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High Stakes Assessment Comparing the

States (grades 6-12)

- Dr. Eric Milou 2006 NCTM Annual - St. Louis

Rowan University (NJ) milou_at_rowan.edu

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

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

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

Utah (MCE)

- http//www.schools.utah.gov/eval/DOCUMENTS/UBSCT_S

ubtest_Math2.pdf - Simplify this expression
- 12 9(2 25)
- Simplify this expression

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

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

California (SBE)

- If x is an integer, what is the solution to

x-3 lt 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

Texas (SBE)

- TAKS
- http//www.tea.state.tx.us/student.assessment/reso

urces/release/taks/2004/gr11taksjulyb.pdf - All multiple choice

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

Hermans 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 gt 0
- B) c lt 0
- C) c 0
- D) c 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

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

Connecticut (SBE)

- Connecticut Academic Performance Test (CAPT)
- http//www.csde.state.ct.us/public/cedar/assessmen

t/capt/resources/released_items/2005/Released_Math

_Items2.pdf - Released open ended items, sample student work,

and rubrics

Connecticut (SBE)

- Delias 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.

Which is correct?

Triangle ABC is not isosceles

A few more

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

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 915 am to 540 pm.

Hours Charges

0 lt h 1

1 lt h 2

2 lt h 3

3 lt h 4

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

South Carolina (SBE)

- HSAP
- http//www.myscschools.com/offices/assessment/Prog

rams/HSAP/releaseitems.htm - Open ended items

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

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

Washington (SBE)

- WASL
- Sample test and open ended items
- http//www.k12.wa.us/assessment/WASL/WASLPractice-

Teacher.aspx

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 players 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.

Game results

T1 1

T2 2

T3 3

T4 4

T5 5

T6 6

H1 2

H2 4

H3 6

H4 8

H5 10

H6 12

- Probability of getting 6 points?
- 2/12 1/6
- Better question What is the probability of

getting at least 6 points

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.

Massachusetts (SBE)

- MCAS
- http//www.doe.mass.edu/mcas/2005/release/
- Sample test with open ended items

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.

Massachusetts (SBE)

- In a report on the history of irrational numbers,

Celine compared three different values that have

been used to approximate p. 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 p. 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 p is approximately

3.1415927. Place the four approximations in

order from least to greatest.

Idaho (SBE)

- Direct Mathematics Assessments (DMA)
- http//www.sde.state.id.us/instruct/math/statewide

test.htm

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

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.

New York (EOC)

- Multiple Choice and Open-Ended
- January 2006 Math A
- http//www.nysedregents.org/testing/mathre/a106.pd

f - January 2006 Math B
- http//www.nysedregents.org/testing/mathre/b106.pd

f

New York (EOC) - Math A

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.

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.

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 p,

where x is expressed in radians. - Solve algebraically for all values of x in the

interval 0 x p, where the height of the

opening, f(x), is 6. Express your answer in terms

of p. If the x-axis represents the base of the

tunnel, what is the maximum height of the

entrance of the tunnel?

f(x) 8 sin x 2

- Maximum height (p/2, 10)

Tennessee (EOC)

- Secondary TCAP Assessment
- http//www.tennessee.gov/education/assessment/pdf/

Math20Item20Sampler2006.pdf - Multiple Choice only

Tennessee (EOC)

- Melissa is sewing a quilt using this pattern. To

continue the pattern, which piece should she

place at the arrow?

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?

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?

Virginia (EOC)

- SOL end-of-course assessments
- Algebra I Geometry
- http//www.pen.k12.va.us/VDOE/Assessment/Release20

05/RIB_EOCA1_WEB.pdf - Multiple Choice

Virginia (EOC)

- What property makes this equation true?
- A) Reflexive
- B) Associative
- C) Commutative
- D) Distributive

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)

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?

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.

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.

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.

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.

Other Required Reading

- Multiple Measures Approaches to High School

Graduation - The School Redesign Network at Stanford

University - Do Graduation Tests Measure Up? A Closer Look at

State High School Exit Exams - Achieve

Summary

- As of June 2005 19 states required an exit exam

for graduation - By 2012, 26 states will require an exit exam (75

of the students in America) - Majority of exit exams contain open ended items,

but this number is decreasing - End of Courses exams are gaining popularity
- My website with links to all states released

items http//www.rowan.edu/math/milou/STATES/Resea

rchstatehsexam.html

Thank You!

- Dr. Eric Milou
- Rowan University
- milou_at_rowan.edu
- REMINDER Speaker proposal deadline for NCTM 07

in Atlanta May 1, 2006