Using Curriculum-Based
Measurement for Progress
Monitoring in Math
Todd Busch
Tracey Hall
Pamela Stecker
Progress Monitoring

Progress monitoring (PM) is
conducted frequently and
designed to:
– Estimate rates of student
improvement.
– Identify students who are not
demonstrating adequate progress.
– Compare the efficacy of different
forms of instruction and design more
effective, individualized instructional
programs for problem learners.
2
What Is the Difference Between Traditional
Assessments and Progress Monitoring?

Traditional Assessments:
– Lengthy tests.
– Not administered on a regular basis.
– Teachers do not receive immediate
feedback.
– Student scores are based on
national scores and averages and a
teacher’s classroom may differ
tremendously from the national
student sample.
3
What Is the Difference Between Traditional
Assessments and Progress Monitoring?

Curriculum-Based Measurement
(CBM) is one type of PM.
– CBM provides an easy and quick
method for gathering student
progress.
– Teachers can analyze student
scores and adjust student goals and
instructional programs.
– Student data can be compared to
teacher’s classroom or school district
data.
4
Curriculum-Based Assessment

Curriculum-Based Assessment
(CBA):
– Measurement materials are aligned
with school curriculum.
– Measurement is frequent.
– Assessment information is used to
formulate instructional decisions.

CBM is one type of CBA.
5
Progress Monitoring


Teachers assess students’
academic performance using brief
measures on a frequent basis.
The main purposes are to:
– Describe the rate of response to
instruction.
– Build more effective programs.
6
Focus of This Presentation
Curriculum-Based
Measurement
The scientifically validated form of
progress monitoring.
7
Teachers Use Curriculum-Based
Measurement To . . .



Describe academic competence at
a single point in time.
Quantify the rate at which students
develop academic competence
over time.
Build more effective programs to
increase student achievement.
8
Curriculum-Based Measurement



The result of 30 years of research
Used across the country
Demonstrates strong reliability,
validity, and instructional utility
9
Research Shows . . .




CBM produces accurate, meaningful
information about students’ academic
levels and their rates of improvement.
CBM is sensitive to student
improvement.
CBM corresponds well with high-stakes
tests.
When teachers use CBM to inform their
instructional decisions, students
achieve better.
10
Most Progress Monitoring:
Mastery Measurement
Curriculum-Based
Measurement is
NOT
Mastery
Measurement
Mastery Measurement:
Tracks Mastery of Short-Term Instructional
Objectives

To implement Mastery
Measurement, the teacher:
– Determines the sequence of skills in
an instructional hierarchy.
– Develops, for each skill, a criterionreferenced test.
12
Hypothetical Fourth Grade
Math Computation Curriculum
1.
2.
3.
4.
Multidigit addition with regrouping
Multidigit subtraction with regrouping
Multiplication facts, factors to nine
Multiply two-digit numbers by a one-digit
number
5. Multiply two-digit numbers by a two-digit number
6. Division facts, divisors to nine
7. Divide two-digit numbers by a one-digit number
8. Divide three-digit numbers by a one-digit number
9. Add/subtract simple fractions, like denominators
10. Add/subtract whole numbers and mixed numbers
13
Multidigit Addition Mastery Test
14
Mastery of Multidigit Addition
Number of digits correct
in 5 minutes
10
Multidigit Addition
Multidigit Subtraction
8
6
4
2
0
2
4
6
8
10
12
14
WEEKS
15
Hypothetical Fourth Grade
Math Computation Curriculum
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Multidigit addition with regrouping
Multidigit subtraction with regrouping
Multiplication facts, factors to nine
Multiply two-digit numbers by a one-digit number
Multiply two-digit numbers by a two-digit number
Division facts, divisors to nine
Divide two-digit numbers by a one-digit number
Divide three-digit numbers by a one-digit number
Add/subtract simple fractions, like denominators
Add/subtract whole numbers and mixed numbers
16
Multidigit Subtraction Mastery Test
Date:
Name:
Subtracting
6521
375
5429
634
8455
756
6782
937
7321
391
5682
942
6422
529
3484
426
2415
854
4321
874
17
Mastery of Multidigit Addition
and Subtraction
of problems
Number of
digits correct
correct
Number
in 5 minutes
10
Multidigit Subtraction
Multidigit
Addition
Multiplication
Facts
8
6
4
2
0
2
4
6
8
10
12
14
WEEKS
18
Problems with Mastery
Measurement





Hierarchy of skills is logical, not
empirical.
Performance on single-skill
assessments can be misleading.
Assessment does not reflect
maintenance or generalization.
Assessment is designed by teachers or
sold with textbooks, with unknown
reliability and validity.
Number of objectives mastered does
not relate well to performance on highstakes tests.
19
Curriculum-Based Measurement Was
Designed to Address These Problems
An Example of CurriculumBased Measurement:
Math Computation
20
Hypothetical Fourth Grade Math
Computation Curriculum
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Multidigit addition with regrouping
Multidigit subtraction with regrouping
Multiplication facts, factors to nine
Multiply two-digit numbers by a one-digit number
Multiply two-digit numbers by a two-digit number
Division facts, divisors to nine
Divide two-digit numbers by a one-digit number
Divide three-digit numbers by a one-digit number
Add/subtract simple fractions, like denominators
Add/subtract whole numbers and mixed numbers
21
Computation 4
Sheet #1
Password: ARM
Name:
Date:
A
B
3
7


