math assessments increasing rigor february 20, 2013 & february 21, 2013
TRANSCRIPT
Math Assessme
ntsIncreasing RigorFebruary 20, 2013
&February 21, 2013
Task Sort ActivityDirections: 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
Discussing the Task SortTask A B C D E F G H I J
Low
High
Criteria for a low level task
Criteria for a high level task
Math Assessments & Rigor
Discussing the Task SortTask A B C D E F G H I J
Low
High
Criteria for a low level task
Computation, mechanical explanationsOne step, roteSkill oriented, Clear directions/taskBasic concepts
Criteria for a high level task
Multi-task, reasoning, connections, stepsInterpret/process info/analyzeJustifyCreate ‘new’ itemExtraneous info included
Math Assessments & Rigor
Task Analysis GuideLower-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
Task Analysis GuideHigher-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 solutionsAdapted 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
Instruction, Assessment, and Backwards Design
STEPS1. Analyze an SOL and Curriculum Framework
- what students should be able to do
2. Brainstorm ways to assess the SOL3. Develop an assessment4. Brainstorm instructional strategies 5. Develop instructional resources/lesson plans
Math Assessments & Rigor
1. Identify the nouns and verbs in the SOL2. Review the Curriculum Framework3. Examine the Essential Knowledge and Skills4. 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 SOLWhat should students be able to
do?
Math Assessments & Rigor
Assessment Templates
Math Assessments & Rigor
Instruction, Assessment, and Backwards Design
STEPS1. Analyze an SOL and Curriculum Framework
- what students should be able to do
2. Brainstorm ways to assess the SOL3. Develop an assessment4. Brainstorm instructional strategies 5. Develop instructional resources/lesson plans
Math Assessments & Rigor
SlopeComparative 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.
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
Modifying Assessment Items
Math Assessments & Rigor
Modifying Assessment Items
Math Assessments & Rigor
Modifying Assessment Items
Math Assessments & Rigor
Modifying Assessment Items
Math Assessments & Rigor
Modifying Assessment Items
Math Assessments & Rigor
Modifying Assessment Items
Math Assessments & Rigor
Where can I get ideas for quality assessment items?
NAEP released items (searchable database) http://nces.ed.gov/nationsreportcard/
PISA released items http://www.oecd.org/dataoecd/14/10/38709418.pdf
APEC Mathematics Assessment Database http://hrd.apec.org/index.php/Mathematics_Assessments
Heinemann Mathematics (not free, but cheap) 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
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Math Assessments & Rigor
Instruction, Assessment, and Backwards Design
STEPS1. Analyze an SOL and Curriculum Framework
- what students should be able to do
2. Brainstorm ways to assess the SOL3. Develop an assessment4. Brainstorm instructional strategies 5. Develop instructional resources/lesson plans
Math Assessments & Rigor
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
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
Assessment Templates
http://teachers.henrico.k12.va.us/math/Teacher/Materials11.html
Math Assessments & Rigor
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
1. Analyze an SOL and Curriculum Framework- what students should be able to do
2. Brainstorm ways to assess the SOL3. Develop assessment items4. Brainstorm instructional strategies 5. Develop instructional resources
Math Assessments & Rigor
Instruction, Assessment, and Backwards Design
1. Analyze an SOL and Curriculum Framework- what students should be able to do
2. Brainstorm ways to assess the SOL3. Develop assessment items4. Brainstorm instructional strategies 5. Develop instructional resources
Math Assessments & Rigor
Instruction, Assessment, and Backwards Design