learning progressions and formative assessment ... · • assist teachers in incorporating lp-based...

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Learning Progressions and Formative Assessment: Helping Mathematics Teachers Transition to

the Common Core State Standards

Jeff Haberstroh

Copyright © 2013 by Educational Testing Service. All rights reserved.

Jeff HaberstrohCaroline Wylie

ETS

CCSSO National Conference on Student Assessment

June 21, 2013

• Objectives

• General plan

Cognitively-Based Assessmentof, for, and as Learning (CBAL)

Copyright © 2013 by Educational Testing Service. All rights reserved.Copyright © 2013 by Educational Testing Service. All rights reserved.

General plan

• Details

• Results

• Increase the capacity of the teacher to accurately analyze and interpret evidence of mathematical understanding that the student produces

• Provide the teacher with specific cognitively-based insights into the nature of student misunderstandings of key

th ti l t

Objectives


mathematical concepts

• Help to estimate where on a hypothetical learning progression student understanding may be located

• Inform teacher how to better advance understanding of more sophisticated mathematical content

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• Focus on students’ understanding of proportional reasoning at grades 6-7

• Common Core State Standards- 6.RP: Understand ratio concepts and use ratio reasoning to solve

problems- 7.RP: Analyze proportional relationships and use them to solve

General Planfor Achieving Objectives


y p p preal-world and mathematical problems

• Build teachers’ deep understanding of proportional reasoning learning progression

• Assist teachers in incorporating LP-based materials into local mathematics curriculum

• Provide LP-based assessment support materials

• Initial 2-day meeting with teachers- Orient teachers to project and learning progression- Provide opportunities for teachers apply understanding of learning progression

• Administer pre-assessment- Generates snapshot of student location on learning progression

F ll 1 d ti ith t h

Details of Plan


• Follow-up 1-day meeting with teachers- Review pre-assessment results and consider instructional implications- Finalize pilot implementation plans for materials

• Administer post-assessment- Generates snapshot of student location on learning progression after use of pilot

materials

• Results of post-assessment

How many scoops of punch mix are needed to fill a 150 cup jug using Malcolm’s punch recipe?

Malcolm’s Recipe

Number of Ratio of

Scoops of Mix

Cups of Water

Scoops of Mix

Cups of Water

3 3

Malcolm’s recipe for making punch uses a ratio of 3 scoops of punch mix to every 5 cups of water.

Workshop Warm-Up


Show your work.

3 5 35

6 10 610

15 25 1525

30 50 3050

scoops

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Strategies Observed

- Set up a correct proportion and “cross multiply”

- Extend the table using an additive reasoning strategy

- Use various forms of multiplicative reasoning


reasoning

- Apply percents

- Incorporate pictorial representations

Connection between strategy employed and understanding relative toimplications for instructional adjustments not always apparent.

• Help teachers to understanding details of proportional reasoning learning progression in the context of specific student responses

• Assist teachers in understanding the structure of and rationale behind proportional reasoning scenario-based tasks

• Model how scenario-based tasks might be implemented in the classroom

Workshop Agenda


g pv.v.

- observing and interpreting student work, and

- making instructional decisions

• Discuss various options for use of available resources

Available Resources and Plan Leading to Post-Assessment

Pre‐Assessment: Use CBAL

Anotherincremental

task

Copyright © 2013 by Educational Testing Service. All rights reserved.Copyright © 2013 by Educational Testing Service. All rights reserved.9

Feedback w.r.t. levels in PR model

Use incremental tasks*, if

appropriate

Proportional Punch Task in sections

Instructional support during task

Complete full task

Incremental extension

task

Repeat as necessary * supported by the Institute of Education Sciences, U.S. Department of Education, through Grant Reference R305A100518 to ETS.

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Has generalized model

Understands covariance and invariance in ratios

Level 5

Level 4

Proportional Reasoning Learning


Recognizes multiplicative relationships

Begins to quantify

Simplistic qualitative understanding

Level 3

Level 2

Level 1

gProgression

Level 5: Generalized

Model of Proportionality

Level 4: Understand

covariance and invariance in

ratios

ther

ooning

c. Task

Inc. Task

Tasks and Levels of Learning Progression


Level 3:Multiplicative Relationships

Level 2: Early

Quantification

Level 1: Simplistic

Qualitative

Proportional Punch

Ratios Rule

Zi

Carto

Inc. Task

Inc. Task

In

• As part of the pilot activity, teachers were required to administer the pre-assessment, the Proportional Punch formative assessment CBAL task, and the post-assessment

• Teachers could use other proportional reasoning tasks as needed (i.e., extended tasks from CBAL and shorter tasks from CAMA) as appropriate to help refine estimated learning progression level support deepening learning

Teacher’s Toolkit of Materials


help refine estimated learning progression level, support deepening learning of proportionality, and check for student progress to next level

• Teacher Handbooks and annotated guides accompanied the CBAL extended tasks and CAMA shorter tasks

• Teacher learning communities were promoted as a way to support the implementation of the materials

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One of the Featured Tasks –Proportional Punch



Proportional Punch


Level 1 on the learning progression: Qualitative understanding

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Proportional Punch


Level 2: Beginning to work with quantities.

Proportional Punch


May be level 3 or level 4: Need to examine student’s response to determine

Proportional Punch


Level 4/5: Moving toward a generalized model for proportional reasoning

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• 18 MC/CR items targeting levels 2‐4 of the proportional reasoning learning progression

• Provided reports to teachers in table and graphical form.

f f di i i l

Pre-assessment results


• Met face‐to‐face to discuss reports, instructional implications and next steps in terms of integrating the resources into instruction.

• In general students around level 2 of the LP although considerable variation within and across classes.

15

20

25

30

Students

Total Score Frequencies by Grade


0

5

10

15

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33

Number of

Total Score

6th grade students

7th grade students

20

50%

60%

70%

80%

Level 2 Level 3 Level 4


0%

10%

20%

30%

40%

1 2 4 8 11 12 18 3 5 6 10 15 17 7 9 13 14 16

Item number

6th grade students

7th grade students

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200%

250%

300%

Pre-Assessment Results for Mrs. X's 7th Grade Class


0%

50%

100%

150%

% of max level 2 % of max level 3 % of max level 4

• Single-class period online extended scenario-based task

• Context similar to Proportional Punch

• Task involved online paint mixing tool

Post-Assessment


• Culminating question in post-assessment task required complex proportional reasoning while dealing with multiple conditions

ResultsPercentageofStudents(District)at

EstimatedLearningProgressionLevelsforthisAssessmentTask

Level4 5%Level3 19%ApproachingLevel3 19%SomeevidenceofLevel1and/orLevel2understanding 11%Noevidenceofunderstanding(Note:Studentsinthiscategorywereunabletoearncreditformostofthequestionsinthetask.) 24%Insufficientevidencetoassignalevel(Note:Studentsinthiscategorymayactuallyhavebeenatlevel4,3,2,1,orbelowlevel1.Theirpatternofresponsesinthistaskdidnotclearlysuggestunderstandingatoneparticularlevel.Follow‐up


y gg g p pinstructionmayhelptodetermineanestimatedlevel.) 22%

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• Movement of students along the learning progression

• Improved teacher conceptual understanding

• Two teachers at the middle school level were designated ‘teacher leaders” but still had a full-time load. This limited the amount of support they could provide to peers.

Lessons Learned


• Technology struggles - similar to what we have seen in other first year pilots with CBAL materials. In second and third year of implementation teachers are more successful at integrating into instruction.

• Need to help teachers learn to transfer ideas from the tasks we provide to their other teaching materials in order to emphasize conceptual understanding.

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