Transcript Using CBM for Progress Monitoring

Introduction to
Using CurriculumBased Measurement
for Progress
Monitoring in Math
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
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
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
Finding CBMs That Work
for You:
 Creating CBM probes is timeconsuming!
 We recommend utilizing these
resources to obtain ready-made
probes:
– NCSPM Tools chart
– www.interventioncentral.org
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
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
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
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 gradelevel expectations.
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.
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.
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.
Kindergarten and Grade 1
 Number Identification
 Quantity Discrimination
 Missing Number
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.
Number Identification: Student
Form
 Student’s copy
of a Number
Identification
test:
– Actual student
copy is 3 pages
long.
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.
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.
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.
Quantity Discrimination:
Student Form
 Student’s copy
of a Quantity
Discrimination
test:
 Actual student
copy is 3
pages long.
Quantity Discrimination:
Scoring Form
 Lin’s Quantity
Discrimination
score sheet:
– Thirty-eight items
attempted.
– Five items are
incorrect.
– Lin’s score is 33.
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.
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.
Missing Number: Student
Form
 Student’s copy
of a Missing
Number test:
– Actual student
copy is
3 pages long.
Missing Number: Scoring
Form
 Thomas’s
Missing Number
score sheet:
– Twenty-six items
attempted.
– Eight items are
incorrect.
– Thomas’s score
is 18.
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.
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.
Computation: Student Form
Computation: Time Limits
 Length of test
varies
by grade.
Grade
1
Time limit
2 minutes
2
2 minutes
3
3 minutes
4
3 minutes
5
5 minutes
6
6 minutes
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.
Computation: Scoring
Example
 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
Computation: Scoring
Different Operations
 Scoring different operations:
9
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).
Computation: Division
Scoring Examples
 Scoring division with remainders:
Correct Answer
403R52
Student’s Answer
43R5
(1 correct digit)

23R15
43R5


(2 correct digits)
Computation: Scoring
Decimals
 Start at the decimal point and
work outward in both directions
Computation: Scoring
Fractions
 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.
Computation: Fraction
Scoring Examples
 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)
Computation: Student
Example
 Samantha’s
Computation test:
– Fifteen problems
attempted.
– Two problems
skipped.
– Two problems
incorrect.
– Samantha’s
correct digit score
is 49.
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.
Concepts and Applications:
Student Form
 Student copy of
a Concepts and
Applications
test:
– This sample is
from a secondgrade test.
– The actual
Concepts and
Applications test
is 3 pages long.
Concepts and Applications:
Time Limits
 Length of test
varies by
grade.
Grade
2
Time limit
8 minutes
3
6 minutes
4
6 minutes
5
7 minutes
6
7 minutes
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.
Concepts and Applications:
Scoring a Student Example
Concepts and Applications:
Scoring a Student Example
 Quinten’s fourthgrade Concepts
and Applications
test:
– Twenty-four
blanks answered
correctly.
– Quinten’s score
is 24.
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.
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 www.interventioncentral.org
for tips
A Math CBM Master
Graph
The vertical axis is labeled with
the range of student scores.
The horizontal axis is labeled with
the number of instructional weeks.
Digits Correct in 3 Minutes
25
20
15
10
5
0
1
2
3
4
5
6
7
8
9
Weeks of Instruction
10
11
12
13
14
Plotting CBM Data
 Student scores are plotted on the graph,
and a line is drawn between the scores.
Digits Correct in 3 Minutes
25
20
15
10
5
0
1
2
3
4
5
6
7
8
9
Weeks of Instruction
10
11
12
13
14
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
Using End-of-Year
Benchmarks to Set 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
Using National Norms to
Set Ambitious Goals
 National norms:
– For typically
developing
students, a
table of median
rates of weekly
increase can be
used to find the
end-of-year
performance
goal.
Grade
Computation:
Digits
Concepts and
Applications:
Blanks
1
0.35
N/A
2
0.30
0.40
3
0.30
0.60
4
0.70
0.70
5
0.70
0.70
6
0.40
0.70
Using National Norms to
Set Goals: Example
 National norms:
– Median is 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
1
0.35
N/A
2
0.30
0.40
3
0.30
0.60
4
0.70
0.70
5
0.70
0.70
6
0.40
0.70
Using an Intra-Individual
Framework to Set 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.
– Added to student’s baseline score to
produce end-of-year performance goal.
Example: Using an IntraIndividual 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
= 0.435.
 Multiply by weeks left: 0.435 × 14 = 6.09.
 Product is added to the first median: 3 +
6.09 = 9.09.
 The end-of-year performance goal is 9.
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.
Example of a Graphed
Goal
 Drawing a goal-line:
Digits Correct in 5 Minutes
– A goal-line is the desired path of measured behavior to
reach the performance goal over time.
25
20
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.
X
15
10
5
0
1
2
3
4
5
6
7
8
9
Weeks of Instruction
10
11
12
13
14
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.
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.
Tukey Method: A
Graphed Example
Digits Correct in 5 Minutes
25
20
15
X
10
X
5
X
X
0
1
2
3
4
5
6
7
8
Weeks of Instruction
9
10
11
12
13
14
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
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.
The 4-point Rule
 Based on four most recent
consecutive points:
– If scores are above the goal-line, endof-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 4-point Rule: Example 1
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
Weeks of Instruction
9
10
11
12
13
14
The 4-point Rule: Example 2
Digits Correct in 7 Minutes
30
25
X
20
15
Goal-line
10
5
Most recent 4 points
0
1
2
3
4
5
6
7
8
Weeks of Instruction
9
10
11
12
13
14
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.
Decision-Making with Trendand Goal-Lines (Example 1)
Digits Correct in 7 Minutes
30
25
Trend-line
20
X
15
X
10
Goal-line
5
0
1
2
3
4
5
6
7
8
Weeks of Instruction
9
10
11
12
13
14
Decision-Making with Trendand Goal-Lines (Example 2)
Digits Correct in 7 Minutes
30
25
20
15
X
X
10
5
Goal-line
Trend-line
0
1
2
3
4
5
6
7
8
Weeks of Instruction
9
10
11
12
13
14
Decision-Making with Trendand Goal-Lines (Example 3)
Digits Correct in 7 Minutes
30
25
X
20
15
X
X
10
Goal-line
5
Trend-line
0
1
2
3
4
5
6
7
8
Weeks of Instruction
9
10
11
12
13
14
Step 7: Use Data to Describe
Student Strengths and
Weaknesses
 Students’ completed probes can be
analyzed to examine mastery of
specific skills.
Examining Computation
CBM
4507
2146
2361
4507
2146
2461
  

4 correct
digits

3 correct
digits
4507
2146
2441


2 correct
digits
Skills Profiles
 Available with some progress
monitoring software programs.
 Skills profile provides a visual display
of a student’s progress by skill area.
Example: Class Skills
Profile
Example: Individual Skills
Profile
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
The End
Thank you for participating in this
training module.
© 2008, National Center on Student Progress Monitoring