Random
numerals
within
problems
Random
placement
of problem
types on
page
2
=
7
F
C
6
1 + 3=
7
H
6
x7
9
x0
L
2 )5 0
P
M
Q
95 22 5
+ 75 26 8
U
O
6
x0
S
11 56
28 24
83
+
W
98 2
97
5 )2 0
N
R
V
3
1
+
=
5
5
J
6 )4 8
33
x 10
8 )3 2
87 5
x 7
I
24 4
x 7
61 44
44 20
E
6 )7 8
4) 6
G
K
D
T
4
7 - 2=
7
X
9
x5
7 )3 0
38
x 33
Y
4
x1
7 )5 6
22
Computation 4
Sheet #2
Password: AIR
Name:
Date:
A
B
9 )24


Random
numerals
within
problems
Random
placement of
problem types
on page
C
D
5 2 85 2
+ 6 4 70 8
F
G
9
x0
H
6 )30
L
P
8
x6
Q
10 7
x 3
U
7
x9
5 )65
2) 9
T
5 + 3
11 11 =
X
9 )8 1
1
3 =
34 - 1=
7
6 )3 0
41 6
44
15 0 4
14 4 1
2
3
O
S
W
82 8 5
43 0 4
90
+
J
N
R
V
41 + 6 =
2
4
x5
M
32
x 23
4 ) 72
I
35
x 74
K
E
6
x2
Y
13 0
x 7
5 )10
23
Donald’s Progress in Digits Correct
Across the School Year
24
Name _______________________________
Date ________________________
(1)
Column B
(5)
Write a number in the blank.
Write the letter in each blank.
1 week = _____ days
•
(A) line segment
Z
•K
•M
One Page of a
3-Page CBM in
Math Concepts
and
Applications (24
Total Blanks)
Test 4 Page 1
Applications 4
Column A
L
•
•N
(B) line
(6)
Vacation Plans for Summit
School Students
(C) point
Summer
School
(D) ray
Camp
(2)
Look at this numbers.:
Travel
356.17
Stay home
Which number is in the hundredths place?
0
10
20
30
40
50
60
70
80
90 100
Number of Students
(3)
Solve the problem by estimating the sum or
difference to the nearest ten.
Jeff wheels his wheelchair for 33 hours
a week at school and for 28 hours a week
in his neighborhood. About how many
hours does Jeff spend each week wheeling
his wheelchair?
(4)
Write the number in each blank.
Use the bar graph to answer the questions.
The P.T.A. will buy a Summit School
T-Shirt for each student who goes
to summer school. Each shirt costs
$4.00. How much money will the
P.T.A. spend on these T shirts?
$ .00
How many students are planning to
travel during the summer?
How many fewer students are planning
to go to summer school than planning
to stay home?
(7)
3 ten thousands, 6 hundreds, 8 ones
2 thousands, 8 hundreds, 4 tens, 6 ones
To measure the distance of the bus
ride from school to your house you
would use
(A) meters
(B) centimeters
(C) kilometers
25
D
Donald’s Graph and Skills Profile
Donald Ross
Computation 4
70

Darker
boxes
equal a
greater
level of
mastery.
D
I
G
I
T
S
60
50
38
40
30
20
10
0
Sep
Oct
Nov
Dec
Jan
Feb
Mar
Apr
May
A1
S1
M1
M2
M3
D1
D2
D3
F1
F2
26
Sampling Performance on Year-Long
Curriculum for Each Curriculum-Based
Measurement . . .





Avoids the need to specify a skills
hierarchy.
Avoids single-skill tests.
Automatically assesses
maintenance/generalization.
Permits standardized procedures for
sampling the curriculum, with known
reliability and validity.
SO THAT: CBM scores relate well to
performance on high-stakes tests.
27
Curriculum-Based Measurement’s Two
Methods for Representing Year-Long
Performance
Method 1:
 Systematically sample items from the
annual curriculum (illustrated in Math
CBM, just presented).
Method 2:
 Identify a global behavior that
simultaneously requires the many skills
taught in the annual curriculum
(illustrated in Reading CBM, presented
next).
28
Hypothetical Second Grade
Reading Curriculum

Phonics
– CVC patterns
– CVCe patterns
– CVVC patterns


Sight Vocabulary
Comprehension
– Identification of who/what/when/where
– Identification of main idea
– Sequence of events

Fluency
29
Second Grade Reading CurriculumBased Measurement





Each week, every student reads aloud
from a second grade passage for 1
minute.
Each week’s passage is the same
difficulty.
As a student reads, the teacher marks
the errors.
Count number of words read correctly.
Graph scores.
30
Curriculum-Based Measurement




Not interested in making kids read
faster.
Interested in kids becoming better
readers.
The CBM score is an overall indicator
of reading competence.
Students who score high on CBMs are
better:
– Decoders
– At sight vocabulary
– Comprehenders

