FEA/PSA - Judith T. Brendel - Spring 2014
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Transcript of FEA/PSA - Judith T. Brendel - Spring 2014
The PARCC Institute – High School Math:
Preparing for PARCC!NJ’s Next Generation Standardized
Assessment SystemFEA/PSA - Judith T. Brendel - Spring 2014
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Welcome…
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Desired outcomes…
•understand the overall substance, design and technical aspects of next generation PARCC assessments
•gain access and practice with PARCC tasks and related resources
•better enable educators to effectively lead the transition to CCSS and PARCC assessments.
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“…revolutionary transformation rather than evolutionary tinkering.” US DOE, NETP 2010
What should teaching and learning in the 21
st century look like?”
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Education for a Contemporary Age
Preparing a Globally Competent and Innovative Workforce
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A Changing World…
A growing need for a paradigm shift in the way we teach and learn…
• A Nation at Risk (1983) http://www2.ed.gov/pubs/NatAtRisk/findings.html
http://www.ed.gov/pubs/NatAtRisk/index.html
• SCANS Report and America 2000 http://wdr.doleta.gov/SCANS/whatwork/whatwork.pdf
(What Work Requires of Schools)
“The best time to plant a tree is twenty years ago; the second best time is today.” (Ancient Chinese Proverb)
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A Changing Student… (recommended resources)
• Digital Natives, Digital Immigrants – Parts I and II – Do They Really Think Differently? (Prensky, 2001) http://www.marcprensky.com/writing/default.asp
• Marc Prensky’s Essential 21st Century Skills http://www.marcprensky.com/writing/Prensky-Essential_21stCenturySkills.pdf
“Different kinds of experiences lead to different brain structures.” Dr. Bruce D. Perry, Baylor College of Medicine
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A Changing Student… (recommended resources)
•Authentic Intellectual Work and Standardized Tests: Conflict or Coexistence (2001) http://ccsr.uchicago.edu/content/publications.php?pub_id=38#
•How People Learn: Brain, Mind, Experience and School (1999, 2003) http://www.nap.edu/openbook.php?record_id=6160
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Listen to our students!
“I am a 21st Century Learner!”
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How? Fostering essential skills…
• Communication• Collaborative
problem solving• Critical thinking• Creativity• Innovation
… through innovative pedagogy and ubiquitous technology.
• Global competence
• Content knowledge
• Entrepreneurship• Adaptability• Interpersonal
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“I do not teach my students; I simply create the conditions for their learning.”
(Albert Einstein)2006 Innovative Teachers Forum. Retrieved May 10, 2010 on : http://www.edlabgroup.org/tl/resources/InnovativeTeachers2006.pdf
What conditions will foster these skills?
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21st learn
ing
…
…what should it look like?
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21st learn
ing
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http://www.pascack.k12.nj.us/cms/lib5/NJ01000238/Centricity/Domain/87/Writing%20Equations%202.swf
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Common standards,…
…common (online) assessments, and common instruction that promote the essential skills.
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Reflection…•What trends will continue to shape the world in which our students will live and work?
•What skills will our students need to succeed in their future?
•What type of learning environments would best support to development of these skills?
…what are your thoughts?
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Let’s take a (quick) break!
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Let’s get to work…
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Let’s take our… (page-3)
PARCC Pre-Assessment!
Item 9: grade-7 level math w/new CCSS (What’s different?)ADD H.S. EXAMPLE
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A (Quick) Walk through the PARCC!
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Race to the Top Assessment Grants:• $350 million of Race-to-the-Top Fund to consortia of states to design and
develop common K-12 assessment systems aligned to CCSS
• In September 2010, the U.S. Department of Education awarded grants to:
• Partnership for Assessment of Readiness for College and Careers (PARCC) – 18 States, & DC
• Smarter Balanced Assessment Consortium (SBAC)
• Winning consortia - four years - to develop assessments systems,
• States participating will administer new assessments statewide by 2014-2015
• ACHIEVE was selected through a competitive bid process, by PARCC to be the Project Manager.
