1. Introduction to Using Curriculum-Based Measurement for Progress Monitoring in Math
Welcome to the National Center on Student Progress Monitoring’s online course, Introduction to Using Curriculum-Based Measurement for Progress Monitoring in Math.

2. Overview 7-step process for monitoring student progress using Math CBM
Math CBM instruments for different grade levels
Monitoring progress, graphing scores, and setting goals
Decision-making using progress monitoring data
This training module will be organized around a 7-step process for monitoring student progress using Math CBM. You’ll learn how to select, administer, and score different math CBM instruments for different grade levels; how to monitor progress; graph scores, and set goals; and how to make decisions about modifying goals and instruction based on math CBM data.

3. CBM Review Brief and easy to administer
All tests are different, but assess the same skills at the same difficulty level within each grade level
Monitors student progress throughout the school year: Probes are given at regular intervals
Weekly, bi-weekly, monthly
Teachers use student data to quantify short- and long-term goals
Scores are graphed to make decisions about instructional programs and teaching methods for each student
Let’s begin by reviewing the characteristics of curriculum-based measurement, or CBM.
CBM tests are brief and easy to administer.
All tests are different, but they assess the same skills at the same difficulty level within each grade level.
CBM is used to monitor student progress throughout the school year: Students are given probes at regular intervals. These can be weekly, bi-weekly, or monthly depending on the needs of the student.
Teachers use the student data that is collected to quantify short- and long-term goals for the student.
CBM scores are graphed for teachers to use to make decisions about instructional programs and teaching methods for each student
You may want to view the online training module: Using Curriculum-Based Measurement for Student Progress Monitoring

4. CBM Is Used to: Identify at-risk students
Help general educators plan more effective instruction
Help special educators design more effective instructional programs
Document student progress for accountability purposes, including IEPs
Communicate with parents or other professionals about student progress
CBM’s convenience and versatility make it suitable for a variety of uses. CBM can be used to:
Identify at-risk students who may need additional services;
Help general educators plan more effective instruction;
Help special educators design more effective instructional programs for students who do not respond to general education;
Document student progress for accountability purposes, including IEPs; and
Communicate with parents or other professionals about student progress.

5. Finding CBMs That Work for You:
Creating CBM probes is time-consuming!
We recommend utilizing these resources to obtain ready-made probes:
NCSPM Tools chart
Because progress monitoring using CBM requires multiple alternate forms at the same difficulty level, it would take a lot of time and effort for teachers to create their own probes. There are many ways to obtain ready-made Math CBM probes, which we recommend as an alternative.
The National Center on Student Progress Monitoring’s Tools chart contains information about several commercially-available progress monitoring tools. Schools or districts can purchase these tools. The tools generally include both probes and graphing software to make teachers’ administration, scoring, and interpretation of CBM data easier.
Another great resource for finding CBM probes is the CBM warehouse at Computer graphing tools are also included here.

6. Steps to Conducting Progress Monitoring Using Math CBM
Step 1: Place students in a mathematics CBM task for progress monitoring
Step 2: Identify the level of material for monitoring progress
Step 3: Administer and score Mathematics CBM probes
Step 4: Graph scores
Step 5: Set ambitious goals
Step 6: Apply decision rules to graphed scores to know when to revise programs and increase goals
Step 7: Use the CBM database qualitatively to describe students’ strength and weaknesses
This module will introduce seven steps for conducting progress monitoring with Math CBM.
Step 1: You will learn how to place students in a mathematics CBM task for progress monitoring.
Step 2: You will learn how to identify the level of material for monitoring progress for computation and concepts and applications.
Step 3: You will learn how to administer and score mathematics CBM probes.
Step 4: You will learn how to graph scores.
Step 5: You will learn how to set ambitious goals.
Step 6: You will learn how to apply decision rules to graphed scores to know when to revise programs and increase goals.
Step 7: You will learn how to use the CBM database qualitatively to describe students’ strengths and weaknesses.

7. Uses of Math CBM for Teachers
Describe academic competence at a single point in time
Quantify the rate at which students develop academic competence over time
Build more effective programs to increase student achievement
The purpose of using the 7-step progress monitoring process is to help teachers:
Describe an individual student’s math competence at a single point in time,
Quantify the rate at which students develop math competence over time,
And build more effective programs to increase student achievement.

