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Using Curriculum-Based Measurement for Progress Monitoring in Math

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Using Curriculum-Based Measurement for Progress Monitoring in Math

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  1. Using Curriculum-Based Measurement for Progress Monitoring in Math Todd Busch Tracey Hall Pamela Stecker

  2. Progress Monitoring • Progress monitoring (PM) is conducted frequently and designed to: • Estimate rates of student improvement. • Identify students who are not demonstrating adequate progress. • Compare the efficacy of different forms of instruction and design more effective, individualized instructional programs for problem learners.

  3. What Is the Difference Between Traditional Assessments and Progress Monitoring? • Traditional Assessments: • Lengthy tests. • Not administered on a regular basis. • Teachers do not receive immediate feedback. • Student scores are based on national scores and averages and a teacher’s classroom may differ tremendously from the national student sample.

  4. What Is the Difference Between Traditional Assessments and Progress Monitoring? • Curriculum-Based Measurement (CBM) is one type of PM. • CBM provides an easy and quick method for gathering student progress. • Teachers can analyze student scores and adjust student goals and instructional programs. • Student data can be compared to teacher’s classroom or school district data.

  5. Curriculum-Based Assessment • Curriculum-Based Assessment (CBA): • Measurement materials are aligned with school curriculum. • Measurement is frequent. • Assessment information is used to formulate instructional decisions. • CBM is one type of CBA.

  6. Progress Monitoring • Teachers assess students’ academic performance using brief measures on a frequent basis. • The main purposes are to: • Describe the rate of response to instruction. • Build more effective programs.

  7. Focus of This Presentation Curriculum-Based Measurement The scientifically validated form of progress monitoring.

  8. Teachers Use Curriculum-Based Measurement To . . . • 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.

  9. Curriculum-Based Measurement • The result of 30 years of research • Used across the country • Demonstrates strong reliability, validity, and instructional utility

  10. Research Shows . . . • CBM produces accurate, meaningful information about students’ academic levels and their rates of improvement. • CBM is sensitive to student improvement. • CBM corresponds well with high-stakes tests. • When teachers use CBM to inform their instructional decisions, students achieve better.

  11. Most Progress Monitoring: Mastery Measurement Curriculum-Based Measurement is NOT Mastery Measurement

  12. Mastery Measurement: Tracks Mastery of Short-Term Instructional Objectives • To implement Mastery Measurement, the teacher: • Determines the sequence of skills in an instructional hierarchy. • Develops, for each skill, a criterion-referenced test.

  13. Hypothetical Fourth Grade Math Computation Curriculum 1. Multidigit addition with regrouping 2. Multidigit subtraction with regrouping 3. Multiplication facts, factors to nine 4. Multiply two-digit numbers by a one-digit number 5. Multiply two-digit numbers by a two-digit number 6. Division facts, divisors to nine 7. Divide two-digit numbers by a one-digit number 8. Divide three-digit numbers by a one-digit number 9. Add/subtract simple fractions, like denominators 10. Add/subtract whole numbers and mixed numbers

  14. Multidigit Addition Mastery Test

  15. Mastery of Multidigit Addition Multidigit Subtraction Multidigit Addition 10 8 6 in 5 minutes Number of digits correct 4 2 0 4 8 10 12 14 6 2 WEEKS

  16. Hypothetical Fourth Grade Math Computation Curriculum 1. Multidigit addition with regrouping 2. Multidigit subtraction with regrouping 3. Multiplication facts, factors to nine 4. Multiply two-digit numbers by a one-digit number 5. Multiply two-digit numbers by a two-digit number 6. Division facts, divisors to nine 7. Divide two-digit numbers by a one-digit number 8. Divide three-digit numbers by a one-digit number 9. Add/subtract simple fractions, like denominators 10. Add/subtract whole numbers and mixed numbers

