curriculum-based measurement, common assessments, and the common core mathematics assessment and...

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

•Standardized administration▫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 academic competence over time•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 individually administered.

•Teacher grades mathematics probe.•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 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

Try a Computation CBM

Computation•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•Students receive 1 point for each

problem answered correctly.•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 answer: 450721462461

450721462361

450721462441

4 correct digits

3 correct digits

2 correct digits

ü ü ü ü ü ü ü ü ü

Concepts and Applications

• 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.

Try a Concept and Applications CBM

Concepts and Applications

•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

Students receive 1 point for each blank answered correctly.

The number of correct answers within the time limit is the student’s score.

Quinten’s fourth-grade Concepts and Applications test: – Twenty-four blanks

answered correctly.– Quinten’s score is 24.

Concepts and Applications

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 answered correctly in 1 minute.

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 answered correctly in 1 minute.

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 answered correctly in 1 minute.

Missing Number

•Thomas’s Missing Number score sheet: ▫Twenty-six

items attempted.

▫Eight items are incorrect.

▫Thomas’s scoreis 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

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

Corr

ect

in 3

Min

ute

s

How to Graph Scores

•Student scores are plotted on the graph, and a line is drawn between the scores.

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 score-lowest score/number of data points (8).

▫Baseline rate is multiplied by 1.5.▫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.

Ambitious Rate of Growth

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 GoalsTukey 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:▫ 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.

How to Set Ambitious Goals• 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.

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.

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

Corr

ect

in 5

Min

ute

s

XX

How to Set Ambitious Goals

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

Corr

ect

in 7

Min

ute

s

Goal-line

Most recent 4 points

How to Apply Decision Rules to Graphed Scores to Know When to Revise Programs and Increase Goals

Change in year end goal needed

How to Apply Decision Rules to Graphed Scores to Know When to Revise Programs and Increase Goals

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

Corr

ect

in 7

Min

ute

s

Goal-line

Most recent 4 points

X

Change in instructional program needed

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•In your Reflective Journal

▫How will the implementation of the common core affect your assessment practices?

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, long-term, authentic▫ Open-ended▫ Complex▫ Performance

tasks

Worth being familiar withImportant to know and do

Enduring Understandin

g

In your grade level groups

•Using the Common Core for your grade level, 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

•Use the first page of your grade level to help focus the concepts and skills

•Summarize on chart paper

Your Assignment

•In grade level groups, create a 25 item computation CBM and a Concepts and Applications CBM for your grade level based on the Common Core. Create the scoring keys and blank graphs to accompany the assessments.

A Programming Note

•Bring some of your classroom level data next time we meet.