8. Kindergarten and Grade 1:
Step 1: Place Students in a Mathematics CBM Task for Progress Monitoring
Kindergarten and Grade 1:
Number Identification
Quantity Discrimination
Missing Number
Grades 1–6:
Computation
Grades 2–6:
Concepts and Applications
Now lets begin the 7-step process of conducting progress monitoring using Math CBM.
The first decision for implementing CBM in mathematics 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 mathematics, here are examples of recommended CBM tasks by grade level.
For kindergarten and first-grade students, Number Identification, Quantity Discrimination, and Missing Number can be administered individually or in combination with each 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.
CBM Computation is typically used in Grades 1–6 and CBM Concepts and Applications is typically used in Grades 2–6. Once again, these can be administered alone or in combination with each another.
I’ll describe each of these tasks in more detail later.
Note that, though it is acceptable to use more than one type of probe as progress is being monitored, students should be administered the same type or types of math CBM for the entire school year. In other words, scores for computation cannot be compared to scores for concepts and applications.

9. Step 2: Identify the Level of Material for Monitoring Progress
Generally, students use the CBM materials prepared for their grade level.
However, some students may need to use probes from a different grade level if they are well below grade-level expectations.
Now that you have learned what math CBM tasks to use for various grade levels, the second step for implementing math CBM is to learn how to identify the level of material for monitoring progress.
Generally, teachers use CBM probes at the student’s current grade level. However, if a student is well below grade-level expectations, the teacher may need to use lower-grade probes. If teachers are worried that a student is too delayed in mathematics to make the grade-level probes appropriately, then they must find the appropriate CBM level by following these steps.

10. Identifying the Level of Material for Monitoring Progress
To find the appropriate CBM level:
On two separate days, administer a CBM test (either Computation or Concepts and Applications) at the grade level at which you expect the student to be functioning at year’s end. Use the correct time limit for the test at the lower grade level.
If the student’s average score is between 10 and 15 digits or blanks, then use this lower grade-level test.
If the student’s average score is less than 10 digits or blanks, then move down one more grade level.
If the average score is greater than 15 digits or blanks, then reconsider grade-appropriate material.
First, on two separate days, administer a Computation or Concepts and Applications CBM at the grade level at which you expect the student to be functioning by year’s end. 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 correct, then you have selected the appropriate grade level at which to monitor progress.
If the average score is less than 10 digits or blanks, then move down one more grade level. You might consider repeating two administrations at this lower grade level to confirm.
If the average score is greater than 15 digits or blanks, then reconsider using math CBM at the student’s actual grade level.
Maintain the student on this grade level and type of math CBM for the purpose of progress monitoring for the entire school year.

11. Identifying the Level of Material for Monitoring Progress
If students are not yet able to compute basic facts or complete concepts and applications problems, then consider using the early numeracy measures.
However, teachers should move students on to the computation and concepts and applications measures as soon as the students are completing these types of problems.
You might be wondering, when should the early math CBMs, like number identification, be used? If the student is not yet able to compute basic math facts or if the student cannot read the concepts and applications problems, then the early numeracy measures are appropriate. In most cases, students will be ready for computation CBM by first or second grade.

12. Step 3: Administer and Score Mathematics CBM Probes
Computation and Concepts and Applications probes can be administered in a group setting, and students complete the probes independently. Early numeracy probes are individually administered.
Teacher grades mathematics probe.
The number of digits correct, problems correct, or blanks correct is calculated and graphed on student graph.
The third step for implementing progress monitoring with CBM is to administer and score math CBM probes.
With mathematics CBM, students work on problems for a prescribed amount of time. After the probes are administered, the teacher grades each probe and graphs the score on a student graph.

13. Kindergarten and Grade 1
Number Identification
Quantity Discrimination
Missing Number
The first CBM tasks we’ll discuss are the early numeracy measures, Number Identification, Quantity Discrimination, and Missing Number. These measures are appropriate for monitoring the progress of students in kindergarten and 1st grade.

14. Number Identification
For students in kindergarten and Grade 1:
Student is presented with 84 items and asked to orally identify the written number between 0 and 100.
After completing some sample items, the student works for 1 minute.
Teacher writes the student’s responses on the Number Identification score sheet.
The Number Identification test for kindergarten students consists of 84 items that require the student to identify numbers between 0 and Number Identification measures have been used as screening tools, but schools may also 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.

15. Number Identification: Student Form
Student’s copy of a Number Identification test:
Actual student copy is 3 pages long.
This is and excerpt of the student’s copy of the Number Identification test.
The teacher says to the student: “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. 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 numbers 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.

