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Welcome Math Leaders Mac Scoring Training Year 14 …analyzing student thinking and improving instruction
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)
MAC Update 2012 • • 50 School Districts plus other states 65, 000 students locally 1500 -1600 teachers locally Now include grades Kinder through Algebra 2
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
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
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
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
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.
You’re the District Ambassadors! • Promote reliability and consistency. • Provide opportunities for professional development in mathematics and reflections and insights for improving instruction.
Leading Scoring is a difficult job. Phases of a Scoring Session • Resistance • Search for evidence • Ideas for changing classroom instruction Understanding the Audience • Care about students • Desire for student success • Uncomfortable with the mathematics • Change from normal classroom practices
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.
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?
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?
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
Didactic Contract Fred’s Flat Fred’s flat has five rooms. The total floor area is 60 sq. meters. Draw a plan of Fred’s flat. Label each room and show the dimensions (length and width of all rooms).
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.
Task Design • Entry level part - allow access • Ramp up - not all parts are equal • Meeting Standards - not based on percentage - so doesn’t meet that internal rubric of 90% A • Meeting Standards based on professional judgment of National Board
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
Professional Development Opportunities to Learn • Every square has two sides plus the two pieces at the end of the row: 2 X+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
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?
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
“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
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 don’t benefit from your ideas or questions
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 thinktime to see if you can find a reason for the official scoring decision. Then we will have an open discussion of the issue.
Scoring Marks √ x √ft ^ () m. r. correct answer or comment incorrect answer or comment correct answer based upon previous incorrect answer called a follow through correct but incomplete work - no credit points awarded for partial credit. student misread the item. Must not lower the demands of the task -1 deduction
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 you figured it out. 3. How much will it cost for everyone to have a cupcake and soda? ________. Show you figured it out. 4. They just remembered to buy a 50¢ party bag for each friend. Show to find the total cost for the party.
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 person? _____. Show you figured it out. The Party - Pts 1. 11 people 1 1 How much will it cost for everyone at the party to have a cupcake and soda? _____. Show you figured it out. 2. $2. 25 1 Shows work such as: $1. 50 + 75¢ 3. Sec tion 1 3. $24. 75 1 f. t. Shows work such as: 11 • $2. 25 2 2 3 4. They just remembered to buy a 50¢ party bag for everyone at the party. Show to find the total cost for the party. 4. Shows work such as: 11 • 50¢ = $4. 50 + $24. 75 = $29. 25 2 partial credit only shows 11 • 50¢ (1) 2 Total Points 8
The Party - The Party 1. 2. 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 √ 1 They are buying cupcakes and cans of soda. Cupcakes cost $1. 50 and soda costs 75¢. How much does it cost person? $2. 50. Show you figured it out. x 3. How much will it cost for everyone at the party to have a cupcake and soda? $27. 50 √ Show you figured it out. 11 • $2. 50 4. √ 1 2. $2. 25 1 Shows work such as: $1. 50 + 75¢ 1 3. $24. 75 1 f. t. Shows work such as: 11 • $2. 25 2 0 1 ft 4. Shows work such as: 11 • 50¢ = $4. 50 + $24. 75 = $29. 25 (1) x 2 3 2 They just remembered to buy a 50¢ party bag for everyone at the party. Show to find the total cost for the party. 11 • 50¢ = $4. 50 √ 1. 11 people Sec tion 1 1 $1. 50 + 75¢ = $2. 50 √ Pts 2 partial credit only shows 11 • 50¢ (1) 2 6 Total Points 8