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Welcome Math Leaders Mac Scoring Training Year 14 …analyzing student thinking and improving instruction

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What is MARS? Mathematics Assessment Resource Service - Nottingham, England not outer space MAC = Mathematics Assessment Colloborative, part of the Silicon Valley Mathematics Initiative - Marin, San Mateo, Santa Clara, Santa Cruz, Alameda Counties, Contra Costa County, and Monterey County Tests are often called MAC tests or BAM (Balanced Assessment in Mathematics)

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MAC Update School Districts plus other states 65,000 students locally teachers locally Now include grades Kinder through Algebra 2

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MAC Core Ideas TIMMS results 5 areas of emphasis –Number Properties –Number Operations (Mathematical Reasoning) –Algebra –Geometry –Data and Statistics (Probability) –This year test was designed to the new National Core Standards in Mathematics

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Why more tests? Difference between Standardized Tests and purposes and Performance Testing and purposes Learning from student work Developing meaningful feedback for students and teachers

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Goals of Assessment We must ensure that tests measure what is of value, not just what is easy to test. If we want students to investigate, explore, and discover, assessment must not measure just mimicry mathematics. Everybody Counts

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Link Assessment and Learning Assessment should be an integral part of teaching. It is the mechanism whereby teachers can learn how students think about mathematics as well as what students are able to accomplish. Everybody Counts

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Purpose of Scoring Gather data about student thinking to inform and improve instruction. Rubrics designed by international team to reflect shared values and perspectives. Rubrics provide one means of analyzing student work and giving teachers feedback. Scoring consistency allows us to capture data and gain insight into student thinking.

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Youre the District Ambassadors! Promote reliability and consistency. Provide opportunities for professional development in mathematics and reflections and insights for improving instruction.

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Leading Scoring is a difficult job. Resistance Search for evidence Ideas for changing classroom instruction Care about students Desire for student success Uncomfortable with the mathematics Change from normal classroom practices Phases of a Scoring Session Understanding the Audience

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Changing the Didactic Contract: For most teachers and students, this is changing what is fair or normal to ask in the classroom. This is no longer business as usual. Change is uncomfortable.

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What does it mean to understand a mathematical idea? Think of mathematics as a set of tools. Tool Possession? Tool Understanding? Tool Application? Tool Selection?

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What it means to do mathematics The Verbs of Mathematics: conjecture, solve, justify, represent, explain, describe, verify, use… Expanding the Didactic Contract - What is considered fair and reasonable in your classroom?

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Changing the Didactic Contract What is fair to ask in the classroom? –Types of tasks –Types of task demands What is needed to justify an answer? Different from curriculum specific tests/rather a check for transference Opportunity to show off what you know

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Didactic Contract Freds Flat Freds flat has five rooms. The total floor area is 60 sq. meters. Draw a plan of Freds flat. Label each room and show the dimensions (length and width of all rooms).

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Scoring Principles Different from other scoring systems Points are awarded throughout a task to emphasize varying aspects of doing mathematics Is there more evidence of understanding or not understanding? Mathematically equivalent expressions or alternative strategies get full credit. If you need to debate what the student was doing, the explanation was not complete.

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Task Design Entry level part - allow access Ramp up - not all parts are equal Meeting Standards - not based on percentage - so doesnt meet that internal rubric of 90% A Meeting Standards based on professional judgment of National Board

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Rubrics Embody value judgments and explicit Computation and representation How to tackle an unfamiliar problem Interpret and evaluate solutions Communicate results and reasoning to others Carefully considered evaluation of performance

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Professional Development Opportunities to Learn Every square has two sides plus the two pieces at the end of the row:2X+2 The end squares have three sides, middle squares have two sides: 2(X-2) + 6 The right end square has three sides, middle squares have two sides and the right end square one extra piece: 2(X-1) + 4

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Take time to examine student work. Ask teachers to analyze student understandings and misconceptions. Think about what strategies helped students who were successful. What experiences do students need to help overcome the misconceptions?

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Reliability Issues Green Sheets - are participants consistent enough to start scoring real student work Post new solutions/solutions paths as they are discovered & other decisions Reliability checks within the session –First folders –Periodic spot checks –Re-calibrate after breaks

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Effective mathematics teaching requires understanding what students know and need to learn and then challenging and supporting them to learn it well. Assessment should support the learning of important mathematics and furnish useful information to both teachers and students. NCTM Principles and Standards

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Scoring Norms Resist side conversations: The dilemma and making your own choice is part of the learning. When you talk over scoring with a neighbor the rest of us dont benefit from your ideas or questions

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Scoring Norms Work task, then take a moment to write out the big mathematical ideas being assessed. When there is a question, everyone should take a moment of quiet think- time to see if you can find a reason for the official scoring decision. Then we will have an open discussion of the issue.

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Scoring Marks correct answer or comment x incorrect answer or comment ft correct answer based upon previous incorrect answer called a follow through ^ correct but incomplete work - no credit ( )points awarded for partial credit. m.r. student misread the item. Must not lower the demands of the task -1 deduction

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The Party 1.Darren and Cindy are planning a party for their friends. They have 9 friends coming to the party. How many people will be at the party? ____________. 2.They are buying cupcakes and cans of soda. Cupcakes cost $1.50 and soda costs 75¢. How much does it cost for each person? __________. Show how you figured it out. 3.How much will it cost for everyone to have a cupcake and soda? ________________. Show how you figured it out. 4. They just remembered to buy a 50¢ party bag for each friend. Show how to find the total cost for the party.

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The Party 1.Darren and Cindy are planning a party for their friends. They have 9 friends coming to the party. How many people will be at the party? ______. 2.They are buying cupcakes and cans of soda. Cupcakes cost $1.50 and soda costs 75¢. How much does it cost per person? __________. Show how you figured it out. 3.How much will it cost for everyone at the party to have a cupcake and soda? __________. Show how you figured it out. 4. They just remembered to buy a 50¢ party bag for everyone at the party. Show how to find the total cost for the party. The Party - PtsSec tio n people $2.25 Shows work such as: $ ¢ $24.75 Shows work such as: 11 $ f.t Shows work such as: 11 50¢ = $4.50 $ $24.75 = $29.25 partial credit only shows 11 50¢ 2 (1) 2 Total Points8

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The Party 1.Darren and Cindy are planning a party for their friends. They have 9 friends coming to the party. How many people will be at the party? 11 2.They are buying cupcakes and cans of soda. Cupcakes cost $1.50 and soda costs 75¢. How much does it cost per person? $2.50. Show how you figured it out. $ ¢ = $ How much will it cost for everyone at the party to have a cupcake and soda? $27.50 Show how you figured it out. 11 $ They just remembered to buy a 50¢ party bag for everyone at the party. Show how to find the total cost for the party ¢ = $4.50 The Party - PtsSec tio n people $2.25 Shows work such as: $ ¢ $24.75 Shows work such as: 11 $ f.t Shows work such as: 11 50¢ = $4.50 $ $24.75 = $29.25 partial credit only shows 11 50¢ 2 (1) 2 Total Points8 1 x x ft 2 (1) 6

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