  17. Multidigit Subtraction Mastery Test Date: Name: Subtracting 6 5 2 1 5 4 2 9 8 4 5 5 6 7 8 2 7 3 2 1 3 7 5 6 3 4 7 5 6 9 3 7 3 9 1 5 6 8 2 6 4 2 2 3 4 8 4 2 4 1 5 4 3 2 1 9 4 2 5 2 9 4 2 6 8 5 4 8 7 4

  18. Mastery of Multidigit Addition and Subtraction Multidigit Subtraction Multidigit Subtraction Multiplication Multiplication Multidigit Multidigit 10 10 Facts Facts Addition Addition 8 8 6 6 Number of problems correct in 5 minutes in 5 minutes Number of digits correct 4 4 2 2 0 0 4 4 8 8 10 10 12 12 14 14 6 6 2 2 WEEKS WEEKS

  19. Problems with Mastery Measurement • Hierarchy of skills is logical, not empirical. • Performance on single-skill assessments can be misleading. • Assessment does not reflect maintenance or generalization. • Assessment is designed by teachers or sold with textbooks, with unknown reliability and validity. • Number of objectives mastered does not relate well to performance on high-stakes tests.

  20. Curriculum-Based Measurement Was Designed to Address These Problems An Example of Curriculum-Based Measurement: Math Computation

  21. Hypothetical Fourth Grade Math Computation Curriculum 1. Multidigit addition with regrouping 2. Multidigit subtraction with regrouping 3. Multiplication facts, factors to nine 4. Multiply two-digit numbers by a one-digit number 5. Multiply two-digit numbers by a two-digit number 6. Division facts, divisors to nine 7. Divide two-digit numbers by a one-digit number 8. Divide three-digit numbers by a one-digit number 9. Add/subtract simple fractions, like denominators 10. Add/subtract whole numbers and mixed numbers

  22. Random numerals within problems • Random placement of problem types on page

  23. Computation 4 Sheet #2 Password: AIR Name: Date: A B C D E ) 5 5 2 2 8 8 5 5 2 2 9 ) 8 2 8 5 9 2 4 4 7 2 + + 6 6 4 4 7 7 0 0 8 8 4 3 0 4 x 0 9 0 + J F G H I ) 3 5 4 7 2 1 6 3 0 = x 7 4 x x 3 3 5 9 K L M N O 4 8 3 2 ) ) 5 6 5 3 1 6 3 0 - = 7 x x 2 3 6 P Q S T R 1 0 7 ) 4 1 6 5 3 2 9 6 + = 3 x 4 4 1 1 1 1 x 2 U V W X Y 1 5 0 4 1 1 3 0 ) 9 8 1 4 + 6 = 1 4 4 1 ) 5 1 0 2 7 x • Random numerals within problems • Random placement of problem types on page

  24. Donald’s Progress in Digits CorrectAcross the School Year

  25. One Page of a 3-Page CBM in Math Concepts and Applications (24 Total Blanks)

  26. Darker boxes equal a greater level of mastery. Donald’s Graph and Skills Profile

  27. Sampling Performance on Year-Long Curriculum for Each Curriculum-Based Measurement . . . • Avoids the need to specify a skills hierarchy. • Avoids single-skill tests. • Automatically assesses maintenance/generalization. • Permits standardized procedures for sampling the curriculum, with known reliability and validity. • SO THAT: CBM scores relate well to performance on high-stakes tests.

  28. Curriculum-Based Measurement’s Two Methods for Representing Year-Long Performance Method 1: • Systematically sample items from the annual curriculum (illustrated in Math CBM, just presented). Method 2: • Identify a global behavior that simultaneously requires the many skills taught in the annual curriculum (illustrated in Reading CBM, presented next).

  29. Hypothetical Second Grade Reading Curriculum • Phonics • CVC patterns • CVCe patterns • CVVC patterns • Sight Vocabulary • Comprehension • Identification of who/what/when/where • Identification of main idea • Sequence of events • Fluency

  30. Second Grade Reading Curriculum-Based Measurement • Each week, every student reads aloud from a second grade passage for 1 minute. • Each week’s passage is the same difficulty. • As a student reads, the teacher marks the errors. • Count number of words read correctly. • Graph scores.

