Using Curriculum-Based Measurement for Progress Monitoring in Math Todd Busch Tracey Hall Pamela Stecker
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. 2
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. 3
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. 4
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. 5
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. 6
Focus of This Presentation Curriculum-Based Measurement The scientifically validated form of progress monitoring. 7
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. 8
Curriculum-Based Measurement The result of 30 years of research Used across the country Demonstrates strong reliability, validity, and instructional utility 9
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. 10
Most Progress Monitoring: Mastery Measurement Curriculum-Based Measurement is NOT Mastery Measurement
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 criterionreferenced test. 12
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 13
Multidigit Addition Mastery Test 14
Mastery of Multidigit Addition 10 Multidigit Addition Multidigit Subtraction Number of digits correct in 5 minutes 8 6 4 2 0 2 4 6 8 10 12 14 WEEKS 15
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 16
Multidigit Subtraction Mastery Test Name: Date: Subtracting 6521 375 5429 634 8455 756 6782 937 7321 391 5682 942 6422 529 3484 426 2415 854 4321 874 17
Mastery of Multidigit Addition and Subtraction Number of problems digits correct correct in 5 minutes 10 8 6 4 2 Multidigit Addition Multidigit Subtraction Multiplication Facts 0 2 4 6 8 10 12 14 WEEKS 18
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 highstakes tests. 19
Curriculum-Based Measurement Was Designed to Address These Problems An Example of Curriculum- Based Measurement: Math Computation 20
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 21
Random numerals within problems Random placement of problem types on page Sheet Password: Name: A #1 3737 27= 2727= ARM B CComputation 4 1+ 67 3 = 4)6 Date: D 6)78 E x8757 F x67 G x90 H x2447 I 6)48 J 5)20 K 2)50 L 6144 4420 M x33 10 N x60 O 7) 30 P +95225 +75268 Q 8)32 R +83 1156 2824 S 7-47 2 = T x 38 33 U 35 + 15= V 982 97 W x 95 X x 41 Y 7) 56 22
Random numerals within problems Random placement of problem types on page Sheet Password: Name: A #2AIRB+52852 +64708 CComputation 4 9)24 Date: x90 D4)72 E +90 8285 4304 F6)30 G x35 74 H x45 I x79 J2313= K x32 23 L x86 M5)65 N6)30 O3-47 1= P 1073 x Q2) 9 R 416 44 S113 5+11= T x62 U4+ 12 6= V 1504 1441 W 9)81 X 1307 x Y 5)10 23
Donald s Progress in Digits Correct Across the School Year D I G I T S 70 60 50 40 30 20 10 0 Donald Ross Computation 4 Sep Oct Nov Dec Jan Feb Mar Apr May 24
One Page of a 3-Page CBM in Math Concepts and Applications (24 Total Blanks) Column Name (1) A Date Write the Applications Test 4 4 Column Page B1 M N L Z Z K letter Lin each N (B) (A) blank. (C) (D)point segment(5) ray line Write a number in the blank. (6) 1 week = days (2) Look at this numbers.: Summer SchoolVacation Students Plans for Summit (3) Which 356.17 Solve number in the hundredths place? Jeff a week wheels the at problem school his wheelchair and by estimating for 28 for hours 33 the hours a sum weekor Stay Travel Camp home0 difference in his neighborhood. to the nearest About ten. hours does Jeff spend each how week many wheeling The 10 20 30405060708090100 his wheelchair? T-Shirt Number of Students to $4.00. Use summer P.T.A. the How for bar each school. will much graph buy student money Each a to Summit answer who will goes the School costs the questions. (4)Write the number in each blank. P.T.A. travel during spend students the on summer? these are T planning shirts? to $.00 2 3 thousands, ten thousands, 8 hundreds, 6 hundreds, 4 tens, 8 ones 6 ones (7) How to go stay To many to summer fewer school students than are ride home? planning would measure from useschool the distance to your (A) (B) of centimeters the bus (C) house kilometers you 25
Donald s Graph and Skills Profile Darker boxes equal a greater level of mastery. D I G I T S 10 20 30 40 50 60 70 0 A1 S1 M1 M2 M3 D1 D2 D3 F1 F2 Donald Ross Computation 4 38 Sep Oct Nov Dec Jan Feb Mar Apr May 38 26
