Using Curriculum-Based Measurement for Progress Monitoring in Math

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. Progress monitoring focuses on individualized decision making in general and special education with respect to academic skill development at the elementary grades. Progress monitoring is conducted frequently (at least monthly) and is designed to: Estimate rates of improvement. Identify students who are not demonstrating adequate progress and, therefore, require additional or alternative forms of instruction. Compare the efficacy of different forms of instruction and, thereby, design more effective, individualized instructional programs for problem learners.

Traditional Assessments:
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. Traditional assessments used in schools are generally lengthy tests that are not administered on a regular basis. Many times, traditional assessments are administered to students once per year, and teachers do not receive their students’ scores until weeks or months later, sometimes after the school year is complete. Because teachers do not receive immediate feedback, they cannot use these assessments to adapt their teaching methods or instructional programs in response to the needs of their students.

Curriculum-Based Measurement (CBM) is one type of PM.
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. One type of progress monitoring, CBM, is an alternative to commercially prepared traditional assessments that are administered at one point in time. CBM provides teachers with an easy and quick method of obtaining empirical information on the progress of their students. With frequently obtained student data, teachers can analyze student scores to adjust student goals and revise their instructional programs. That way, instruction can be tailored to best fit the needs of each student. One problem with traditional assessments is that student scores are based on national scores and averages. In fact, the students in a teacher’s classroom may differ tremendously from a national sample of students. CBM allows teachers to compare an individual student’s data to data on other students in their classroom. Schools or school districts may also collect normative data on the students within their own school or district to provide teachers with a local normative framework for interpreting scores.

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. Curriculum-based assessment (CBA) is a broader term than CBM. As defined by Tucker (1987), CBM meets the three curriculum-based assessment requirements: Measurement materials are aligned with the school’s curriculum. Measurement is frequent. Assessment information is used to formulate instructional decisions. CBM is just one type of CBA. Resource: Tucker, J. (1987). Curriculum-based assessment is not a fad. The Collaborative Educator, 1, 4, 10.

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.

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

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.

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

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.

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

To implement Mastery Measurement, the teacher:
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.

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

Multidigit Addition Mastery Test

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

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

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

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.

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

Random numerals within problems
Random placement of problem types on page

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

Donald’s Progress in Digits Correct Across the School Year

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

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

Avoids the need to specify a skills hierarchy.
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.

Curriculum-Based Measurement’s Two Methods for Representing Year-Long Performance
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).

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

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.

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.

CBM Passage for Correct Words per Minute

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.

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

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

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

Kindergarten Letter 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 …

First Grade Word Identification Fluency
Teacher: Read these words. Time: 1 minute

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

CBM Passage for Correct Words per Minute

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.

Computer Maze

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

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. CBM is a distinctive form of CBA because of two additional properties. First, each CBM test is an alternate form of equivalent difficulty. Each test samples the year-long curriculum in exactly the same way using prescriptive methods for constructing the tests. In fact, CBM is usually conducted with “generic” tests, designed to mirror popular curricula. By contrast, other forms of CBA require teachers to design their own assessment procedures. The creation of those CBA tests can be time consuming for teachers because the measurement procedures change each time a student masters an objective and can differ across pupils in the same classroom. The second distinctive feature of CBM is that it is highly prescriptive and standardized. This guarantees reliable and valid scores. CBM provides teachers with a standardized set of materials that have been researched to produce meaningful and accurate information. By contrast, the adequacy of teacher-developed CBA tests and commercial CBA tests is largely unknown. It is uncertain whether scores on those CBA tests represent performance on meaningful, important skills and whether the student would achieve a similar score if the test were re-administered.

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. CBM is used to monitor student progress across the entire school year. Students are given standardized reading probes at regular intervals (weekly, biweekly, monthly) to produce accurate and meaningful results that teachers can use to quantify short- and long-term student gains toward end-of-year goals. With CBM, teachers establish long-term (i.e., end-of-year) goals indicating the level of proficiency students will demonstrate on by the end of the school year.

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. CBM tests (also called probes) are relatively brief and easy to administer. The probes are administered the same way every time. Each probe is a different test, but the probes assess the same skills at the same difficulty level. The reading probes have been prepared by researchers or test developers to represent curriculum passages and be of equivalent difficulty from passage to passage within each grade level. Probes are scored for reading accuracy and speed, and student scores are graphed for teachers to consider when making decisions about the instructional programs and teaching methods for each student in the class. CBM provides a doable and technically strong approach for quantifying student progress. Using CBM, teachers determine quickly whether an educational intervention is helping a student.

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. Research has demonstrated that when teachers use CBM to inform their instructional decisionmaking students learn more, teacher decisionmaking improves, and students are more aware of their own performance (Fuchs, Deno, & Mirkin, 1984). CBM research, conducted over the past 30 years, has also shown CBM to be reliable and valid (Deno, 1985; Germann & Tindal, 1985; Marston, 1988; Shinn, 1989). A more in-depth bibliography of CBM research is available in the CBM manual. Resources: Deno, S. L. (1985). Curriculum-based measurement: The emerging alternative. Exceptional Children, 52, 211–232. Fuchs, L. S., Deno, S. L., & Mirkin, P. K. (1984). Effects of frequent curriculum-based measurement of evaluation on pedagogy, student achievement, and student awareness of learning. American Educational Research Journal, 21, 441–460. Germann G., & Tindal, G. (1985). An application on curriculum-based assessment: The use of direct and repeated measurement. Exceptional Children, 52, 241–265. Marston, D. (1988). The effectiveness of special education: A time-series analysis of reading performance in regular and special education settings. The Journal of Special Education, 21, 11–26. Shinn, M.R. (Ed.). (1989). Curriculum-based measurement: Assessing special children. New York: Guilford Press.

Steps to Conducting Curriculum-Based Measurements
Step 1: How to Place Students in a Math 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 Math Curriculum-Based Measurement Probes Step 4: How to Graph Scores The following are the seven steps needed to conduct CBM. We’ll highlight each of the steps, but a more in-depth explanation of each step is in the CBM manual. Step 1 discusses how to place students in a math CBM task for progress monitoring (page 9 of CBM manual). Step 2 discusses how to identify the level for material for monitoring progress for computation and concepts and applications (page 10 of CBM manual). Step 3 discusses how to administer and score math CBM (page 11 of CBM manual). Step 4 discusses how to graph scores (page 59 of CBM manual).

Steps to Conducting Curriculum-Based Measurements
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 Step 5 discusses how to set ambitious goals (page 62 of CBM manual). Step 6 discusses how to apply decision rules to graphed scores to know when to revise programs and increase goals (page 71 of CBM manual). Step 7 discusses how to use the CBM database qualitatively to describe students’ strengths and weaknesses (page 77 of CBM manual).