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Race to the Top Assessment Grants:
• New Jersey is PARCC Governing Board State:
• Will administer the assessment system statewide 2014-15 school year.
• Will field test assessment items spring 2014.
• Governing Board meets quarterly. The chief state school officer for each of the governing states sits on the PARCC Governing Board. This to make major policy, operational, design and financial decisions regarding PARCC.
• Executive Committee meets weekly. (Governing Board Members from 6 states)
• ACHIEVE won competitive bid, selected by PARCC to be the Project Manager.
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Why New Common Assessments?
Current Assessment Systems…
• Too many tests, often with disconnected purposes (e.g., instructional improvement vs. accountability vs. college admissions)
• Not challenging enough to measure CCR
• Do not measure the full range of college- and career-ready knowledge and skills (such as research, analysis, critical thinking, and collaboration)
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Why New Common Assessments?
Current Assessment Systems…
• Fail to generate information for educators and students quickly enough or at all
• Are widely inconsistent across states making results impossible to compare
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Why New Common Assessments?
Next-Generation Common Assessment Systems will…
• Measure students’ mastery of Common Core State Standards
• Provide a common measure of college and career readiness
• Include a range of item types that allow for the assessment of higher-order skills
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Why New Common Assessments?
Next-Generation Common Assessment Systems will…
• Leverage new technologies in assessment and reporting to get actionable student data to educators and parents in real time
• Mitigate challenges associated with student mobility by ensuring students will have the same expectations wherever they live
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PARCC Assessment Consortium
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K-2 formative assessment
being developed,
aligned to the PARCC system
Timely student achievement data showing students, parents and educators
whether ALL students are on-track to college and
career readiness
ONGOING STUDENT SUPPORTS/INTERVENTIONS
College readiness score to identify who
is ready for college-level coursework
SUCCESS IN FIRST-YEAR,
CREDIT-BEARING,
POSTSECONDARY COURSEWORK
Targeted interventions &
supports:•12th-grade bridge courses• PD for educators
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What does it mean? “Students are on-track or ready for college and careers” (Math)
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Assessment Transition Timeline
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Assessment Transition Timeline
Spring 2012
NJ ASK Aligned to NJCCCS
Spring 2013
NJ ASK
Aligned to the CCSS and NJCCCS
(Except Gr. 6-8 Math)
Spring 2014
NJ ASK
Aligned to the CCSS
SY 2014-15
Full administration
of PARCC assessments
“Transitional Assessments”
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The PARCC Commitment…
PARCC is designed to promote quality instruction aligned to the CC Standards, so the assessment is worthy of preparation rather than a distraction from good work.
TEACHING to the TEST may be a GOOD THING!
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Understanding the Common Core State Standards …is to understand PARCC
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Why Common Core State Standards?
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"The standards are designed to be robust and relevant to the real world, reflecting the knowledge and skills that our young people need for success in college and careers," which will place American students in a position in which they can compete in a global economy.
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Why Common Core State Standards?• Before Common Core State Standards we had
standards, but rarely did we have standards-based instruction.
Long lists of broad, vague statements Mysterious assessments Coverage mentality Focused on teacher behaviors – “the inputs”
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Principles of the CCSS…
FEWER - CLEARER - HIGHER•Aligned to requirements for College and Career Readiness•Based on evidence•Honest about time
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The CCSS Difference: Grade 8 Mathematics
Before: NJCCCS (2004)
1. Understand and apply the Pythagorean Theorem.
After: CCSS (2010)
1. Explain a proof of the Pythagorean Theorem and its converse.
1. Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
• Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.
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a2 + b2 = c2
a
b
c
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4 16
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a = 4
b = 3
c = ?
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Implications of the CCSS on WHAT and HOW to teach…
What are the Critical Shifts to Consider?
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COMMON CORE SHIFTS in ASSESSMENTS
Shift 1: Focus Priority standards = focus of the assessments. Other standards deemphasized.
Shift 2: Coherence Assessments will reflect the progression of content and concepts as depicted in the standards across grade levels.
