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

2. 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)

3. MAC Update 2012 50 School Districts plus other states
65,000 students locally
teachers locally
Now include grades Kinder through Algebra 2

4. 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

5. 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

6. 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
Notes on study in Australia. Correlation to STAR testing. Predicting goes only one way. False positive.

7. 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

8. 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.

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

10. Leading Scoring is a difficult job.
Phases of a Scoring Session
Understanding the Audience
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

11. 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.

12. 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?

13. 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?

14. 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

15. 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).
Think about this task. What might your students do?

16. America - country of lawyers, didactic contract what is the minimum that meets each word of the task.

17. Australia - show thinking and how numbers are derived.

18. Netherlands- show thinking and fit a real world context.
Sweden - opportunity to show off what knowledge? Think of extensions or further exploration.

19. 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.

20. 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

21. 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

22. 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

23. 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?

24. 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

25. “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

26. 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

27. 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.

28. 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

29. The Party
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? ____________.
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? ________________.
4. They just remembered to buy a 50¢ party bag for each friend. Show how to find the total cost for the party.

30. The Party The Party - Pts Section 1. 11 people 1 2. $2.25
2. $2.25
Shows work such as:
$ ¢ 2
3. $24.75
11 • $2.25
1 f.t. 3
4. Shows work such as:
11 • 50¢ = $4.50
$ $24.75 = $29.25
partial credit
only shows 11 • 50¢
(1)
Total Points 8
The Party
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? ______.
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.
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.

31. The Party The Party - Pts Section 1. 11 people 1 2. $2.25
2. $2.25
Shows work such as:
$ ¢ 2
3. $24.75
11 • $2.25
1 f.t. 3
4. Shows work such as:
11 • 50¢ = $4.50
$ $24.75 = $29.25
partial credit
only shows 11 • 50¢
(1)
Total Points 8
The Party
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
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.
$ ¢ = $2.50
3. 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 • $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.
11 • 50¢ = $4.50 √ 1 x 1 √ √
1 ft 2 √ √
(1) x 6