Kindergarten and first grade:
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 The first decision for implementing CBM in math is to decide which task is developmentally appropriate for each student to be monitored over the academic year. For students who are developing at a typical rate in math, the correct CBM tasks are as follows. For kindergarten or first grade, the following probes can be administered alone or in combination with one another. Number Identification asks students to identify numeric characters. Quantity Discrimination asks students to identify the bigger number in a pair of numbers. Missing Number asks students to identify the missing number in a sequence of four numbers. It should be noted that the Number Identification, Quantity Discrimination, and Missing Number tasks presented in the manual have limited data related to their technical adequacy at this time. The measures (as presented here) have recently been developed and are currently being examined with respect to their reliability and validity (Lembke & Foegen, 2005). Early data indicate that the measures show promise as indicators of student performance in math, but the effectiveness of the measures for monitoring student progress has not been assessed at the time. CBM Computation (Grades 1–6) and CBM Concepts and Applications Computation (Grades 2–6) can be administered alone or in combination with one another. Students in the earlier grades should use the Computation probes until the Concepts and Applications probes are appropriate for the grade-level material from the curriculum. For grades 1–6, once you select a task for CBM progress monitoring stick with that task (and level of probes) for the entire year. Resources: Lembke, E. S. & Foegen, A. (2005). Creating measures of early numeracy. Presentation at the annual Pacific Coach Research Conference. San Diego, CA.

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. For Computation and Concepts and Applications probes, teachers use CBM probes for the student’s current grade level. However, if a student is well below grade-level expectations, he or she may need to use lower-grade probes. If teachers are worried that a student is too delayed in math to make the grade-level probes appropriately, then they must find the appropriate CBM level by following these steps.

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 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, 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. Determine the grade level probe at which you expect the student to competently perform in math by year’s end. 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 average score is between 10 and 15 digits or blanks, then use this lower grade level. If the average score is less than 10 digits or blanks, move down one more level or stay at the original lower grade level and repeat this procedure. If the average score is greater than 15 digits or blanks, reconsider grade-appropriate material. Maintain the student on this level of text for the purpose of progress monitoring for the entire school year.

Students answer math problems. Teacher grades math probe.
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. With math CBM, students work on selected math problems for a set amount of time. After the probes are administered, the teacher grades each probe and graphs the score on a student graph. The CBM score is a general overall indicator of the student’s math competency. In math, the following CBM tasks are available at these grade levels. Kindergarten and first grade: Number Identification Quantity Discrimination Missing Number Grades 1–6: Computation Grades 2–6: Concepts and Applications We will discuss each of these six CBM tasks.

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. The fifth CBM task is Computation. Computation is used to monitor student progress during grades 1–6. The math CBM Computation probes include tests at each grade level for grades 1–6. Each test consists of 25 math computation problems representing the year-long grade-level math computation curriculum. Within each grade level, the type of problems represented on each test remains constant from test to test. For example, for third grade, each Computation test includes five multiplication facts with factors zero through five and four multiplication facts with factors six through nine. However, the facts to be tested and their positions on the test are selected randomly. Other types of problems remain similarly constant. CBM Computation can be administered to a group of students at one time. The administrator presents each student with a CBM Computation test. Students have a set amount of time to answer the math problems on the Computation test. Timing the CBM Computation test correctly is critical to ensure consistency from test to test. See Figure 4 in the manual for the time limit for each grade. The administrator times the students during the test and scores the tests later.

Computation Student Copy of a First Grade Computation Test
This is a first grade student copy of the Computation test. This would be the copy presented to the student.

Computation This is a second grade Computation test. On the right is a third grade Computation test. For grades 1–6, the teacher gives the class directions and allows the students to work for a set amount of time. The teacher says to the students: “It’s time to take your weekly math test. As soon as I give you your test, write your first name, your last name, and the date. After you’ve written your name and the date on the test, turn your paper over and put your pencil down so I know you are ready. “I want you to do as many problems as you can. Work carefully and do the best you can. Remember, start at the first problem and work left to right. Some problems will be easy for you; others will be harder. When you come to a problem you know you can do, do it right away. When you come to a problem that’s hard for you, skip it, and come back later. “Go through the entire test doing the easy problems. Then, go back and try the harder ones. Remember that you can get points for getting part of a problem right. So, even after you have done all the easy problems, go back and try the harder problems. Do this even if you think you can’t get the whole problem right. (For appropriate grade levels, say “Remember to reduce fractions to lowest terms unless the problem specifies to do something differently. And be sure to write out your remainder if the division problem has one.”) When I say, ‘Begin,’ turn your test over and start to work. Work for the whole test time. Write your answers so I can read them! If you finish early, check your answers. When I say, ‘Stop,’ put your pencil down and turn your test face down.” At that point, the teacher triggers the stopwatch and the student works for a specified amount of time.

Computation Grade Time limit First 2 min. Second Third 3 min. Fourth
Fifth 5 min. Sixth 6 min. Length of test varies by grade. The length of the Computation test varies by grade. This table shows the length of time students in grades 1–6 should be allowed to work on the Computation test.

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. When the teacher scores the student test, students receive 1 point for each digit answered correctly. The total number of correct digits is the student’s score. Although we can score total problems correct, scoring each digit correct in the answer is a more sensitive index of student change. We typically can evaluate overall student growth (or deterioration) earlier by evaluating correct digits in the answers.

Computation Correct Digits: Evaluate Each Numeral in Every Answer 4507 4507 4507 2146 2146 2146 2 61 2361 4 2 44 1 Score only each digit in the answer. Do not score other digits written during the calculation of the problem. ü 4 correct 3 correct 2 correct digits digits digits

Computation Scoring Different Operations Examples: 22 18 23 8 184 x 43
16 24 22 x 43 66 880 946 4 1 1 18 +16 34 158 29 129 When scoring addition, subtraction, and multiplication problems, evaluate each digit in the answer working in the direction from right to left. This direction follows how most people would work the problem. However, for division problems, score digits in the answer from left to right, the same direction a student would follow when working the problem. A slightly different method is used when scoring a quotient with a remainder as explained in the next slide. 2 correct digits 3 correct digits 3 correct digits 2 correct digits

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). When giving directions, tell students that they should use remainders for problems rather than carrying out long division to decimals. When scoring remainders, the direction follows from right to left, similar to what a student would do (i.e., subtracting) to find the remainder portion of the answer. The first part of the quotient, however, is scored left to right, following the same direction as one would use in working the problem.

Computation Scoring Examples: Division with Remainders Correct Answer
Student ’ s Answer 4 0 3 R 5 2 4 3 R 5 (1 correct digit) ü 2 3 R 1 5 4 3 R 5 ü ü (2 correct digits)

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. For decimal problems, decimal placement is the critical feature. Therefore, the teacher starts scoring from the decimal in the answer and moves out in either direction, digit by digit. The decimal point itself is not considered a digit. It just marks where scoring begins. Unless specified otherwise for a particular problem, tell students they should reduce fractional answers to lowest terms in order to get full credit.

Computation Scoring Examples: Decimals

Computation Scoring Examples: Fractions Correct Answer Student ’
s Answer 6 7 / 1 2 8 / 1 1 (2 correct digits) 5 6 / 1 2 ü 1 / 2 Scoring Examples: Fractions

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. Look at the following fifth grade CBM Computation score sheet. Samantha answered 13 problems correctly in 5 minutes but got 49 digits correct. We would graph 49 as Samantha’s score for this probe.

