Learning Maps: Tools for

Formative Assessment

Practice

National Council of Supervisors of Mathematics

2014 Annual Meeting

New Orleans, LA

Angela Broaddus, Ph.D.

Julia Shaftel, Ph.D.

Anu Sharma, Ph.D.

Zachary Conrad, M.Ed.

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Who We Are

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Key Features of the DLM

• Learning maps

• Testlets

• Instructional relevance

• Embedded and year-end assessments

• Multiple entry points

• Dynamic assessment

• Assessment technology system (KITE)

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Connected Knowledge

Demonstrate simple ratio relationship

Recognize unit

Recognize many to one ratio

Partition shape into equal parts

Explain unit

fraction

Explain ratio

Extend number pattern

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A Portion of the Math Learning Map

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Components of the Learning Map

• Nodes specify individual skills and understandings that were drawn from the research in Mathematics and English Language Arts.

• Connections indicate relationships between nodes and are indicated by arrows in the learning map.

• Alternate pathways acknowledge that students do not all necessarily follow the same sequence of learning.

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Quick Facts about the Mathematics Map

• 141 foundational nodes

• 2,316 mathematics

nodes

• 4,838 connections

HOW DOES THE MAP RELATE TO

THE FORMATIVE ASSESSMENT?

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Formative Assessment

“Formative assessment is a process used by teachers and students during instruction that provides feedback to adjust ongoing teaching

and learning to improve students’ achievement of intended instructional

outcomes.”

CCSSO (2012)

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Key Elements of Formative

Assessment

• Systematic collection of evidence of student learning

• Quality teacher feedback provided to students

• Involvement of students in the assessment and learning process

Heritage (2008)

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Attributes of Formative Assessment

• Learning goals and criteria for success should be clearly identified and communicated to students.

• Learning progressions should clearly articulate the sub-goals of the ultimate learning goal.

• Evidence of learning is elicited during instruction in terms of the steps outlined in the learning progression.

FAST SCASS (2012)

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Attributes of Formative Assessment

• Descriptive feedback should be provided with evidence-based feedback that is linked to the intended instructional outcomes and criteria for success.

• Self- and peer-assessment are important for providing students an opportunity to think meta-cognitively about their learning.

• Collaboration – A classroom culture in which teachers and students are partners in learning should be established.

FAST SCASS (2012)

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Learning Goals in the Learning Map

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Fractions Case Study

Count by fractional parts

Calculate least common

denominator

Explain the fraction relationship x/y

Explain common denominator

Explain least common

denominator

Explain unit fraction

Recognize fraction as division

Calculate common denominator

Add/subtract fractions with common denominators

Add/subtract fractions with unlike

denominators

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Activity

• How does the learning map help you collect evidence of student thinking and learning in: – place value?

– operations with fractions?

– operations and algebraic thinking?

• Select at least two nodes and design two interactive activities for each node that would elicit evidence of student thinking.

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Discussion

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How the Map Supports Teachers’

Formative Assessment Practice?

• Deepen mathematical content

knowledge

• Recognize learning sequences made

explicit in the map

• Raise awareness about prerequisite skills

and connections to future learning

• Identify voids in student understanding

• View multiple pathways in support of

differentiated instruction

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Thank you!

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References

FAST SCASS. (2012). Distinguishing formative assessment from other educational assessment labels. Retrieved on 03/25/2014 from http://www.ccsso.org/Resources/Publications FAST SCASS. (2008). Attributes of effective formative assessment. Retrieved on 03/25/2014 from http://www.ccsso.org/Resources/Publications Heritage, M. (2008). Learning progressions: Supporting instruction and formative assessment. Retrieved on 03/25/2014 from http://www.ccsso.org/Resources/Publications