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Oklahoma Mathematics Educator Workshop

Oklahoma Mathematics Educator Workshop. September 28-October 2, 2009. Who’s Who?. Teachers of Grades 3 through 8 Oklahoma State Department of Education Data Recognition Corporation . Goals.

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Oklahoma Mathematics Educator Workshop

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  1. Oklahoma Mathematics Educator Workshop September 28-October 2, 2009 Data Recognition Corporation Copyright 2009

  2. Who’s Who? Teachers of Grades 3 through 8 Oklahoma State Department of Education Data Recognition Corporation Data Recognition Corporation Copyright 2009

  3. Goals • Provide educators with an overview of how mathematics test items are developed and aligned to the PASS standards. • Increase understanding and use of the Mathematics Test and Item Specification documents. • Work collaboratively with educators to create and discuss aligned test items. • Inform educators about various resources for their classrooms. Data Recognition Corporation Copyright 2009

  4. Agenda • Large Group Session • Lunch • Breakout Session Data Recognition Corporation Copyright 2009

  5. OCCT Test Development Cycle Writing of Item Build Test Oper. & Field Test and Item Specs Content & Bias Review Scoring & Reporting Review Item Pool TESTING Data Review Data Recognition Corporation Copyright 2009

  6. Walkthrough of the Guiding Documents PASS Mathematics Standards/Objectives Alignment and validity Mathematics Test Blueprints Percent emphasis of content Mathematics Test and Item Specifications New combined document Clarifies assessment limits, guides item development, and provides sample items Data Recognition Corporation Copyright 2009

  7. Mathematics Test and Item Specifications • Provide parameters and guidelines for item writers and DRC mathematics assessment specialists to design the PASS Math items. • Provide Oklahoma educators and SDE staff with guidance to judge whether or not items are appropriate for field testing.

  8. Mathematics Test and Item Specifications • Components • Emphasis • Assessment Limits • Format for Items • Distractor Domains • Sampling of Items Data Recognition Corporation Copyright 2009

  9. Parts of an Item • Multiple-choice items • Stem • Response Options • Correct Answer • Distractors • Graphics/Artwork (if applicable)

  10. Parts of an Item

  11. What Makes a Good Multiple-Choice Item? Oklahoma Mathematics Educator Workshop September 28-October 2, 2009 Data Recognition Corporation Copyright 2009

  12. Is there clear primary standard alignment? John earned $37.50 for 5 hours of babysitting. At this rate, how much will he earn for 8 hours of babysitting? This item addresses the primary standard of solving a proportion and the non-primary standard of using multiplication and division. Data Recognition Corporation Copyright 2009

  13. Is there clear primary standard alignment? John earned $37.50 for 5 hours of babysitting. At this rate, how much will he earn for 8 hours of babysitting? A $1.07 (5/37.50 = x/8) B $23.44 (5/8 = x/37.50) C $40.50 (5+3=8 so 37.50+3) D $60.00 (correct) Answer options must only reflect errors related to the standard being tested. Data Recognition Corporation Copyright 2009

  14. Is there clear primary standard alignment? Ryan’s garden is 3 feet long and 2 feet wide. What is the area of Ryan’s garden in square inches? This item tests two standards: calculating area and converting units. It should test only one standard. Data Recognition Corporation Copyright 2009

  15. Is the stem context-based? Use this figure to answer the question. What is the area of the square? 11 feet Data Recognition Corporation Copyright 2009

  16. Melissa wants to carpet the floor of a square-shaped room. How many square feet of carpet are needed to cover the floor of Melissa’s room? Is the stem context-based? 11 feet Data Recognition Corporation Copyright 2009

  17. Is the item written as an interrogative? Declarative Form This table shows the number of points Jim scored in 5 games. Find the mean number of points Jim scored. Data Recognition Corporation Copyright 2009

  18. Is the item written as an interrogative? Interrogative Form This table shows the number of points Jim scored in 5 games. What is the mean number of points Jim scored? Data Recognition Corporation Copyright 2009

  19. Is there one and only one correct response? Leticia drew a triangle with two sides of equal length. What type of triangle did Leticia draw? A scalene B isosceles C equilateral D right Data Recognition Corporation Copyright 2009