  31. Curriculum-Based Measurement • Not interested in making kids read faster. • Interested in kids becoming better readers. • The CBM score is an overall indicator of reading competence. • Students who score high on CBMs are better: • Decoders • At sight vocabulary • Comprehenders • Correlates highly with high-stakes tests.

  32. CBM Passage for Correct Words per Minute

  33. What We Look for in Curriculum-Based Measurement Increasing Scores: • Student is becoming a better reader. Flat Scores: • Student is not profiting from instruction and requires a change in the instructional program.

  34. Sarah’s Progress on Words Read Correctly Sarah Smith Reading 2 180 160 140 120 100 Words Read Correctly 80 60 40 20 0 Sep Oct Nov Dec Jan Feb Mar Apr May

  35. Jessica’s Progress on Words Read Correctly Jessica Jones Reading 2 180 160 140 120 100 Words Read Correctly 80 60 40 20 0 Sep Oct Nov Dec Jan Feb Mar Apr May

  36. Reading Curriculum-Based Measurement • Kindergarten: Letter sound fluency • First Grade: Word identification fluency • Grades 1–3: Passage reading fluency • Grades 1–6: Maze fluency

  37. KindergartenLetter Sound Fluency p U z L y • Teacher: Say the sound that goes with each letter. • Time: 1 minute i t R e w O a s d f v g j S h k m n b V Y E i c x …

  38. First GradeWord Identification Fluency • Teacher: Read these words. • Time: 1 minute

  39. Grades 1–3 Passage Reading Fluency • Number of words read aloud correctly in 1 minute on end-of-year passages.

  40. CBM Passage for Correct Words per Minute

  41. Grades 1–6 Maze Fluency • Number of words replaced correctly in 2.5 minutes on end-of-year passages from which every seventh word has been deleted and replaced with three choices.

  42. Computer Maze

  43. Donald’s Progress on Words Selected Correctly for Curriculum-Based Measurement Maze Task

  44. Curriculum-Based Measurement • CBM is distinctive. • Each CBM test is of equivalent difficulty. • Samples the year-long curriculum. • CBM is highly prescriptive and standardized. • Reliable and valid scores.

  45. The Basics of Curriculum-Based Measurement • CBM monitors student progress throughout the school year. • Students are given reading probes at regular intervals. • Weekly, biweekly, monthly • Teachers use student data to quantify short- and long-term goals that will meet end-of-year goals.

  46. The Basics of Curriculum-Based Measurement • CBM tests are brief and easy to administer. • All tests are different, but assess the same skills and difficulty level. • CBM scores are graphed for teachers to use to make decisions about instructional programs and teaching methods for each student.

  47. Curriculum-Based Measurement Research • CBM research has been conducted over the past 30 years. • Research has demonstrated that when teachers use CBM for instructional decision making: • Students learn more. • Teacher decision making improves. • Students are more aware of their performance.

  48. Steps to Conducting Curriculum-Based Measurements Step 1: How to Place Students in aMath Curriculum-BasedMeasurement Task forProgress Monitoring Step 2: How to Identify the Level ofMaterial for Monitoring Progress Step 3: How to Administer and ScoreMath Curriculum-BasedMeasurement Probes Step 4: How to Graph Scores

  49. Steps to Conducting Curriculum-Based Measurements Step 5: How to Set Ambitious Goals Step 6: How to Apply Decision Rulesto Graphed Scores to KnowWhen to Revise Programsand Increase Goals Step 7: How to Use the Curriculum-Based MeasurementDatabase Qualitatively toDescribe Students’ Strengthsand Weaknesses

  50. Step 1: How to Place Students in a Math Curriculum-Based Measurement Task for Progress Monitoring • Grades 1–6: • Computation • Grades 2–6: • Concepts and Applications • Kindergarten and first grade: • Number Identification • Quantity Discrimination • Missing Number