High Stakes Assessment: Comparing the States (grades 6-12)

1. High Stakes Assessment: Comparing the States(grades 6-12) Dr. Eric Milou2006 NCTM Annual - St. Louis Rowan University (NJ)milou@rowan.edu

2. Types of Exit Exams • MCEs - Minimum Competency Exams • Basic Skill below the HS level • SBEs - Standards Based Exams • Aligned with state standards - usually at 9th/10th grade level • EOCs - End-of-Course Exams • Standards Based but given after a student completes a specific HS course

3. Exit Exams & Graduation • Successful Exit Exam score required for diploma • Exit Exam required but alternative assessments are available as a pathway to graduation • Alternative assessments available for students with disabilities and ELL • Exam is considered in the graduation decision, but it is NOT used to deny a diploma • State exit exam results and/or local performance assessments • Differentiated diplomas or diploma endorsements

4. What follows in this study? • Descriptive (not evaluative) • Based on released tests or just released items • Why were certain states/problems selected? • Range of level (basic skill to higher order) • To show commonalities • Uniqueness/Differences • A wealth of open-ended problems

5. Utah (MCE) • http://www.schools.utah.gov/eval/DOCUMENTS/UBSCT_Subtest_Math2.pdf • Simplify this expression • 12 – 9(2 × 25) • Simplify this expression

6. Utah (MCE) • Lucy wants to treat her pond for mosquitoes. What is the best estimate of the area of her pond? • A. 12 sq. km • B. 18 sq. km • C. 24 sq. km • D. 30 sq. km

7. California (SBE) • California High School Exit Examination (CAHSEE) • http://www.cde.ca.gov/ta/tg/hs/mathrtq05.asp • All Multiple Choice questions • Some sample items are similar to a MCE • 3/4 - 1/6

8. California (SBE) • If x is an integer, what is the solution to |x-3| < 1 • If perimeter, P, of a square may be found by using the formula where A is the area of the square. What is the perimeter of the square with an area of 36 square inches? 24

9. Texas (SBE) • TAKS • http://www.tea.state.tx.us/student.assessment/resources/release/taks/2004/gr11taksjulyb.pdf • All multiple choice

10. Texas (SBE) • Herman claimed that the square of a number is always greater than or equal to the number. Which of the following examples disproves Herman’s claim? • A) A comparison of (-1.5)2 with -1.5 • B) A comparison of (-0.5)2 with -0.5 • C) A comparison of (0.5)2 with 0.5 • D) A comparison of (1.5)2 with 1.5 • The graph of y = 11x2 + c is a parabola with a vertex at the origin. Which of the following is true about the value of c? • A) c > 0 • B) c < 0 • C) c = 0 • D) c = 11

11. Texas (SBE) • The 12-foot-long bed of a dump truck loaded with debris must rise to an angle of 30° before the debris will spill out. Approximately how high must the front of the bed rise for the debris to spill out? 6 ft

12. Texas (SBE) • Start with a 1-unit-by-1-unit unshaded square. In each iteration, the following steps occur for the smallest unshaded squares resulting from the previous iteration. • Step 1: Divide the square into a 3-by-3 grid of squares • Step 2: Shade only the center square of this 3-by-3 grid • What fraction of the 1-unit-by-1-unit square is shaded after the second iteration? 17/81

13. Connecticut (SBE) • Connecticut Academic Performance Test (CAPT) • http://www.csde.state.ct.us/public/cedar/assessment/capt/resources/released_items/2005/Released_Math_Items2.pdf • Released open ended items, sample student work, and rubrics

14. Connecticut (SBE) • Delia’s drafting teacher gave her these instructions for drawing a geometric figure to be used in a design for a birdhouse. • Draw isosceles triangle ABC so that angle A is a right angle • Draw line l through point A that is parallel to BC • Draw line m through point B that is perpendicular to BC • Label a point E at the intersection of lines l and m • Draw the geometric figure in the space provided in your answer booklet. • Delia was asked the measure of angle EBA. What is the degree measure of angle EBA? • Show your work or explain how you found your answer.

15. Which is correct? Triangle ABC is not isosceles

16. A few more…

17. Statewide results • 4-point rubric (0-3 scale) • 3 pts - 30% of students • 2 pts - 15% of students • 1 pt - 14% of students • 0 pts - 29% of students • omitted - 12% of students

18. Connecticut (SBE) • Elena plans to rent a motorbike at the beach. She uses a rental service that charges a fixed fee of $25 plus $15 for each hour or part of an hour that she uses the bike. Fill in the table and extend the patterns to show the total charges if she works from 9:15 am to 5:40 pm.

