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


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 ... – PowerPoint PPT presentation

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

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
  • 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
  • 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

Texas (SBE)
  • TAKS
  • http//www.tea.state.tx.us/student.assessment/reso
  • 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
  • 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?

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

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
  • 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

3 x 4 x 2 24
South Carolina (SBE)
  • HSAP
  • http//www.myscschools.com/offices/assessment/Prog
  • 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.

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-

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
  • Egyptian approximation. Chinese
  • 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

  • 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
  • c. Explain how you would determine the number of
    diagonals in a 15-sided polygon.

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

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
  • 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/
  • 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
  • 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
  • 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
  • Districts devote the most time and energy to
    in-school remediation and test prep classes,
    rather than after-school or summer school
  • 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
  • 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
  • The School Redesign Network at Stanford
  • Do Graduation Tests Measure Up? A Closer Look at
    State High School Exit Exams
  • Achieve

  • 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

Thank You!
  • Dr. Eric Milou
  • Rowan University
  • milou_at_rowan.edu
  • REMINDER Speaker proposal deadline for NCTM 07
    in Atlanta May 1, 2006
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