Computation Sixth Grade Computation Test Let’s practice.
Let’s practice Computation. In your materials packet, handout 1 is a sixth grade Computation test. Here’s what happens. The teacher introduces the activity to the student. I’ll be the teacher for this activity. All of the students will begin working at the same time. I’ll time 6 minutes for everyone. [Teacher reads from script.] Are all the Students ready? Great. Go ahead and begin. [Time for 6 minutes.]

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. [At the end of 6 minutes] Great! Now, switch Computation tests with the person sitting next to you. Use this key to grade the student’s work. The key is also on handout 2. Score just the digits correct in the answers and ignore any other computational work. Remember to score right to left for addition, subtraction, and multiplication. Score left to right for division—except for the remainder part, which is scored right to left. Make sure students know to write remainders when appropriate. For decimals, start at the decimal point and work outward from the decimal point in both directions. For fractions, score each digit right to left for the whole number part, for the numerator, and for the denominator separately. Then, add together all the digits correct from each part. Be sure students know that fractions should be reduced (or simplified) to their lowest terms unless specified differently by the problem (e.g., renaming to an improper fraction). If the student gets every digit correct on this probe, the student would earn a total of 104 digits correct (or 25 problems). Then, the teacher would graph 104 as the student’s score for this probe.

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 math curriculum. Student works for set amount of time (time limit varies by grade). Teacher grades test after student finishes. The sixth CBM task is Concepts and Applications. Concepts and Applications is used to monitor student progress during grades 2–6. The math CBM Concepts and Applications probes include tests at each grade level for grades 2–6. Each test consists of 18–25 math computation problems representing the year-long grade-level math concepts and applications curriculum. Each test is 3 pages long. Within each grade level, the type of problems represented on each test remains constant from test to test. For example, for third grade, every Concepts and Applications test includes two problems dealing with charts and graphs and three problems dealing with number concepts. Other types of problems remain similarly constant. The placement of the various types of items is random from test to test, and the actual problems differ from test to test. CBM Concepts and Applications can be administered to a group of students at one time. The administrator presents each student with a CBM Concepts and Applications test. Students have a set amount of time to answer the math problems on the test. Timing the CBM Concepts and Applications test correctly is critical to ensure consistency from test to test. The administrator monitors the students during the test and scores each test later. The score is the number of blanks answered correctly.

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. This is the student copy of the Concepts and Applications test. The actual test is 3 pages long. This would be the copy presented to the student. For grades 2–6, the teacher gives the class directions and allows the students to work for a set amount of time. The teacher says to the students: “It’s time to take your weekly math test. As soon as I give you your test, write your first name, your last name, and the date. After you’ve written your name and the date on the test, turn your paper over and put your pencil down so I’ll know you are ready. “I want you to do as many problems as you can. Work carefully and do the best you can. Remember, start at the first problem, work down the first column and then down the second column. Then move on to the next page. Some problems will be easy for you; others will be harder. When you come to a problem you know you can do, do it right away. When you come to a problem that’s hard for you, skip it, and come back later. Remember, some problems have more than one blank. You get credit for each blank that you answer, so be sure to fill in as many blanks as you can. The answers to some word problems may be an amount of money. When you write your answer to a money problem, be sure to use the correct symbols for money in order to get credit for your answer.” Note that no “digits” are awarded for the actual symbols indicating money. Only the digits in the answers will be scored. However, without the monetary symbol for appropriate word problems, the answer should not be scored. “Go through the entire test doing the easy problems. Then go back and try the harder ones. When I say, ‘Begin,’ turn your test over and start to work. Work for the whole test time. Write your answers so I can read them! If you finish early, check your answers. When I say, ‘Stop,’ put your pencil down and turn your test face down.” At that point, the teacher triggers the stopwatch and the student works for a specified amount of time.

Grade Time limit Second 8 min. Third 6 min. Fourth Fifth 7 min. Sixth Length of test varies by grade. The length of the Concepts and Applications test varies by grade. This table shows the length of time students in grades 2–6 should be allowed to work on the Concepts and Applications test.

Students receive 1 point for each blank answered correctly. The number of correct answers within the time limit is the student’s score. When the teacher scores the student test, students receive 1 point for each blank answered correctly. The total number of correct blanks is the student’s score.

Quinten’s Fourth Grade Concepts and Applications Test Twenty-four blanks answered correctly. Quinten’s score is 24. Look at the following fourth grade CBM Concepts and Applications score sheet. Quinten answered a total of 24 blanks correctly. Twenty-four is Quinten’s math score for this probe. Note that on problem 9, Quinten missed both blanks. The whole problem is marked wrong. However, Quinten’s teacher could have marked each blank separately.

These are pages 2 and 3 of Quinten’s Concepts and Applications test.

Fifth Grade Concepts and Applications Test—1 Let’s practice. Let’s practice Concepts and Applications. In your materials packet, handouts 3–5 are a fifth grade Concepts and Applications test. Here’s what happens. The teacher introduces the activity to the student. I’ll be the teacher for this activity. All of the students will begin working at the same time. I’ll time 7 minutes for everyone. [Teacher reads from script.] Are all the students ready? Great. Go ahead and begin. [Time for 7 minutes.]

Fifth Grade Concepts and Applications Test—Page 2

Fifth Grade Concepts and Applications Test—Page 3 Let’s practice.

Problem Answer 10 3 11 A ADC C BFE 12 0.293 13   14 28 hours 15 790,053 16 451 CDLI 17 7 18 $10.00 in tips 20 more orders 19 4.4 20 21 5/6 dogs or cats 22 1 m 23 12 ft Answer Key Problem Answer 1 54 sq. ft 2 66,000 3 A center C diameter 4 28.3 miles 5 7 6 P 7 N 10 0 $5 bills 4 $1 bills 3 quarters 8 1 millions place 3 ten thousands place 9 697 [At the end of 7 minutes] Great! Now, switch Concepts and Applications tests with the person sitting next to you. This answer key is also on handout 22. Subtract any incorrect blanks from the total number of blanks attempted in 7 minutes. The number of blanks the student got correct is the student’s Concepts and Applications score. If the student has every blank correct, his or her score is 32.

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. The second CBM task is Number Identification. Number Identification is used to monitor student progress during kindergarten. The Number Identification test for kindergarten students consists of 84 items that require the student to identify numbers between 0 and 100. Number Identification includes three alternate forms. Number Identification measures have been researched as screening tools, but schools may want to use them for progress monitoring. Number Identification is administered individually. The administrator presents the student with a student copy of the Number Identification test. The administrator places the administrator copy of the Number Identification test on a clipboard and positions it so the student cannot see what the administrator records.

Student Copy of a Number Identification test Actual student copy is 3 pages long. This is the student copy of the Number Identification test. The actual Number Identification test is 3 pages long. This would be the copy presented to the student. The teacher says to the students: “The paper in front of you has boxes with numbers in them. When I say begin, I want you to tell me what number is in each box. Start here and go across the page [demonstrate by pointing]. Try each one. If you come to one that you don’t know, I’ll tell you what to do. Are there any questions? Put your finger on the first one. Ready, begin.” At that point, the teacher triggers the stopwatch and the student identifies the number of dots for 1 minute. When scoring Number Identification, if a student correctly identifies the number, score the item as correct. If the student hesitates or struggles with a problem for 3 seconds, prompt the student to continue to the next problem and score the item as incorrect.

