1. National Center on Response to Intervention Using CBM in a Response to Intervention Framework Introduction to Using CBM for Progress Monitoring in Math

2. National Center on Response to Intervention Module Series  This module is intended to be used in conjunction with a series of modules. – Introduction to CBM – CBM in the Content Areas  Reading  Math  Written Expression – Other Ways to Use CBM Data – Using CBM to Determine RTI

3. National Center on Response to Intervention You Will Learn:  The seven step process for implementing CBM in Math for grades K-6.

4. National Center on Response to Intervention Note About This Presentation  Although we use progress monitoring measures in this presentation to illustrate methods, we are not recommending or endorsing any specific product.

5. National Center on Response to Intervention Steps to Conducting CBM Step 1:How to Place Students in a Mathematics Curriculum-Based Measurement Task for Progress Monitoring Step 2:How to Identify the Level of Material for Monitoring Progress Step 3:How to Administer and Score Mathematics Curriculum-Based Measurement Probes Step 4:How to Graph Scores

6. National Center on Response to Intervention Steps to Conducting CBM Step 5:How to Set Ambitious Goals Step 6:How to Apply Decision Rules to Graphed Scores to Know When to Revise Programs and Increase Goals Step 7:How to Use the Curriculum-Based Measurement Database Qualitatively to Describe Students’ Strengths and Weaknesses

7. National Center on Response to Intervention Step 1: How to 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

8. National Center on Response to Intervention Step 2: How to 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.

9. National Center on Response to Intervention Step 2: How to Identify the Level of Material for Monitoring Progress  To find the appropriate CBM level: – Determine the grade level at which you expect the student to perform in mathematics competently by year’s end. OR – On two separate days, administer a CBM test (either Computation or Concepts and Applications) at the grade level lower than the student’s grade-appropriate level. Use the correct time limit for the test at the lower grade level, and score the tests according to the directions.  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 or stay at the original lower grade and repeat this procedure.  If the average score is greater than 15 digits or blanks, then reconsider grade-appropriate material.

10. National Center on Response to Intervention Step 2: How to Identify 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.

11. National Center on Response to Intervention Step 3: How to 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.

12. National Center on Response to Intervention 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.

13. National Center on Response to Intervention Computation

14. National Center on Response to Intervention Computation  Length of test varies by grade. GradeTime limit 12 minutes 2 33 minutes 4 55 minutes 66 minutes

15. National Center on Response to Intervention Computation  Students receive 1 digit for each problem answered correctly.  The number of digits correct within the time limit is the student’s score.

16. National Center on Response to Intervention Computation  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

17. National Center on Response to Intervention Computation  Scoring different operations: 9

18. National Center on Response to Intervention Computation  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).

19. National Center on Response to Intervention Computation  Scoring examples: 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) 

20. National Center on Response to Intervention Computation  Scoring decimals and fractions: – Decimals: Start at the decimal point and work outward in both directions. – Fractions: Score right to left for each portion of the answer. Evaluate digits correct in the whole number part, numerator, and denominator. Then add digits together.  When giving directions, be sure to tell students to reduce fractions to lowest terms.

21. National Center on Response to Intervention Computation  Scoring examples: Decimals:

22. National Center on Response to Intervention Computation  Scoring examples: Fractions: Correct AnswerStudent’s Answer 67 / 1 28 / 1 1 (2 correct digits) 56 / 1 2 (2 correct digits) 6 51 / 2

23. National Center on Response to Intervention Computation Samantha’s Computation test: Fifteen problems attempted. Two problems skipped. Two problems incorrect. Samantha’s score is 13 problems. However, Samantha’s correct digit score is 49.

24. National Center on Response to Intervention Computation  Sixth-grade Computation test: –Let’s practice.

25. National Center on Response to Intervention Computation Answer Key: –Possible score of 21 digits correct in first row –Possible score of 23 digits correct in the second row –Possible score of 21 digits correct in the third row –Possible score of 18 digits correct in the fourth row –Possible score of 21 digits correct in the fifth row –Total possible digits on this probe: 104

26. National Center on Response to Intervention 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.

27. National Center on Response to Intervention Concepts and Applications  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.

