The Essential Skillof Mathematics

Using the Math Scoring Guide: An Introduction for High School Content Teachers

1. IntroduceOregon’s Math Problem Solving Scoring GuidePrinciples of math instruction and assessment

in content area classesClassroom uses of the Math Scoring Guide

2. ExamineEssential Skill of Mathematics requirementsStudent work samples

3. 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 and

accurately

• (C) Apply mathematics

OAR: 581-22-0615

Essential Skill DefinitionApply 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 defendthe verified process

Essential Skill Proficiency

1. OAKS Statewide Mathematics Assessment

• Score of 236 or higher

2. Other approved standardized assessments

Three options for diploma requirement Test 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 earn a score of 4 or higher in each dimension for 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 LOOK AT 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 solving the problem

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

Communicating Reasoning

Clearly identify and support the 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 mathematics5 – Thoroughly developed4 – Work is proficient (not perfect)3 – Work is partially effective or partially complete2 – Work is underdeveloped or sketchy1 – Work is ineffective, minimal,

or not-evident

What does a Math Work Sample look like?

Mathematics Problem SolvingWork Samples

•Present complex, often multi-step tasks that could not be presented in a multiple choice test format

•Designed to judge student abilities to apply specific knowledge & skills

•Allow a variety of problem-solving approaches

•May simulate real-word mathematics problems

Mr. Gerard’s Oil TankMr. Gerard bought a

house that contained an empty heating oil tank with the dimensions shown in the drawing. The left and right arcs of the tank are perfect semi-circles. If heating oil costs $3.50 per gallon, how much would it cost Mr. Gerard to fill this tank? (There are 231 cubic inches in a gallon.)

Share your solution!

Scoring the First Anchor PaperThis anchor paper met the achievement standard in each dimension of the scoring guide.

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 Dimensions . . .What differentiates a 3 from a 4?

Scoring

Scoring Papers 3, 4, & 5 Use the scoring guide to rate each paper.

What scores did these papers earn?

Roof VentsHow many roof vents will it take to properly vent an attic with a span of 32 feet, a length of 62 feet, and an 8/12 roof pitch? Industry standards determine that one vent is needed for every 660 cubic feet of air space.

Share your solution!

Scoring the First Anchor Paper

This anchor paper almost met the achievement standard.

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.

Scoring Papers 3, 4, & 5 Use the scoring guide to rate each paper.

What scores did these papers earn?

Purposes1. Instructional Tool2. Formative Assessment3. Summative Assessment4. Demonstrate Proficiency in the

Essential Skill of Apply Math to earn an Oregon Diploma

The Mathematics Scoring Guide

Multiple Uses for the Scoring Guide Instructional Tool

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

from website or other examples

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 AssessmentThe Scoring Guide can

help to identify strengths and weaknesses.

Students learn where to focus to improve math skills.

Teachers learn where additional instruction is needed.

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. Highlighting Oregon’s Scoring

GuideSTUDENT REVISION:3. Students are allowed to revise

and resubmit their work samples following scoring/feedback.

4. Most papers should be revised only 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 yourinformation here)

Resources & Coming Attractions

A Parting Thought

The cowboys have a way of trussing up a steer or a pugnacious bronco which fixes the brute so that it can neither move nor think.  This is the hog-tie, and it is what Euclid did to geometry.

~Eric Bell, The Search for Truth