Number Identification Score Sheet This is the teacher score sheet for the Number Identification test. When scoring Number Identification, if a student correctly identifies the number, score the item as correct. At 1 minute, underline the last problem completed.

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. During the Number Identification test, if the student hesitates or struggles with a problem for 3 seconds, prompt the student to continue to the next problem and score the item as incorrect. Do not correct student errors.

Jamal’s Number Identification Score Sheet Skipped items are marked with a (-). Fifty-seven items attempted. Three incorrect. Jamal’s score is 54. Look at the following Number Identification score sheet. Jamal answered 54 items correctly in 1 minute. Fifty-four is Jamal’s math score for this probe.

Teacher Score Sheet Let’s practice. Let’s practice Number Identification. In your materials packet, handout 21 is a teacher score sheet for Number Identification test. Handouts 22–24 are a student copy of the Number Identification test. Choose a partner. One of you is the teacher. The teacher uses the teacher script and teacher score sheet. The other person is the student. Place the student copy of the Number Identification test in front of the student. Here’s what happens. The teacher introduces the activity to the student. Then for timing purposes, all of the students begin working at the same time. I’ll time 1 minute for everyone. The teacher marks errors on the score sheet. Go ahead and read from the script. [Allow time for teachers to read from script.]

Student Sheet—Page 1 Let’s practice. Are all the students ready to say the number? Great. Go ahead and begin. [Time for 1 minute. Teachers mark errors as students work.] [At the end of 1 minute] Great! Now, teachers, underline the last problem completed. Subtract any errors from the total number of items attempted in 1 minute. That is the student’s score.

Student Sheet—Page 2 Let’s practice.

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. The third CBM task is Quantity Discrimination. Quantity Discrimination is used to monitor student progress during kindergarten. The Quantity Discrimination test for kindergarten students consists of 63 items that require the student to identify the bigger number from a pair of numbers 0 through 20. Quantity Discrimination includes three alternate forms. Quantity Discrimination measures have been researched as screening tools, but schools may want to use them for progress monitoring. Quantity Discrimination is administered individually. The administrator presents the student with a student copy of the Quantity Discrimination test. The administrator places the administrator copy of the Quantity Discrimination test on a clipboard and positions it so the student cannot see what the administrator records.

Student Copy of a Quantity Discrimination test Actual student copy is 3 pages long. This is the student copy of the Quantity Discrimination test. The actual Quantity Discrimination test is 3 pages long. This would be the copy presented to the student. The teacher says to the students: “The paper in front of you has boxes with two numbers in each box. When I say begin, I want you to tell me which number is bigger. Start here and go across the page [demonstrate by pointing]. Try each one. If you come to one that you don’t know, I’ll tell you what to do. Are there any questions? Put your finger on the first one. Ready, begin.” At that point, the teacher triggers the stopwatch and the student identifies the number of dots for 1 minute. When scoring Quantity Discrimination, if a student correctly identifies the bigger number, score the item as correct. If the student hesitates or struggles with a problem for 3 seconds, prompt the student to continue to the next problem and score the item as incorrect.

Quantity Discrimination Score Sheet This is the teacher score sheet for the Quantity Discrimination test. When scoring Quantity Discrimination, if a student correctly identifies the bigger number, score the item as correct. At 1 minute, underline the last problem completed.

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. During the Quantity Discrimination test, if the student hesitates or struggles with a problem for 3 seconds, prompt the student to continue to the next problem and score the item as incorrect. Do not correct student errors.

Lin’s Quantity Discrimination Score Sheet Thirty-eight items attempted. Five incorrect. Lin’s score is 33. Look at the following Quantity Discrimination score sheet. Lin answered 33 items correctly in 1 minute. Thirty-three is Lin’s math score for this probe.

Teacher Score Sheet Let’s practice. Let’s practice Quantity Discrimination. In your materials packet, handout 25 is a teacher score sheet for the Quantity Discrimination test. Handouts 26–28 are a student copy of the Quantity Discrimination test. Choose a partner. One of you is the teacher. The teacher uses the teacher script and teacher score sheet. The other person is the student. Place the student copy of the Quantity Discrimination test in front of the student. Here’s what happens. The teacher introduces the activity to the student. Then for timing purposes, all of the students begin working at the same time. I’ll time 1 minute for everyone. The teacher marks errors on the score sheet. Go ahead and read from the script. [Allow time for Teachers to read from script.]

Student Sheet—Page 1 Let’s practice. Are all the students ready to say the bigger number? Great. Go ahead and begin. [Time for 1 minute. Teachers mark errors as students work.] [At the end of 1 minute] Great! Now, teachers, underline the last problem completed. Subtract any errors from the total number of items attempted in 1 minute. That is the student’s score.

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. The fourth CBM task is Missing Number. Missing Number is used to monitor student progress at kindergarten. The Missing Number test for kindergarten students consists of 63 items that require the student to identify the missing number in a sequence of four numbers. The sequences includes counting by 1-digit increments with numbers 0 through 10, counting by 2-digit increments with numbers 0 through 20, counting by 5-digit increments with numbers 0 through 50, and counting by 10-digit increments with numbers 0 through 100. Missing Number includes three alternate forms. Missing Number measures have been researched as screening tools, but schools may want to use them for progress monitoring. Missing Number is administered individually. The administrator presents the student with a student copy of the Missing Number test. The administrator places the administrator copy of the Missing Number test on a clipboard and positions it so the student cannot see what the administrator records.

Missing Number Student Copy of a Missing Number Test
Actual student copy is 3 pages long. This is the student copy of the Missing Number test. The actual Missing Number test is 3 pages long. This would be the copy presented to the student. The teacher says to the students: “The paper in front of you has boxes with three numbers and a blank in each of them. When I say begin, I want you to tell me what number goes in the blank in each box. Start here and go across the page [demonstrate by pointing]. Try each one. If you come to one that you don’t know, I’ll tell you what to do. Are there any questions? Put your finger on the first one. Ready, begin.’ At that point, the teacher triggers the stopwatch and the student identifies the number of dots for 1 minute. When scoring Missing Number, if a student correctly identifies the missing number, score the item as correct. If the student hesitates or struggles with a problem for 3 seconds, prompt the student to continue to the next problem and score the item as incorrect.

Missing Number Missing Number Score Sheet
This is the teacher score sheet for the Missing Number test. When scoring Missing Number, if a student correctly identifies the missing number, the item is scored as correct. At 1 minute, the administrator underlines the last problem completed.

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. During the Missing Number test, if the student hesitates or struggles with a problem for 3 seconds, the student is prompted to continue to the next problem and the item is scored as incorrect. The administrator does not correct student errors.

Missing Number Thomas’s Missing Number Score Sheet
Twenty-six items attempted. Eight incorrect. Thomas’s score is 18. Look at the following Missing Number score sheet. Thomas answered 18 items correctly in 1 minute. Eighteen is Thomas’ math score for this probe.

