the essential skill of mathematics
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The Essential Skill of Mathematics. Using the New Math Scoring Guide: An Introduction for High School Math Teachers. Goals for this workshop. 1 . Review Oregon’s Math Problem Solving Scoring Guide Classroom uses of the Math Scoring Guide - PowerPoint PPT PresentationTRANSCRIPT
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The Essential Skillof MathematicsUsing the New Math Scoring Guide: An Introduction for High School Math Teachers
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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
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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 andaccurately
• (C) Apply mathematics
OAR: 581-22-0615
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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
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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
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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….
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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.”
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1. Make sense of problems and persevere insolving 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
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Essential Skill ProficiencyThree 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
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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
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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 REVIEW 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 solvingthe 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 supportthe 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 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
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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?
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• Share your solution
Share your solution!
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Scoring the First Anchor Paper
This anchor paper met the achievement standard in each trait.
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 Traits . . .What differentiates a 3 and 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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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?
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Share your solution!
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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?
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Scoring the 2nd Anchor PaperFor Bike Rental
What scores did this paper earn?
This anchor paper also met the achievement standard.
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Scoring Papers 8, 9, & 10 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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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
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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 Screening Tool
• Help determine likelihood of reaching proficiency – on target, need assistance, at risk
• Help determine whichstudents need additionalinstruction and coaching
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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).
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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 math strengths and weaknesses.
Students learn where to focus to improve math skills.
Teachers learn where additional instruction is needed.
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AssessmentDoes your school have an assessment plan? Explain
Does your school have a data analysis & use plan? Explain
Benchmark
Formative
Interim and Predictive
Summative
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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. 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
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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 your information here)
Resources & Coming Attractions
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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