Shift 3: Fluency It will be assumed students possess required fluencies through grade 8; as such, students will not be allowed to use calculators in grades 3-5.
Students will be allowed to use four-function calculators with a square root key or scientific calculators in grade 6 and scientific calculators in grades 7-8.
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CC SHIFTS in ASSESSMENTS continued ….
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Shift 4: Deep UnderstandingEach standard will be assessed from multiple perspectives, while not veering from the primary target of measurement for the standard.
Shift 5: Application
Shift 6: Dual Intensity
Students will be expected to know grade-level mathematical content with fluency and to know which mathematical concepts to employ to solve real-world mathematics problems.
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PARCC sample prototypes with Task Type
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TASK TYPES – PARCC
I – Computation, Skills, Process
(x – 2)2 + 6 = 75 2x2 - 5x – 6 = 0
II – Mathematical Reasoning
xxx
xxxx
III – Modeling, Combined Standards, Applications
Compare the 3 sets of data (graph, chart, and equation) and defend the argument that ….
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TASK TYPE-ITasks assessing concepts, skills and procedures.
- include a balance of conceptual understanding, fluency, and application. These tasks can involve any or all mathematical practice standards.
- will be machine scorable and will include innovative, computer-based formats.
-will appear on the End-of-Year and Performance Based Assessment components and generate evidence for measuring major, additional, and supporting content with connections to the mathematical practices as indicated in the PARCC Model Content Frameworks for Mathematics.*
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Mathematics online Sample Item/Prototypes:
PARCC TYPE-I TASKS (1, 2, or 4 point questions)
HS – FunctionsS
HS – Seeing Structure in Quadratic Equation
HS – Picture Frame (Algebra-I/Math 2) http://www.parcconline.org/sites/parcc/files/HS-Alg1Math2PictureFrame.pdf
HS – Myla’s Swimming Poole (Algebra-I)
HS – Green Tea Observation Study (Algebra-2/Math 3)
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TYPE II: Tasks assessing expressing mathematical reasoning.
- tasks call for written arguments/justifications, critique of reasoning, or precision in mathematical statements (MP. 3, 6). These tasks can also involve other mathematical practice standards.
- tasks may include a mix of innovative, machine scored and hand scored responses.
- tasks will be included on the Performance Based Assessment component and generate evidence for measuring mathematical reasoning with connections to content.
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Mathematics online Sample Item/Prototypes:
PARCC TYPE-II TASKS (4 point questions)
•HS – Graphs of Functions (Algebra-II/Math III) Nov. 2013 HS.C.6.2, A.REI.D, MP.3, 7 with 4-point scoring rubrichttp://www.parcconline.org/sites/parcc/files/HighSchoolAlg2Math3-GraphsofFunctions.pdf
•HS – Michelle’s Conjectures (Algebra-II/Math III)http://www.parcconline.org/sites/parcc/files/PARCC_SampleItems_Mathematics_HSAlgIMathIIMichelleConjecture_081913_Final_0.pdf
•HS – Geometric Construction Connection (Geometry/Math III)PARCC_SampleItems_Mathematics_HSGeoMathIIIGeometricConnection_081913_Final_0.pdf
http://www.parcconline.org/sites/parcc/files
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TYPE III: Tasks assessing modeling/applications. (3 or 6 point questions)
- tasks call for modeling/application in a real-world context or scenario (MP.4) and can also involve other mathematical practice standards.
- tasks may include a mix of innovative, machine scored and hand scored responses.
-tasks will be included on the Performance Based Assessment component and generate evidence for measuring mathematical modeling/application with connections to content.
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TYPE-I PARCC TASKSinclude a balance of conceptual understanding, fluency, and application, and can involve any or all Math Practice Standards. will be machine scorable and will include innovative, computer-based formats. will appear on the End of Year and Performance Based Assessment components and generate evidence for measuring major, additional, and supporting content with connections to the mathematical practices as indicated in the
PARCC Model Content Frameworks for Mathematics.*
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Functions http://www.parcconline.org/samples/mathematics/high-school-functions
Given f(x) as a graphed parabola and g(x) as table of values
1.Compare y-intercepts 2.Compare f(3) and g(3)3.Compare maximum values of each w/in range -5 ≤ x ≤ 54.Compare
A type I PARCC task
COURSE
?