Missing Number Teacher Score Sheet Let’s practice.
Let’s practice Missing Number. In your materials packet, handout 13 is a teacher score sheet for the Missing Number test. Handouts 14–16 are a student copy of the Missing Number test. Choose a partner. One of you is the teacher. The teacher uses the teacher script and teacher score sheet. The other person is the student. Place the student copy of the Missing Number test in front of the Student. Here’s what happens. The teacher introduces the activity to the student. Then for timing purposes, all of the students begin working at the same time. I’ll time 1 minute for everyone. The teacher marks errors on the score sheet. Go ahead and read from the script. [Allow time for teachers to read from script.]

Missing Number Student Sheet—Page 1 Let’s practice.
Are all the students ready to say the missing number? Great. Go ahead and begin. [Time for 1 minute. Teachers mark errors as students work.] [At the end of 1 minute] Great! Now, teachers, underline the last problem completed. Subtract any errors from the total number of items attempted in 1 minute. That is the student’s score.

Missing Number Student Sheet—Page 2 Let’s practice.

Missing Number Student Sheet—Page 3 Let’s practice.

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. Step 4 discusses how to graph scores. Once the CBM data for each student have been collected, it is time to begin graphing student scores. Graphing the scores of every CBM on an individual student graph is a vital aspect of the CBM program. These graphs give teachers a straightforward way of reviewing a student’s progress, monitoring the appropriateness of the student’s goals, judging the adequacy of the student’s progress, and comparing and contrasting successful and unsuccessful instructional aspects of the student’s program. CBM graphs help teachers make decisions about the short- and long-term progress of each student. Frequently, teachers underestimate the rate at which students can improve (especially in special education classrooms); therefore, the CBM graphs help teachers set ambitious, but realistic, goals. Without graphs and decision rules about the scores on a student graph, teachers often stick with low goals. By using a CBM graph, teachers can use a set of standards to create more ambitious student goals and help improve student achievement. Also, CBM graphs provide teachers with actual data to help them revise and improve a student’s instructional program.

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. Teachers have two options for creating CBM graphs of the individual students in the classroom. The first option is that teachers and schools can purchase CBM graphing software that graphs student data and helps interpret the data for teachers. The second option is that teachers can create their own student graphs using graph paper and pencil. To create student graphs, teachers create a master CBM graph, in which the vertical axis accommodates the range of the scores of all students in the class, from 0 to the highest score. A table of highest scores for the vertical axis is available in the CBM manual. On the horizontal axis, the number of weeks of instruction is listed. Once the teacher creates the master graph, it can be copied and used as a template for every student.

It is easy to graph student CBM scores on teacher-made graphs. Teachers create a student graph for each individual CBM student so they can interpret the CBM scores of every student and see their progress or lack thereof. Again, the vertical axis is labeled with the range of student scores. The horizontal axis is labeled with the number of instructional weeks for the year.

5 10 15 20 25 1 2 3 4 6 7 8 9 11 12 13 14 Weeks of Instruction Digits Correct in 3 Minutes Every time a CBM probe is administered, the teacher scores the probe and then records the score on a CBM graph. Look at this graph. A line can be drawn connecting each data point to easily see the differences between scores. Student scores are plotted on graph and a line is drawn between scores.

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 Once a few CBM scores have been graphed, it is time for the teacher to decide on an end-of-year performance goal for the student. There are three options. Two options are utilized after at least three CBM scores have been graphed. One option is utilized after at least eight CBM scores have been graphed.

End-of-Year Benchmarking For typically developing students, a table of benchmarks can be used to find the CBM end-of-year performance goal. The first option for making an end-of-year performance goal is to use End-of-Year Benchmarking. For typically developing students at the grade level where the student is being monitored, identify the end-of-year CBM benchmark as provided in this table. This table is also included in the CBM manual. This benchmark is the end-of-year performance goal. The benchmark, or end-of-year performance goal, is represented on the graph by an X at the date marking the end of the year. A goal-line is then drawn between the median of at least the first three CBM-graphed scores and the end-of-year performance goal.

Grade Probe Maximum score Benchmark Kindergarten Data not yet available First Computation 30 20 digits Second 45 Concepts and Applications 32 20 blanks Third 30 digits 47 30 blanks Fourth 70 40 digits 42 Fifth 80 15 blanks Sixth 105 35 digits 35 These are the maximum scores and benchmarks for first through sixth grade Computation and Concepts and Applications tests.

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. The second option for making an end-of-year performance goal is to use an Intra-Individual Framework. Identify the weekly rate of improvement for the target student under baseline conditions, using at least eight CBM data points. Multiply this baseline rate by 1.5. Take this product and multiply it by the number of weeks until the end of the year. Add this product to the student’s baseline score. This sum is the end-of-year goal.

First eight scores: 3, 2, 5, 6, 5, 5, 7, and 4. Difference: 7 – 2 = 5. Divide by weeks: 5 ÷ 8 = Multiply by baseline: × 1.5 = Multiply by weeks left: × 14 = Product is added to median: = The end-of-year performance goal is 18 (rounding). For example, a student’s first eight CBM scores were 3, 2, 5, 6, 5, 5, 7, and 4. To calculate the weekly rate of improvement, find the difference between the highest and lowest scores. In this instance, 7 is the highest score and 2 is the lowest score: 7 – 2 = 5. Since eight scores have been collected, divide the difference between the highest and lowest scores by the number of weeks: 5 ÷ 8 = That quotient is then multiplied by 1.5: × 1.5 = Multiply that product by the number of weeks until the end of the year. If there are 14 weeks left until the end of the year: × 14 = The median score of the first eight data points was The sum of and the median score is the end-of-year performance goal: = The student’s end-of-year performance goal would be 18.

Grade Computation: Digits Concepts and Applications: Blanks First 0.35 N/A Second 0.30 0.40 Third 0.60 Fourth 0.70 Fifth Sixth 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. The third option for making an end-of-year performance goal is to use National Norms. For typically developing students at the grade level where the student is being monitored, identify the average rate of weekly increase from a national norm chart. This is a copy of a Norm Chart. It is also available in the CBM manual.

Grade Computation: Digits Concepts and Applications: Blanks First 0.35 N/A Second 0.30 0.40 Third 0.60 Fourth 0.70 Fifth Sixth National Norms Median: 14 Fourth Grade Computation Norm: 0.70 Multiply by weeks left: 16 × 0.70 = 11.2 Add to median: = 25.2 The end-of-year performance goal is 25 For example, let’s say that a fourth grade student’s median score from his first three CBM Computation probes is 14. The norm for fourth grade students is (See Figure 58 in the CBM manual.) The 0.70 is the weekly rate of growth for fourth graders. To set an ambitious goal for the student, multiply the weekly rate of growth by the number of weeks left until the end of the year. If there are 16 weeks left, multiply 16 by 0.70: 16  0.70 = Add 11.2 to the baseline median of 14 ( = 25.2). This sum (25) is the end-of-year performance goal.

