The Essential Skillof MathematicsUsing the New Math Scoring Guide:

An Introduction for High School Math Teachers

1. ReviewOregon’s Math Problem Solving Scoring GuideClassroom uses of the Math Scoring GuideSupporting colleagues in using math work samples in

content classes

2. UnderstandOptions for Demonstrating Proficiency in the Essential

Skill of Mathematics for the Oregon Diploma

3. Score student papers and calibrate to scoring standards

4. Set the stage for follow-up training

Goals for this workshop

For students first enrolled in grade 9 during the 2010-2011 school year [and subsequent years], school districts and public charter schools shall require students to demonstrate proficiency in the Essential Skills listed

• (A) Read and comprehend a variety of text; and

• (B) Write clearly andaccurately

• (C) Apply mathematics

OAR: 581-22-0615

Essential SkillDefinition

Apply Mathematicsin a variety of settings

Interpret a situation and apply workable mathematical concepts and strategies, using appropriate technologies where applicable.

Produce evidence, such as graphs, data, or mathematical models, to obtain and verify a solution.

Communicate and defend the verified process

The Common Core State Standards For Mathematics

describe varieties of expertise... that rest on important “processes and proficiencies” …[including the] NCTM process standards of

–problem solving–reasoning and proof–communication–representation–and connections

Make sense of problems and persevere in solving them

“Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution….

They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt.”

1. Make sense of problems and persevere in

solving them.

2. Reason abstractly and quantitatively.

3. Construct viable arguments and critique

the reasoning of others.

4. Model with mathematics.

5. Use appropriate tools strategically.

6. Attend to precision.

7. Look for and make use of structure.

8. Look for and express regularity in

repeated reasoning.

Mathematical Practices

From Common Core State Standards for Mathematics

Essential Skill Proficiency

Three options for diploma requirement

1. OAKS Statewide Mathematics Assessment• Score of 236 or higher

2. Other approved standardized assessmentsTest Score

ACT or PLAN 19/19

WorkKeys 5

Compass 66 (College Alg. test)

Asset 41 (Int. Alg. test)

SAT/PSAT 450/45

AP & IB various

Option 3 Math Work Samples

Students must earna score of 4 or higherin each dimensionfor each work sample

Two Mathematics Work Samples Required: algebra, geometry, statistics

Mathematics Work Sample scored using Official State Scoring Guide

Work samples must meet the level of rigor required on the OAKS assessment.

Work samples provide an optional means to demonstrate proficiency not an easier means.

Level of Rigor

LET’S REVIEW THE SCORING GUIDE !

Background In use since 1988 (minor

revisions in 2000) 2009-2010 new version based

on Oregon Mathematics Content Standards

2010-11 aligned to the Common Core State Standards

Adopted by Oregon State Board of Education May 2011

The Math Problem Solving Scoring Guide

Mathematics Problem Solving Scoring Guide

Making Sense of the Problem

Representing and Solving the Problem

Communicating Reasoning

Accuracy

Reflecting and Evaluating

Interpret the concepts of the task and translate them into mathematics

Making sense of the problem

Use models, pictures, diagrams, and/or symbols to represent the problem and select an effective strategy to solve the problem.

Representing and solvingthe problem

Communicate mathematical reasoning coherently and clearly use the language of mathematics.

Communicating Reasoning

Clearly identify and supportthe solution.

Accuracy

State the solution in the context of the problem.

Defend the process. Evaluate and interpret the reasonableness of the solution

Reflecting and Evaluating

Simplified Mathematics Scoring Guide

Beginning1

2

3

4

5

Emerging

Developing

Proficient

Strong

6Exemplary

Another way to

look at scores

6 −Enhanced or connected to other mathematics

5 – Thoroughly developed

4 – Work is proficient (not perfect)

3 – Work is partially effective or partially complete

2 – Work is underdeveloped or sketchy

1 – Work is ineffective, minimal,

or not-evident

What does a Math Work Sample look like?

Mathematics Problem Solving Work Samples

•Present complex, multi-step tasks•Are designed to judge student abilities to apply specific knowledge & skills

•Allow a variety of problem-solving approaches

•May simulate real-word mathematics problems

Farmer JohnThe Task: Farmer John has a rectangular holding pen that measures 10 yards long and 5 yards wide to contain his cattle. He is acquiring more cattle from the neighboring farmer and wants to add the same amount of fencing to each side to create a new holding pen that encloses 176 square yards. How much should Farmer John add on to each side of his existing holding pen to achieve his goal?

