### 3 Curriculum-Based Measurement, Common Assessments, and the

Curriculum-Based
Measurement, Common
Assessments, and the
Common Core
Mathematics Assessment and
Intervention
Much of the information on this topic was found
on the National Center on Student Progress
Monitoring website at
http://www.studentprogress.org/default.asp
• Specific information was also gleaned from
presentations by Pam Fernstrom, Sarah Powell,
Lynn Fuchs, Pamela Stecker, and Ingrid Oxaal
What is Curriculum-Based
Measurement
• Curriculum-based measurement is assessment
that samples elements of the curriculum over
time to monitor student progress.
Characteristics of CBM
▫ Time
▫ Directions
•
•
•
•
Results are graphed
Aligned with curriculum (criterion referenced)
Repeated measures
Low inference (25 correct digits means 25
correct digits)
The Basics of CBM
•
•
•
•
•
Monitors progress throughout the school year
Measures at regular intervals
Uses data to determine goals
Provides parallel and brief measures
Displays data graphically
Uses of CBM for Teachers
• Describe academic competence at a single point
in time
• Quantify the rate at which students develop
• Build more effective programs to increase
student achievement
How to 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
• The number of digits correct, problems correct,
or blanks correct is calculated and graphed on
student graph.
Computation
• For students in Grades 1–6:
▫ Student is presented with 25 computation
mathematics curriculum.
▫ Student works for set amount of time (time limit
▫ Teacher grades test after student finishes.
Computation
Try a Computation CBM
Computation
• Length of test varies
1
Time limit
2 minutes
2
2 minutes
3
3 minutes
4
3 minutes
5
5 minutes
6
6 minutes
Computation
• Students receive 1 point for each problem
• 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.
Computation
• Correct digits: Evaluate each numeral in every
4507
4507
2146
2361
2146
2461
  

4 correct
digits

3 correct
digits
2146
2441


2 correct
digits
Concepts and Applications
• Student copy of a
Concepts and
Applications test:
▫ This sample is
▫ The actual
Concepts and
Applications test
is 3 pages long.
Try a Concept and Applications CBM
Concepts and Applications
• Length of test
2
Time limit
8 minutes
3
6 minutes
4
6 minutes
5
7 minutes
6
7 minutes
Concepts and Applications
 Students receive 1 point for each blank
 The number of correct answers within
the time limit is the student’s score.
Concepts and Applications

Concepts and
Applications test:
– Twenty-four blanks
– Quinten’s score is 24.
Concepts and Applications
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’s copy of a
Number
Identification test:
▫ Actual student
copy is 3 pages
long.
Number Identification
• Number
Identification
score sheet
Number Identification
• 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
Number Identification
• 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.
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’s copy
of a Quantity
Discrimination
test:
• Actual student
copy is 3 pages
long.
Quantity Discrimination
• Quantity
Discrimination
score sheet
Quantity Discrimination
• 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
Quantity Discrimination
• Lin’s Quantity
Discrimination
score sheet:
▫ Thirty-eight
items attempted.
▫ Five items are
incorrect.
▫ Lin’s score is 33.
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’s copy of
a Missing
Number test:
▫ Actual student
copy is
3 pages long.
Missing Number
• 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
Missing Number
• Thomas’s
Missing Number
score sheet:
▫ Twenty-six items
attempted.
▫ Eight items are
incorrect.
▫ Thomas’s score
is 18.
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.
How to Graph Scores
• Teachers can use computer graphing programs.
• Teachers can create their own graphs.
▫ A template can be created for student graphs.
▫ The same template can be used for every student
in the classroom.
▫ Vertical axis shows the range of student scores.
▫ Horizontal axis shows the number of weeks.
How to Graph Scores
How to Graph Scores
• 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
10
Weeks of Instruction
11
12
13
14
How to Set Ambitious Goals
• Once baseline data has 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 (commercial test)
▫ Intra-individual framework
▫ National norms (commercial test)
How to Set Ambitious Goals
• Intra-individual framework:
▫ Weekly rate of improvement is calculated using at
least eight data points.
▫ Weekly rate of improvement = highest scoreAmbitious
lowest score/number of data points (8).
Rate
▫ Baseline rate is multiplied by 1.5.
of Growth
▫ 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.
How to Set Ambitious Goals
First eight scores: 3, 2, 5, 6, 5, 5, 7, 4.
Difference between high and low: 7-2=5
Divide by (# data points): 5 ÷ (8) = 0.625
Multiply by typical growth rate: 0.625 × 1.5 = 0.9375.
Multiply by weeks left: 0.9375 × 20 = 18.75.
Product is added to the median of the first 8 scores: 5 +
18.75 = 23.75.
• The end-of-year performance goal is 24.
•
•
•
•
•
•
How to Set Ambitious Goals
Tukey Method
•
•
•
•
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.
How to Set Ambitious Goals
• 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
How to Set Ambitious Goals
• After drawing the goal-line, teachers continually monitor
student graphs.
• After seven or eight CBM scores, teachers draw a trendline 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.
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.
Mark with an X on the median instructional week.
Draw a line between the first group X and third group X.
This line is the trend-line.
How to Set Ambitious Goals
Digits Correct in 5 Minutes
25
20
15
10
5
X
X
X
0
1
2
3
4
5
6
7
8
9
Weeks of Instruction
10
11
12
13
14
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
Weeks of Instruction
Change in year end goal needed
10
11
12
13
14
How to Apply Decision Rules to Graphed Scores to
Know When to Revise Programs and Increase Goals
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
9
Weeks of Instruction
Change in instructional program needed
10
11
12
13
14
Using Data to Make Instructional Decisions
• You can disaggregate the data by objective and
plot growth.
• Then instruction can be focused on student
needs.
Assessment and the Common Core
▫ How will the implementation of the common core
Common Core
• What do you know or have heard about the
common core?
• Do you think it is an improvement as a guide to
math instruction?
• Does the common core dictate assessment
methods?
Common Core Information
Aligning Priorities & Evidence
• Informal, quick,
or contrived
▫ Paper/pencil
▫ Observation
▫ Selected
response
quiz/test
• Formal, longterm, authentic
▫ Open-ended
▫ Complex
▫ Performance
Worth being
familiar with
Important to
know and do
Enduring
Understanding
identify the essential computation skills that
students need to master
• Identify the essential concepts and applications
that students need to understand.
• Identify standards that cannot be assessed using
a paper and pencil assessment