  20. Is there one and only one correct response? Leticia drew a triangle with exactly two sides of equal length. What type of triangle did Leticia draw? A scalene B isosceles C equilateral D equiangular Data Recognition Corporation Copyright 2009

  21. Do items that require estimation contain qualifiers? What is the approximate value of ? A 5 B 7 C 8 D 10 “Approximate” is too vague. (rounded to nearest 5) (rounded to nearest 1) (rounded up to nearest 1) (rounded up to nearest 5) Data Recognition Corporation Copyright 2009

  22. Do items that require estimation contain qualifiers? Which is closest to the value of ? A 5 B 7 C 8 D 10 closest Data Recognition Corporation Copyright 2009

  23. Do the distractors reflect plausible errors? A rectangular garden is shown. What is the perimeter of the garden? A. 7 feet C. 15 feet B. 8 feet D. 46 feet 8 feet 15 feet Data Recognition Corporation Copyright 2009

  24. Do the distractors reflect plausible errors? A rectangular garden is shown. What is the perimeter of the garden? A. 23 feet C. 60 feet B. 46 feet D. 120 feet (½ area) (area) (½ per.) (correct) 8 feet 15 feet Data Recognition Corporation Copyright 2009

  25. Can authentic data and information be used? What is the mode of the data shown? 5, 13, 20, 8, 9, 15, 13, 17 Data Recognition Corporation Copyright 2009

  26. The normal high temperatures, in ºF, each month in Oklahoma are shown. 47, 54, 62, 71, 79, 87, 93, 93, 84, 74, 60, 50 What is the mode of the temperatures? Can authentic data and information be used? Data Recognition Corporation Copyright 2009

  27. Is the item teaching the student? A board foot is defined as the volume of a piece of square-cut lumber with a top surface area of 1 ft2 and a thickness of 1 in. A lumber company sells pine lumber for $1.25 per board foot. What is the cost of a pine board that is 8 ft. long, 1 ft. wide, and ¾ in. thick? Data Recognition Corporation Copyright 2009

  28. Is the item the specified complexity? Complexity of an item is relative to the grade and developmental levels of the students. Do not confuse difficulty and complexity. Data Recognition Corporation Copyright 2009

  29. Can the item be completed in the time specified? All multiple-choice items must be written so a typical student can complete each item in 1½ minutes or less. Data Recognition Corporation Copyright 2009

  30. Is the item grammatically and structurally correct? Watch for: Tense Number style Plural/singular Third person Data Recognition Corporation Copyright 2009

  31. Is the item testing mathematics or reading? To minimize the influence of student reading ability: Be concise Be direct Maintain linguistic simplicity Use appropriate vocabulary Use simple sentences Write in a positive sense Data Recognition Corporation Copyright 2009

  32. Is the item testing mathematics or reading? Pat is baking cupcakes for the Hyland Elementary School annual fundraiser. Pat’s recipe calls for 2½ cups of flour to make 2 dozen cupcakes. Pat will double the recipe. How many cups of flour does Pat need to make 48 cupcakes? Data Recognition Corporation Copyright 2009

  33. Is the item testing mathematics or reading? Pat is baking cupcakes. The recipe calls for 2½ cups of flour to make 24 cupcakes. How many cups of flour does Pat need to make 48 cupcakes? Data Recognition Corporation Copyright 2009

  34. Is the item bias-free? Bias is the existence of some characteristic of an item and/or test that could result in two individuals of the same ability but from different subgroups performing differently. Data Recognition Corporation Copyright 2009

  35. Is the item bias-free? Types of Bias Stereotyping Gender Bias Regional or Geographic Bias Ethnic Bias Cultural Bias Religious Bias Socioeconomic Bias Age Bias Bias Against Persons with Disabilities Experiential Bias Data Recognition Corporation Copyright 2009

  36. Is the item bias-free? The number of yards rushed each game by Adrian Peterson during the 2008 regular season is shown. 103, 160, 77, 101, 32, 111, 121, 139, 192, 85, 80, 103 What was Peterson’s average number of rushing yards per game for the 2008 regular season? Data Recognition Corporation Copyright 2009