19. Connecticut (SBE) • Three-course dinner special $9.95 - choose one dish from each group below • Salad: Mixed Greens, Waldorf, Caesar • Main Dish: Eggplant, Salmon, Pork, Chicken • Dessert: Chocolate Mousse, Pecan Pie • How many different three-course meals are possible? • The manager wants to add one item to the menu that will increase the number of possible three-course meals. What should he add to give the greatest possible choices of three course meals? 3 x 4 x 2 = 24 Dessert

20. South Carolina (SBE) • HSAP • http://www.myscschools.com/offices/assessment/Programs/HSAP/releaseitems.htm • Open ended items

21. South Carolina (SBE) • Mr. Jones is planning to put a fence around a rectangular part of his yard. He wants the area to be 216 square feet. The fenced part of his yard has a length of 18 feet. • a.How many feet should the width of the fenced yard be? Show your work to support your answer. • b.Mr. Jones wants to put a 3-foot gate on one side of the fenced yard. How many feet of fencing does he need for the rest of the fenced yard? Show your work to support your answer. 12 57

22. South Carolina (SBE) • Which of the following will always represent a subset of integers? • Ⓐ minimum wage • Ⓑ grocery receipt total • Ⓒ amount of gas in a car • Ⓓ number of students in the lunchroom

23. Washington (SBE) • WASL • Sample test and open ended items • http://www.k12.wa.us/assessment/WASL/WASLPractice-Teacher.aspx

24. Washington (SBE) • Joseph and Cindy made up a game in their mathematics class. To earn points in the game, each player rolls a six-sided cube with numbers 1 through 6 on the sides and then flips a coin. When the coin lands “tails up,” the player gets a total number of points equal to the number at the top of the cube. When the coin lands “heads up,” the player’s points are doubled for that turn. In the box below, list all the possible outcomes for each turn. Then indicate the probability of a player getting 6 points in one turn.

25. Game results • Probability of getting 6 points? • 2/12 = 1/6 • Better question: What is the probability of getting at least 6 points

26. Washington (SBE) • Briefly describe the changes that took place for one group during the entire time period shown. Name the group and describe the changes using numbers and years in your description. • Describe one way that any two of the groups changed in relation to one another during a particular period of time. Name the two groups. Give the time period you are considering. Describe how the two groups changed in relation to one another during that particular time period.

27. Massachusetts (SBE) • MCAS • http://www.doe.mass.edu/mcas/2005/release/ • Sample test with open ended items

28. Massachusetts (SBE) • The graph below shows the number of milligrams of a medication in the bloodstream from the time it was administered to 300 minutes after administration. Using the information from the graph, which of the following statements is true? • A. The maximum amount of medication in the bloodstream was 12 milligrams. • B. The minimum amount of medication was in the bloodstream 300 minutes after administration. • C. The amount of medication in the bloodstream increased at a faster rate than it decreased. • D. The maximum amount of medication was in the bloodstream 100 minutes after administration.

29. Massachusetts (SBE) • In a report on the history of irrational numbers, Celine compared three different values that have been used to approximate π. The values are listed below. • Egyptian approximation……. Chinese approximation…… • Archimedes’ approximation (Greek)…….. • a. Celine compared the approximation used by the Egyptians to a value (22/7) often used for π. She converted both to decimals rounded to four decimal places (nearest ten-thousandth). To the nearest ten-thousandth, what is the absolute value of the difference between them. Show or explain how you got your answer. • b. Celine also compared the approximation used by the Chinese to 22/7. To the nearest ten-thousandth, what is the absolute value of the difference between them. • c. Celine knows that π is approximately 3.1415927. Place the four approximations in order from least to greatest.

30. Idaho (SBE) • Direct Mathematics Assessments (DMA) • http://www.sde.state.id.us/instruct/math/statewidetest.htm

31. Idaho(SBE) • a. In the space provided, draw in the diagonals for the six-sided polygon. • b. How many diagonals are there in an 8-sided polygon? Show or explain how you found your answer. • c. Explain how you would determine the number of diagonals in a 15-sided polygon. 9

32. Idaho (SBE) • A new game called Right Triangle Toss is becoming very popular. Take a beanbag and toss it onto the board while blindfolded. The object is to toss three beanbags into the same region. What is the area of each colored region? Show or explain how you find your answer. • What is the probability of one beanbag being tossed into the red region? The blue region? The yellow region? • Find the probability of a beanbag landing in the yellow region three times in a row.