DIFFICULTY?
POINTS?
STANDARDS?
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Seeing Structure in a Quadratic Equations http://www.parcconline.org/samples/mathematics/high-school-seeing-structure-quadratic-equation
(3x - 2)2 = 6x – 4
a Type-I PARCC task
COURSE
?DIFFICULTY
?POINTS?
STANDARDS?
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Seeing Structure in Equations http://www.parcconline.org/samples/mathematics/high-school-seeing-structure-equation
24 + 10x – x2 = p – (x – 5)2 Solve for p
a Type I PARCC task
COURSE
?DIFFICULTY
?
POINTS?STANDARDS?
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PICTURE FRAME http://www.parcconline.org/sites/parcc/files/HS-Alg1Math2PictureFrame.pdf
a Type I PARCC task
COURSE
?DIFFICULTY
?POINTS?
STANDARDS?
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GREEN TEA TYPEhttp://www.parcconline.org/sites/parcc/files/PARCC_SampleItems_Mathematics_HSAlgIIMathIIIGreenTeaStudy_081913_Final_0.pdf
a Type I PARCC task
COURSE
? DIFFICULTY
?
POINTS?
STANDARDS?
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TYPE-II PARCC TASKS
call for written arguments/justifications, critique of reasoning, or precision in mathematical statements (MP. 3, 6). These tasks can also involve other mathematical practice standards. may include a mix of innovative, machine scored and hand scored responses. will be included on the Performance Based Assessment component and generate evidence for measuring mathematical reasoning with connections to content.
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GRAPH of FUNCTIONS (posted November 2013)
http://www.parcconline.org/sites/parcc/files/HighSchoolAlg2Math3-GraphsofFunctions.pdf
a Type-II PARCC Task
COURSE
?POINTS ?
DIFFICULTY?
STANDARDS?
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GEOMETRY CONSTRUCTION CONNECTION
http://www.parcconline.org/sites/parcc/files/PARCC_SampleItems_Mathematics_HSGeoMathIIIGeometricConnection_081913
_Final_0.pdf
a Type-II PARCC Task
POINTS ?
DIFFICULTY
?STANDARDS?
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MICHELLE’S CONJECTURES (Aug.19, 2013)
http://www.parcconline.org/sites/parcc/files/PARCC_SampleItems_Mathematics_HSAlgIMathIIMichelleConjecture_081913_Final_0.pdf
a Type-II PARCC Task
COURSE
? POINTS ?
DIFFICULTY?
STANDARDS?
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TYPE-III PARCC TASKS
call for modeling/application in a real-world context or scenario (MP.4) and can also involve other mathematical practice standards.
may include a mix of innovative, machine scored and hand scored responses.
will be included on the Performance Based Assessment component and generate evidence for measuring mathematical modeling/application with connections to content.
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MINI GOLF PRICES
(November, 2013)
http://www.parcconline.org/sites/parcc/files/HSAlg1Math2MiniGolfPrices.pdf
a Type-III PARCC Task
COURSE
? POINTS ?
DIFFICULTY?
STANDARDS?
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BRETT’S RACE
(November, 2013)
http://www.parcconline.org/sites/parcc/files/HSMathematicsSampleItemBR.pdf
a Type-III PARCC Task
COURSE
? POINTS ?DIFFICULTY
?
STANDARDS?
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POPCORN INVENTORY (NOVEMBER 2013)
http://www.parcconline.org/sites/parcc/files/HSAlg1Math1PopcornInventory.pdf
COURSE
? POINTS ?
DIFFICULTY?
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TEMPERATURE CHANGES
http://www.parcconline.org/sites/parcc/files/PARCC_SampleItems_Mathematics_HSAlgIIMathIIITemperatureChange_081913_
Final_0.pdf
COURSE
? POINTS ?
DIFFICULTY?
