how best to prepare students to take the sat mathematics test nctm annual meeting atlanta march 24,...

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

Sections Questions Time

Section 1 20 5-choice 25 minutes

Section 2 8 5-choice

10 SPR25 minutes

Section 3 16 5-choice 20 minutes

Total44 5-choice

10 SPR70 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

InitialSubmissionFromOutsideItemWriter

16

AfterFirstTestSpecialistReview

17

FinalVersionofItem

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, Chair Illinois State University, Normal, IL

Lynne M. Butler Haverford College, Haverford, PA

James R. Choike Oklahoma State University, Stillwater, OK

Louis P. D’Angelo, Jr. Archmere Academy, Claymont, DE

Ruth Haas Smith College, Northampton, MA

Roger E. Howe Yale University, New Haven, CT

Kenneth J. Koehler Iowa State University, Ames, IA

Karen Longhart Flathead High School, Kalispell, MT

Daniel V. Lotesto Riverside University High School, Milwaukee, WI

Alfred B. Manaster University of California–San Diego, La Jolla, CA

Monique A. Morton Woodrow Wilson Senior High School, Washington DC

Jorge A. Perez LaGuardia Community College, Long Island City, NY

Deborah E. Poss Lassiter High School, Marietta, GA

Betty P. Travis University of Texas at San Antonio, San Antonio, TX

Charles Vonder Embse Central Michigan University, Mount Pleasant, MI

22

Current SAT Mathematics TD Committee James R. Choike, Chair Oklahoma State University,

Stillwater, OK Deborah Hughes Hallett University of Arizona, Tucson, AZ

Roger E. Howe Yale University, New Haven, CT

Karen Longhart Flathead 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 StudentsPrepare for the SAT Mathematics

Section

• 10 Be familiar with the calculator you bring to the test

38

Top 10 Ways To Help Your StudentsPrepare for the SAT Mathematics

Section• 9 Know 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 StudentsPrepare for the SAT Mathematics

Section• 9 Know when and when not to use the

calculator

Calculator can be used to perform the arithmetic

Key = B

180 – 3(12) = 144

144 / 4 = 36

40

Top 10 Ways To Help Your StudentsPrepare for the SAT Mathematics

Section• 8 Understand what content could

appear on the SAT and what content will NOT appear on the SAT

41

Top 10 Ways To Help Your StudentsPrepare for the SAT Mathematics

SectionWhat 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 StudentsPrepare for the SAT Mathematics

SectionMore Advanced Algebra

Key = B

43

Top 10 Ways To Help Your StudentsPrepare for the SAT Mathematics

Section• 7 For 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 StudentsPrepare for the SAT Mathematics

Section

• 6 Don’t spend too much time on any one question

45

Top 10 Ways To Help Your StudentsPrepare for the SAT Mathematics

Section• 5 For every question (especially Student- Produced Response) ask yourself, “Is my answer reasonable?” “Did I answer the question asked?”

Key: 2035 N = 51,492 Pop 1: 2040 N = 9,733 Pop 2: 45 N = 3,808 Pop 3: 2030 N = 2,504

46

Top 10 Ways To Help Your StudentsPrepare for the SAT Mathematics

Section

• 4 Read the SAT Preparation Booklet from Cover to Cover

47

Top 10 Ways To Help Your StudentsPrepare for the SAT Mathematics

Section

• 3 Take the Sample Test in the SATPreparation Booklet under timed conditions

48

Top 10 Ways To Help Your StudentsPrepare for the SAT Mathematics

Section• 2 Understand 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 StudentsPrepare for the SAT Mathematics

Section• 2 Understand

what item types are in the test, and what formulas are given

50

Top 10 Ways To Help Your StudentsPrepare for the SAT Mathematics

Section• 2 Understand what item types are in the test, and what formulas are given

51

Top 10 Ways To Help Your StudentsPrepare for the SAT Mathematics

Section• 1 For 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

rocallaghan@collegeboard.org