33. New York (EOC) • Multiple Choice and Open-Ended • January 2006: Math A • http://www.nysedregents.org/testing/mathre/a106.pdf • January 2006: Math B • http://www.nysedregents.org/testing/mathre/b106.pdf

34. New York (EOC) - Math A

35. NY - Math A • As shown in the accompanying diagram, a ladder is leaning against a vertical wall, making an angle of 70° with the ground and reaching a height of 10.39 feet on the wall. • Find, to the nearest foot, the length of the ladder. • Find, to the nearest foot, the distance from the base of the ladder to the wall.

36. NY - Math B • On the accompanying diagram, draw a mapping of a relation from set A to set B that is not a function. Explain why the relationship you drew is not a function.

37. NY - Math B • An architect is using a computer program to design the entrance of a railroad tunnel. The outline of the opening is modeled by the function f(x) = 8 sin x + 2, in the interval 0 ≤ x ≤ π, where x is expressed in radians. • Solve algebraically for all values of x in the interval 0 ≤ x ≤ π, where the height of the opening, f(x), is 6. Express your answer in terms of π. If the x-axis represents the base of the tunnel, what is the maximum height of the entrance of the tunnel?

38. f(x) = 8 sin x + 2 • Maximum height (π/2, 10)

39. Tennessee (EOC) • Secondary TCAP Assessment • http://www.tennessee.gov/education/assessment/pdf/Math%20Item%20Sampler%2006.pdf • Multiple Choice only

40. Tennessee (EOC) • Melissa is sewing a quilt using this pattern. To continue the pattern, which piece should she place at the arrow?

41. Tennessee (EOC) • The graph shows the weight of a puppy as a function of age in weeks. What is the domain of the function shown on the graph?

42. Tennessee (EOC) • When his bus arrives, Calvin is 40 ft east of the corner. The door of the bus is 30 ft north of the corner. If Calvin runs directly across the field to the bus, how far will he run?

43. Virginia (EOC) • SOL end-of-course assessments • Algebra I & Geometry • http://www.pen.k12.va.us/VDOE/Assessment/Release2005/RIB_EOCA1_WEB.pdf • Multiple Choice

44. Virginia (EOC) • What property makes this equation true? • A) Reflexive • B) Associative • C) Commutative • D) Distributive

45. Virginia (EOC) • The ordered pairs in the sets shown below are of the form (x, y). In which set is y a function of x? • A) {(1, 3) , (2, 6) , (3, 1) , (6, 3)} • B) {(1, 3) , (3, 1) , (3, 4) , (4, 3)} • C) {(1, -2) , (1, 0) , (1, 5) , (1, 7)} • D) {(0, 3) , (1, 4) , (2, 4) , (2, 8)}

46. Virginia (EOC) • Sam and Max sell bags of peanuts and popcorn at baseball games. One matrix (bottom left) shows the number of bags they sold during the July 1st game. The second matrix shows the number of bags sold during the July 2nd games. Which matrix shows how many more bags were sold during the second games than in the first?

47. Center on Education Policy • How have High School Exit Exams changed our Schools? Perspectives from Virginia and Maryland • Exams have had a “noticeable impact,” leading to significant changes in instructional content and methods, allocation of resources, staffing patterns, and school climate. • Teachers and principals – even those who disagree with the exit exam policy – seem committed to helping students pass the exams. • Educators spend more time emphasizing topics and skills likely to be tested and on test taking skills, bringing greater focus to instruction but potentially inhibiting more in-depth learning and time for non-tested topics.

48. Center on Education Policy • While students are generally aware of the exam requirements and remediation options, some did not know about key aspects including the content likely to be covered on the tests. • Schools have changed staffing patterns to assign some of their strongest teachers to teach tested subjects and to make staff available for remediation. • Districts devote the most time and energy to in-school remediation and test prep classes, rather than after-school or summer school programs. • Districts emphasized the need for more resources to cover additional costs related to exit exams.

49. Mixed Messages • What State High School Tests Communicate About Student Readiness for College • Center for Educational Policy Research (University of Oregon) • States should undertake studies of students scores on state tests and subsequent performance in college • State tests should be revised to include additional optional items for college bound students. • States should work closer with representations from postsecondary education to help promote greater alignment with college entrance skills.

50. Wall Street Journal: March 23, 2006 • Florida and Houston, Texas have adopted plans tying teacher salaries to student test scores. • Denver, Colorado and some districts in Minnesota are basing teacher salaries on a variety of performance criteria, including test scores.