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. The teacher creates an end-of-year performance goal for the student using one of the three options we just discussed. The performance goal is marked on the student graph at the year-end date with an X. A goal-line is then drawn between the median of the initial graphed scores and the end-of-year performance goal. The goal-line shows the teacher and students how quickly CBM scores should be increasing to reach the year-end goal. Let’s look at an example graph.

Drawing a Goal-Line For this student, the end-of-year performance goal on CBM Concepts and Applications would be 18. An X is marked at 18 and a dotted line is drawn from the median of the student’s first few scores to the X. The student’s progress should follow this dotted line. We’ll talk about what to do if the student’s progress is above or below the goal-line (the dotted line) in a little while. Goal-line: The desired path of measured behavior to reach the performance goal over time.

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. After deciding on an end-of-year performance goal and drawing the goal-line, teachers continually monitor the student graph to determine whether student progress is adequate. This tells the teacher whether the instructional program is effective. When at least seven to eight CBM scores have been graphed, teachers draw a trend-line to represent the student’s actual progress. By drawing the trend-line, teachers can compare the goal-line (desired rate of progress) to the trend-line (actual rate of progress). 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.

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. To draw a trend-line, teachers use a procedure called the Tukey method. The Tukey method provides a fairly accurate idea of how the student is progressing. Teachers use the Tukey method after at least seven to eight CBM scores have been graphed. First, the teacher counts the number of charted scores and divides the scores into three fairly equal groups. If the scores cannot be split into three groups equally, try to make the groups as equal as possible. Draw two vertical lines to divide the scores into three groups. Look at the first and third groups of data points. Find the median (middle) data point for each group and mark this point with an X. To draw the trend-line, draw a line through the two Xs.

Look at this graph. The data points were divided into three fairly equal groups. Two vertical lines were drawn to divide the three groups. The median (middle) data point for the first group and third group were marked with an X. Then, a trend-line was drawn through the two Xs. After the initial seven to eight data points are graphed and the Tukey method is used to create a trend-line, the student graphs should be reevaluated using the Tukey method every seven to eight additional data points. Instructional decisions for students are based on the ongoing evaluation of student graphs.

Practice 1 5 10 15 20 25 1 2 3 4 6 7 8 9 11 12 13 14 Weeks of Instruction Digits Correct in 5 Minutes Look in your materials packet at handout 11. You’re going to practice drawing a trend-line using the Tukey method in two different graphs. Remember to divide the data points into three fairly equal groups. Then mark the median (middle) data point for the first group and third group with an X and draw the trend-line. Go ahead and practice on the first graph.

Practice 1 Your graph should look similar to this one. Does anyone have questions?

Practice 2 5 10 15 20 25 1 2 3 4 6 7 8 9 11 12 13 14 Weeks of Instruction Digits Correct in 5 Minutes Let’s practice another one. Practice using the Tukey method on handout 28.

Practice 2 Your graph should look similar to this one. Does anyone have questions?

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. CBM computer management programs are available for schools to purchase. The computer scoring programs create graphs for individual students after the student scores are entered into the program and aid teachers in making performance goals and instructional decisions. Other computer programs actually collect and score the data. Various types of computer assistance are available at varying fees. Information on how to obtain the computer programs is in Appendix A.

Standard decision rules help with this process.
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. Step 6 discusses how to apply decision rules to graphed scores. CBM can judge the adequacy of student progress and the need to change instructional programs. Researchers have demonstrated that CBM can be used to improve the scope and usefulness of program-evaluation decisions and develop instructional plans that enhance student achievement. After teachers draw CBM graphs and trend-lines, they use graphs to evaluate student progress and formulate instructional decisions. Standard CBM-decision rules guide decisions about the adequacy of student progress and the need to revise goals and instructional programs.

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, 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). Decision rules can used two ways. These decision rules are based on the four most recent consecutive scores: If the four most recent consecutive CBM scores are above the goal-line, the student’s end-of-year performance goal needs to be increased. If the four most recent consecutive CBM scores are below the goal-line, the teacher needs to revise the instructional program.

Step 6: How to Apply Decision Rules to Graphed Scores to Know When to Revise Programs and Increase Goals 5 10 15 20 25 30 1 2 3 4 6 7 8 9 11 12 13 14 Weeks of Instruction Digits Correct in 7 Minutes Goal-line Most recent 4 points Look at this graph. The four most recent consecutive CBM scores are above the goal-line, so the teacher needs to increase the student’s end-of-year performance goal. The teacher increases the desired rate (or goal) to boost the actual rate of student progress. The point of the goal increase is notated on the graph as a dotted vertical line. This allows teachers to visually note when the student’s goal was changed. The teacher reevaluates the student graph in another seven to eight data points to determine whether the student’s new goal is appropriate or whether a teaching change is needed.

Step 6: How to Apply Decision Rules to Graphed Scores to Know When to Revise Programs and Increase Goals 5 10 15 20 25 30 1 2 3 4 6 7 8 9 11 12 13 14 Weeks of Instruction Digits Correct in 7 Minutes Goal-line On this graph, the four most recent scores are below the goal-line. Therefore, the teacher needs to change the student’s instructional program. The end-of-year performance goal and goal-line never decrease, they can only increase. The instructional program should be tailored to bring a student’s scores up so they match or surpass the goal-line. The teacher draws a dotted vertical line when making an instructional change. This allows teachers to visually note when changes to the student’s instructional program were made. The teacher reevaluates the student graph in another seven to eight data points to determine whether the change was effective. Most recent 4 points

Based on the student’s trend-line:
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. Decision rules can used two ways. These decision rules are based on the student’s trend-line: If the student’s trend-line is steeper than the goal-line, the student’s end-of-year performance goal needs to be increased. If the student’s trend-line is flatter than the goal-line, the teacher needs to revise the instructional program. If the student’s trend-line and goal-line are the same, no changes need to be made.

Step 6: How to Apply Decision Rules to Graphed Scores to Know When to Revise Programs and Increase Goals On this graph, the trend-line is steeper than the goal-line. Therefore, the student’s end-of-year performance goal needs to be adjusted. The teacher increases the desired rate (or goal) to boost the actual rate of student progress. The new goal-line can be an extension of the trend-line. The point of the goal increase is notated on the graph as a dotted vertical line. This allows teachers to visually note when the student’s goal was changed. The teacher reevaluates the student graph in another seven to eight data points to determine whether the student’s new goal is appropriate or whether a teaching change is needed.

Step 6: How to Apply Decision Rules to Graphed Scores to Know When to Revise Programs and Increase Goals On this graph, the trend-line is flatter than the performance goal-line. The teacher needs to change the student’s instructional program. Again, the end-of-year performance goal and goal-line are never decreased. A trend-line below the goal-line indicates that student progress is inadequate to reach the end-of-year performance goal. The instructional program should be tailored to bring a student’s scores up so they match or surpass the goal-line. The point of the instructional change is represented on the graph as a dotted vertical line. This allows teachers to visually note when the student’s instructional program was changed. The teacher reevaluates the student graph in another seven to eight data points to determine whether the change was effective.