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. 27
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). 28
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 29
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. 30
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. 31
CBM Passage for Correct Words per Minute Mom was going to have a baby. Another one! That is all we need thought Samantha who was ten years old. Samantha had two little brothers. They were brats. Now Mom was going to have another one. Samantha wanted to cry. I will need your help, said Mom. I hope you will keep an eye on the boys while I am gone. You are my big girl! Samantha told Mom she would help. She did not want to, though. The boys were too messy. They left toys everywhere. They were too loud, too. Samantha did not want another baby brother. Two were enough. Dad took Samantha and her brothers to the hospital. They went to Mom s room. Mom did not feel good. She had not had the baby. The doctors said it would be later that night. I want to wait here with you, said Samantha. Thank you Samantha. But you need to go home. You will get too sleepy. Go home with Grandma. I will see you in the morning, said Mom. That night Samantha was sad. She knew that when the new baby came home that Mom would not have time for her. Mom would spend all of her time with the new baby. The next day Grandma woke her up. Your mom had the baby last night, Grandma said. We need to go to the hospital. Get ready. Help the boys get ready, too. Samantha slowly got ready. She barely had the heart to get dressed. After she finished, she helped the boys. They sure were a pain! And now another one was coming. Oh brother! Soon they were at the hospital. They walked into Mom s room. Mom was lying in the bed. Her tummy was much Smaller. Samantha... 32
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. 33
Sarah s Progress on Words Read Correctly Words Read Correctly 180 160 140 120 100 80 60 40 20 0 Sarah Smith Reading 2 Sep Oct Nov Dec Jan Feb Mar Apr May 34
Jessica s Progress on Words Read Correctly Words Read Correctly 180 160 140 120 100 80 60 40 20 0 Jessica Jones Reading 2 Sep Oct Nov Dec Jan Feb Mar Apr May 35
Reading Curriculum-Based Measurement Kindergarten: Letter sound fluency First Grade: Word identification fluency Grades 1 3: Passage reading fluency Grades 1 6: Maze fluency 36
Kindergarten Letter Sound Fluency Teacher: Say the sound that goes with each letter. Time: 1 minute p U z L y 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 37
First Grade Word Identification Fluency Teacher: Read these words. Time: 1 minute two for come because last from... 38
Grades 1 3 Passage Reading Fluency Number of words read aloud correctly in 1 minute on end-ofyear passages. 39
CBM Passage for Correct Words per Minute Jason Fry ran home from school. He had to pack his clothes. He was going to the beach. He packed a swimsuit and shorts. He packed tennis shoes and his toys. The Fry family was going to the beach in Florida. The next morning Jason woke up early. He helped Mom and Dad pack the car, and his sister, Lonnie, helped too. Mom and Dad sat in the front seat. They had maps of the beach. Jason sat in the middle seat with his dog, Ruffie. Lonnie sat in the back and played with her toys. They had to drive for a long time. Jason looked out the window. He saw farms with animals. Many farms had cows and pigs but some farms had horses. He saw a boy riding a horse. Jason wanted to ride a horse, too. He saw rows of corn growing in the fields. Then Jason saw rows of trees. They were orange trees. He sniffed their yummy smell. Lonnie said she could not wait to taste one. Dad stopped at a fruit market by the side of the road. He bought them each an orange. 40
Grades 1 6 Maze Fluency Number of words replaced correctly in 2.5 minutes on end-ofyear passages from which every seventh word has been deleted and replaced with three choices. 41
Computer Maze 42
Donald s Progress on Words Selected Correctly for Curriculum-Based Measurement Maze Task W O R D S C O R R E C T 60 50 40 30 20 10 0 Donald Ross Reading 4 Sep Oct Nov Dec Jan Feb Mar Apr May 43