16. Number Identification: Scoring Form
Jamal’s Number Identification score sheet:
Skipped items are marked with a (-).
Fifty-seven items attempted.
Three items are incorrect.
Jamal’s score is 54.
This is the teacher’s 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.
On this score sheet, We can see that the last item Jamal attempted was number 57. He got 3 items incorrect. Therefore, to compute his score, subtract 3 from 57 to get 54. Jamal answered 54 items correctly in 1 minute. Fifty-four is Jamal’s score for this probe, which his teacher would add to his progress monitoring graph.

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

18. Quantity Discrimination
For students in kindergarten and Grade 1:
Student is presented with 63 items and asked to orally identify the larger number from a set of two numbers.
After completing some sample items, the student works for 1 minute.
Teacher writes the student’s responses on the Quantity Discrimination score sheet.
The next early numeracy CBM task is Quantity Discrimination.
The Quantity Discrimination test consists of 63 items that require the student to identify the bigger number from a pair of numbers between zero and 20. Quantity Quantity Discrimination measures have been used 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.

19. Quantity Discrimination: Student Form
Student’s copy of a Quantity Discrimination test:
Actual student copy is 3 pages long.
This is and excerpt of the student’s copy of the Quantity Discrimination test.
The teacher says to the student: “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. 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 larger numbers 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.

20. Quantity Discrimination: Scoring Form
Lin’s Quantity Discrimination score sheet:
Thirty-eight items attempted.
Five items are incorrect.
Lin’s score is 33.
This is the teacher’s 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.
On this score sheet, We can see by the line that was drawn that Lin’s last item to attempt was number 38. But she got 5 of the items incorrect. So to compute the score subtract 5 from 38 to get 33. Lin answered 33 items correctly in 1 minute, therefore, thirty-three is Lin’s mathematics score for this probe.

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

22. Missing Number For students in kindergarten and Grade 1:
Student is presented with 63 items and asked to orally identify the missing number in a sequence of four numbers.
Number sequences primarily include counting by 1s, with fewer sequences counting by 5s and 10s
After completing some sample items, the student works for 1 minute.
Teacher writes the student’s responses on the Missing Number score sheet.
Now lets move on to Missing Number. This is the third early numeracy CBM task.
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 include counting by 1-digit increments with numbers 0–10, counting by 2-digit increments with numbers 0–20, counting by 5-digit increments with numbers 0–50, and counting by 10-digit increments with numbers 0–100. Missing Number measures have also been used 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.

23. Missing Number: Student Form
Student’s copy of a Missing Number test:
Actual student copy is 3 pages long.
This is the student copy of the Missing Number test.
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. 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.’
Then the teacher triggers the stopwatch, and the student identifies the number of dots for 1 minute.
When scoring the Missing Number test, if a student correctly identifies the missing number, then score the item as correct. If the student hesitates or struggles with a problem for 3 seconds, then prompt the student to continue to the next problem and score the item as incorrect.

24. Missing Number: Scoring Form
Thomas’s Missing Number score sheet:
Twenty-six items attempted.
Eight items are incorrect.
Thomas’s score is 18.
This is the teacher’s score sheet for the Missing Number test.
When scoring Missing Number, if a student correctly identifies the missing number, then the item is scored as correct.
At 1 minute, the administrator underlines the last problem completed.
On this score sheet The line under number 26 tells us that this is where Thomas stopped. So we count the number of incorrect responses. There are 8 of them. 26 minus 8 equals 18. So, Thomas answered 18 items correctly in 1 minute. Eighteen is Thomas’ mathematics score for this probe.

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

26. For students in Grades 1–6:
Computation
For students in Grades 1–6:
Student is presented with 25 computation problems representing the year-long, grade-level mathematics curriculum.
Student works for set amount of time (time limit varies for each grade).
Teacher grades test after student finishes.
Now we will move on to math CBM for older students. Computation is used to monitor student progress for students in Grades 1–6.
CBM Computation includes probes at each grade level for Grades 1–6. Each probe consists of 25 mathematics computation problems representing the year-long grade-level mathematics 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 0–5 and four multiplication facts with factors 6–9. 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 mathematics problems on the Computation test. Timing the CBM Computation test correctly is critical to ensure consistency from test to test. We will look at the time allocations for each grade level in just a minute.
The administrator times the students during the test and scores the tests later.