Step 6: How to Apply Decision Rules to Graphed Scores to Know When to Revise Programs and Increase Goals If the trend-line matches the goal-line, then no change is currently needed for the student. The teacher reevaluates the student graph in another seven to eight data points to determine whether an end-of-year performance goal or instructional change needs to take place.

Student completes Computation or Concepts and Applications tests.
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. Step 7 discusses how to use CBM data qualitatively to describe student strengths and weaknesses. Teachers can use a Skills Profile to describe the strengths and weaknesses of each student in the classroom. A Skills Profile is a visual display of a student’s progress by each skill area. Each box on the Skills Profile represents performance for each skill for every 1-week interval for the entire school year. The Skills Profile can help teachers formulate instructional decisions for individual students by identifying skills to target for instruction.

Step 7: How to Use Curriculum-Based Measurement Data Qualitatively to Describe Student Strengths and Weaknesses A Class Skills Profile provides information in specific skills for each student in the class, averaged across the most recent two assessments. Each box represents the student’s mastery status on a particular skill.

Step 7: How to Use Curriculum-Based Measurement Data Qualitatively to Describe Student Strengths and Weaknesses An individual Skills Profile (like this one) provides the teacher with information on the individual students in his or her classroom. The labels at the top of the chart (A1–F2) stand for addition, subtraction, multiplication, division, and fractions. As Mrs. Marshall looks at the boxes for each student, she can see that increasingly dark boxes show increasing mastery of skill.

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 Now, we are going to discuss three additional ways to use the CBM database. The first topic we will discuss is “How To Use the CBM Database To Accomplish Teacher and School Accountability and for Formulating Policy Directed at Improving Student Outcomes.” The second topic we will discuss is “How To Incorporate Decision Making Frameworks To Enhance General Educator Planning.” The third topic we will discuss is “How To Use Progress Monitoring To Identify Nonresponders Within a Response-to-Intervention Framework To Identify Disability.”

CBM can be used to fulfill the AYP evaluation in math.
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. Let’s talk about how to use the CBM database to accomplish teacher and school accountability and for formulating policy directed at improving student outcomes. Federal law requires schools to show that they are achieving Adequate Yearly Progress (AYP) toward the No Child Left Behind proficiency goal. AYP is the annual minimum growth rate needed to eliminate the discrepancy between a school’s initial proficiency status and universal proficiency within the established time frame. Schools must determine the measure(s) to be used for AYP evaluation and the criterion for deeming an individual student “proficient” on this measure. Schools must quantify AYP for achieving the goal of universal proficiency by the school year 2013–2014. CBM can be used to fulfill the AYP evaluation in math.

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. Schools can assess every student using CBM to identify the number of students who initially meet benchmarks. This number of students represents a school’s initial proficiency status. Then, the discrepancy between initial proficiency and universal proficiency can be calculated.

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. Once the discrepancy between initial and universal proficiency is calculated, the discrepancy is divided by the number of years available before meeting the 2013–2014 goal. The resulting answer gives the number of additional students who must meet CBM end-of-year benchmarks each year.

Advantages of using CBM for AYP:
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. Relying on CBM for specifying AYP provides several advantages. First, the CBM measures are simple to administer, and examiners can be trained to administer the tests in a reliable fashion in a short amount of time. Second, because the tests are brief, schools can measure an entire student body relatively efficiently and frequently. Routine testing allows a school to track its own progress over the school year. Progress can be examined at the school, teacher, or student level. Using CBM for multilevel monitoring can transform AYP from a procedural compliance burden into a useful tool for guiding education reform at the school level, guiding the instructional decisionmaking of individual teachers about their reading programs, and ensuring that the reading progress of individual students is maximized.

Across-Year School Progress
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 CBM provides a multilevel monitoring system that helps schools ensure greater levels of reading success. Here are a few examples of how CBM can be used in conjunction with a school’s AYP. CBM can be used to monitor across-year progress in achieving AYP (and toward achieving universal proficiency by the 2013–2014 deadline). On this graph, it is easy for the school to see the progress it is making towards its universal proficiency goal of 497 students.

Within-Year School Progress
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 (281) CBM can be used to monitor a school’s within-year progress towards achieving the AYP for the year. On this graph, the number of students, 281, who need to meet CBM benchmarks by the end of the school year is marked with an X on the graph. The month-by-month breakdown of the progress towards the yearly AYP goal is highlighted on this graph.

Within-Year Teacher Progress
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 CBM can be used to monitor a teacher’s within-year progress. This graph provides each individual teacher with a month-by-month look at how many of his or her students are meeting CBM benchmarks.

Within-Year Special Education Progress
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 CBM can be used to monitor a school’s special education performance within a school year. This graph provides a month-by-month look at the progress of all the special education students in the school and how many students are meeting CBM benchmarks.

Within-Year Student Progress
How to Use Curriculum-Based Measurement Data to Accomplish Teacher and School Accountability for Formulating Policy Directed at Improving School Outcomes Within-Year Student Progress Like we’ve already discussed, CBM can monitor a student’s within-year progress. Graphs like these, prepared individually for each student, can provide the teacher with information about a student’s reading progress.

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 high-performing students CBM score averages List of students who may need additional intervention Let’s talk about how to incorporate decision-making frameworks to enhance general educator planning. Some CBM Class Reports that are prepared by computer can provide the teacher with information about his or her class that he or she can use to enhance his or her classroom planning. CBM Reports give the teacher student CBM raw scores; graphs of the low-, middle- and high-performing students; CBM score averages; and a list of students who many need additional intervention.

This page of the CBM Class Report shows three graphs: one for the progress of the lower-performing readers, another for the middle-performing readers, and one for the higher-performing readers. The report also gives teachers a list of students to watch. These are students who are in the bottom 25 percent of their class.

This second page of the CBM Class Report provides teachers with a ranked list of the students in their classrooms that includes the student’s score and their growth from the previous Computation test.

This third page of the CBM Class Report provides teachers with an average of the students in the classroom and identifies students who are performing below their classroom peers both in terms of the level (“Score”) of their CBM performance and their rate (“Slope”) of CBM improvement.

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. Now let’s talk about how to use progress monitoring to identify nonresponders within a response-to-intervention framework to identify disability. The traditional assessment framework for identifying students with learning disabilities relies on discrepancies between intelligence and achievement tests. This framework has been scrutinized and attacked due to measurement and conceptual differences. An alternative framework is one in which a learning disability is conceptualized as nonresponsiveness to otherwise effective instruction. It requires that special education be considered only when a student’s performance reveals a dual discrepancy: The student not only performs below the level demonstrated by classroom peers but also demonstrates a learning rate substantially below that of classmates.

All students do not achieve the same degree of math competence.
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. Educational outcomes differ across a population of learners and a low-performing student may ultimately perform not as well as his or her peers. All students do not achieve the same degree of reading competence. Just because reading growth is low, it does not mean the student should automatically receive special education services. If a low-performing student is learning at a rate similar to the growth rate of other students in the same classroom environment, he or she is demonstrating the capacity to profit from the educational environment. Additional intervention is unwarranted.