28. National Center on Response to Intervention Concepts and Applications  Length of test varies by grade. GradeTime limit 28 minutes 36 minutes 4 57 minutes 6

29. National Center on Response to Intervention Concepts and Applications  Students receive 1 point for each blank answered correctly.  The number of correct answers within the time limit is the student’s score.

30. National Center on Response to Intervention  Quinten’s fourth- grade Concepts and Applications test: –Twenty-four blanks answered correctly. –Quinten’s score is 24. Concepts and Applications

31. National Center on Response to Intervention Concepts and Applications

32. National Center on Response to Intervention Concepts and Applications  Fifth-grade Concepts and Applications test—page 1: –Let’s practice.

33. National Center on Response to Intervention Concepts and Applications  Fifth-grade Concepts and Applications test—page 2

34. National Center on Response to Intervention Concepts and Applications  Fifth-grade Concepts and Applications test—page 3: –Let’s practice.

35. National Center on Response to Intervention Concepts and Applications ProblemAnswer 103 11A  ADC C  BFE 120.293 13  1428 hours 15790,053 16451 CDLI 177 18$10.00 in tips 20 more orders 194.4 20  215/6 dogs or cats 221 m 2312 ft ProblemAnswer 154 sq. ft 266,000 3A center C diameter 428.3 miles 57 6P 7 N 10 70 $5 bills 4 $1 bills 3 quarters 81 millions place 3 ten thousands place 9697 Answer Key

36. National Center on Response to Intervention 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.

37. National Center on Response to Intervention Number Identification  Student’s copy of a Number Identification test: –Actual student copy is 3 pages long.

38. National Center on Response to Intervention Number Identification  Number Identification score sheet

39. National Center on Response to Intervention Number Identification  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.

40. National Center on Response to Intervention Number Identification  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.

41. National Center on Response to Intervention Number Identification  Teacher’s score sheet: –Let’s practice.

42. National Center on Response to Intervention Number Identification  Student’s sheet—page 1: –Let’s practice.

43. National Center on Response to Intervention Number Identification  Student’s sheet— page 2: –Let’s practice.

44. National Center on Response to Intervention Number Identification  Student’s sheet— page 3: –Let’s practice.

45. National Center on Response to Intervention 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.

46. National Center on Response to Intervention Quantity Discrimination  Student’s copy of a Quantity Discrimination test:  Actual student copy is 3 pages long.

47. National Center on Response to Intervention Quantity Discrimination  Quantity Discrimination score sheet

48. National Center on Response to Intervention Quantity Discrimination  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.

49. National Center on Response to Intervention Quantity Discrimination  Lin’s Quantity Discrimination score sheet:  Thirty-eight items attempted.  Five items are incorrect.  Lin’s score is 33.

50. National Center on Response to Intervention Quantity Discrimination  Teacher’s score sheet: –Let’s practice.

51. National Center on Response to Intervention Quantity Discrimination  Student’s sheet—page 1: –Let’s practice.

52. National Center on Response to Intervention Quantity Discrimination  Student’s sheet—page 2: –Let’s practice.

53. National Center on Response to Intervention Quantity Discrimination  Student’s sheet— page 3: –Let’s practice.

54. National Center on Response to Intervention 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.

55. National Center on Response to Intervention Missing Number  Student’s copy of a Missing Number test: –Actual student copy is 3 pages long.

56. National Center on Response to Intervention Missing Number  Missing Number score sheet

57. National Center on Response to Intervention Missing Number  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.

58. National Center on Response to Intervention Missing Number  Thomas’s Missing Number score sheet: –Twenty-six items attempted. –Eight items are incorrect. –Thomas’s score is 18.

59. National Center on Response to Intervention Missing Number  Teacher’s score sheet: –Let’s practice.

60. National Center on Response to Intervention Missing Number  Student’s sheet—page 1: –Let’s practice.

61. National Center on Response to Intervention Missing Number  Student’s sheet—page 2: –Let’s practice.

62. National Center on Response to Intervention Missing Number  Student ‘s sheet—page 3: –Let’s practice.

63. National Center on Response to Intervention Step 4: How to 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. –Compare and contrast successful and unsuccessful instructional aspects of a student’s program.