27. Computation: Student Form
On the left-hand side is a first-grade Computation test. On the right is a third-grade Computation test. You can see that the difficulty of the problems increases with each grade level.
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.” “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 the specified amount of time.

28. Computation: Time Limits
Length of test varies by grade.
Grade
Time limit 1
2 minutes 2 3
3 minutes 4 5
5 minutes 6
6 minutes
The length of the Computation test varies by grade. This table shows the length of time for which students in Grades 1–6 should be allowed to work on the Computation test.

29. Computation: Scoring
Computation tests can also be scored by awarding 1 point for each digit answered correctly.
The number of digits correct within the time limit is the student’s score. or
Students receive 1 point for each problem answered correctly.
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. In other words, we can evaluate overall student growth earlier by evaluating correct digits in the answers.

30. Computation: Scoring Example
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.
Look at the 1st problem. The student got the whole problem correct and since there are 4 digits in the problem, she got 4 digits correct.
Now look at the 2nd problem.. This student has three digits correct in her answer
Now look at the 3rd problem. This student does not yet understand regrouping; the answer has only 2 digits correct. ü
4 correct
3 correct
2 correct
digits
digits
digits

31. Computation: Scoring Different Operations9
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.

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

33. Computation: Division Scoring Examples
Scoring division with remainders: ü
Correct Answer
Student ’
s Answer
4 0 3 R 5 2
4 3 R 5
(1 correct digit)
2 3 R 1 5
(2 correct digits)
Re-Record Slide
Look at these scoring examples for division with remainders. The quotient is scored left to right, and the remainder is scored right to left.
On the 1st example, the answer is four-hundred-three with a remainder of 52. The student’s answer is 43 with a remainder of 5. We start scoring by looking at the quotient from left to right. The first digit should be a 4 and this is what the student has, so it is correct. The next digit should be 0, but the student’s next digit is 3, so this is incorrect. The student’s answer does not have any more digits in the quotient, so now we move on to the remainder.
On the remainder we work right to left. The correct remainder is 52 so the first digit we score is 2. The student’s first digit is a 5, so this is incorrect. The student does not have a 2nd digit, so we stop here. In this problem, the student got 1 digit correct.
Now lets look at the 2nd problem. The answer is 23 with a reminder of 15. First let’s score the quotient looking at the digits from left to right. The first digit we score should be a 2. The student has this incorrect. The second digit we score should be a 3. The student did get this right.
Now look at the remainder. The correct answer is remainder 15 and we score is from right to left. Therefore the first digit on the right should be a 5. The student has a 5 as the first digit on the right, so this digit is correct. The student does not have another digit, so we stop scoring here. In this problem the student got 2 digits correct.

34. Computation: Scoring Decimals
Start at the decimal point and work outward in both directions
For decimal problems, decimal placement is the critical feature. 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.
Look at the first example. The correct answer is The students answer is Start by looking at the first digit to the left of the decimal. The correct answer is a 3. This is what the student has, therefore they have this digit correct. The next digit should be a 0. But the student has a 4, so this is incorrect. Not look at the first digit to the right of the decimal. It should be a 5. This is what the student has so it is correct. The next digit should be a 2, but the student does not have anything so no more scoring is done. In this problem, the student got 2 digits correct.
Now look at the 2nd example. Look at the first digit to the left of the decimal. The digit should be a 3, but the student has a 0. This is incorrect. The next digit should be a 0, but the student has a 4. This is incorrect. Now look at the first digit to the right of the decimal. The digit should be a 5, but the student has a 4. This digit is incorrect. The next digit should be a 2. the student does have a 2 as the next digit, so this digit is correct. In this problem the student got 1 digit correct.

35. Computation: Scoring Fractions
Score right to left for each portion of the answer. Evaluate digits correct in the whole number, numerator, and denominator. Then add digits together.
When giving directions, be sure to tell students to reduce fractions to lowest terms.
When scoring fractions, score right to left for each portion of the answer. You are going to score digits correct in the whole number, the numerator and the denominator. Then you add all the digits correct together.
Unless specified otherwise for a particular problem, tell students they should reduce fractional answers to lowest terms to get full credit.

