1. Introduction to Using Curriculum- Based Measurement for Progress Monitoring in Math

2. Overview  7-step process for monitoring student progress using Math CBM  Math CBM instruments for different grade levels  Monitoring progress, graphing scores, and setting goals  Decision-making using progress monitoring data

3. CBM Review  Brief and easy to administer  All tests are different, but assess the same skills at the same difficulty level within each grade level  Monitors student progress throughout the school year: Probes are given at regular intervals –Weekly, bi-weekly, monthly  Teachers use student data to quantify short- and long-term goals  Scores are graphed to make decisions about instructional programs and teaching methods for each student

4. CBM Is Used to:  Identify at-risk students  Help general educators plan more effective instruction  Help special educators design more effective instructional programs  Document student progress for accountability purposes, including IEPs  Communicate with parents or other professionals about student progress

5. Finding CBMs That Work for You:  Creating CBM probes is time- consuming!  We recommend utilizing these resources to obtain ready-made probes: –NCSPM Tools chartNCSPM Tools chart –www.interventioncentral.orgwww.interventioncentral.org

6. Steps to Conducting Progress Monitoring Using Math CBM Step 1: Place students in a mathematics CBM task for progress monitoring Step 2: Identify the level of material for monitoring progress Step 3: Administer and score Mathematics CBM probes Step 4: Graph scores Step 5: Set ambitious goals Step 6: Apply decision rules to graphed scores to know when to revise programs and increase goals Step 7: Use the CBM database qualitatively to describe students’ strength and weaknesses

7. Uses of Math CBM for Teachers  Describe academic competence at a single point in time  Quantify the rate at which students develop academic competence over time  Build more effective programs to increase student achievement

8. Step 1: Place Students in a Mathematics CBM Task for Progress Monitoring  Kindergarten and Grade 1: –Number Identification –Quantity Discrimination –Missing Number  Grades 1–6: –Computation  Grades 2–6: –Concepts and Applications

9. Step 2: Identify the Level of Material for Monitoring Progress  Generally, students use the CBM materials prepared for their grade level.  However, some students may need to use probes from a different grade level if they are well below grade- level expectations.

10. Identifying the Level of Material for Monitoring Progress  To find the appropriate CBM level: –On two separate days, administer a CBM test (either Computation or Concepts and Applications) at the grade level at which you expect the student to be functioning at year’s end. Use the correct time limit for the test at the lower grade level. If the student’s average score is between 10 and 15 digits or blanks, then use this lower grade-level test. If the student’s average score is less than 10 digits or blanks, then move down one more grade level. If the average score is greater than 15 digits or blanks, then reconsider grade-appropriate material.

11. Identifying the Level of Material for Monitoring Progress  If students are not yet able to compute basic facts or complete concepts and applications problems, then consider using the early numeracy measures.  However, teachers should move students on to the computation and concepts and applications measures as soon as the students are completing these types of problems.

12. Step 3: Administer and Score Mathematics CBM Probes  Computation and Concepts and Applications probes can be administered in a group setting, and students complete the probes independently. Early numeracy probes are individually administered.  Teacher grades mathematics probe.  The number of digits correct, problems correct, or blanks correct is calculated and graphed on student graph.

13. Kindergarten and Grade 1  Number Identification  Quantity Discrimination  Missing Number

14. Number Identification  For students in kindergarten and Grade 1: –Student is presented with 84 items and asked to orally identify the written number between 0 and 100. –After completing some sample items, the student works for 1 minute. –Teacher writes the student’s responses on the Number Identification score sheet.

15. Number Identification: Student Form  Student’s copy of a Number Identification test: –Actual student copy is 3 pages long.

16. Number Identification: Scoring Form  Jamal’s Number Identification score sheet: –Skipped items are marked with a (-). –Fifty-seven items attempted. –Three items are incorrect. –Jamal’s score is 54.

17. Number Identification Administration and Scoring Tips  If the student does not respond after 3 seconds, then point to the next item and say, “Try this one.”  Do not correct errors.  Teacher writes the student’s responses on the Number Identification score sheet. Skipped items are marked with a hyphen (-).  At 1 minute, draw a line under the last item completed.  Teacher scores the task, putting a slash through incorrect items on score sheet.  Teacher counts the number of items that the student answered correctly in 1 minute.