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. 44
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. 45
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. 46
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. 47
Steps to Conducting Curriculum- Based Measurements Step 1: Step 2: Step 3: Step 4: How to Place Students in a Math Curriculum-Based Measurement Task for Progress Monitoring How to Identify the Level of Material for Monitoring Progress How to Administer and Score Math Curriculum-Based Measurement Probes How to Graph Scores 48
Steps to Conducting Curriculum- Based Measurements Step 5: Step 6: Step 7: How to Set Ambitious Goals How to Apply Decision Rules to Graphed Scores to Know When to Revise Programs and Increase Goals How to Use the Curriculum- Based Measurement Database Qualitatively to Describe Students Strengths and Weaknesses 49
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 50
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. 51
Step 2: How to Identify the Level of Material for Monitoring Progress To find the appropriate CBM level: Determine the grade-level probe at which you expect the student to perform in math 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 gradeappropriate 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, 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, reconsider grade-appropriate material. 52
Step 3: How to Administer and Score Math Curriculum-Based Measurement Probes Students answer math problems. Teacher grades math probe. The number of digits correct, problems correct, or blanks correct is calculated and graphed on student graph. 53
Computation For students in grades 1 6. Student is presented with 25 computation problems representing the year-long, grade-level math curriculum. Student works for set amount of time (time limit varies for each grade). Teacher grades test after student finishes. 54
Computation Student Copy of a First Grade Computation Test 55
Computation 56
Computation Length of test varies by grade. Grade First Second Third Fourth Fifth Sixth Time limit 2 min. 2 min. 3 min. 3 min. 5 min. 6 min. 57
Computation Students receive 1 point for each problem answered correctly. 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. 58
Computation Correct Digits: Evaluate Each Numeral in Every Answer 4507 2146 2361 4507 2146 2461 4507 2146 2441 4 correct digits 3 correct digits 2 correct digits 59
Computation Scoring Different Operations Examples: 1 18 +16 34 4 1 158-29 129 22 x 43 66 880 946 23 8 184 16 24 24 0 2 correct digits 3 correct digits 3 correct digits 2 correct digits 60
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). 61
Computation Scoring Examples: Division with Remainders Correct Answer Student s Answer 4 0 3 R 5 2 4 3 R 5 (1 correct digit) 2 3 R 1 5 4 3 R 5 (2 correct digits) 62
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. 63
Computation Scoring Examples: Decimals 64
Computation Scoring Examples: Fractions Correct Answer Student s Answer 6 7 / 1 2 6 8 / 1 1 (2 correct digits) 5 1 / 2 5 6 / 1 2 (2 correct digits) 65
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. 66
Computation Sixth Grade Computation Test Let s practice. 67
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. 68
Concepts and Applications For students in grades 2 6. Student is presented with 18 25 Concepts and Applications problems representing the yearlong grade-level math curriculum. Student works for set amount of time (time limit varies by grade). Teacher grades test after student finishes. 69
Concepts and Applications Student Copy of a Concepts and Applications test This sample is from a third grade test. The actual Concepts and Applications test is 3 pages long. 70
Concepts and Applications Length of test varies by grade. Grade Second Third Fourth Fifth Sixth Time limit 8 min. 6 min. 6 min. 7 min. 7 min. 71
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. 72
Concepts and Applications Quinten s Fourth Grade Concepts and Applications Test Twenty-four blanks answered correctly. Quinten s score is 24. 73
Concepts and Applications 74
Concepts and Applications Fifth Grade Concepts and Applications Test 1 Let s practice. 75