Correlates highly with high-stakes
tests.
31
CBM
Passage
for Correct
Words per
Minute
Mom was going to have a baby. Another one! That is all we need
thought Samantha who was ten years old. Samantha had two little brothers. They
were brats. Now Mom was going to have another one. Samantha wanted to cry.
“I will need your help,” said Mom. “I hope you will keep an eye on the
boys while I am gone. You are my big girl!”
Samantha told Mom she would help. She did not want to, though. The
boys were too messy. They left toys everywhere. They were too loud, too.
Samantha did not want another baby brother. Two were enough.
Dad took Samantha and her brothers to the hospital. They went to
Mom’s room. Mom did not feel good. She had not had the baby. The doctors said it
would be later that night. “I want to wait here with you,” said Samantha. “Thank
you Samantha. But you need to go home. You will get too sleepy. Go home with
Grandma. I will see you in the morning,” said Mom.
That night Samantha was sad. She knew that when the new baby came
home that Mom would not have time for her. Mom would spend all of her time
with the new baby.
The next day Grandma woke her up. “Your mom had the baby last
night,” Grandma said. “We need to go to the hospital. Get ready. Help the boys get
ready, too.”
Samantha slowly got ready. She barely had the heart to get dressed.
After she finished, she helped the boys. They sure were a pain! And now another
one was coming. Oh brother!
Soon they were at the hospital. They walked into Mom’s room. Mom
was lying in the bed. Her tummy was much Smaller. Samantha . . .
32
What We Look for in CurriculumBased Measurement
Increasing Scores:
 Student is becoming a better
reader.
Flat Scores:
 Student is not profiting from
instruction and requires a change
in the instructional program.
33
Sarah’s Progress on Words Read
Correctly
Words Read Correctly
180
Sarah Smith
Reading 2
160
140
120
100
80
60
40
20
0
Sep
Oct
Nov
Dec
Jan
Feb
Mar
Apr
May
34
Jessica’s Progress on Words Read
Correctly
Words Read Correctly
180
Jessica Jones
Reading 2
160
140
120
100
80
60
40
20
0
Sep
Oct
Nov
Dec
Jan
Feb
Mar
Apr
May
35
Reading Curriculum-Based
Measurement




Kindergarten: Letter sound fluency
First Grade: Word identification
fluency
Grades 1–3: Passage reading
fluency
Grades 1–6: Maze fluency
36
Kindergarten
Letter Sound Fluency


Teacher: Say
the sound that
goes with each
letter.
Time: 1 minute
p
i
O
v
k
Y
…
U
t
a
g
m
E
z
R
s
j
n
i
L
e
d
S
b
c
y
w
f
h
V
x
37
First Grade
Word Identification Fluency


Teacher: Read
these words.
Time: 1 minute
two
for
come
because
last
from
...
38
Grades 1–3
Passage Reading Fluency

Number of words read aloud
correctly in 1 minute on end-ofyear passages.
39
Jason Fry ran home from school. He had to pack his
clothes. He was going to the beach. He packed a swimsuit and
shorts. He packed tennis shoes and his toys. The Fry family was
going to the beach in Florida.
CBM
Passage
for Correct
Words per
Minute
The next morning Jason woke up early. He helped Mom
and Dad pack the car, and his sister, Lonnie, helped too. Mom and
Dad sat in the front seat. They had maps of the beach. Jason sat in
the middle seat with his dog, Ruffie. Lonnie sat in the back and
played with her toys.
They had to drive for a long time. Jason looked out the
window. He saw farms with animals. Many farms had cows and
pigs but some farms had horses. He saw a boy riding a horse.
Jason wanted to ride a horse, too. He saw rows of corn growing in
the fields. Then Jason saw rows of trees. They were orange trees.
He sniffed their yummy smell. Lonnie said she could not wait to
taste one. Dad stopped at a fruit market by the side of the road.
He bought them each an orange.
40
Grades 1–6
Maze Fluency

Number of words replaced
correctly in 2.5 minutes on end-ofyear passages from which every
seventh word has been deleted
and replaced with three choices.
41
Computer Maze
42
Donald’s Progress on Words Selected
Correctly for Curriculum-Based
Measurement Maze Task
W 60
O
R 50
D
S 40
30
C
O 20
R
R 10
E
0
C
T
Reading 4
Donald Ross
Sep
Oct
Nov
Dec
Jan
Feb
Mar
Apr
May
43
Curriculum-Based Measurement

CBM is distinctive.
– Each CBM test is of equivalent
difficulty.
• Samples the year-long curriculum.
– CBM is highly prescriptive and
standardized.
• Reliable and valid scores.
44
The Basics of Curriculum-Based
Measurement


CBM monitors student progress
throughout the school year.
Students are given reading probes
at regular intervals.
– Weekly, biweekly, monthly

Teachers use student data to
quantify short- and long-term
goals that will meet end-of-year
goals.
45
The Basics of Curriculum-Based
Measurement



CBM tests are brief and easy to
administer.
All tests are different, but assess
the same skills and difficulty level.
CBM scores are graphed for
teachers to use to make decisions
about instructional programs and
teaching methods for each
student.
46
Curriculum-Based Measurement
Research


