the essential skill of mathematics
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The Essential Skill of Mathematics. Using the Math Scoring Guide: An Introduction for High School Content Teachers. Goals for this workshop. 1 . Introduce Oregon’s Math Problem Solving Scoring Guide Principles of math instruction and assessment in content area classes - PowerPoint PPT PresentationTRANSCRIPT
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The Essential Skillof Mathematics
Using the Math Scoring Guide: An Introduction for High School Content Teachers
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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
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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
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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
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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
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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
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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
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LET’S LOOK AT THE SCORING GUIDE !
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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
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Mathematics Problem Solving Scoring Guide
Making Sense of the Problem
Representing and Solving the Problem
Communicating Reasoning
Accuracy
Reflecting and Evaluating
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Interpret the concepts of the task and translate them into mathematics
Making sense of the problem
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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
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Communicate mathematical reasoning coherently and clearly use the language of mathematics.
Communicating Reasoning
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Clearly identify and support the solution.
Accuracy
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State the solution in the context of the problem.
Defend the process. Evaluate and interpret the reasonableness of the solution
Reflecting and Evaluating
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Simplified Mathematics Scoring Guide
Beginning1
2
3
4
5
Emerging
Developing
Proficient
Strong
6Exemplary
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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
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What does a Math Work Sample look like?
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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
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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.)
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Share your solution!
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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?
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Scoring the 2nd Anchor Paper
What scores did this paper earn?
This anchor paper did not meet the achievement standard.
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Within the Dimensions . . .What differentiates a 3 from a 4?
Scoring
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Scoring Papers 3, 4, & 5 Use the scoring guide to rate each paper.
What scores did these papers earn?
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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.
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Share your solution!
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Scoring the First Anchor Paper
This anchor paper almost met the achievement standard.
Why did this paper earn these scores?
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Scoring the 2nd Anchor Paper
What scores did this paper earn?
This anchor paper did not meet the achievement standard.
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Scoring Papers 3, 4, & 5 Use the scoring guide to rate each paper.
What scores did these papers earn?
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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
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Multiple Uses for the Scoring Guide Instructional Tool
• Makes targets explicit to students• Opportunities to show students models
from website or other examples
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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
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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.
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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
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• 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
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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
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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
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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
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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
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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