2013 Mathematics Standards of Learning Institutes Analyzing and Modifying Assessments

Learning Outcomes Participants will be able to analyze assessments modify existing assessments to raise the level of cognitive demand modify existing resources to promote problem solving

Assessment Analysis Sample Assessment Morning Session Assessment Analysis Sample Assessment Is this a good assessment? Complete the assessment individually and then discuss in small groups. Be able to justify your group’s conclusions. Method of sharing varies

Assessment Analysis Share and Reflect Morning Session Assessment Analysis Share and Reflect Share your conclusions and justifications with the whole group

Assessment Analysis Guiding Questions Morning Session 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? Wrap in the vertical articulation documents

Assessment Analysis Guiding Questions Morning Session 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)

Assessment Analysis – Level of Cognitive Demand Morning Session Assessment Analysis – Level of Cognitive Demand Small Group discussion Brainstorm and record characteristics of mathematics tasks/problems that require a high level of cognitive demand.

Assessment Analysis – Level of Cognitive Demand Morning Session Assessment Analysis – Level of Cognitive Demand Share and Reflect Share your conclusions and justifications with the whole group

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 Adapted 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 Adapted 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 DOING Mathematics Adapted 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

Assessment Analysis Small Group discussion Morning Session Assessment Analysis Small 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.

Assessment Analysis Share and Reflect Morning Session Assessment Analysis Share and Reflect Share your conclusions and justifications with the group Record responses somewhow.

Assessment Analysis – Level of Cognitive Demand Morning Session 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? Record responses somewhow.

Level of Cognitive Demand in Activities High Level of Cognitive Demand Med Med Low

Level of Cognitive Demand in Activities Write a real-world problem using this expression. Is the value of this expression more or less than 1? How do you know? Simplify.

Modifying Assessment Items Morning Session 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. Need a balance of cognitive demand on the assessment

Modifying Assessment Items Morning Session Modifying Assessment Items Share and Reflect Share your modified problems using the document camera Post assessment item using chart paper

Modifying Assessment Items Morning Session Modifying Assessment Items Reflect What are some of the strategies you used to raise the level of cognitive demand? 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 Record responses somehow.

Balancing Assessments Morning Session Balancing Assessments Modify the original assessment Select replacement items from modified assessments posted to balance the level of cognitive demand required in the assessment.