  37. Is the item bias-free? Mrs. Rogers bought a new car for $45,000. She will make car payments of $700 every month. At this rate, how many months will it take Mrs. Rogers to pay for her car? Data Recognition Corporation Copyright 2009

  38. Are response options such as “none of the above” used? NO! Use of phrases like • “none of the above” • “all of the above” • “A and C” are not necessary and tend to decrease the validity of an item. Data Recognition Corporation Copyright 2009

  39. Questions? Data Recognition Corporation Copyright 2009

  40. Grade 3, Objective 2.2aCompare and order whole numbers up to 4 digits. The heights of four mountains are shown in the table. What is the order of the heights from least to greatest? A 12,970 1,300 2,420 29,030 (ordered by first 2 digits) B 29,030 1,300 2,420 12,970 (ordered by last 3 digits) C 1,300 2,420 12,970 29,030 (correct) D 12,970 1,300 2,420 29,030 (ordered 1st, then 2nd digit) Data Recognition Corporation Copyright 2009

  41. Data Recognition Corporation Copyright 2006

  42. Grade 6, Objective 2.1Multiply and divide fractions and mixed numbers to solve problems using a variety of methods. Simone needs 2½ cups of flour for one recipe and 1¾ cups for another. She will double both recipes. How many cups of flour does Simone need in all? A 2 8/17 cups (error converting 17/2) B 3 1/2 cups (converted 4¼ to 9/4) C 7 2/3 cups (adding error) D 8 1/2 cups (correct) Data Recognition Corporation Copyright 2009

  43. Grade 4, Objective 4.3a: Describe the effects on two- and three-dimensional objects when they slide (translate), flip (reflect), and turn (rotate). Fred made a design by reflecting the letter F over a line. Which shows a reflection of the letter F over a line? A B C D F F F F F F F F Data Recognition Corporation Copyright 2009

  44. Grade 7, Objective 1.1Identify and apply the commutative, associative, distributive, inverse, and identity properties. Which shows a use of the commutative property? A (3 + 2) + 4 = 3 + (2 + 4) B (3 + 2) x 4 = 3 x 4 + 2 x 4 C 3 + 2 + 4 = 3 + 4 + 2 D 3 + 2 + 4 = 2 + 3 + 4 Data Recognition Corporation Copyright 2009

  45. Grade 5, Objective 3.2b: Multiply and divide whole numbers and decimal numbers with 1- or 2-digit multipliers or divisors to solve problems. Loren and four friends decided to go out for pizza to celebrate the end of the school year. They bought three large pizzas and five pops. The total cost was $35.60. The 5 friends split the bill evenly. How much did each friend pay? A $0.71 B $7.01 C $7.12 D $712 Data Recognition Corporation Copyright 2009

  46. Grade 5, Objective 3.2b: Multiply and divide whole numbers and decimal numbers with 1- or 2-digit multipliers or divisors to solve problems. Loren and his friends bought pizzas and pop. The total cost was $35.60. The 5 friends divided the cost evenly. How much did each friend pay? A $0.71 B $7.01 C $7.12 D $712 Data Recognition Corporation Copyright 2009

  47. Grade 8, Objective 1.1aModel, write, and solve 2-step linear equations using a variety of methods. Marti has a dog-walking business called Marti’s Marching Mutts. She walks dogs one hour a day, five days a week. She gets paid $7 per hour for each dog. Plus, she gets a $3 bonus each week. Which equation can be used to find the number of weeks, w, it will take Marti to earn $100? A 35w + 3 = 100 B 3w + 35 = 100 C 35w – 3 = 100 D 3w – 35 = 100 Data Recognition Corporation Copyright 2009

  48. Grade 8, Objective 1.1aModel, write, and solve 2-step linear equations using a variety of methods. Marti has $4 and earns $32 a week raking leaves. Which equation can be used to find the number of weeks, w, it will take Marti to have a total of $100? A 32w + 4 = 100 B 4w + 32 = 100 C 32w – 4 = 100 D 4w – 32 = 100 Data Recognition Corporation Copyright 2009

  49. Questions? Data Recognition Corporation Copyright 2009

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