Concepts and Applications Fifth Grade Concepts and Applications Test Page 2 76
Concepts and Applications Fifth Grade Concepts and Applications Test Page 3 Let s practice. 77
Concepts and Applications Problem Answer Answer Key 10 11 3 A ADC C BFE Problem 1 Answer 54 sq. ft 12 13 0.293 < > 2 66,000 14 28 hours 3 4 5 6 7 8 A center C diameter 28.3 miles 7 P 7 N 10 0 $5 bills 4 $1 bills 3 quarters 1 millions place 3 ten thousands place 15 16 17 18 19 20 21 22 790,053 451 CDLI 7 $10.00 in tips 20 more orders 4.4 > < 5/6 dogs or cats 1 m 9 697 23 12 ft 78
Number Identification For kindergarten or first grade students. Student is presented with 84 items and is 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. 79
Number Identification Student Copy of a Number Identification test Actual student copy is 3 pages long. 80
Number Identification Number Identification Score Sheet 81
Number Identification If the student does not respond after 3 seconds, 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 correct answers in 1 minute. 82
Number Identification Jamal s Number Identification Score Sheet Skipped Fifty-seven Three Jamal s items are marked with a (-). items attempted. incorrect. score is 54. 83
Number Identification Teacher Score Sheet Let s practice. 84
Number Identification Student Sheet Page 1 Let s practice. 85
Number Identification Student Sheet Page 2 Let s practice. 86
Number Identification Student Sheet Page 3 Let s practice. 87
Quantity Discrimination For kindergarten or first grade students. 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. 88
Quantity Discrimination Student Copy of a Quantity Discrimination test Actual student copy is 3 pages long. 89
Quantity Discrimination Quantity Discrimination Score Sheet 90
Quantity Discrimination If the student does not respond after 3 seconds, 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 correct answers in a minute. 91
Quantity Discrimination Lin s Quantity Discrimination Score Sheet Thirty-eight items attempted. Five incorrect. Lin s score is 33. 92
Quantity Discrimination Teacher Score Sheet Let s practice. 93
Quantity Discrimination Student Sheet Page 1 Let s practice. 94
Quantity Discrimination Student Sheet Page 2 Let s practice. 95
Quantity Discrimination Student Sheet Page 3 Let s practice. 96
Missing Number For kindergarten or first grade students. Student is presented with 63 items and asked to orally identify the missing number in a sequence of four numbers. After completing some sample items, the student works for 1 minute. Teacher writes the student s responses on the Missing Number score sheet. 97
Missing Number Student Copy of a Missing Number Test Actual student copy is 3 pages long. 98
Missing Number Missing Number Score Sheet 99
Missing Number If the student does not respond after 3 seconds, 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 correct answers in I minute. 100
Missing Number Thomas s Missing Number Score Sheet Twenty-six items attempted. Eight incorrect. Thomas s score is 18. 101
Missing Number Teacher Score Sheet Let s practice. 102
Missing Number Student Sheet Page 1 Let s practice. 103
Missing Number Student Sheet Page 2 Let s practice. 104
Missing Number Student Sheet Page 3 Let s practice. 105
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. 106
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. Create template for student graph. Use same template for every student in the classroom. Vertical axis shows the range of student scores. Horizontal axis shows the number of weeks. 107
Step 4: How to Graph Scores 108
Step 4: How to Graph Scores 25 Digits Correct in 3 Minutes 20 15 10 5 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Weeks of Instruction Student scores are plotted on graph and a line is drawn between scores. 109
Step 5: How to Set Ambitious Goals Once a few scores have been graphed, 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 110
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. 111