36. Computation: Fraction Scoring Examples
Scoring examples: Fractions:
Correct Answer
Student ’
s Answer 6
7 / 1 2 6
8 / 1 1 ü ü
(2 correct digits)
Let’s look at these scoring examples for fractions. All the scoring for fractions takes place from right to left.
In the first example the correct answer is 6 and 7 twelfths. First look at the whole number. The first digit in the whole number is 6. The student has this correct. Now look at the numerator. The first digit in the numerator is 7. The student, however, has 8 so this digit is incorrect. Now look at the denominator. The first digit in the denominator, when working right to left is a 2. The student has a 1 so this digit is incorrect. The next digit in the denominator is a 1. The student has this digit correct. So the student has 2 digits correct in this answer.
Now look at the 2nd example. Start with the whole number. There is only one digit, a 5, and the student has this correct. Now look at the numerator. The first digit is a 1. The student has a 6 for the numerator so this digit is incorrect. Move on to the denominator now. The first digit is a 2. If you look at the students denominator, moving right to left, the first digit is a 2, so this digit is correct. The student does not get credit for the 1 in the denominator.
Note in this example, that even though the student has the correct answer, it is not correct because it was not reduced. But they do get 2 digits correct. 5
1 / 2 5
6 / 1 2 ü ü
(2 correct digits)

37. Computation: Student Example
Samantha’s Computation test:
Fifteen problems attempted.
Two problems skipped.
Two problems incorrect.
Samantha’s correct digit score is 49.
Let’s look at a completed Computation probe. Samantha answered 13 problems correctly in 5 minutes and got 49 digits correct. We would graph 49 as Samantha’s score for this probe.

38. Concepts and Applications
For students in Grades 2–6:
Student is presented with 18–25 Concepts and Applications problems representing the year-long, grade-level mathematics curriculum.
Student works for set amount of time (time limit varies by grade).
Teacher grades test after student finishes.
Re-Record Slide
Now we are going to move on and look at the CBM task of Concepts and Applications. Concepts and Applications is used to monitor student progress during Grades 2–6.
The CBM Concepts and Applications probes include tests at each grade level for Grades 2–6. Each test consists of 18–25 mathematics computation problems representing the year-long, grade-level mathematics concepts and applications curriculum. 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 mathematics 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.

39. Concepts and Applications: Student Form
Student copy of a Concepts and Applications test:
This sample is from a second-grade test.
The actual Concepts and Applications test is 3 pages long.
This is an excerpt of the student’s copy of the Concepts and Applications test.
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 mathematics 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.”
“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.

40. Concepts and Applications: Time Limits
Length of test varies by grade.
Grade
Time limit 2
8 minutes 3
6 minutes 4 5
7 minutes 6
The time limits of the Concepts and Applications test vary by grade. This table shows the length of time for which students in Grades 2–6 should be allowed to work on the Concepts and Applications test.

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

42. Concepts and Applications: Scoring a Student Example
Here is any example. These are pages 2 and 3 of Quinten’s Concepts and Applications test. Note that on some problems there is more than one blank.

43. Concepts and Applications: Scoring a Student Example
Quinten’s fourth-grade Concepts and Applications test:
Twenty-four blanks answered correctly.
Quinten’s score is 24.
This is page 1 of Quinten’s Concepts and Applications score sheet. Quinten answered a total of 24 blanks correctly. Twenty-four is his mathematics score for this probe.

44. Step 4: Graph Scores Graphing student scores is vital.
Graphs provide teachers with a straightforward way to:
Review a student’s progress.
Monitor the appropriateness of student goals.
Judge the adequacy of student progress.
Determine the need for instructional change.
Now that we have covered Step 3, administering and scoring probes, we can move on to Step 4 and learn how to graph scores.
Graphing the scores of every CBM on an individual student graph is a vital aspect of progress monitoring using CBM. 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 determining the need for instructional changes.
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 classroom. 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.

45. How to Graph CBM Scores Teachers can use computer graphing programs.
See the NCSPM Tools Chart
Teachers can create their own graphs.
Using paper and pencil:
Vertical axis has range of student scores
Horizontal axis has number of weeks
Create template for student graph
Use same template for every student in the classroom
Or using computer graphing programs.
Microsoft Excel
ChartDog
See the CBM Warehouse on for tips
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 Student Progress Monitoring Center’s Tools Chart is a good place to find information about progress monitoring tools.
The second option is that teachers can create their own student graphs.
To create student graphs using paper and pencil, teachers create a master CBM graph, in which the vertical axis accommodates the range of the scores of all students, from 0 to the highest score. 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.
Alternatively, teachers can create their own databases and graphs using Microsoft Excel or software such as ChartDog. Visit for tips and tools.

