Introduction to Using Curriculum- Based Measurement for Progress Monitoring in Math

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

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1 2 3 4 5 6 7 8 9 10 11 12 13 14

Weeks of Instruction

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The vertical axis is labeled with the range of student scores.

The horizontal axis is labeled with the number of instructional weeks.

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1 2 3 4 5 6 7 8 9 10 11 12 13 14

Weeks of Instruction

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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.

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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

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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

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Goal-line

Most recent 4 points

The 4-point Rule: Example 2

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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)

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Goal-line

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Trend-line

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Trend-line

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Decision-Making with Trend- and Goal-Lines (Example 2)

Decision-Making with Trend- and Goal-Lines (Example 3)

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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