12 during 2010-11 school year.

The SAT Mathematics Test

SAT Mathematics Content Areas

• Number and Operations (20–25%)• Algebra and Functions (35–40%)• Geometry and Measurement (25–30%)• Data Analysis, Statistics, and Probability

(10–15%) 

Multiple Choice

Key = E

Student-Produced Response

Key = 9.8, 49/5

SPR Answer Grid

The SAT Mathematics Development Committee

College Board Committees

• A Committee in the early 1990s advised the College Board on 1994 changes to the SAT.

• A Committee formed in 2002 to advise the College Board on introducing changes to the SAT.

• The present Committee continues to advise the College Board on the SAT.

SAT Mathematics TD Committee

Deborah Hughes Hallett, co-chair University of Arizona, Tucson, AZJ. T. Sutcliffe, co-chair Saint Mark’s School, Dallas, TX

Ann Davidian General Douglas MacArthur HS, Levittown, NY

Katherine Halvorsen Smith College, Northhampton, MA

Paul J. Karafiol Walter Payton College Prep HS, Chicago, IL

Kenneth Millett University of California, Santa Barbara, Santa Barbara, CA

Jose Molina Bellarmine College Preparatory, San Jose, CA

Thomas Morley Georgia Tech, Atlanta, GA

Dwight Pierre Borough of Manhattan Community College, New York, NY

Committee Decisions

• The SAT should remain a reasoning test. • There will not be a no-calculator section of

the SAT.• Students should be able to bring the

calculator they use in their classroom.• Questions admitting multiple solution

strategies (including those involving the calculator) are encouraged.

• Questions involving multiple representations of material are encouraged.

What is the Calculator Policy for the SAT?

The Calculator Policy

• Every question on these tests can be solved without a calculator; however, using a calculator on some questions may be helpful to students. A scientific or graphing calculator is recommended.

• Calculator use is permitted on all sections of the SAT Mathematics test.

• Most calculators are permitted, including those with (CAS) computer algebra systems.

The Calculator/Equity Issue

• The SAT Mathematics test contains questions requiring students to simplify algebraic expressions or to solve equations.

• Students can do this algebra “by hand.”• Students who have and can use a calculator

equipped with CAS (computer algebra system) may be able do this algebra by “pushing buttons.”

What is the Calculator/Equity

Study ?

Questions to be Answered

• What effect, if any, does CAS have on mathematics performance on the SAT?

• What models of calculators are students using on the SAT?

• How are students using their calculators on the SAT?

• Do students who have calculators with CAS have an advantage?

The Study Design

• A short survey at the end of one SAT administration to be answered by all students at that administration

• Two specially designed variable sections, each given to a subset of students at the administration; one pretest contains 6 CAS-active questions; the other contains 6 algebra questions of comparable difficulty

The Study Design

Survey questions:• What calculator did you use on the

Mathematics sections of the test?• Is this the calculator that you use in your

classroom?• How did you use your calculator?

Types of Calculators Brought

Examples of Possible CAS-active Questions

Examples of Algebraic

Translation Problems

P+ = 10%

P+ = 57%

P+ = 15%

P+ = 11%

P+ = 27%

P+ = 34%

Possibly CAS-active but Easy

P+ = 71%

P+ = 71%

P+ = 72%

Calculator Not an Advantage

P+ = 22%

P+ = 10%

P+ = 11%

P+ = 20%

P+ = 11%

P+ = 23%

Calculator Used with Reasoning

P+ = 31%

P+ = 40%

P+ = 23%

YourQuestions

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