CBM research has been
conducted over the past 30 years.
Research has demonstrated that
when teachers use CBM for
instructional decision making:
– Students learn more.
– Teacher decision making improves.
– Students are more aware of their
performance.
47
Steps to Conducting CurriculumBased Measurements
Step 1:
Step 2:
Step 3:
Step 4:
How to Place Students in a
Math Curriculum-Based
Measurement Task for
Progress Monitoring
How to Identify the Level of
Material for Monitoring Progress
How to Administer and Score
Math Curriculum-Based
Measurement Probes
How to Graph Scores
48
Steps to Conducting CurriculumBased Measurements
Step 5:
Step 6:
Step 7:
How to Set Ambitious Goals
How to Apply Decision Rules
to Graphed Scores to Know
When to Revise Programs
and Increase Goals
How to Use the CurriculumBased Measurement
Database Qualitatively to
Describe Students’ Strengths
and Weaknesses
49
Step 1: How to Place Students in a Math
Curriculum-Based Measurement Task for
Progress Monitoring

Grades 1–6:
– Computation

Grades 2–6:
– Concepts and Applications

Kindergarten and first grade:
– Number Identification
– Quantity Discrimination
– Missing Number
50
Step 2: How to Identify the Level of
Material for Monitoring Progress


Generally, students use the CBM
materials prepared for their grade
level.
However, some students may
need to use probes from a
different grade level if they are
well below grade-level
expectations.
51
Step 2: How to Identify the Level of
Material for Monitoring Progress

To find the appropriate CBM level:
– Determine the grade-level probe at which you
expect the student to perform in math competently
by year’s end.
OR
– On two separate days, administer a CBM test
(either Computation or Concepts and Applications)
at the grade level lower than the student’s gradeappropriate level. Use the correct time limit for the
test at the lower grade level, and score the tests
according to the directions.
•If the student’s average score is between 10 and 15
digits or blanks, then use this lower grade-level test.
•If the student’s average score is less than 10 digits or
blanks, move down one more grade level or stay at
the original lower grade and repeat this procedure.
•If the average score is greater than 15 digits or
blanks, reconsider grade-appropriate material.
52
Step 3: How to Administer and Score Math
Curriculum-Based Measurement Probes



Students answer math problems.
Teacher grades math probe.
The number of digits correct,
problems correct, or blanks correct
is calculated and graphed on
student graph.
53
Computation




For students in grades 1–6.
Student is presented with 25
computation problems representing
the year-long, grade-level math
curriculum.
Student works for set amount of time
(time limit varies for each grade).
Teacher grades test after student
finishes.
54
Computation
Student Copy of a
First Grade
Computation Test
55
Computation
56
Computation

Length of test
varies by grade.
Grade
First
Time
limit
2 min.
Second
2 min.
Third
3 min.
Fourth
3 min.
Fifth
5 min.
Sixth
6 min.
57
Computation



Students receive 1 point for each
problem answered correctly.
Computation tests can also be
scored by awarding 1 point for
each digit answered correctly.
The number of digits correct within
the time limit is the student’s
score.
58
Computation
Correct Digits: Evaluate Each
Numeral in Every Answer
4507
2146
2361
4507
2146
2461
  

4 correct
digits

3 correct
digits
4507
2146
2441


2 correct
digits
59
Computation
Scoring Different Operations
Examples:
1
18
+16
34
2 correct
digits
41
158
- 29
129
3 correct
digits
22
x 43
66
880
946
3 correct
digits
23
8 184
16
24
24
0
2 correct
digits
60
Computation
Division Problems with Remainders


When giving directions, tell students to write
answers to division problems using R for
remainders when appropriate.
Although the first part of the quotient is scored
from left to right (just like the student moves
when working the problem), score the
remainder from right to left (because
student would likely subtract to calculate
remainder).
61
Computation
Scoring Examples: Division with
Remainders
Correct Answer
403R52
Student’s Answer
43 R 5
(1 correct digit)

23 R 15
43 R 5


(2 correct digits)
62
Computation
Scoring Decimals and Fractions

Decimals: Start at the decimal point and work
outward in both directions.

Fractions: Score right to left for each portion
of the answer. Evaluate digits correct in the
whole number part, numerator, and
denominator. then add digits together.
– When giving directions, be sure to tell students to
reduce fractions to lowest terms.
63
Computation
Scoring Examples: Decimals
64
Computation
Scoring Examples: Fractions
Correct Answer
Student’s Answer
6
6
7/12

5
1/2
5

8/11
(2 correct digits)

6/12
 (2 correct digits)
65
Computation
Samantha’s
Computation
Test





Fifteen problems
attempted.
Two problems
skipped.
Two problems
incorrect.
Samantha’s score
is 13 problems.
However,
Samantha’s
correct digit score
is 49.
66
Computation
Sixth Grade
Computation
Test

Let’s practice.
67
Computation
Answer Key






Possible score of 21 digits correct in first row.
Possible score of 23 digits correct in the second
row.
Possible score of 21 digits correct in the third row.
Possible score of 18 digits correct in the fourth
row.
Possible score of 21 digits correct in the fifth row.
Total possible digits on this probe: 104.
68
Concepts and Applications




For students in grades 2–6.
Student is presented with 18–25
Concepts and Applications
problems representing the yearlong grade-level math curriculum.
Student works for set amount of
time (time limit varies by grade).
Teacher grades test after student
finishes.
69
Concepts and Applications
Student Copy of a
Concepts and
Applications test


This sample is from
a third grade test.
The actual Concepts
and Applications test
is 3 pages long.
70
Concepts and Applications

Length of test
varies by grade.
Grade
Second
Time
limit
8 min.
Third
6 min.
Fourth
6 min.
Fifth
Sixth
7 min.
7 min.
71
Concepts and Applications