First Kindergarten Grade Second Sixth Fifth Fourth Third Probe Computation Computation Concepts Concepts Computation Concepts Computation Concepts Computation Concepts Computation and Applications and Applications and Applications and Applications and Applications Data Maximum not yet Data not yet 30 available score 45 available 32 47 45 42 70 105 32 80 35 Benchmark 20 digits 20 20 30 30 blanks digits 30 40 blanks digits 15 30 blanks digits 15 35 blanks digits blanks digits Step 5: How to Set Ambitious Goals 112
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. 113
Step 5: How to Set Ambitious Goals First eight scores: 3, 2, 5, 6, 5, 5, 7, and 4. Difference: 7 2 = 5. Divide by weeks: 5 8 = 0.625. Multiply by baseline: 0.625 1.5 = 0.9375. Multiply by weeks left: 0.9375 14 = 13.125. Product is added to median: 13.125 + 5 = 18.125. The end-of-year performance goal is 18 (rounding). 114
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. Grade First Second Third Fourth Fifth Sixth Computation: Digits 0.35 0.30 0.30 0.70 0.70 0.40 Concepts and Applications: Blanks N/A 0.40 0.60 0.70 0.70 0.70 115
Step 5: How to Set Ambitious Goals National Norms Median: 14 Fourth Grade Computation Norm: 0.70 Multiply by weeks left: 16 0.70 = 11.2 Grade First Second Third Fourth Computation : Digits 0.35 0.30 0.30 0.70 Concepts and Applications: Blanks N/A 0.40 0.60 0.70 Add to median: 11.2 + 14 = 25.2 The end-of-year performance goal is 25 Fifth Sixth 0.70 0.40 0.70 0.70 116
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. 117
Step 5: How to Set Ambitious Goals Drawing a Goal-Line Goal-line: The desired path of measured behavior to reach the performance goal over time. 118
Step 5: How to Set Ambitious Goals After drawing the goal-line, teachers continually monitor student graphs. After seven to eight CBM scores, teachers draw a trend-line to represent actual student progress. The goal-line and trend-line are compared. The trend-line is drawn using the Tukey method. Trend-line: A line drawn in the data path to indicate the direction (trend) of the observed behavior. 119
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 and median instructional week. Locate the place on the graph where the two values intersect and mark with an X. Draw a line between the first group X and third group X. This line is the trend-line. 120
Step 5: How to Set Ambitious Goals 121
Step 5: How to Set Ambitious Goals Practice 1 25 Digits Correct in 5 Minutes 20 15 10 5 0 Weeks of Instruction 1 2 3 4 5 6 7 8 9 10 11 12 13 14 122
Step 5: How to Set Ambitious Goals Practice 1 123
Step 5: How to Set Ambitious Goals Practice 2 25 Digits Correct in 5 Minutes 20 15 10 5 0 Weeks of Instruction 1 2 3 4 5 6 7 8 9 10 11 12 13 14 124
Step 5: How to Set Ambitious Goals Practice 2 125
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. Listed in Appendix A of manual. 126
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. 127
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 goalline, the end-of-year performance goal needs to be increased. If all four most recent scores fall below the goal-line, the student's instructional program needs to be revised. If these four most recent scores fall both above and below the goal-line, continue collecting data (until the four-point rule can be used or a trend-line can be drawn). 128
Step 6: How to Apply Decision Rules to Graphed Scores to Know When to Revise Programs and Increase Goals 30 Digits Correct in 7 Minutes 25 20 15 10 5 0 Most recent 4 points Weeks of Instruction Goal-line 1 2 3 4 5 6 7 8 9 10 11 12 13 14 129
Step 6: How to Apply Decision Rules to Graphed Scores to Know When to Revise Programs and Increase Goals 30 Digits Correct in 7 Minutes 25 20 15 10 5 0 Goal-line Weeks of Instruction Most recent 4 points 1 2 3 4 5 6 7 8 9 10 11 12 13 14 130
Step 6: How to Apply Decision Rules to Graphed Scores to Know When to Revise Programs and Increase Goals Based on the student s trend-line: If the trend-line is steeper than the goal line, the end-of-year performance goal needs to be increased. If the trend-line is flatter than the goal line, the student s instructional program needs to be revised. If the trend-line and goal-line are fairly equal, no changes need to be made. 131
Step 6: How to Apply Decision Rules to Graphed Scores to Know When to Revise Programs and Increase Goals 132