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PARCC RELEASED TASKS include elsewhere? Use this slide to ‘hold’ sites
file://localhost/Users/jbrendel/Desktop/PARCC%20HS%20Functions.html (November/December 2013)
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https://www.teachingchannel.org/videos/laws-of-sines-cosines-lesson# 14-min lesson “fly quadcopters” math/science/engineering … a 4-month project … Ms. Brookins and Mr. James GRADE-11
How/if .. .include here?
https://www.teachingchannel.org/videos/statistical-analysis-lessonStatistical analysis to rank baseball players GRADES 11-12CCSS Standards: Math SID. 1, 2 and 3
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What you SHOULD NOT see !
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ZN
x
y
>
<
Slope =
slope =
(3,6)
(3,2)
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BRAINSTORM in GROUPS
What should teachers NOT be doing?
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READING CCSS and Mathematics
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•In “Casey at the Bat,” Casey strikes out. Describe a time when you failed at something.
•In “Letter from a Birmingham Jail,” Dr. King discusses nonviolent protest. Discuss, in writing, a time when you wanted to fight against something that you felt was unfair.
•In “The Gettysburg Address” Lincoln says the nation is dedicated to the proposition that all men are created equal. Why is equality an important value to promote?
What makes Casey’s experiences at bat humorous?
What can you infer from King’s letter about the letter that he received?
“The Gettysburg Address” mentions the year 1776. According to Lincoln’s speech, why is this year significant to the events described in the speech?
Not Text-Dependent in ELA Text-Dependent in ELA
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Text-Dependent in mathematics
December 2, 2013 author: J. Brendel Material not to be duplicated.
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Regular Practice with Complex Text and its Academic Language
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Regular Practice with Complex Text and its Academic Language
Cramer’s Rule for solving systems of equations uses determinants to solve for each variable. D is the determinant of the coefficient matrix. Dy is the determinant formed by replacing the coefficients of y in D with the constant terms.
Algebra-II
Sample academic language in a basic statistics task: measure of central tendency, skewed, mean, median, mode, outlier, bimodal, quartiles, box-and-whisker plot, percentile, random sample, … New to Pre-Algebra, Algebra I or II
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Regular Practice with Complex Text and its Academic Language (“Adult Language”)
Example: Phone company ‘A’ charges an initiation fee plus a charge per minute. The cost of using 300 minutes (plus initiation fee) is $25 and the cost of 700 minutes (plus initiation fee) is $33.
•Write an equation to represent the cost. •What is the initiation fee? •What is the cost per minute?•Is this company’s offer better than the new phone company ‘B’s?•Explain or compare with charts and graphs.
Pre-Algebra, Algebra
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Regular Practice with Complex Text and its Academic Language
Basic constructions w/triangles using protractors, compasses or online with simulation tools: Students construct, do proofs and solve problems involving:
Medians, vertex angle, balancing point, centroid
Altitudes, acute triangles, obtuse triangles, right triangles, orthocenter, interior, exterior or ….
Perpendicular Bisectors, concurrent lines, point of concurrency, circumcenter of a triangle
Angle Bisectors, incenter, equidistant, …. Geometry
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Adjusting Math Language to the CCSS• Old habit to eliminate: Defining equality as “same as.” The problem: This is mathematically incorrect and leads to
misconceptions. New habit to adopt: Defining equality as “same value as.”
• Old habit to eliminate: “Addition makes things get bigger.” The problem: When negative numbers are introduced, the old habit
has to be debugged. New habit to adopt: Addition is about combining.
• Old habit to eliminate: “Subtraction makes things get smaller.” The problem: As with addition, negative numbers make this wrong. New habit to adopt: Subtraction is about difference.
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Regular Practice With Complex Text and its Academic Language: Why?
• Gap between complexity of college and high school texts is huge.
• What students can read, in terms of complexity is greatest predictor of success in college (ACT study).
• Too many students are reading at too low a level.
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What are the Features of Complex Text?
