Welcome Math Leaders

Mac Scoring TrainingYear 17

…analyzing student thinking and improving instruction

What is MARS?

• Mathematics Assessment Resource Service• MAC = Mathematics Assessment Colloborative,

part of the Silicon Valley Mathematics Initiative –Districts throughout California

MAC Update 2015

• Over 150 School Districts• 65,000 students• Grown from 3,5,7, and 9• Now include grades kinder, first through –

Algebra 2 with special high school version for Integrated Courses

• Written to Common Core Standards and Mathematical Practices

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

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.

• 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

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• This year’s test is written to Common Core

Standards and Mathematical Practices

Mathematical Practices

• Make sense and persevere.• Reason abstractly and quantitatively.• Construct viable arguments.• Use appropriate tools.• Attend to precision.• Look for and make use of structure.• Look for express regularity.

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

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?

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

Developing Common Standards

• Takes more than writing standards• Tasks help define the language of the

standards• Rubrics help express changes in expectations

as students move up in grade levels• Gives us an opportunity to discuss values

explicitly – develop a common understanding as a professional community

Goals for the Day

• To develop a consistent approach to scoring tasks, understanding the underlying big mathematical ideas, and fairly scoring student work.

• To make this work, we need to move out the realm of what do I do in my classroom or what might my students do . . . . And think about clarifying questions . . .

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 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.

Helpful Strategies for Running a scoring training session

• Why do you think it was scored that way? • What is the mathematics you want to see or

mathematics being assessed?• What strategies did you use for . . .(get a

collection of strategies to help scorers see and understand student work)

• Make list of equivalent expressions, equations, or strategies

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

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.

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 - Pts Section

1. 11 people 1

1

2. $2.25

Shows work such as: $1.50 + 75¢

1

1 2

3. $24.75

Shows work such as: 11 • $2.25

1 f.t.

23

4. Shows work such as: 9 • 50¢ = $4.50 $4.50 + $24.75 = $29.25

partial credit only shows 9 • 50¢

(Accept 30.25 with correct work)

2

(1)

22

Total Points 8

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.

$1.50 + 75¢ = $2.50

3. How much will it cost for everyone at the party to have a cupcake and soda? $27.50Show how you figured it out.

11 • $2.50

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.

9 • 50¢ = $4.50

The Party - Pts Section

1. 11 people 1

1

2. $2.25

Shows work such as: $1.50 + 75¢

1

1 2

3. $24.75

Shows work such as:11 • $2.25

1 f.t.

23

4. Shows work such as: 9 • 50¢ = $4.50 $4.50 + $24.75 = $29.25

partial credit only shows 9 • 50¢

2

(1)2

Total Points 8

√ 1

√

√

x

√

√

x

0

1

1 ft

2

(1)

6

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

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