CURRICULUM-BASED
MEASURES: MATH
Kat Nelson, M.Ed
University of Utah
Objectives
1. You will be able to define a CBM and articulate
the big ideas of using math CBM with the CCSS
and the MTSS model.
2. You will be able to administer and score
screener and progress monitoring probes.
3. You will be able to use the problem solving
process to interpret the data produced from the
math CBM.
CBM: Big Ideas
(Kelly, Hosp, Howell, 2008)
• “CBM is a quick and reliable method for
gathering information about student
performance and progress.”
• CBM is…
• Aligned with Curriculum
• Valid and Reliable
• Standardized measures
• Provides low-inference Information
CBM: Big Ideas
(Kelly, Hosp, Howell, 2008)
• CBM probes are repeated measures that
are efficient, and sensitive to growth.
• Sensitivity to growth = Informing your
instruction frequently.
• Information about performance and growth
can be easily shared with stakeholders
• Indicator of future reading and math
achievement
Curriculum-Based Measurement
And The Common Core State
Standarads
Big Ideas
Common Core & CBM
(Shinn, 2012)
• The Common Core State Standards (CCSS) provide sets of College
and Career focused outcomes and annual Criterion Referenced Tests
to measure student learning as a summative evaluation.
• The assessment implications of CCSS are clearly related to
summative evaluation and accountability
• No single test is sufficient for all the data-based decisions,
screenings, intervention planning/diagnosis, progress monitoring,
accountability/program evaluation that schools make in their attempts
to identify student learning needs.
Common Core & CBM
(Shinn, 2012)
• Assessment of CCSS need not be separate items or tests
for each standard, but may include “rich tasks” that
address a number of separate standards.
• AIMSweb’s Curriculum-Based Measurement (CBM) tests
typically are based on these rich tasks that are validated
as “vital signs” or “indicators” of general basic skill
outcomes.
Common Core & CBM
(Shinn, 2012)
• AIMSweb’s CBM tests are consistent with the CCSS.
They are content valid.
• AIMSweb’s CBM tests are complementary to the
assessment requirements to attain proficiency on the
CCSS.
Curriculum BasedMeasurement And Multi-tier
System Of Support
Big Ideas
Multi-Tiered System of Support
• Schools identify students at risk for poor learning
outcomes
• Monitor student progress
• Provide evidence based interventions and adjust
the intensity and nature of those interventions
depending on a student’s responsiveness.
(NCRtI, 2010)
Key Features of MTSS
(Sugai, 2008)
• Universal Design
• Data-based decision making and problem solving
• Continuous progress monitoring
• Focus on successful student outcomes
• Continuum of evidence-based interventions
• A core curriculum is provided for all students
• A modification of this core is arranged for students who are
identified as non-responsive
• A specialized and intensive curriculum for students with intensive
needs
• Focus on fidelity of implementation
Problem Solving Process
Using CBM within MTSS
• Tier 1 Universal Screening
• Establishes benchmarks three times throughout the school year
• Tier 2 Progress monitoring
• Monitoring students at-risk by assessing monthly
• Tier 3 Intensive Progress monitoring
• Frequent assessment for students at risk or significant needs
Conducting A Math
CBM
Directions and Scoring Procedures
Selecting the Measure
• At Kindergarten or Grade 1
• Oral Counting
• Quantity Array
• Number Identification
• Quantity Discrimination
• Missing Number
• At Grade 1-8
• Computation (Mixed and/or Facts)
• Concepts & Applications
• As appropriate (Grade 9?)
• Algebra
• Early Numeracy
Measures
Let’s take
a Look
• Concepts and
Applications or M-Cap
Let’s Take a
Look
• Computation
Let’s
Take a
Look
Administration of Computation Probe
•
•
The number of correctly written digits in 2 minutes from the end-of-year
curriculum
Correct digits
•
Not correct problems or answers
• Why?
•
2 minutes
•
Depends on grade and publisher
Computation
• Student(s) are given a sheet of math
problems and pencil
• Student(s) complete as many math
problems as they can in 2 minutes
• At the end of 2 minutes the number of
correctly written digits is counted
Directions for Computation
•
•
Give the child(ren) a math sheet(s) and pencil
Say
“The sheet on your desk is math facts. There are
several types of problems on the sheet. Some are
(insert types of problems on sheet). Look at each
problem carefully before you answer it. When I say
‘please begin’, start answering the problems. Begin with
the first problem and work across the page. Then go to
the next row. If you cannot answer the problem, mark
an ‘X’ through it and go to the next one. If you finish a
page, turn the page and continue working. Are there
any questions?”
Directions – Your Turn
• The sheet on your desk is math facts. There are several
types of problems on the sheet. Some are (insert types of
problems on sheet). Look at each problem carefully
before you answer it. When I say ‘please begin’, start
answering the problems. Begin with the first problem and
work across the page. Then go to the next row. If you
cannot answer the problem, mark an ‘X’ through it and go
to the next one. If you finish a page, turn the page and
continue working. Are there any questions?”