• Subtle and/or frequent transitions
• Multiple and/or subtle themes and purposes
• Density of information
• Unfamiliar settings, topics or events
• Lack of repetition, overlap or similarity in words and sentences
• Complex sentences
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What are the Features of Complex Text? (cont.)
• Uncommon vocabulary
• Lack of words, sentences or paragraphs that review or pull things together for the student
• Longer paragraphs
• Any text structure which is less narrative and/or mixes structures
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It all boils down to…
Texts Worth Reading…and
Questions Worth Answering!
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Let’s take a quick break!
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Understanding the Common Core Math Standards …is to understand PARCC Math!
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The Common Core Standards: Classroom Video Illustration
High School School
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The Standards are NOT new names for old ways of doing things…
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• A different topic every day
• Every topic/concept treated as equally important
• Elementary students dipping into advanced topics at the expense of mastering fundamentals
• Infinitesimal advance in each grade; endless review
• Incoherence and illogic – bizarre associations, or lacking a thread
NOT …
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Dan Meyer:Math Class Needs a Makeover
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NOT
Lack of rigor
• Reliance on rote learning at expense of concepts
• Aversion to repetitious practice
• Severe restriction to stereotyped problems lending themselves to mnemonics or tricks
• Lack of quality applied problems and real-world contexts
• Lack of variety in what students produce
• E.g., overwhelmingly only answers are produced, not arguments, diagrams, models, etc.
From.... To….856 = ___ hundreds, ___ tens, ___ ones 1 hundredth = ___ tenths
x2 + 10x + 21 = 0 ¾ c(c –1) = c
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1. Focus: Focus strongly where the Standards focus.
2. Coherence: Think across grades, and link to major topics within grades.
3. Rigor: In major topics, pursue:
1.conceptual understanding;
2.procedural skill and fluency; and
3.application with equal intensity.
Three (3) Significant Shifts in Mathematics:
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Activity No. 3: Shifts Happen - Mathematics
What is this shift?Why this shift?
Opportunities Challenges
Focus: Focus strongly where the Standards focus.
Coherence: Think across grades, and link to major topics within grades.
Rigor: In major topics, pursue conceptual understanding, procedural skill and fluency, and application with equal intensity.
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1. Focus: Focus strongly where the Standards focus.
2. Coherence: Think across grades, and link to major topics within grades.
3. Rigor: In major topics, pursue:
• conceptual understanding;
• procedural skill and fluency; and
• application with equal intensity.
Three (3) Significant Shifts in Mathematics:
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FOCUS continued
70% or more of the assessment will measure the major work in grades 3-8
Focus allows for a variety of problem types (task types) to get at a concept
in multiple ways.
Students will have more time to master concepts at a deeper level.
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Mathematics topics intended at each grade by at least two-thirds of A+ countries
Mathematics topics intended at each grade by at least two-thirds of 21 U.S. states
The shape of math in A+ countries…
1 Schmidt, Houang, & Cogan, “A Coherent Curriculum: The Case of Mathematics.” (2002).
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K 12Number and Operations
Measurement and Geometry
Algebra and Functions
Statistics and Probability
Traditional U.S. Approach…
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Focusing attention within Number and Operations
Operations and Algebraic Thinking
Expressions and Equations
Algebra
Number and Operations—Base Ten
The Number System
Number and Operations—Fractions
K 1 2 3 4 5 6 7 8 High School
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GradeFocus Areas in Support of Rich Instruction and Expectations of Fluency and Conceptual Understanding
K–2Addition and subtraction - concepts, skills, and problem solving and place value
3–5Multiplication and division of whole numbers and fractions – concepts, skills, and problem solving
6Ratios and proportional reasoning; early expressions and equations
7Ratios and proportional reasoning; arithmetic of rational numbers
8Linear algebra, linear functions
Priorities in Mathematics (CCSS)
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ALG. - 1Focus Areas in Support of Rich Instruction and Expectations of Fluency and Conceptual Understanding
UNIT-1 Relationships Between Quantities and Reasoning with Equations
UNIT-2 Linear Relationships
UNIT-3 Expressions and Equations
UNIT-4 Quadratic Functions and Modeling
UNIT-5 Functions and Descriptive Statistics
Priorities in Mathematics (CCSS)- MS/HS
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GEOMETRYFocus Areas in Support of Rich Instruction and Expectations of Fluency and Conceptual Understanding
UNIT-1 Congruence, Proof, and Constructions
UNIT-2 Similarity, Proof, and Trigonometry
UNIT-3 Extending to Three Dimensions
UNIT-4 Connecting Algebra and Geometry Through Coordinates
UNIT-5 Circles With and Without Coordinates
UNIT-6Applications of Probability
Priorities in Mathematics (CCSS) - HS
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ALG. - 2Focus Areas in Support of Rich Instruction and Expectations of Fluency and Conceptual Understanding
UNIT-1 Polynomial, Rational, and Radical Relationships
UNIT-2 Trigonometric Functions
UNIT-3 Modeling with Functions
UNIT-4 Inferences and Conclusions from Data
Priorities in Mathematics (CCSS) – HS
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1. Focus: Focus strongly where the Standards focus.
