2013 Mathematics Standards of Learning Institutes Analyzing and Modifying Assessments.

2013 Mathematics Standards of Learning Institutes

Analyzing and Modifying Assessments

Learning OutcomesParticipants will be able to• analyze assessments • modify existing assessments to raise the level

of cognitive demand• modify existing resources to promote problem

solving

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Assessment AnalysisSample Assessment• Is this a good assessment? Complete the

assessment individually and then discuss in small groups.

• Be able to justify your group’s conclusions.

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Assessment AnalysisShare and Reflect• Share your conclusions and justifications with

the whole group

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Assessment Analysis Guiding Questions• SOL Alignment

– Does the assessment assess the standard?– Does the assessment assess targeted components

of the Essential Knowledge and Skills found in the Curriculum Framework?

– Does the assessment reflect the requirements of the verbs found in the Curriculum Framework?

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Assessment Analysis Guiding Questions• Level of Cognitive Demand

– Does the assessment have an appropriate variety of questions requiring various levels of cognitive demand?

– Does the assessment require students to explain, justify, and use multiple representations?

• Format – Does the assessment provide various ways for students

to demonstrate understanding? (open response, multiple choice, fill-in-the-blank, shading, sorting, etc)

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Assessment Analysis – Level of Cognitive DemandSmall Group discussion• Brainstorm and record characteristics of

mathematics tasks/problems that require a high level of cognitive demand.

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Assessment Analysis – Level of Cognitive DemandShare and Reflect• Share your conclusions and justifications with

the whole group

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Characteristics of Lower-level Tasks• Involve recall or memory of facts, rules, formulae,

procedures, or definitions• Involve exact reproduction of previously seen-material• No connection of facts, rules, formulae, procedures, or

definitions to concepts or underlying understandings.• Require limited cognitive demand• Focused on producing correct answers rather than

developing mathematical understandings• Require no explanations or explanations that focus only

on describing the procedure used to solve

9Adapted from Stein, M.K., Smith, M.S., Henningsen, M.A., & Silver, E.A. (2000). Implementing standards-based mathematics instruction: A casebook for professional development. New York, NY: Teachers College Press

Characteristics of Higher-level Tasks

• Focus on use of procedures for developing deeper levels of understanding of concepts and ideas

• Suggest broad general procedures with connections to conceptual ideas (not narrow algorithms)

• Provide multiple representations to develop understanding and connections

• Require complex, non-algorithmic thinking and considerable cognitive effort

10Adapted from Stein, M.K., Smith, M.S., Henningsen, M.A., & Silver, E.A. (2000). Implementing standards-based mathematics instruction: A casebook for professional development. New York, NY: Teachers College Press

Characteristics of Higher-level Tasks• Require exploration and understanding of concepts,

processes, or relationships• Require accessing and applying prior knowledge and relevant

experiences to facilitate connections and problem solving• Require task analysis and identification of limits to solutions

11Adapted from Stein, M.K., Smith, M.S., Henningsen, M.A., & Silver, E.A. (2000). Implementing standards-based mathematics instruction: A casebook for professional development. New York, NY: Teachers College Press

DOING

Mathematics

Assessment AnalysisSmall Group discussion• Identify whether or not each problem is

aligned to the intended SOL, using the Curriculum Framework to justify.

- and -• Identify the level of cognitive demand of each

problem as “low,” “medium,” or “high.” Be able to justify your groups’ consensus.

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Assessment AnalysisShare and Reflect• Share your conclusions and justifications with

the group

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Assessment Analysis – Level of Cognitive Demand

Discussion• Does the assessment have a variety of

problems requiring various levels of cognitive demand? Is there a balance?

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Level of Cognitive Demand in ActivitiesLe

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Low

Med

Med

High

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Level of Cognitive Demand in ActivitiesLe

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ogni

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and

Simplify.

Is the value of this expression more or less than 1? How do you know?

Write a real-world problem using this expression.

Modifying Assessment Items Group work• Select two of the low-level problems and

modify them to raise the level of cognitive demand to a “high-level.”

• Record your modified problems on the handout to share and on chart paper to post.

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Modifying Assessment ItemsShare and Reflect• Share your modified problems using the

document camera• Post assessment item using chart paper

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Modifying Assessment ItemsReflect• What are some of the strategies you used to

raise the level of cognitive demand?

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• Providing context/requiring application • Choosing numbers intentionally• Increasing the number of required steps• Changing the unknown/given information• Allowing for multiple solutions• Requiring students to explain, justify, and make

connections between representations

Balancing AssessmentsModify the original assessment• Select replacement items from modified

assessments posted to balance the level of cognitive demand required in the assessment.

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