64. National Center on Response to Intervention Step 4: How to Graph Scores  Teachers can use computer graphing programs. –List available in Appendix A of manual.  Teachers can create their own graphs. –A template can be created for student graphs. –The same template can be used for every student in the classroom. –Vertical axis shows the range of student scores. –Horizontal axis shows the number of weeks.

65. National Center on Response to Intervention Step 4: How to Graph Scores

66. National Center on Response to Intervention 0 5 10 15 20 25 1234567891011121314 Weeks of Instruction Digits Correct in 3 Minutes Step 4: How to Graph Scores  Student scores are plotted on the graph, and a line is drawn between the scores.

67. National Center on Response to Intervention Step 5: How to Set Ambitious Goals  Once baseline data has 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 –Intra-individual framework –National norms

68. National Center on Response to Intervention Step 5: How to Set Ambitious Goals  End-of-year benchmarking: –For typically developing students, a table of benchmarks can be used to find the CBM end-of-year performance goal.

69. National Center on Response to Intervention Step 5: How to Set Ambitious Goals

70. National Center on Response to Intervention Step 5: How to Set Ambitious 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. –Product is added to the student’s baseline rate to produce end-of-year performance goal.

71. National Center on Response to Intervention Step 5: How to Set Ambitious 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.

72. National Center on Response to Intervention Step 5: How 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.

73. National Center on Response to Intervention Step 5: How to Set Ambitious Goals  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.

74. National Center on Response to Intervention Step 5: How to Set Ambitious Goals  National norms: –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.

75. National Center on Response to Intervention Step 5: How to Set Ambitious Goals  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.

76. National Center on Response to Intervention Step 5: How to Set Ambitious Goals  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.

77. National Center on Response to Intervention Step 5: How to Set Ambitious Goals  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. –Mark with an X on the median instructional week. –Draw a line between the first group X and third group X. –This line is the trend-line.

78. National Center on Response to Intervention X 0 5 10 15 20 25 1234567891011121314 Weeks of Instruction Digits Correct in 5 Minutes X X Step 5: How to Set Ambitious Goals

79. National Center on Response to Intervention Step 5: How to Set Ambitious Goals 0 5 10 15 20 25 1234567891011121314 Weeks of Instruction Digits Correct in 5 Minutes Practice Graph:

80. National Center on Response to Intervention Step 5: How to Set Ambitious Goals Practice Graph: 0 5 10 15 20 25 1234567891011121314 Weeks of Instruction Digits Correct in 5 Minutes X X X

81. National Center on Response to Intervention Step 5: How to Set Ambitious Goals  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.  Programs are listed in Appendix A of manual.

82. National Center on Response to Intervention Step 6: How to Apply Decision Rules to Graphed Scores to Know When to Revise Programs and Increase Goals  After trend-lines have been drawn, teachers use graphs to evaluate student progress and formulate instructional decisions.  Standard decision rules help with this process.

83. National Center on Response to Intervention Step 6: How to Apply Decision Rules to Graphed Scores to Know When to Revise Programs and Increase Goals  If at least 3 weeks of instruction have occurred and at least six data points have been collected, examine the four most recent consecutive points: –If all four most recent scores fall above the goal-line, then the end-of-year performance goal needs to be increased. –If all four most recent scores fall below the goal- line, then the student's instructional program needs to be revised. –If the four most recent scores fall both above and below the goal-line, then continue collecting data (until the four-point rule can be used or a trend-line can be drawn).