18. Quantity Discrimination  For students in kindergarten and Grade 1: –Student is presented with 63 items and asked to orally identify the larger number from a set of two numbers. –After completing some sample items, the student works for 1 minute. –Teacher writes the student’s responses on the Quantity Discrimination score sheet.

19. Quantity Discrimination: Student Form  Student’s copy of a Quantity Discrimination test:  Actual student copy is 3 pages long.

20. Quantity Discrimination: Scoring Form  Lin’s Quantity Discrimination score sheet: –Thirty-eight items attempted. –Five items are incorrect. –Lin’s score is 33.

21. Quantity Discrimination Administration and Scoring Tips  If the student does not respond after 3 seconds, then point to the next item and say, “Try this one.”  Do not correct errors.  Teacher writes student’s responses on the Quantity Discrimination score sheet. Skipped items are marked with a hyphen (-).  At 1 minute, draw a line under the last item completed.  Teacher scores the task, putting a slash through incorrect items on the score sheet.  Teacher counts the number of items that the student answered correctly in 1 minute.

22. Missing Number  For students in kindergarten and Grade 1: –Student is presented with 63 items and asked to orally identify the missing number in a sequence of four numbers. –Number sequences primarily include counting by 1s, with fewer sequences counting by 5s and 10s –After completing some sample items, the student works for 1 minute. –Teacher writes the student’s responses on the Missing Number score sheet.

23. Missing Number: Student Form  Student’s copy of a Missing Number test: –Actual student copy is 3 pages long.

24. Missing Number: Scoring Form  Thomas’s Missing Number score sheet: –Twenty-six items attempted. –Eight items are incorrect. –Thomas’s score is 18.

25. Missing Number Administration and Scoring Tips  If the student does not respond after 3 seconds, then point to the next item and say, “Try this one.”  Do not correct errors.  Teacher writes the student’s responses on the Missing Number score sheet. Skipped items are marked with a hyphen (-).  At 1 minute, draw a line under the last item completed.  Teacher scores the task, putting a slash through incorrect items on the score sheet.  Teacher counts the number of items that the student answered correctly in 1 minute.

26. Computation  For students in Grades 1–6: –Student is presented with 25 computation problems representing the year-long, grade-level mathematics curriculum. –Student works for set amount of time (time limit varies for each grade). –Teacher grades test after student finishes.

27. Computation: Student Form

28. Computation: Time Limits  Length of test varies by grade. GradeTime limit 12 minutes 2 33 minutes 4 55 minutes 66 minutes

29. Computation: Scoring  Computation tests can also be scored by awarding 1 point for each digit answered correctly.  The number of digits correct within the time limit is the student’s score.or  Students receive 1 point for each problem answered correctly.

30. Computation: Scoring Example  Correct digits: Evaluate each numeral in every answer: 4507 2146 2 4 61 4507 2146 2361 4507 2146 2 44 1 4 correct digits 3 correct digits 2 correct digits

31. Computation: Scoring Different Operations  Scoring different operations: 9

32. Computation: Scoring Division  Division problems with remainders: –When giving directions, tell students to write answers to division problems using “R” for remainders when appropriate. –Although the first part of the quotient is scored from left to right (just like the student moves when working the problem), score the remainder from right to left (because student would likely subtract to calculate remainder).

33. Computation: Division Scoring Examples  Scoring division with remainders: Correct AnswerStudent’s Answer 4 0 3 R 5 24 3 R 5 (1 correct digit) 2 3 R 1 54 3 R 5 (2 correct digits) 

34. Computation: Scoring Decimals  Start at the decimal point and work outward in both directions

35. Computation: Scoring Fractions  Scoring fractions: –Score right to left for each portion of the answer. Evaluate digits correct in the whole number, numerator, and denominator. Then add digits together. When giving directions, be sure to tell students to reduce fractions to lowest terms.

36. Computation: Fraction Scoring Examples  Scoring examples: Fractions: Correct AnswerStudent’s Answer 67 / 1 28 / 1 1 (2 correct digits) 56 / 1 2 (2 correct digits) 6 51 / 2

37. Computation: Student Example  Samantha’s Computation test: –Fifteen problems attempted. –Two problems skipped. –Two problems incorrect. –Samantha’s correct digit score is 49.