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. However, when a low-performing student is not manifesting growth in a situation where others are thriving, consideration of special intervention is warranted. Alternative instructional methods must be tested to address the apparent mismatch between the student’s learning requirements and those represented in the conventional instructional program. CBM is a promising tool for identifying treatment responsiveness due to its capacity to model student growth, evaluate treatment effects, and simultaneously inform instructional programming.

Case Study 1: Alexis Now, we’re going to look at come case studies that utilize some of the CBM topics we have discussed. This case study is on pages 31–32 of your materials packet. Mrs. Taylor has been monitoring her entire class using weekly CBM Computation tests. She has been graphing student scores on individual student graphs. Mrs. Taylor used the Tukey method to draw a trend-line for Alexis’ CBM Computation scores. This is Alexis’ graph.

Case Study 1: Alexis Since Alexis’ trend-line is flatter than her goal-line, Mrs. Taylor needs to make a change to Alexis’ instructional program. She has marked the week of the instructional change with a dotted vertical line. To decide what type of instructional change might benefit Alexis, Mrs. Taylor decides to use the Skills Profile provided by the MBSP Scoring Program to find her strengths and weaknesses as a math student. Based on the Skills Profile, what instructional program changes should Mrs. Taylor introduce into Alexis’ math program?

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. The second case study is on pages 33–36 of your materials packet. In this case study, Mr. Singh is the principal of Darby Valley Elementary School. He has decided, along with the school teachers and district administration, to use CBM to monitor progress towards reaching Adequate Yearly Progress toward their school’s No Child Left Behind proficiency goal. During school year 2002–2003, all 378 students at the school were assessed using CBM Passage Reading Fluency at the appropriate grade level. One hundred and twenty-five students initially met CBM benchmarks, therefore, 125 represents Darby Valley’s initial proficiency status. The discrepancy between initial proficiency and universal proficiency is 253 students. To find the number of students who must meet CBM benchmarks each year before the 2013–2014 deadline, the discrepancy of 253 students is divided by the number of years until the deadline (11): 253 ÷ 11 = 23. Twenty-three students need to meet CBM benchmarks each year in order for the school to demonstrate AYP.

Across-Year School Progress
Case Study 2: Darby Valley Elementary Across-Year School Progress End of School Year 100 200 300 400 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 X (378) Number Students Meeting CBM Benchmarks (125) During the 2003–2004 school year, Mr. Singh is provided with these CBM graphs based on the performance of the students in his school. Based on this graph, what can Mr. Singh decide about his school’s progress since the initial year of benchmarks? [Allow for discussion.]

Within-Year School Progress
Case Study 2: Darby Valley Elementary Within-Year School Progress X (148) Based on this graph, what can Mr. Singh decide about his school’s progress since the beginning of the school year? [Allow for discussion.]

Ms. Main (Teacher) Case Study 2: Darby Valley Elementary
Mr. Singh receives the next two graphs from two different second grade teachers. What information can he gather from these graphs? [Allow for discussion.]

Mrs. Hamilton (Teacher)
Case Study 2: Darby Valley Elementary Mrs. Hamilton (Teacher) [Allow for discussion.]

Special Education Case Study 2: Darby Valley Elementary 5 10 15 20 25
5 10 15 20 25 Sept Oct Nov Dec Jan Feb Mar Apr May June 2004 School-Year Month Number Students on Track to Meet CBM Benchmarks This is the graph that Mr. Singh receives based on the performance of Darby Valley’s Special Education students. What should he learn from this graph? [Allow for discussion.]

Cynthia Davis (Student)
Case Study 2: Darby Valley Elementary Cynthia Davis (Student) Mr. Singh receives a graph for every student in the school. He gives these graphs to the respective teachers of each student. How can the teachers use the graphs? [Allow for discussion.]

Dexter Wilson (Student)
Case Study 2: Darby Valley Elementary Dexter Wilson (Student) How can the teachers use this student graph? [Allow for discussion.]

Case Study 3: Mrs. Smith This third case study utilizes computer CBM Reports. It is on page 37–40 of your materials packet. Mrs. Smith has conducted CBM since the beginning of the school year with all of the students in her classroom. She has received the following printout from the MBSP computer software program. This is the first page of Mrs. Smith’s CBM Class Report. How would you characterize how her class is doing? How can she use this information to improve the math skills of the students in her classroom? [Allow for discussion.]

Case Study 3: Mrs. Smith This is the second page of Mrs. Smith’s Class Report. How can she use this class report to improve her classroom instruction? [Allow for discussion.]

Case Study 3: Mrs. Smith This is the third page of Mrs. Smith’s Class Report. What information does she learn on this page? How can she use this information? [Allow for discussion.]

Case Study 3: Mrs. Smith This is the fourth page of Mrs. Smith’s Class Report. What information does she learn on this page? How can she use this information? [Allow for discussion.]

Case Study 4: Marcus The fourth case study is on page 41–42 in your materials packet. Mrs. Fritz has been using CBM to monitor the progress of all of the students in her classroom for the entire school year. She has one student, Marcus, who has been performing extremely below his classroom peers, even after two instructional changes. Look at Marcus’ CBM graph. After 8 weeks, Mrs. Fritz determined that Marcus’ trend-line was flatter than his goal-line, so she made an instructional change to Marcus’ math program. This instructional change included having Marcus work on basic math facts that he was counting on his fingers. The instructional change is the first thick, vertical line on Marcus’ graph. After another 8 weeks, Mrs. Fritz realized that Marcus’ trend-line was still flatter than his goal-line. His graph showed that Marcus had made no improvement in math. So, Mrs. Fritz made another instructional change to Marcus’ math program. This instructional change included having Marcus work on math fact flash cards. The second instructional change is the second thick, vertical line on Marcus’ graph.

Case Study 4: Marcus 5 10 15 20 25 30 1 2 3 4 6 7 8 9 11 12 13 14 16 17 18 19 21 22 23 24 Weeks of Instruction Digits Correct in 5 Minutes High-performing math students Middle-performing math students Low-performing math students Mrs. Fritz has been conducting CBM for 20 weeks and still has yet to see any improvement with Marcus’ math despite two instructional teaching changes. What could this graph tell Mrs. Fritz about Marcus? Pretend you’re at a meeting with your principal and Individual Education Program team members, what would you say to describe Marcus’ situation? What would you recommend as the next steps? How could Mrs. Fritz use this class graph to help her with her decisions about Marcus? [Allow for discussion.]

Curriculum-Based Measurement Materials
AIMSweb/Edformation Yearly ProgressProTM/McGraw-Hill Monitoring Basic Skills Progress/ Pro-Ed, Inc. Research Institute on Progress Monitoring, University of Minnesota (OSEP Funded) Vanderbilt University The various CBM reading measures and computer software may be obtained from the following sources. A list of the CBM materials and/or computer assistance that each source provides, along with contact information, is available in Appendix A of your materials packet.

Curriculum-Based Measurement Resources
List on pages 31–34 of materials packet Appendix B of CBM manual A list of CBM research articles is available in Appendix B of your materials packet. It is also included in Appendix B of the CBM Manual.

Using Curriculum-Based Measurement for Progress Monitoring in Math

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