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 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. GradeTime limit 12 minutes 2 33 minutes 4 55 minutes 66 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: correct digits 3 correct digits 2 correct digits

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. GradeTime limit 28 minutes 36 minutes 4 57 minutes 6

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

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 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

Weeks of Instruction Digits Correct in 3 Minutes 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) = Multiply by typical growth rate: × 1.5 = Multiply by weeks left: × 20 = Product is added to the median of the first 8 scores: = 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) = Multiply by typical growth rate: 0.29 × 1.5 = Multiply by weeks left: × 14 = Product is added to the first median: = 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. 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.

X Weeks of Instruction Digits Correct in 5 Minutes X X How to Set Ambitious Goals

Weeks of Instruction Digits Correct in 7 Minutes 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 Weeks of Instruction Digits Correct in 7 Minutes 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 with Important to know and do Enduring Understanding

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.