46. A Math CBM Master Graph 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
The vertical axis is labeled with the range of student scores.
The horizontal axis is labeled with the number of instructional weeks.
Here is an example of a master graph that a teacher could make to reproduce and hand-graph scores for each student.
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.

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

48. Step 5: Set Ambitious Goals
Once baseline data have been collected (best practice is to administer three probes and use the median score), the teacher decides on an end-of-year performance goal for each student.
Three options for making performance goals:
End-of-year benchmarking
National norms
Intra-individual framework
Step 5 in the process of monitoring student progress with math CBM is to set ambitious goals using graphed data.
Once a few CBM scores have been graphed, the teacher should decide on an end-of-year performance goal for the student. There are three options for determining these goals. Two options, end-of-year benchmarking and national norms, are utilized after at least three CBM scores have been graphed. The third option, the intra-individual framework, is utilized after at least 8 CBM scores have been graphed.

49. Using End-of-Year Benchmarks to Set Goals
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
The first option for making an end-of-year performance goal is to use End-of-Year Benchmarking.
The teacher can identify the end-of-year CBM benchmark for the appropriate math CBM grade level and instrument. This table displays benchmarks based on recent research. The benchmark is the end-of-year performance goal, and it can be plotted on the CBM graph with an X at the x-axis value corresponding to the end of the year. A goal-line is then drawn between the median of the student’s first three CBM scores and the end-of-year performance goal. An example will be shown later.

50. Using National Norms to Set Ambitious Goals
For typically developing students, a table of median rates of weekly increase can be used to find the end-of-year performance goal.
Grade
Computation: Digits
Concepts and Applications: Blanks 1
0.35
N/A 2
0.30
0.40 3
0.60 4
0.70 5 6
The second option for making an end-of-year performance goal is to use National Norms.
Teachers can use a resource like this research-based norms table to identify the average expected rate of weekly increase for students at each grade level. For example this table indicates that a 1st grade student would be expected compute 0.35 additional digits correct each week on Computation probes. A 4th grade student would be expected to compute an additional 0.70 digits correct on computation probes and 0.70 additional blanks correct on Concepts and Applications probes.

51. Using National Norms to Set Goals: Example
Median is 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.
Grade
Computation: Digits
Concepts and Applications: Blanks 1
0.35
N/A 2
0.30
0.40 3
0.60 4
0.70 5 6
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 0.70 meaning that a fourth grader is expected to compute 0.70 additional digits correct each week. 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 which is Add 11.2 to the baseline median of 14 and the sum is 25. The end-of-year performance goal for this student would be set at 25.

52. Using an Intra-Individual Framework to Set Goals
Weekly rate of improvement is calculated using at least eight data points.
Baseline rate is multiplied by 1.5.
Product is multiplied by the number of weeks until the end of the school year.
Added to student’s baseline score to produce end-of-year performance goal.
The third option for making an end-of-year performance goal is to use an Intra-Individual Framework.
This option is most appropriate for students who have an identified math or developmental disability and are functioning below their actual grade level.
First the teacher needs to identify the weekly rate of improvement for the student under baseline conditions, using at least eight CBM data points. This baseline rate is multiplied by 1.5., which is the minimum amount of weekly progress we would like to expect from a student receiving specialized math instruction. This product should then be multiplied by the number of instructional weeks until the end of the school year. Add this product to the student’s median baseline score to get the end-of-year goal.

53. Example: Using an Intra-Individual Framework to Set Goals
First eight scores: 3, 2, 5, 6, 5, 5, 7, 4.
Difference between medians: 5 – 3 = 2.
Divide by (# data points – 1): 2 ÷ (8-1) = 0.29.
Multiply by typical growth rate: 0.29 × 1.5 =
Multiply by weeks left: × 14 = 6.09.
Product is added to the first median: = 9.09.
The end-of-year performance goal is 9.
Here is an example to illustrate using an intra-individual framework to set a goal.
A student’s first eight CBM scores were 3, 2, 5, 6, 5, 5, 7, and 4. To calculate the current weekly rate of improvement, or slope, we can use the Tukey method. We will learn more about the Tukey method in a few minutes.
First, divide the scores into three roughly equal groups. There are 8 initial data points in this example, so the data are grouped into groups of 3, 2, and 3 data points. Now subtract the median of the first group from the median value of the last group. In this instance, 5 is the third median and 3 is the first median. 5 – 3 = 2. We then divide 2 by the number of weeks of instruction in this example minus 1, which is 7 in this case because the data are from 8 weeks. 2 divided by 7 is 0.29.
0.29 is multiplied by 1.5 to yield Multiply the by the number of weeks until the end of the year. If there are 14 weeks left until the end of the year, then × 14 = The median score of the first three data points was 3. Add 6.09 to the first median score for the end-of-year performance goal: = The student’s end-of-year performance goal would be 9.