Step 6: How to Apply Decision Rules to Graphed Scores to Know When to Revise Programs and Increase Goals 133
Step 6: How to Apply Decision Rules to Graphed Scores to Know When to Revise Programs and Increase Goals 134
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. 135
Step 7: How to Use Curriculum-Based Measurement Data Qualitatively to Describe Student Strengths and Weaknesses 136
Step 7: How to Use Curriculum-Based Measurement Data Qualitatively to Describe Student Strengths and Weaknesses 137
Other Ways to Use the Curriculum-Based Measurement Database How to Use the Curriculum-Based Measurement Database to Accomplish Teacher and School Accountability and for Formulating Policy Directed at Improving Student Outcomes How to Incorporate Decision Making Frameworks to Enhance General Educator Planning How to Use Progress Monitoring to Identify Nonresponders Within a Response-to-Intervention Framework to Identify Disability 138
How to Use Curriculum-Based Measurement Data to Accomplish Teacher and School Accountability for Formulating Policy Directed at Improving School Outcomes No Child Left Behind requires all schools to show Adequate Yearly Progress (AYP) toward a proficiency goal. Schools must determine measure(s) for AYP evaluation and the criterion for deeming an individual student proficient. CBM can be used to fulfill the AYP evaluation in math. 139
How to Use Curriculum-Based Measurement Data to Accomplish Teacher and School Accountability for Formulating Policy Directed at Improving School Outcomes Using Math CBM: Schools can assess students to identify the number of initial students who meet benchmarks (initial proficiency). The discrepancy between initial proficiency and universal proficiency is calculated. 140
How to Use Curriculum-Based Measurement Data to Accomplish Teacher and School Accountability for Formulating Policy Directed at Improving School Outcomes The discrepancy is divided by the number of years before the 2013 2014 deadline. This calculation provides the number of additional students who must meet benchmarks each year. 141
How to Use Curriculum-Based Measurement Data to Accomplish Teacher and School Accountability for Formulating Policy Directed at Improving School Outcomes Advantages of using CBM for AYP: Measures are simple and easy to administer. Training is quick and reliable. Entire student body can be measured efficiently and frequently. Routine testing allows schools to track progress during school year. 142
How to Use Curriculum-Based Measurement Data to Accomplish Teacher and School Accountability for Formulating Policy Directed at Improving School Outcomes Across-Year School Progress Number of Students Meeting CBM Benchmarks 500 400 300 200 100 0 (257) 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 End of School Year X (498) 143
How to Use Curriculum-Based Measurement Data to Accomplish Teacher and School Accountability for Formulating Policy Directed at Improving School Outcomes Within-Year School Progress Number of Students Meeting CBM Benchmarks 500 400 300 200 100 0 X (281) Sept Oct Nov Dec Jan Feb Mar Apr May June 2005 School-Year Month 144
How to Use Curriculum-Based Measurement Data to Accomplish Teacher and School Accountability for Formulating Policy Directed at Improving School Outcomes Within-Year Teacher Progress Number Students on Track to Meet CBM Benchmarks 25 20 15 10 5 0 Sept Oct Nov Dec Jan Feb Mar Apr May June 2005 School-Year Month 145
How to Use Curriculum-Based Measurement Data to Accomplish Teacher and School Accountability for Formulating Policy Directed at Improving School Outcomes Within-Year Special Education Progress Number Students on Track to Meet CBM Benchmarks 25 20 15 10 5 0 Sept Oct Nov Dec Jan Feb Mar Apr May June 2005 School-Year Month 146
How to Use Curriculum-Based Measurement Data to Accomplish Teacher and School Accountability for Formulating Policy Directed at Improving School Outcomes CBM Score: Grade 3 Concepts and Aplications Within-Year Student Progress 30 25 20 15 10 2005 School-Year Month 5 0 Sept Oct Nov Dec Jan Feb Mar Apr May June 147
