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Introduction to Using Curriculum-Based 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 time-
consuming! 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 todescribe 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 grade-level 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 Time limit
1 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.
oror Students receive 1 point for each
problem answered correctly.
Computation: Scoring Example
Correct digits: Evaluate each numeral in every answer:
450721462461
450721462361
450721462441
4 correct digits
3 correct digits
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 Student’s Answer
4 0 3 R 5 2 4 3 R 5(1 correct digit)
2 3 R 1 5 4 3 R 5(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 7 / 1 2 8 / 1 1(2 correct digits)
5 6 / 1 2(2 correct digits)
6
51 / 2
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 second-grade test.
– The actual Concepts and Applications test is 3 pages long.
Concepts and Applications: Time Limits
Length of test varies by grade.
Grade Time limit
2 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
Quinten’s fourth-grade Concepts and Applications test: – Twenty-four
blanks answered correctly.
– Quinten’s score is 24.
Concepts and Applications: Scoring a Student Example
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
0
5
10
15
20
25
1 2 3 4 5 6 7 8 9 10 11 12 13 14
Weeks of Instruction
Dig
its
Co
rrec
t in
3 M
inu
tes
The vertical axis is labeled with the range of student scores.
The horizontal axis is labeled with the number of instructional weeks.
0
5
10
15
20
25
1 2 3 4 5 6 7 8 9 10 11 12 13 14
Weeks of Instruction
Dig
its
Co
rrec
t in
3 M
inu
tes
Plotting CBM Data
Student scores are plotted on the graph, and a line is drawn between the scores.
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
Grade Probe Maximum score
Benchmark
Kindergarten
Data not yet available
First Computation 30 20 digits
First 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 End-of-Year Benchmarks to Set Goals
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.
GradeComputation:
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.
GradeComputation:
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 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
= 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:– A goal-line is the desired path of measured behavior to
reach the performance goal over time.
0
5
10
15
20
25
1 2 3 4 5 6 7 8 9 10 11 12 13 14
Weeks of Instruction
Dig
its
Co
rrec
t in
5 M
inu
tes
X
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.
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.
X0
5
10
15
20
25
1 2 3 4 5 6 7 8 9 10 11 12 13 14
Weeks of Instruction
Dig
its
Co
rre
ct
in 5
Min
ute
s
XX
Tukey Method: A Graphed Example
X
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, 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 4-point Rule: Example 1
0
5
10
15
20
25
30
1 2 3 4 5 6 7 8 9 10 11 12 13 14
Weeks of Instruction
Dig
its
Co
rre
ct
in 7
Min
ute
s
Goal-line
Most recent 4 points
The 4-point Rule: Example 2
0
5
10
15
20
25
30
1 2 3 4 5 6 7 8 9 10 11 12 13 14
Weeks of Instruction
Dig
its
Co
rre
ct
in 7
Min
ute
s
Goal-line
Most recent 4 points
X
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 Trend- and Goal-Lines (Example 1)
0
5
10
15
20
25
30
1 2 3 4 5 6 7 8 9 10 11 12 13 14
Weeks of Instruction
Dig
its
Co
rre
ct
in 7
Min
ute
s
Goal-line
X
X
Trend-line
0
5
10
15
20
25
30
1 2 3 4 5 6 7 8 9 10 11 12 13 14
Weeks of Instruction
Dig
its
Co
rre
ct
in 7
Min
ute
s
Goal-line
Trend-line
XX
Decision-Making with Trend- and Goal-Lines (Example 2)
Decision-Making with Trend- and Goal-Lines (Example 3)
0
5
10
15
20
25
30
1 2 3 4 5 6 7 8 9 10 11 12 13 14
Weeks of Instruction
Dig
its
Co
rre
ct
in 7
Min
ute
s
Goal-line
Trend-line
X
X
X
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
450721462461
450721462361
450721462441
4 correct digits
3 correct digits
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