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Math Assessments Increasing Rigor February 20, 2013 & February 21, 2013
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Task Sort Activity Directions: Individually, read each task. Sort and record the provided tasks as high or low cognitive demand. Record your answers in the google form. Discuss your results as a table group and come to a consensus. Describe the criteria you used to sort each task. How did you communicate your reasoning to your table group? List the criteria in your task analysis guide. Math Assessments & Rigor
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Discussing the Task Sort TaskABCDEFGHIJ Low High Criteria for a low level task Criteria for a high level task Math Assessments & Rigor
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Discussing the Task Sort TaskABCDEFGHIJ Low High Criteria for a low level task Computation, mechanical explanations One step, rote Skill oriented, Clear directions/task Basic concepts Criteria for a high level task Multi-task, reasoning, connections, steps Interpret/process info/analyze Justify Create ‘new’ item Extraneous info included Math Assessments & Rigor
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Task Analysis Guide Lower-level Demands Involve recall or memory of facts, rules, formulae, or definitions Involve exact reproduction of previously seen material No connection of facts, rules, formulae, or definitions to concepts or underlying understandings. 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 Math Assessments & Rigor
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Task Analysis Guide Higher-level Demands Focus on developing deeper understanding of concepts Use multiple representations to develop understanding and connections Require complex, non-algorithmic thinking and considerable cognitive effort Require exploration of concepts, processes, or relationships Require accessing and applying prior knowledge and relevant experiences to facilitate connections Require critical analysis of the task and solutions 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 DOING Mathematics Math Assessments & Rigor
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Instruction, Assessment, and Backwards Design STEPS 1. Analyze an SOL and Curriculum Framework - what students should be able to do 2. Brainstorm ways to assess the SOL 3. Develop an assessment 4. Brainstorm instructional strategies 5. Develop instructional resources/lesson plans Math Assessments & Rigor
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1. Identify the nouns and verbs in the SOL 2. Review the Curriculum Framework 3. Examine the Essential Knowledge and Skills 4. List at least 5 different things that students should know and be able to do. Good news! The Assessment Templates are already set up for you. Step 1: Analyze the SOL What should students be able to do? Math Assessments & Rigor
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Assessment Templates Math Assessments & Rigor
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Instruction, Assessment, and Backwards Design STEPS 1. Analyze an SOL and Curriculum Framework - what students should be able to do 2. Brainstorm ways to assess the SOL 3. Develop an assessment 4. Brainstorm instructional strategies 5. Develop instructional resources/lesson plans Math Assessments & Rigor
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Slope Comparative Questions What is the slope of the line that passes through the points (2, 3) and (5, 7)? Write a linear equation that is parallel to the given line 3x + 2y = 24. Access ramps must be built to meet specifications with regard to slope. Federal regulations states that for every 12 inches along the base of a ramp, the height cannot rise more than 1 inch. Design an access ramp for a doctor’s office that extends no more than 108 inches. Include your solution and a scaled diagram to illustrate your design.
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Modifying Assessment Items Use these guiding questions to “upgrade” the following SOL questions How could an old test item be revised to reflect the new rigor? How could a test item writer ask this in a TEI format? What types of classroom activities or assessments could I use to prepare students? Math Assessments & Rigor
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Modifying Assessment Items Math Assessments & Rigor
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Modifying Assessment Items Math Assessments & Rigor
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Modifying Assessment Items Math Assessments & Rigor
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Modifying Assessment Items Math Assessments & Rigor
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Modifying Assessment Items Math Assessments & Rigor
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Modifying Assessment Items Math Assessments & Rigor
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Where can I get ideas for quality assessment items? NAEP released items (searchable database) http://nces.ed.gov/nationsreportcard/ http://nces.ed.gov/nationsreportcard/ PISA released items http://www.oecd.org/dataoecd/14/10/38709418.pdf http://www.oecd.org/dataoecd/14/10/38709418.pdf APEC Mathematics Assessment Database http://hrd.apec.org/index.php/Mathematics_Assessments http://hrd.apec.org/index.php/Mathematics_Assessments Heinemann Mathematics (not free, but cheap) http://books.heinemann.com/math/ http://books.heinemann.com/math/ JMU Center for STEM Education Outreach (by SOL in Algebra I, Geometry, Algebra II) http://www.jmu.edu/stem/outreach/features/pivotalquestions. html http://www.jmu.edu/stem/outreach/features/pivotalquestions. html 19 Math Assessments & Rigor
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Instruction, Assessment, and Backwards Design STEPS 1. Analyze an SOL and Curriculum Framework - what students should be able to do 2. Brainstorm ways to assess the SOL 3. Develop an assessment 4. Brainstorm instructional strategies 5. Develop instructional resources/lesson plans Math Assessments & Rigor
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Practice SOL Items It is essential that students have experiences with the Practice SOL Items prior to testing. http://www.doe.virginia.gov/testing/sol/practice_items/index.shtml http://www.doe.virginia.gov/testing/sol/practice_items/index.shtml Use of the Practice Item Guides is STRONGLY recommended. Practice Item Guides provide: Guided practice with tools Information specific to TEI functionality Information on item format Math Assessments & Rigor
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Assessment Templates http://teachers.henrico.k12.va.us/math/Teacher/Materials11.html Math Assessments & Rigor
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TEI Creation Math Assessments & Rigor 1. Download the ActivInspire template from the Math Assessments blog posting on the HCPS math website. 2. Individually or as a group, convert the questions to TEI items. Sample Hot Spot Problem
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1. Analyze an SOL and Curriculum Framework - what students should be able to do 2. Brainstorm ways to assess the SOL 3. Develop assessment items 4. Brainstorm instructional strategies 5. Develop instructional resources Math Assessments & Rigor Instruction, Assessment, and Backwards Design
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1. Analyze an SOL and Curriculum Framework - what students should be able to do 2. Brainstorm ways to assess the SOL 3. Develop assessment items 4. Brainstorm instructional strategies 5. Develop instructional resources Math Assessments & Rigor Instruction, Assessment, and Backwards Design
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