Students receive 1 point for each
blank answered correctly.
The number of correct answers
within the time limit is the student’s
score.
72
Concepts and Applications
Quinten’s Fourth
Grade Concepts
and Applications
Test


Twenty-four
blanks answered
correctly.
Quinten’s score
is 24.
73
Concepts and Applications
74
Concepts and Applications
Fifth Grade
Concepts and
Applications
Test—1

Let’s practice.
75
Concepts and Applications
Fifth Grade
Concepts and
Applications
Test—Page 2
76
Concepts and Applications
Fifth Grade
Concepts and
Applications
Test—Page 3

Let’s practice.
77
Concepts and Applications
Problem
Answer Key
Answer
10
3
11
A ADC
C BFE
12
0.293
13


Problem
Answer
1
54 sq. ft
2
66,000
14
28 hours
3
A center
C diameter
15
790,053
16
451 CDLI
4
28.3 miles
17
7
5
7
18
6
P7
N 10
$10.00 in tips
20 more orders
19
4.4
7
0 $5 bills
4 $1 bills
3 quarters
20


8
1 millions place
3 ten thousands place
21
5/6 dogs or cats
22
1m
23
12 ft
9
697
78
Number Identification




For kindergarten or first grade
students.
Student is presented with 84 items and
is asked to orally identify the written
number between 0 and 100.
After completing some sample items,
the student works for 1 minute.
Teacher writes the student’s responses
on the Number Identification score
sheet.
79
Number Identification
Student Copy of
a Number
Identification test

Actual student
copy is 3 pages
long.
80
Number Identification
Number
Identification
Score Sheet
81
Number Identification






If the student does not respond after 3
seconds, point to the next item and say “Try
this one.”
Do not correct errors.
Teacher writes the student’s responses on the
Number Identification score sheet. Skipped
items are marked with a hyphen (-).
At 1 minute, draw a line under the last item
completed.
Teacher scores the task, putting a slash
through incorrect items on score sheet.
Teacher counts the number of correct
answers in 1 minute.
82
Number Identification
Jamal’s Number
Identification
Score Sheet




Skipped items are
marked with a (-).
Fifty-seven items
attempted.
Three incorrect.
Jamal’s score is 54.
83
Number Identification
Teacher Score
Sheet

Let’s practice.
84
Number Identification
Student
Sheet—Page 1

Let’s practice.
85
Number Identification
Student
Sheet—Page 2

Let’s practice.
86
Number Identification
Student
Sheet—Page 3

Let’s practice.
87
Quantity Discrimination




For kindergarten or first grade
students.
Student is presented with 63 items and
asked to orally identify the larger
number from a set of two numbers.
After completing some sample items,
the student works for 1 minute.
Teacher writes the student’s responses
on the Quantity Discrimination score
sheet.
88
Quantity Discrimination
Student Copy of a
Quantity
Discrimination test

Actual student copy
is 3 pages long.
89
Quantity Discrimination
Quantity
Discrimination
Score Sheet
90
Quantity Discrimination






If the student does not respond after 3
seconds, point to the next item and say “Try
this one.”
Do not correct errors.
Teacher writes student’s responses on the
Quantity Discrimination score sheet. Skipped
items are marked with a hyphen (-).
At 1 minute, draw a line under the last item
completed.
Teacher scores the task, putting a slash
through incorrect items on the score sheet.
Teacher counts the number of correct
answers in a minute.
91
Quantity Discrimination
Lin’s Quantity
Discrimination
Score Sheet

Thirty-eight items
attempted.

Five incorrect.

Lin’s score is 33.
92
Quantity Discrimination
Teacher Score
Sheet

Let’s practice.
93
Quantity Discrimination
Student
Sheet—Page 1

Let’s practice.
94
Quantity Discrimination
Student
Sheet—Page 2

Let’s practice.
95
Quantity Discrimination
Student
Sheet—Page 3

Let’s practice.
96
Missing Number




For kindergarten or first grade
students.
Student is presented with 63 items and
asked to orally identify the missing
number in a sequence of four numbers.
After completing some sample items,
the student works for 1 minute.
Teacher writes the student’s responses
on the Missing Number score sheet.
97
Missing Number
Student Copy
of a Missing
Number Test

Actual student
copy is 3
pages long.
98
Missing Number
Missing Number
Score Sheet
99
Missing Number






If the student does not respond after 3
seconds, point to the next item and say “Try
this one.”
Do not correct errors.
Teacher writes the student’s responses on the
Missing Number score sheet. Skipped items
are marked with a hyphen (-).
At 1 minute, draw a line under the last item
completed.
Teacher scores the task, putting a slash
through incorrect items on the score sheet.
Teacher counts the number of correct
answers in I minute.
100
Missing Number
Thomas’s
Missing Number
Score Sheet

Twenty-six items
attempted.

Eight incorrect.

Thomas’s score
is 18.
101
Missing Number
Teacher Score
Sheet

Let’s practice.
102
Missing Number
Student
Sheet—Page 1

Let’s practice.
103
Missing Number
Student
Sheet—Page 2

Let’s practice.
104
Missing Number
Student
Sheet—Page 3

Let’s practice.
105
Step 4: How to Graph Scores


Graphing student scores is vital.
Graphs provide teachers with a
straightforward way to:
– Review a student’s progress.
– Monitor the appropriateness of student
goals.
– Judge the adequacy of student
progress.
– Compare and contrast successful and
unsuccessful instructional aspects of a
student’s program.
106
Step 4: How to Graph Scores

Teachers can use computer graphing
programs.
– List available in Appendix A of manual.