38. Concepts and Applications  For students in Grades 2–6: –Student is presented with 18–25 Concepts and Applications problems representing the year-long, grade-level mathematics curriculum. –Student works for set amount of time (time limit varies by grade). –Teacher grades test after student finishes.

39. Concepts and Applications: Student Form  Student copy of a Concepts and Applications test: –This sample is from a second- grade test. –The actual Concepts and Applications test is 3 pages long.

40. Concepts and Applications: Time Limits  Length of test varies by grade. GradeTime limit 28 minutes 36 minutes 4 57 minutes 6

41. Concepts and Applications: Scoring Rules  Students receive 1 point for each blank answered correctly.  The number of correct answers within the time limit is the student’s score.

42. Concepts and Applications: Scoring a Student Example

43.  Quinten’s fourth- grade Concepts and Applications test: –Twenty-four blanks answered correctly. –Quinten’s score is 24. Concepts and Applications: Scoring a Student Example

44. Step 4: Graph Scores  Graphing student scores is vital.  Graphs provide teachers with a straightforward way to: –Review a student’s progress. –Monitor the appropriateness of student goals. –Judge the adequacy of student progress. –Determine the need for instructional change.

45. How to Graph CBM Scores  Teachers can use computer graphing programs. –See the NCSPM Tools ChartNCSPM Tools Chart  Teachers can create their own graphs. –Using paper and pencil: Vertical axis has range of student scores Horizontal axis has number of weeks Create template for student graph Use same template for every student in the classroom –Or using computer graphing programs. Microsoft Excel ChartDog See the CBM Warehouse on www.interventioncentral.org for tipswww.interventioncentral.org

46. A Math CBM Master Graph 0 5 10 15 20 25 1234567891011121314 Weeks of Instruction Digits Correct in 3 Minutes The vertical axis is labeled with the range of student scores. The horizontal axis is labeled with the number of instructional weeks.

47. 0 5 10 15 20 25 1234567891011121314 Weeks of Instruction Digits Correct in 3 Minutes Plotting CBM Data  Student scores are plotted on the graph, and a line is drawn between the scores.

48. Step 5: Set Ambitious Goals  Once baseline data have been collected (best practice is to administer three probes and use the median score), the teacher decides on an end-of-year performance goal for each student.  Three options for making performance goals: –End-of-year benchmarking –National norms –Intra-individual framework

49. GradeProbeMaximum scoreBenchmark KindergartenData not yet available FirstComputation3020 digits FirstData not yet available SecondComputation4520 digits SecondConcepts and Applications3220 blanks ThirdComputation4530 digits ThirdConcepts and Applications4730 blanks FourthComputation7040 digits FourthConcepts and Applications4230 blanks FifthComputation8030 digits FifthConcepts and Applications3215 blanks SixthComputation10535 digits SixthConcepts and Applications3515 blanks Using End-of-Year Benchmarks to Set Goals

50. Using National Norms to Set Ambitious Goals  National norms: –For typically developing students, a table of median rates of weekly increase can be used to find the end-of-year performance goal. Grade Computation: Digits Concepts and Applications: Blanks 10.35N/A 20.300.40 30.300.60 40.70 5 60.400.70

51. Using National Norms to Set Goals: Example  National norms: –Median is 14. –Fourth-grade Computation norm: 0.70. –Multiply by weeks left: 16 × 0.70 = 11.2. –Add to median: 11.2 + 14 = 25.2. –The end-of-year performance goal is 25. Grade Computation: Digits Concepts and Applications: Blanks 10.35N/A 20.300.40 30.300.60 40.70 5 60.400.70

52. Using an Intra-Individual Framework to Set Goals  Intra-individual framework: –Weekly rate of improvement is calculated using at least eight data points. –Baseline rate is multiplied by 1.5. –Product is multiplied by the number of weeks until the end of the school year. –Added to student’s baseline score to produce end-of-year performance goal.

53. Example: Using an Intra- Individual Framework to Set Goals  First eight scores: 3, 2, 5, 6, 5, 5, 7, 4.  Difference between medians: 5 – 3 = 2.  Divide by (# data points – 1): 2 ÷ (8-1) = 0.29.  Multiply by typical growth rate: 0.29 × 1.5 = 0.435.  Multiply by weeks left: 0.435 × 14 = 6.09.  Product is added to the first median: 3 + 6.09 = 9.09.  The end-of-year performance goal is 9.