• Share your solution

Share your solution!

Scoring the First Anchor Paper

This anchor paper met the achievement standard in each trait.

Why did this paper earn these scores?

Scoring the 2nd Anchor Paper

What scores did this paper earn?

This anchor paper did not meet the achievement standard.

Within the Traits . . .What differentiates a 3 and a 4?

Scoring

Scoring Papers 3, 4, & 5 Use the scoring guide to

rate each paper. What scores did

these papers earn?

Bike RentalA local bicycle rental company charges $12 to rent a bicycle. They normally have 300 rentals per month. The company owner has determined that each increase in price of $2 will decrease the number of rentals by 15. What price will maximize the revenue?

Share your solution!

Scoring the First Anchor Paper for Bike Rental

This anchor paper met the achievement standard in each trait.

Why did this paper earn these scores?

Scoring the 2nd Anchor PaperFor Bike Rental

What scores did this paper earn?

This anchor paper also met the achievement standard.

Scoring Papers 8, 9, & 10

Use the scoring guide to rate each paper.

What scores did these papers earn?

Purposes

1. Instructional Tool

2. Formative Assessment

3. Summative Assessment

4. Demonstrate Proficiency in the Essential Skill of Apply Math to earn an Oregon Diploma

The Mathematics Scoring Guide

Building Consensus on Definitions of Assessments

Assessment Purpose When Administered?

ScreeningIdentify students at risk of mathematics difficulties & provides info to target instruction for all students

Beginning of year or semester; when new students arrive

FormativeSupports learning and informs instruction

Embedded directly in instruction to inform teacher decisions

Multiple Uses for the Scoring Guide

Instructional Tool• Makes targets explicit to students• Opportunities to show students models

from website or other examples Screening Tool

• Help determine likelihood of reaching proficiency – on target, need assistance, at risk

• Help determine whichstudents need additionalinstruction and coaching

Building Consensus on Definitions of Assessments

Assessment Purpose When Administered?

Interim and Predictive

Determine the progress of individuals or groups of students based on focused elements of content

Occasional, based on curriculum & other instructional milestones

SummativeDetermine how much knowledge and skills individuals or groups of students (e.g. programs, schools, districts and states) have acquired.

Periodically after a substantial period of time (e.g. end of the year and end of course).

Multiple Uses for the Scoring Guide

Formative & Interim Assessments– Inform instructional strategies– Provide data on student progress

Classroom/ Summative Assessment– End of unit, course, etc. or Essential Skills

Formative Assessment

The Scoring Guide can help to identify math strengths and weaknesses.

Students learn where to focus to improve math skills.

Teachers learn where additional instruction is needed.

AssessmentDoes your school have an assessment plan? Explain

Does your school have a data analysis & use plan? Explain

Benchmark

Formative

Interim and Predictive

Summative

Requirements for Essential Skill Proficiency UsingMath Work Samples

2 work samples −Algebra, geometry, or statistics

Score of 4 or higher in all dimensions on Official Scoring Guide

• Math Problem Solving Tasks must be carefully designed to provide opportunities for students to demonstrate skills in all dimensions of the scoring guide.

• Math tasks must be at the appropriate difficulty level and address high school content standards.

Work Sample Design

Administration

Work samples must be the product of an individual

Work samples must be supervised by an authorized adult;

Students may not work on work samples outside a supervised setting.

Work Sample Implementation

Scoring All work samples must be

scored using Oregon’s Official Math Scoring Guide.

All raters must have beentrained to use the Scoring Guide.

Only one set of scores is required for a work sample. (Districts may want more than one rater for borderline papers.)

Work Sample Implementation

Feedback and Revision 

FEEDBACK: Only 2 options1. Oregon’s Official Scoring Form2. Oregon’s Scoring Guide (highlight/underline)

STUDENT REVISION:3. Students are allowed to revise and resubmit

their work samples following scoring/feedback.

4. Most papers should be revisedonly once.

Work Sample Implementation

ODE Website: www.ode.state.or.us/go/worksamples

OCTM Website:

http://www.octm.org/ Follow-up workshops

(List any scheduled)Contact information

(List your information here)

Resources & Coming Attractions

It is the duty of all teachers, and of

teachers of mathematics in particular,

to expose their students to problems

much more than to facts.- Paul Halmos

A Parting Thought