How Best to Prepare Students to Take the SAT Mathematics Test NCTM Annual Meeting Atlanta March 24, 2007

2 Speakers: Dan Lotesto: SAT Mathematics Test Development Committee Fred Schuppan: Educational Testing Service Robin O’Callaghan: The College Board

How is the Mathematics Portion of the Test Created ?

4 Test Development Language Item – Test Question Key – Correct Answer Distractor – Incorrect Answer Choice Pretest – Equating Section that does not count toward score Final Form – Operational Test Sections that count toward score

What is the Configuration of the SAT ?

6 SAT Configuration and Timing Content Number of Sections Total Time Mathematics 3 70 minutes Critical Reading 3 70 minutes Writing 3 60 minutes Equating Section 1 25 minutes

What is the Mathematics Section ?

8 Mathematics Section Configuration SectionsQuestionsTime Section choice25 minutes Section choice 10 SPR 25 minutes Section choice20 minutes Total 44 5-choice 10 SPR 70 minutes

9 Content Areas Number and Operations (20 – 25%) Algebra and Functions (35 – 40%) Geometry and Measurement (25 – 30%) Data Analysis, Statistics, and Probability (10 – 15%)

10 Multiple-Choice Key = C

11 Student-Produced Response Key = 5/2, 2.5

12

The Item

14 Pretesting Items are pretested to determine their difficulty and correlation with the operational test. Items are written by a combination of ETS Staff and Outside Item Writers Each pretest item is reviewed by at least 5 ETS Test Specialists and 3 College Board Test Specialists Pretesting is in the “Equating Section” of the SAT to ensure accurate statistics

15 Initial Submission From Outside Item Writer

16 After First Test Specialist Review

17 Final Version of Item Key = 9.8, 49/5

18 Final Form Assembly Assembler and 2 ETS Test Specialists Review each Final Form Test is sent to College Board and SAT Committee to Review 3 College Board Test Specialists Review each Final Form At least 5 SAT Committee Members Review each Final Form

The SAT Mathematics Development Committee

20 SAT Development Committee A Committee in the early 1990’s 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 will continue to advise the College Board on the SAT

21 College Board SAT Mathematics Development Committee John A. Dossey, ChairIllinois State University, Normal, IL Lynne M. ButlerHaverford College, Haverford, PA James R. ChoikeOklahoma State University, Stillwater, OK Louis P. D’Angelo, Jr.Archmere Academy, Claymont, DE Ruth HaasSmith College, Northampton, MA Roger E. Howe Yale University, New Haven, CT Kenneth J. KoehlerIowa State University, Ames, IA Karen LonghartFlathead High School, Kalispell, MT Daniel V. LotestoRiverside University High School, Milwaukee, WI Alfred B. ManasterUniversity of California–San Diego, La Jolla, CA Monique A. MortonWoodrow Wilson Senior High School, Washington DC Jorge A. PerezLaGuardia Community College, Long Island City, NY Deborah E. PossLassiter High School, Marietta, GA Betty P. TravisUniversity of Texas at San Antonio, San Antonio, TX Charles Vonder EmbseCentral Michigan University, Mount Pleasant, MI

22 Current SAT Mathematics TD Committee James R. Choike, Chair Oklahoma State University, Stillwater, OK Deborah Hughes HallettUniversity of Arizona, Tucson, AZ Roger E. Howe Yale University, New Haven, CT Karen LonghartFlathead High School, Kalispell, MT Daniel V. Lotesto University of Wisconsin-Milwaukee, Milwaukee, WI Alfred B. Manaster University of California–San Diego, La Jolla, CA Monique A. Morton Woodrow Wilson Senior High School, Washington DC Roxy Peck California Polytechnic State University, San Luis Obispo, CA Deborah E. Poss Lassiter High School, Marietta, GA Monica Stephens Spelman College, Atlanta, GA

What Does the Committee Do?