84. National Center on Response to Intervention 0 5 10 15 20 25 30 1234567891011121314 Weeks of Instruction Digits Correct in 7 Minutes Goal-line Most recent 4 points Step 6: How to Apply Decision Rules to Graphed Scores to Know When to Revise Programs and Increase Goals

85. National Center on Response to Intervention Step 6: How to Apply Decision Rules to Graphed Scores to Know When to Revise Programs and Increase Goals 0 5 10 15 20 25 30 1234567891011121314 Weeks of Instruction Digits Correct in 7 Minutes Goal-line Most recent 4 points X

86. National Center on Response to Intervention Step 6: How to Apply Decision Rules to Graphed Scores to Know When to Revise Programs and Increase Goals  If the trend-line is steeper than the goal line, then the end-of-year performance goal needs to be increased.  If the trend-line is flatter than the goal line, then the 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.

87. National Center on Response to Intervention Step 6: How to Apply Decision Rules to Graphed Scores to Know When to Revise Programs and Increase Goals 0 5 10 15 20 25 30 1234567891011121314 Weeks of Instruction Digits Correct in 7 Minutes Goal-line X X Trend-line

88. National Center on Response to Intervention 0 5 10 15 20 25 30 1234567891011121314 Weeks of Instruction Digits Correct in 7 Minutes Goal-line Trend-line X X Step 6: How to Apply Decision Rules to Graphed Scores to Know When to Revise Programs and Increase Goals

89. National Center on Response to Intervention Step 6: How to Apply Decision Rules to Graphed Scores to Know When to Revise Programs and Increase Goals 0 5 10 15 20 25 30 1234567891011121314 Weeks of Instruction Digits Correct in 7 Minutes Goal-line Trend-line X X X

90. National Center on Response to Intervention Step 7: How to Use Curriculum-Based Measurement Data Qualitatively to Describe Student Strengths and Weaknesses  Using a skills profile, student progress can be analyzed to describe student strengths and weaknesses.  Student completes Computation or Concepts and Applications tests.  Skills profile provides a visual display of a student’s progress by skill area.

91. National Center on Response to Intervention Step 7: How to Use Curriculum-Based Measurement Data Qualitatively to Describe Student Strengths and Weaknesses

92. National Center on Response to Intervention Step 7: How to Use Curriculum-Based Measurement Data Qualitatively to Describe Student Strengths and Weaknesses

93. National Center on Response to Intervention Case Study 1: Alexis 0 5 10 15 20 25 30 1234567891011121314 Weeks of Instruction Digits Correct in 2 Minutes Alexis’s goal-line Alexis’s trend-line X X

94. National Center on Response to Intervention Case Study 1: Alexis

95. National Center on Response to Intervention Case Study 2: Marcus 0 5 10 15 20 25 30 123456789101112131415161718192021222324 Weeks of Instruction Digits Correct in 5 Minutes Marcus’s goal-line Instructional changes Marcus’s trend-lines

96. National Center on Response to Intervention 0 5 10 15 20 25 30 123456789101112131415161718192021222324 Weeks of Instruction Digits Correct in 5 Minutes High-performing mathematics students Middle-performing mathematics students Low-performing mathematics students Case Study 2: Marcus

97. National Center on Response to Intervention CBM Materials and Research  Appendix A –AIMSweb/Edformation –Yearly ProgressPro TM /McGraw-Hill –Pro-Ed Math Computation and Concepts/Applications CBM –Research Institute on Progress Monitoring, University of Minnesota (OSEP Funded)  Appendix B –Research Articles

98. National Center on Response to Intervention Module Series  This module is intended to be used in conjunction with a series of modules. –Introduction to CBM –CBM in the Content Areas  Reading  Math  Written Expression –Other Ways to Use CBM Data –Using CBM to Determine RTI

99. National Center on Response to Intervention This document was originally developed by the National Center on Student Progress Monitoring under Cooperative Agreement (#H326W0003) and updated by the National Center on Response to Intervention under Cooperative Agreement (#H326E07004) between the American Institutes for Research and the U.S. Department of Education, Office of Special Education Programs. The contents of this document do not necessarily reflect the views or policies of the Department of Education, nor does mention of trade names, commercial products, or organizations imply endorsement by the U.S. Government. This publication is copyright free. Readers are encouraged to copy and share it, but please credit the National Center on Response to Intervention. National Center on Response to Intervention www.rti4success.org