54. Graphing the Goal  Once the end-of-year performance goal has been created, the goal is marked on the student graph with an X.  A goal line is drawn between the median of the student’s scores and the X.

55. Example of a Graphed Goal  Drawing a goal-line: –A goal-line is the desired path of measured behavior to reach the performance goal over time. X The X is the end-of-the-year performance goal. A line is drawn from the median of the first three scores to the performance goal.

56. Graphing a Trend Line  After drawing the goal-line, teachers continually monitor student graphs.  After seven or eight CBM scores, teachers draw a trend-line to represent actual student progress. –A trend-line is a line drawn in the data path to indicate the direction (trend) of the observed behavior. –The goal-line and trend-line are compared.  The trend-line is drawn using the Tukey method.

57. Graphing a Trend Line: Tukey Method  Graphed scores are divided into three fairly equal groups  Two vertical lines are drawn between the groups.  In the first and third groups: –Find the median data point and the median date. –Mark the intersection of these 2 with an X  Draw a line connecting the first group X and third group X.  This line is the trend-line.

58. X 0 5 10 15 20 25 1234567891011121314 Weeks of Instruction Digits Correct in 5 Minutes X X Tukey Method: A Graphed Example X

59. Trend and Goal Lines Made Easy  CBM computer management programs are available.  Programs create graphs and aid teachers with performance goals and instructional decisions.  Various types are available for varying fees.  See the NCSPM Tools ChartNCSPM Tools Chart

60. Step 6: Apply Decision Rules to Graphed Scores  After trend-lines have been drawn, teachers use graphs to evaluate student progress and formulate instructional decisions.  Standard decision rules help with this process.

61. The 4-point Rule  Based on four most recent consecutive points: –If scores are above the goal-line, end- of-year performance goal needs to be increased. –If scores are below goal-line, student instructional program needs to be revised. –If scores are on the goal-line, no changes need to be made.

62. The 4-point Rule: Example 1 0 5 10 15 20 25 30 1234567891011121314 Weeks of Instruction Digits Correct in 7 Minutes Goal-line Most recent 4 points

63. The 4-point Rule: Example 2 0 5 10 15 20 25 30 1234567891011121314 Weeks of Instruction Digits Correct in 7 Minutes Goal-line Most recent 4 points X

64. Using Trend- and Goal-Lines to Inform Decisions  Based on the student’s trend-line: –If the trend-line is steeper than the goal line, end-of-year performance goal needs to be increased. –If the trend-line is flatter than the goal line, student’s instructional program needs to be revised. –If the trend-line and goal-line are fairly equal, then no changes need to be made.

65. Decision-Making with Trend- and Goal-Lines (Example 1) 0 5 10 15 20 25 30 1234567891011121314 Weeks of Instruction Digits Correct in 7 Minutes Goal-line X X Trend-line

66. 0 5 10 15 20 25 30 1234567891011121314 Weeks of Instruction Digits Correct in 7 Minutes Goal-line Trend-line X X Decision-Making with Trend- and Goal-Lines (Example 2)

67. Decision-Making with Trend- and Goal-Lines (Example 3) 0 5 10 15 20 25 30 1234567891011121314 Weeks of Instruction Digits Correct in 7 Minutes Goal-line Trend-line X X X

68. Step 7: Use Data to Describe Student Strengths and Weaknesses  Students’ completed probes can be analyzed to examine mastery of specific skills.

69. Examining Computation CBM 4507 2146 2 4 61 4507 2146 2361 4507 2146 2 44 1 4 correct digits 3 correct digits 2 correct digits

70. Skills Profiles  Available with some progress monitoring software programs.  Skills profile provides a visual display of a student’s progress by skill area.

71. Example: Class Skills Profile

72. Example: Individual Skills Profile

73. Summary  Step 1: Place Students in a Math CBM task for progress monitoring  Step 2: identify the level of material for monitoring progress  Step 3: Administer and score Math CBM  Step 4: Graph scores  Step 5: Set ambitious goals  Step 6: Apply decision rules to graphed scores to know when to revise instructional programs and increase goals  Step 7: Use the CBM data qualitatively to inform instruction

74. The End Thank you for participating in this training module. © 2008, National Center on Student Progress Monitoring