24 Committee Functions Advise on Policy Reasoning vs. achievement? Calculator / noncalculator sections? Final Form Review Item by item decisions Smaller policy decisions

25 Committee Functions Policy Decisions Made Calculator at least at scientific level recommended Knowledge of trigonometry or matrix operations not expected Multiple representations of material encouraged Multiple solution strategies encouraged

26 SAT Committee Review Each final form is mailed to at least 5 SAT Committee members The committee members work the test and return comments by mail Comments are collected and collated by question Committee members meet face-to-face to discuss and resolve comments

How Did You Do on the Practice Test ?

28 Question 1 Key = D Percent Correct: 69%

29 Question 2 Key = E Percent Correct: 51%

30 Question 3 Key = C Percent Correct: 33%

31 Question 4 Key = A Percent Correct: 30%

32 Question 5 Key = 120 < y < 125 Percent Correct: 67%

33 Question 6 Key = 5 Percent Correct: 60%

34 Question 7 Key = 2.5, 5/2 Percent Correct: 28%

35 Question 8 Key = 13/2, 6.5 Percent Correct: 25%

How Can You Help Students Prepare for the Test ?

37 Top 10 Ways To Help Your Students Prepare for the SAT Mathematics Section 10 Be familiar with the calculator you bring to the test

38 Top 10 Ways To Help Your Students Prepare for the SAT Mathematics Section 9Know when and when not to use the calculator Calculator is not helpful in answering the question. Key = C

39 Top 10 Ways To Help Your Students Prepare for the SAT Mathematics Section 9Know when and when not to use the calculator Calculator can be used to perform the arithmetic Key = B 180 – 3(12) = / 4 = 36

40 Top 10 Ways To Help Your Students Prepare for the SAT Mathematics Section 8Understand what content could appear on the SAT and what content will NOT appear on the SAT

41 Top 10 Ways To Help Your Students Prepare for the SAT Mathematics Section What is on the test? More Advanced Algebra Reasoning Questions that Involve Multiple Steps What is NOT on the test? Trigonometry, Logarithms

42 Top 10 Ways To Help Your Students Prepare for the SAT Mathematics Section More Advanced Algebra Key = B

43 Top 10 Ways To Help Your Students Prepare for the SAT Mathematics Section 7For questions you can’t solve, it is in your favor to guess if you can eliminate one or more answer choices If you know the equation is true for k = 0 and k = 1, then A, B and D can be eliminated

44 Top 10 Ways To Help Your Students Prepare for the SAT Mathematics Section 6Don’t spend too much time on any one question

45 Top 10 Ways To Help Your Students Prepare for the SAT Mathematics Section 5For every question (especially Student- Produced Response) ask yourself, “Is my answer reasonable?” “Did I answer the question asked?” Key:2035N = 51,492 Pop 1:2040N = 9,733 Pop 2: 45N = 3,808 Pop 3:2030N = 2,504

46 Top 10 Ways To Help Your Students Prepare for the SAT Mathematics Section 4Read the SAT Preparation Booklet from Cover to Cover

47 Top 10 Ways To Help Your Students Prepare for the SAT Mathematics Section 3Take the Sample Test in the SAT Preparation Booklet under timed conditions

48 Top 10 Ways To Help Your Students Prepare for the SAT Mathematics Section 2Understand the item types in the test, and what formulas are given You should NOT be using test time reading directions. You should know what reference formulas are given and be able to quickly refer to them as needed.

49 Top 10 Ways To Help Your Students Prepare for the SAT Mathematics Section 2Understand what item types are in the test, and what formulas are given

50 Top 10 Ways To Help Your Students Prepare for the SAT Mathematics Section 2Understand what item types are in the test, and what formulas are given

51 Top 10 Ways To Help Your Students Prepare for the SAT Mathematics Section 1For additional practice test material, use “Real SATs”. Only Preparation Publication developed by the makers of the SAT Accurate reflection of the content that may appear in the mathematics questions on an SAT Test Questions are presented in the same style as on the SAT Includes the mathematical reasoning as in the SAT

52 YOUR QUESTIONS Robin O’Callaghan Office of Academic Initiatives and Test Development Mathematics Content Specialist