Teachers can create their own graphs.
– Create template for student graph.
– Use same template for every student in the
classroom.
– Vertical axis shows the range of student
scores.
– Horizontal axis shows the number of
weeks.
107
Step 4: How to Graph Scores
108
Step 4: How to Graph Scores
Digits Correct in 3 Minutes
25
20
15
10
5
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Weeks of Instruction

Student scores are plotted on graph
and a line is drawn between scores.
109
Step 5: How to Set Ambitious Goals


Once a few scores have been graphed,
the teacher decides on an end-of-year
performance goal for each student.
Three options for making performance
goals:
– End-of-Year Benchmarking
– Intra-Individual Framework
– National Norms
110
Step 5: How to Set Ambitious Goals


End-of-Year Benchmarking
For typically developing students, a
table of benchmarks can be used to
find the CBM end-of-year performance
goal.
111
Step 5: How to Set Ambitious Goals
Grade
Probe
Kindergarten
First
Maximum score
Benchmark
Data not yet available
Computation
First
30
20 digits
Data not yet available
Second
Computation
45
20 digits
Second
Concepts and Applications
32
20 blanks
Third
Computation
45
30 digits
Third
Concepts and Applications
47
30 blanks
Fourth
Computation
70
40 digits
Fourth
Concepts and Applications
42
30 blanks
Fifth
Computation
80
30 digits
Fifth
Concepts and Applications
32
15 blanks
Sixth
Computation
105
35 digits
Sixth
Concepts and Applications
35
15 blanks
112
Step 5: How to Set Ambitious Goals
Intra-Individual Framework




Weekly rate of improvement is calculated
using at least eight data points.
Baseline rate is multiplied by 1.5.
Product is multiplied by the number of weeks
until the end of the school year.
Product is added to the student’s baseline
rate to produce end-of-year performance goal.
113
Step 5: How to Set Ambitious Goals







First eight scores: 3, 2, 5, 6, 5, 5, 7, and 4.
Difference: 7 – 2 = 5.
Divide by weeks: 5 ÷ 8 = 0.625.
Multiply by baseline: 0.625 × 1.5 = 0.9375.
Multiply by weeks left: 0.9375 × 14 =
13.125.
Product is added to median: 13.125 + 5 =
18.125.
The end-of-year performance goal is 18
(rounding).
114
Step 5: How to Set Ambitious Goals
Grade
Computation:
Digits
Concepts and
Applications:
Blanks
First
0.35
N/A
Second
0.30
0.40
Third
0.30
0.60
Fourth
0.70
0.70
Fifth
0.70
0.70
Sixth
0.40
0.70
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.
115
Step 5: How to Set Ambitious Goals
National Norms





Median: 14
Fourth Grade
Computation
Norm: 0.70
Multiply by weeks
left: 16 × 0.70 =
11.2
Add to median:
11.2 + 14 = 25.2
The end-of-year
performance goal
is 25
Grade
Computation
: Digits
Concepts and
Applications:
Blanks
First
0.35
N/A
Second
0.30
0.40
Third
0.30
0.60
Fourth
0.70
0.70
Fifth
0.70
0.70
Sixth
0.40
0.70
116
Step 5: How to Set Ambitious Goals
National Norms


Once the end-of-year performance goal has
been created, the goal is marked on the
student graph with an X.
A goal line is drawn between the median of
the student’s scores and the X.
117
Step 5: How to Set Ambitious Goals
Drawing a Goal-Line
Goal-line: The desired path of measured behavior to reach the
performance goal over time.
118
Step 5: How to Set Ambitious Goals


After drawing the goal-line, teachers
continually monitor student graphs.
After seven to eight CBM scores,
teachers draw a trend-line to represent
actual student progress.
– The goal-line and trend-line are compared.

The trend-line is drawn using the Tukey
method.
Trend-line: A line drawn in the data path to indicate the direction
(trend) of the observed behavior.
119
Step 5: How to Set Ambitious Goals

Tukey Method
– Graphed scores are divided into three fairly
equal groups.
– Two vertical lines are drawn between the
groups.

In the first and third groups:
– Find the median data point and median
instructional week.
– Locate the place on the graph where the two
values intersect and mark with an X.
– Draw a line between the first group X and third
group X.
– This line is the trend-line.
120
Step 5: How to Set Ambitious Goals
121
Step 5: How to Set Ambitious Goals
Practice 1
Digits Correct in 5 Minutes
25
20
15
10
5
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Weeks of Instruction
122
Step 5: How to Set Ambitious Goals
Practice 1
123
Step 5: How to Set Ambitious Goals
Practice 2
Digits Correct in 5 Minutes
25
20
15
10
5
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Weeks of Instruction
124
Step 5: How to Set Ambitious Goals
Practice 2
125
Step 5: How to Set Ambitious Goals




CBM computer management programs
are available.
Programs create graphs and aid
teachers with performance goals and
instructional decisions.
Various types are available for varying
fees.
Listed in Appendix A of manual.
126
Step 6: How to Apply Decision Rules to Graphed
Scores to Know When to Revise Programs and
Increase Goals