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

55. Example of a Graphed Goal
The X is the end-of-the-year performance goal. A line is drawn from the median of the first three scores to the performance goal.
Example of a Graphed Goal
Drawing a goal-line:
A goal-line is the desired path of measured behavior to reach the performance goal over time.
For this student, the end-of-year performance goal on CBM Concepts and Applications is 18. An X is marked at the intersection of 18 and the end of the school year. A dotted line representing the goal line is drawn from the point marking the intersection of the median date and value of the student’s first few scores to the X. The student’s progress should follow this dotted line.

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

57. Graphing a Trend Line: Tukey Method
Graphed scores are divided into three fairly equal groups
Two vertical lines are drawn between the groups.
In the first and third groups:
Find the median data point and the median date.
Mark the intersection of these 2 with an X
Draw a line connecting the first group X and third group X.
This line is the trend-line.
To draw a trend-line, teachers can use the Tukey method procedure after at least 7-8 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, then 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, or middle value for each group and mark this point with an X. To draw the trend-line, draw a line connecting the two Xs.

58. Tukey Method: A Graphed Example5 10 15 20 25 1 2 3 4 6 7 8 9 11 12 13 14
Weeks of Instruction
Digits Correct in 5 Minutes X
Here is an example of the Tukey method used on a graph. To draw the trend line, the student’s data points were divided into three fairly equal groups. Two vertical lines were drawn to divide the three groups. The median, or middle data point for the first group and third group were marked with an X. Note that the X should be placed at the intersection of the median time and the median data value. Then, a trend-line was drawn connecting the two Xs.
Instructional decisions for students are based on the ongoing comparisons of trend lines and goal lines. X X X

59. Trend and Goal Lines Made Easy
CBM computer management programs are available.
Programs create graphs and aid teachers with performance goals and instructional decisions.
Various types are available for varying fees.
See the NCSPM Tools Chart
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 help teachers in making performance goals and instructional decisions. Other computer programs actually collect and score the data.
Please visit the Student Progress Monitoring Center’s Tools Chart for more information about available tools.

60. Step 6: Apply Decision Rules to Graphed Scores
After trend-lines have been drawn, teachers use graphs to evaluate student progress and formulate instructional decisions.
Standard decision rules help with this process.
Step 6 in using CBM for progress monitoring in math is to apply decision rules to graphed scores.
CBM can assist teachers in judging 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 to develop instructional plans that enhance student achievement.
After teachers draw CBM graphs, they use graphs to evaluate student progress and inform instructional decisions. Standard CBM-decision rules guide decisions about the adequacy of student progress and the need to revise goals and instructional programs.

61. The 4-point Rule Based on four most recent consecutive points:
If scores are above the goal-line, end-of-year performance goal needs to be increased.
If scores are below goal-line, student instructional program needs to be revised.
If scores are on the goal-line, no changes need to be made.
The most basic decision rules for CBM data can be applied using most recent 4 consecutive scores:
If the four most recent consecutive CBM scores are above the goal-line, then 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, then the teacher needs to revise the instructional program. Note that the student’s goal is never decreased.
If the four most recent consecutive scores are on the goal line, no changes need to be made

62. The 4-point Rule: Example 15 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, which will boost the expected rate of student progress.
The point of the goal increase is noted on the graph as a dashed vertical line. This allows teachers to visually note when the student’s goal was changed. The teacher reevaluates the student graph in another seven or eight data points to determine whether the student’s new goal is appropriate or whether a teaching change is needed.

63. The 4-point Rule: Example 25 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 X
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 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 or eight data points to determine whether the change was effective.