How to Incorporate Decision-Making Frameworks to Enhance General Educator Planning CBM reports prepared by computer can provide the teacher with information about the class: Student CBM raw scores Graphs of the low-, middle-, and highperforming students CBM score averages List of students who may need additional intervention 148
How to Incorporate Decision-Making Frameworks to Enhance General Educator Planning 149
How to Incorporate Decision-Making Frameworks to Enhance General Educator Planning 150
How to Incorporate Decision-Making Frameworks to Enhance General Educator Planning 151
How to Use Progress Monitoring to Identify Non- Responders Within a Response-to-Intervention Framework to Identify Disability Traditional assessment for identifying students with learning disabilities relies on intelligence and achievement tests. Alternative framework is conceptualized as nonresponsiveness to otherwise effective instruction. Dual-discrepancy: Student performs below level of classmates. Student s learning rate is below that of their classmates. 152
How to Use Progress Monitoring to Identify Non- Responders Within a Response-to-Intervention Framework to Identify Disability All students do not achieve the same degree of math competence. Just because math growth is low, the student doesn t automatically receive special education services. If the learning rate is similar to that of the other students, the student is profiting from the regular education environment. 153
How to Use Progress Monitoring to Identify Non- Responders Within a Response-to-Intervention Framework to Identify Disability If a low-performing student is not demonstrating growth where other students are thriving, special intervention should be considered. Alternative instructional methods must be tested to address the mismatch between the student s learning requirements and the requirements in a conventional instructional program. 154
Case Study 1: Alexis 155
Case Study 1: Alexis 156
Case Study 2: Darby Valley Elementary Using CBM toward reading AYP: A total of 378 students. Initial benchmarks were met by 125 students. Discrepancy between universal proficiency and initial proficiency is 253 students. Discrepancy of 253 students is divided by the number of years until 2013 2014: 253 11 = 23. Twenty-three students need to meet CBM benchmarks each year to demonstrate AYP. 157
Case Study 2: Darby Valley Elementary Number Students Meeting CBM Benchmarks 100 200 300 400 0 Across-Year School Progress X (378) 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 (125) End of School Year 158
Case Study 2: Darby Valley Elementary Within-Year School Progress Number Students Meeting CBM Benchmarks 200 150 100 50 0 Sept Oct Nov Dec Jan Feb Mar Apr May June 2004 School-Year Month X (148) 159
Case Study 2: Darby Valley Elementary Ms. Main (Teacher) Number Students on Track to Meet CBM Benchmarks 25 20 15 10 5 0 Sept Oct Nov Dec Jan Feb Mar Apr May June 2004 School-Year Month 160
Case Study 2: Darby Valley Elementary Mrs. Hamilton (Teacher) Number Students on Track to Meet CBM Benchmarks 25 20 15 10 5 0 Sept Oct Nov Dec Jan Feb Mar Apr May June 2004 School-Year Month 161
Case Study 2: Darby Valley Elementary Special Education Number Students on Track to Meet CBM Benchmarks 25 20 15 10 5 0 Sept Oct Nov Dec Jan Feb Mar Apr May June 2004 School-Year Month 162
Case Study 2: Darby Valley Elementary CBM Score: Grade 1 C omputation 30 25 20 15 10 5 0 Cynthia Davis (Student) 2004 School-Year Month Sept Oct Nov Dec Jan Feb Mar Apr May June 163
Case Study 2: Darby Valley Elementary Dexter Wilson (Student) 164
Case Study 3: Mrs. Smith 165
Case Study 3: Mrs. Smith 166
Case Study 3: Mrs. Smith 167
Case Study 3: Mrs. Smith 168
Case Study 4: Marcus 169
Case Study 4: Marcus Digits Correct in 5 Minutes 30 25 20 15 10 5 0 High-performing math students Middle-performing math students Low-performing math students Weeks of Instruction 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 170
Curriculum-Based Measurement Materials AIMSweb/Edformation Yearly ProgressPro TM /McGraw-Hill Monitoring Basic Skills Progress/ Pro-Ed, Inc. Research Institute on Progress Monitoring, University of Minnesota (OSEP Funded) Vanderbilt University 171
Curriculum-Based Measurement Resources List on pages 31 34 of materials packet Appendix B of CBM manual 172