After trend-lines have been drawn,
teachers use graphs to evaluate
student progress and formulate
instructional decisions.
Standard decision rules help with this
process.
127
Step 6: How to Apply Decision Rules to Graphed
Scores to Know When to Revise Programs and
Increase Goals

If at least 3 weeks of instruction have occurred and at
least six data points have been collected, examine the
four most recent consecutive points:
– If all four most recent scores fall above the goalline, the end-of-year performance goal needs to be
increased.
– If all four most recent scores fall below the goal-line,
the student's instructional program needs to be
revised.
– If these four most recent scores fall both above and
below the goal-line, continue collecting data (until
the four-point rule can be used or a trend-line can
be drawn).
128
Step 6: How to Apply Decision Rules to Graphed
Scores to Know When to Revise Programs and
Increase Goals
Digits Correct in 7 Minutes
30
Most recent 4 points
25
20
15
10
Goal-line
5
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Weeks of Instruction
129
Step 6: How to Apply Decision Rules to Graphed
Scores to Know When to Revise Programs and
Increase Goals
Digits Correct in 7 Minutes
30
25
20
15
Goal-line
10
5
Most recent 4 points
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Weeks of Instruction
130
Step 6: How to Apply Decision Rules to Graphed
Scores to Know When to Revise Programs and
Increase Goals

Based on the student’s trend-line:
– If the trend-line is steeper than the goal
line, the end-of-year performance goal
needs to be increased.
– If the trend-line is flatter than the goal line,
the student’s instructional program needs
to be revised.
– If the trend-line and goal-line are fairly
equal, no changes need to be made.
131
Step 6: How to Apply Decision Rules to Graphed
Scores to Know When to Revise Programs and
Increase Goals
132
Step 6: How to Apply Decision Rules to Graphed
Scores to Know When to Revise Programs and
Increase Goals
133
Step 6: How to Apply Decision Rules to Graphed
Scores to Know When to Revise Programs and
Increase Goals
134
Step 7: How to Use Curriculum-Based
Measurement Data Qualitatively to Describe
Student Strengths and Weaknesses



Using a skills profile, student progress
can be analyzed to describe student
strengths and weaknesses.
Student completes Computation or
Concepts and Applications tests.
Skills profile provides a visual display
of a student’s progress by skill area.
135
Step 7: How to Use Curriculum-Based
Measurement Data Qualitatively to Describe
Student Strengths and Weaknesses
136
Step 7: How to Use Curriculum-Based
Measurement Data Qualitatively to Describe
Student Strengths and Weaknesses
137
Other Ways to Use the Curriculum-Based
Measurement Database



How to Use the Curriculum-Based
Measurement Database to Accomplish
Teacher and School Accountability and for
Formulating Policy Directed at Improving
Student Outcomes
How to Incorporate Decision Making
Frameworks to Enhance General
Educator Planning
How to Use Progress Monitoring to
Identify Nonresponders Within a
Response-to-Intervention Framework to
Identify Disability
138
How to Use Curriculum-Based Measurement Data to
Accomplish Teacher and School Accountability for
Formulating Policy Directed at Improving School Outcomes



No Child Left Behind requires all
schools to show Adequate Yearly
Progress (AYP) toward a proficiency
goal.
Schools must determine measure(s)
for AYP evaluation and the criterion
for deeming an individual student
“proficient.”
CBM can be used to fulfill the AYP
evaluation in math.
139
How to Use Curriculum-Based Measurement Data to
Accomplish Teacher and School Accountability for
Formulating Policy Directed at Improving School Outcomes

Using Math CBM:
– Schools can assess students to identify
the number of initial students who meet
benchmarks (initial proficiency).
– The discrepancy between initial
proficiency and universal proficiency is
calculated.
140
How to Use Curriculum-Based Measurement Data to
Accomplish Teacher and School Accountability for
Formulating Policy Directed at Improving School Outcomes
– The discrepancy is divided by the
number of years before the 2013–2014
deadline.
– This calculation provides the number of
additional students who must meet
benchmarks each year.
141
How to Use Curriculum-Based Measurement Data to
Accomplish Teacher and School Accountability for
Formulating Policy Directed at Improving School Outcomes

