Post on 09-Sep-2018
6/14/2013
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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
Copyright © 2013 by Educational Testing Service. All rights reserved.Copyright © 2013 by Educational Testing Service. All rights reserved.
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
Copyright © 2013 by Educational Testing Service. All rights reserved.Copyright © 2013 by Educational Testing Service. All rights reserved.
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
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• 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
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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
Copyright © 2013 by Educational Testing Service. All rights reserved.Copyright © 2013 by Educational Testing Service. All rights reserved.
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
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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
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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
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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
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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
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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
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Copyright © 2013 by Educational Testing Service. All rights reserved.Copyright © 2013 by Educational Testing Service. All rights reserved.
Proportional Punch
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Level 1 on the learning progression: Qualitative understanding
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Proportional Punch
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Level 2: Beginning to work with quantities.
Proportional Punch
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May be level 3 or level 4: Need to examine student’s response to determine
Proportional Punch
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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
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• 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
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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
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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
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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
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• 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
Copyright © 2013 by Educational Testing Service. All rights reserved.Copyright © 2013 by Educational Testing Service. All rights reserved.
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
Copyright © 2013 by Educational Testing Service. All rights reserved.Copyright © 2013 by Educational Testing Service. All rights reserved.
• 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.