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 Robin K. O’Callaghan The College Board

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!

SAT ® Participation: 20 Year Trend + 59% Note: SAT participation data for 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 US SAT Takers US High School Graduates Cohort Source: 2011 College-Bound Seniors Total Group Report; WICHE (2008)

SAT-takers Mathematics and Science Course Work, Over Time or more years of Mathematics78%74%70%68%65% AP or Honors36%31%30%29%23% Pre-calculus29%*50%45%38%32% Calculus25%*28%24%23%19% 4 or more years of Science61%55%49%48%40% AP or Honors34%31%30%29%22% Chemistry89%88%86%84%81% Physics51%53%48%47%44% * Highest level math course taken

Average SAT ® Math Scores by High School GPA 8 Students earning higher grades in high school earned higher math scores on the SAT. Average SAT Math Scores High School GPA

Average SAT ® Math Scores by Average High School Math Grades 9 Average SAT Math Scores Average High School Math Grade 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. Average SAT Math Scores Years of Math Study in High School

Average SAT ® Math Scores by Highest Level Math Course Taken Average SAT Math Scores Highest Level Math Course Taken Average SAT Math Scores 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 2 Subject Test 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 years More than 3 years 3 years 44 multiple choice 10 student produced 44 multiple choice 10 student produced 50 multiple choice Length Years of Study Format Test Attribute 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 Assessed Math content/subject-area knowledge and the ability to apply that knowledge Mathematical reasoning, problem solving & critical thinking

Mathematics Subject Test Selection 13 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 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 Tests AP 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 15 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 in selected districts and states. Administering the test on a school day eliminates barriers of transportation family 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 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-chairUniversity of Arizona, Tucson, AZ J. T. Sutcliffe, co-chair Saint Mark’s School, Dallas, TX Ann DavidianGeneral 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+ = 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%

Your Questions ????