Directions Continued
• Say “Please begin” and start your timer
• Make sure students are not skipping
problems in rows and do not skip around
or answer only the easy problems
• Say “Please stop” at the end of 2 minutes
Scoring
•
If the answer is correct, the student earns the
score equivalent to the number of correct digits
written using the “longest method” taught to
solve the problem, even if the work is not shown
• If a problem has been crossed out, credit is
given for the correct digits written
• If the problem has not been completed, credit is
earned for any correct digits written
Scoring Continued
•
Reversed digits (e.g., 3 as E) or rotated digits,
with the exception of 6 & 9 are counted as
correct
• Parts of the answer above the line (carries or
borrows) are not counted as correct digits
• In multiplication problems, a “0”, “X”, or <blank>
counts as a place holder and is scored as a CD
Scoring Continued
•
A division BASIC FACT is when both the divisor
and the quotient are 9 or less. If the answer is
correct the total CD always equals 1
• In division problems, remainder zeroes (r 0) are
not counted as correct digits
• In division problems, place holders are not
counted as correct digits
Scoring
Computation Scoring – Your Turn
Put It To Practice
Benchmarking, Survey Level Assessment, and
Progress Monitoring
Tier 1- Universal Screening Big Ideas
(Hosp, Hosp, Howell, 2007)
• Provides a reliable and valid way to identify
• Students who are at risk for failure
• Students who are not making adequate
progress
• Students who need additional diagnostic
evaluation
• Students’ instructional level.
• 3 times a year for the entire school
• 3 probes are given and you take the
median score
What is Proficient?
How Much Progress can we Expect?
(Hosp, Hosp, Howell, 2007)
• Benchmarks - Use standards for level
of performance that are empirically
validated by researchers.
• Norms – Compare a student’s score to
the performance of others in her grade
or instructional level
Proficiency Levels or Benchmarks for
Math CBM
(Burns, VanDerHeyden, Jiban, 2006)
Grade
Placement Level
Correct Digits
2-3
Frustration
<14
Instructional
14-31
Mastery
>31
Frustration
<24
Instructional
24-49
Mastery
>49
4-5
Norms for Math CBM: Correct Digits
(AIMSweb, 2006)
Grade
Percentile
Fall (CD)
Winter (CD)
Spring (CD)
2
90%
31
39
43
75%
20
30
42
50%
12
24
24
25%
8
16
17
10%
5
10
12
90%
68
76
85
75%
53
59
69
50%
37
45
52
25%
25
33
39
10%
16
23
27
5
Making Informed Data Based-Decisions
Spring Benchmark Data for 2nd Grade
Student
Median Score
1
22
2
35
3
37
4
10
5
42
6
47
7
13
8
27
9
42
Making Informed Data Based-Decisions
Spring Benchmark Data for 2nd
Grade
Student
Median Score
6
47
9
42
5
42
3
37
2
35
8
27
1
22
7
13
4
10
Survey Level Assessment
(Hosp, 2012)
• Purposes
• To determine the appropriate instructional
placement level for the student
• The highest level of materials that the student can be
expected to benefit from instruction in
• To provide baseline data, or a starting point for
progress monitoring
• In order to monitor progress toward a future goal, you
need to know how the student is currently performing
Survey Level Assessment
(Hosp, 2012)
1. Start with grade level passages/worksheets
(probes)
2. Administer 3 separate probes (at same difficulty
level) using standard CBM procedures
3. Calculate the median (i.e., find the middle score)
4. Is the student’s score within instructional range?
•
•
•
Yes: this is the student’s instructional level
No: if above level (too easy), administer 3 probes at
next level of difficulty
No: if below level (too hard), administer 3 probes at
previous level of difficulty
Survey Level
Assessment
4
2
2 7 12 1010 F
1 25 23 27 25 I
x
x
6/13/13
Progress Monitoring Big Ideas: Tier 2 & 3
• Purpose: (Hosp, Hosp, Howell, 2007)
• To ensure that instruction is working
• To signal when a change is needed
• To guide adjustments in the program
• Frequency:
• Tier 2: Monthly – to show progress and to inform instruction
• Tier 3: Weekly to Bi-Weekly – to ensure that students who are the
most treatment resistant are making progress.
Progress Monitoring:
Determine the Goal
Weekly Growth Rates for Math
CBM: Correct Digits
Calculating Aim Line
• Median Score from
SLA or Benchmark +
(Number of Weeks x
Rate of Improvement)
= Goal
• Student 4
• 25 + (20 x .50) = 35
• Goal = 35 Correct Digits in
20 weeks
Grade
Realistic
Growth
rates per
week (CD)
Ambitious
growth
rates per
week (CD)
1
0.30
0.50
2
0.30
0.50
3
0.30
0.50
4
0.70
1.15
5
0.75
1.20
6
0.45
1.00
(Fuchs, Fuchs, Hamlett, Walz, and Germann 1993)
Your Turn: Calculate Goal for Student 1
2nd grade: Spring Benchmark
Scores
Student
Median Score
6
47
9
42
5
42
3
37
2
35
8
27
*1*
22
7
13
4
10
Calculate
Grade
Realistic
Growth
rates per
week (CD)
Ambitious
growth
rates per
week (CD)
2
0.30
0.50
Median Score from SLA or
Benchmark + (Number of Weeks
x Rate of Improvement) = Goal
Making Informed Data Based-Decisions
35
Student 4
1st Grade Probe
33
30
25
25
27
23
20
15
Student 4
10
5
• Is our intervention working?
• What changes should we
make?
0
---Aimline
Progress Monitoring: Another Look
Student 4: 1st Grade Progress Monitoring
40
35
33
30
25
25
27
35
34
28
27
23
20
15
10
5
0
0
Week Week Week Week Week Week Week Week
1
2
3
4
5
6
7
8
Student 4
Aimline
Intervention
CBM and Web-Based Data Management
Resources
• AIMSWeb
• EasyCBM
• EDCheckup
• Intervention Central
• iSTEEP
• Yearly Progress Pro
• NCRtI
• enumeracy
• PM Focus