Advantages of using CBM for AYP:
– Measures are simple and easy to
administer.
– Training is quick and reliable.
– Entire student body can be measured
efficiently and frequently.
– Routine testing allows schools to track
progress during school year.
142
How to Use Curriculum-Based Measurement Data to
Accomplish Teacher and School Accountability for
Formulating Policy Directed at Improving School Outcomes
Number of Students
Meeting CBM Benchmarks
Across-Year School Progress
500
X
(498)
400
300
200
(257)
100
0
2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014
End of School Year
143
How to Use Curriculum-Based Measurement Data to
Accomplish Teacher and School Accountability for
Formulating Policy Directed at Improving School Outcomes
Number of Students
Meeting CBM Benchmarks
Within-Year School Progress
500
400
300
X
(281)
200
100
0
Sept Oct Nov Dec Jan Feb Mar Apr May June
2005 School-Year Month
144
How to Use Curriculum-Based Measurement Data to
Accomplish Teacher and School Accountability for
Formulating Policy Directed at Improving School Outcomes
Number Students on Track to
Meet CBM Benchmarks
Within-Year Teacher Progress
25
20
15
10
5
0
Sept Oct
Nov
Dec
Jan Feb Mar
Apr May June
2005 School-Year Month
145
How to Use Curriculum-Based Measurement Data to
Accomplish Teacher and School Accountability for
Formulating Policy Directed at Improving School Outcomes
Number Students on Track to
Meet CBM Benchmarks
Within-Year Special Education Progress
25
20
15
10
5
0
Sept Oct
Nov
Dec
Jan Feb Mar
Apr May June
2005 School-Year Month
146
How to Use Curriculum-Based Measurement Data to
Accomplish Teacher and School Accountability for
Formulating Policy Directed at Improving School Outcomes
CBM Score: Grade 3 Concepts and
Applications
Within-Year Student Progress
30
25
20
15
10
5
0
Sept
Oct
Nov
Dec
Jan
Feb
Mar
Apr
May
June
2005 School-Year Month
147
How to Incorporate Decision-Making Frameworks to
Enhance General Educator Planning

CBM reports prepared by computer
can provide the teacher with
information about the class:
– Student CBM raw scores
– Graphs of the low-, middle-, and highperforming students
– CBM score averages
– List of students who may need
additional intervention
148
How to Incorporate Decision-Making Frameworks to
Enhance General Educator Planning
149
How to Incorporate Decision-Making Frameworks to
Enhance General Educator Planning
150
How to Incorporate Decision-Making Frameworks to
Enhance General Educator Planning
151
How to Use Progress Monitoring to Identify NonResponders Within a Response-to-Intervention
Framework to Identify Disability



Traditional assessment for identifying
students with learning disabilities relies on
intelligence and achievement tests.
Alternative framework is conceptualized
as nonresponsiveness to otherwise
effective instruction.
Dual-discrepancy:
– Student performs below level of
classmates.
– Student’s learning rate is below that of their
classmates.
152
How to Use Progress Monitoring to Identify NonResponders Within a Response-to-Intervention
Framework to Identify Disability



All students do not achieve the same
degree of math competence.
Just because math growth is low, the
student doesn’t automatically receive
special education services.
If the learning rate is similar to that of
the other students, the student is
profiting from the regular education
environment.
153
How to Use Progress Monitoring to Identify NonResponders Within a Response-to-Intervention
Framework to Identify Disability


If a low-performing student is not
demonstrating growth where other
students are thriving, special
intervention should be considered.
Alternative instructional methods
must be tested to address the
mismatch between the student’s
learning requirements and the
requirements in a conventional
instructional program.
154
Case Study 1: Alexis
155
Case Study 1: Alexis
156
Case Study 2: Darby Valley
Elementary

Using CBM toward reading AYP:
– A total of 378 students.
– Initial benchmarks were met by 125
students.
– Discrepancy between universal proficiency
and initial proficiency is 253 students.
– Discrepancy of 253 students is divided by
the number of years until 2013–2014:
• 253 ÷ 11 = 23.
– Twenty-three students need to meet CBM
benchmarks each year to demonstrate
AYP.
157
Case Study 2: Darby Valley
Elementary
Meeting CBM Benchmarks
Number Students
Across-Year School Progress
400
X
(378)
300
200
100
(125)
0
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
End of School Year
158
Case Study 2: Darby Valley
Elementary
Number Students
Meeting CBM Benchmarks
Within-Year School Progress
200
150
X
(148)
100
50
0
Sept Oct Nov Dec Jan Feb Mar Apr May June
2004 School-Year Month
159
Case Study 2: Darby Valley
Elementary
Number Students on Track to
Meet CBM Benchmarks
Ms. Main (Teacher)
25
20
15
10
5
0
Sept Oct
Nov
Dec
Jan Feb Mar
Apr May June
2004 School-Year Month
160
Case Study 2: Darby Valley
Elementary
Number Students on Track to
Meet CBM Benchmarks
Mrs. Hamilton (Teacher)
25
20
15
10
5
0
Sept Oct
Nov
Dec
Jan Feb Mar
Apr May June
2004 School-Year Month
161
Case Study 2: Darby Valley
Elementary
Number Students on Track to
Meet CBM Benchmarks
Special Education
25
20
15
10
5
0
Sept
Oct
Nov
Dec
Jan
Feb
Mar
Apr
May June
2004 School-Year Month
162
Case Study 2: Darby Valley
Elementary
Cynthia Davis (Student)
CBM Score: Grade 1
Computation
30
25
20
15
10
5
0
Sept
Oct
Nov
Dec
Jan
Feb
Mar
Apr
May
June
2004 School-Year Month
163
Case Study 2: Darby Valley
Elementary
Dexter Wilson (Student)
164
Case Study 3: Mrs. Smith
165
Case Study 3: Mrs. Smith
166
Case Study 3: Mrs. Smith
167
Case Study 3: Mrs. Smith
168
Case Study 4: Marcus
169
Case Study 4: Marcus
Digits Correct in 5 Minutes
30
High-performing
math students
25
20
Middle-performing
math students
15
10
Low-performing
math students
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Weeks of Instruction
170
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
171
Curriculum-Based Measurement
Resources


List on pages 31–34 of materials
packet
Appendix B of CBM manual
172