64. Using Trend- and Goal-Lines to Inform Decisions
Based on the student’s trend-line:
If the trend-line is steeper than the goal line, end-of-year performance goal needs to be increased.
If the trend-line is flatter than the goal line, student’s instructional program needs to be revised.
If the trend-line and goal-line are fairly equal, then no changes need to be made.
Once a teacher has enough data points to draw a trend line using the Tukey method, she can use similar decision rules when comparing trend- and goal-lines:
If the student’s trend-line is steeper than the goal-line, then the student’s end-of-year performance goal needs to be increased.
If the student’s trend-line is flatter than the goal-line, then the teacher needs to revise the instructional program.
If the student’s trend-line and goal-line are the same, then no changes need to be made.

65. Decision-Making with Trend- and Goal-Lines (Example 1)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 X
Trend-line
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 goal and desired rate of progress 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 noted 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 or eight data points to determine whether the student’s new goal is appropriate or whether an instructional change is needed.

66. Decision-Making with Trend- and Goal-Lines (Example 2)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
Trend-line X
On this graph, the trend-line is flatter than the 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.
Again you can see on this graph that the point of the instructional change is represented as a vertical line. This allows teachers to visually note when the student’s instructional program was changed. The teacher will reevaluate the student graph in another seven or eight data points to determine whether the change was effective.

67. Decision-Making with Trend- and Goal-Lines (Example 3)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
Trend-line X
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 or eight data points to determine whether an end-of-year performance goal or instructional change needs to take place.

68. Step 7: Use Data to Describe Student Strengths and Weaknesses
Students’ completed probes can be analyzed to examine mastery of specific skills.
Step 7 is to use CBM data qualitatively to describe student strengths and weaknesses.
Students’ completed probes can be analyzed to examine mastery of specific skills. Let’s look at an example.

69. Examining Computation CBM
4507
2146 2 4 61
2361 44 1
4 correct
digits
3 correct
2 correct ü
Here is a subtraction problem that was completed by three different students.
The student who completed the first problem mastered subtraction with regrouping.
The student who completed the second problem seems to understand regrouping to the extent that the 0 in the 10s place becomes a 10, but he does not understand that the 5 in the hundreds place needs to become a 4 in the regrouping process.
The student who completed the 3rd problem does not yet understand regrouping.
With this information, the teacher can target instruction appropriately to these students.

70. Skills Profiles
Available with some progress monitoring software programs.
Skills profile provides a visual display of a student’s progress by skill area.
Skills profiles that visually display a student’s progress by each skill area are available with some progress monitoring software programs. Teachers can use a Skills Profile to describe the strengths and weaknesses of each student in the classroom. Skills Profiles can help teachers formulate instructional decisions for individual students by identifying skills to target for instruction.

71. Example: Class Skills Profile
Here is an example of a Class Skills Profile that is available with the Monitoring Basic Skills Progress software. The profile provides information about specific skills for each student in the class, averaged across the most recent two assessments. Each column represents a skill taught in the year. The labels at the top of the chart stand for addition, subtraction, multiplication, division, and fractions. Each box represents the student’s mastery status of that particular skill. The more a box is filled in, the higher the mastery the student has achieved.

72. Example: Individual Skills Profile
Here is an example of an individual Skills Profile displayed along with the student’s software-generated CBM data graph. This example also comes from the Monitoring Basic Skills Progress software.

73. Summary
Step 1: Place Students in a Math CBM task for progress monitoring
Step 2: identify the level of material for monitoring progress
Step 3: Administer and score Math CBM
Step 4: Graph scores
Step 5: Set ambitious goals
Step 6: Apply decision rules to graphed scores to know when to revise instructional programs and increase goals
Step 7: Use the CBM data qualitatively to inform instruction
You have completed this training module on Using Curriculum Based Measurement to Monitor Student Progress in Math. The 7 steps for conducting progress monitoring using CBM were covered in this module.
First you learned about typical math tasks for different grade levels.
Second, I described how to identify the level of math CBM material to use depending on a student’s current level of functioning, whether at or below grade level.
Third, you learned how to administer and score five types of math CBM: Computation for grades 1-6, Concepts and Applications for grades 2-6, and for Kindergarten and first grade you learned about Number Identification, Quantity Discrimination, and Missing Number.
Fourth, you learned about graphing CBM data.
Fifth, I described three methods for setting ambitious goals for students; benchmarks, national norms, and an intra-individual framework.
Sixth, you learned two types of decision rules to apply to graphed scores in relation to the goal line: the four most recent data points and the student trend line.
Finally, I described how to use a Skills Profile to identify students’ math strengths and weaknesses and inform instruction.

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