2. Coherence: Think across grades, and link to major topics within grades.
3. Rigor: In major topics, pursue:
• conceptual understanding;
• procedural skill and fluency; and
• application with equal intensity.
Three (3) Significant Shifts in Mathematics:
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COHERENCE
Integrative tasks draw on multiple standards to ensure students are making important connections.
The Standards are not treated as a checklist.
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COHERENCENeed to include h.s. task(s) that incorporate multiple standards to show connections.
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Coherence and NEW multiple-choice questions.Circle all that are true.
Given: All squaresA.are parallelograms and rectanglesB.have 4 acute anglesC.have only 2 diagonals D.Area = ½ base x height E.Sum of consecutive angles = 180˚F.Perimeter = 2 x Side lengthG.Area > area with the same perimeter.
5 3
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525
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*Activity 4: Work with your group (p. 15. Ex. 8)
What skills and understandings are assessed here?
Do they come from only one standard? One domain?
A. subtraction w/decimals
B. addition then subtraction
C. write % as a decimal; multiply
D. read carefully, add and subtract money
E. know how to find an average
F. know to ÷ or x; compute accurately
G. know to add lowest, then highest; understand concept, recognize > and < symbols
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Coherence: Link to major topics within gradesExample: HIGH SCHOOL performance task; Algebra-I unit 1
Algebra-I Unit-1
A large truck has two fuel tanks, each with a capacity of 150 gallons. One of the tanks is half full, and the other is empty. Fuel is pumped into the tanks until both tanks are full. The pump delivers fuel at a constant rate of 5¾ gallons per minute.
a.Write an equation for the total number of gallons of fuel ….
a.How much fuel is in the tanks after the pump … 8 minutes?
b.Graph the equation … on the coordinate plane … label ….
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1. Focus: Focus strongly where the Standards focus.
2. Coherence: Think across grades, and link to major topics within grades.
3. Rigor: In major topics, pursue:
• conceptual understanding;
• procedural skill and fluency; and
• application with equal intensity.
Three (3) Significant Shifts in Mathematics:
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RIGOR
Need to include h.s. task(s) that incorporate multiple standards to show connections.
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See the Rigor – Early Elementary Grades
Ray’s father has 129 plants in his garden. Billy’s father has 230 plants in his garden. Ray says his father has more plants because 9 is bigger than 2. Is Ray correct? Yes ___ No ___ Explain how you know.
Guess the grade level!
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See the Rigor in Grade-3 Fractions on a Number Line
http://www.illustrativemathematics.org/standards/hs
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See the Rigor in Middle GradesUnderstanding of Fractions
Write a number that is greater than and less than
Hint: Find equivalent fractions for and with denominators of 40 or 100.
Why wasn’t it helpful to use 20 as a denominator? (JB)
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See Rigor in Grade 6: Ratios
PARCC - Grade-6 Slider Ruler: type-I http://www.parcconline.org/samples/mathematics/grade-6-slider-ruler
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ONLINE http://www.parcconline.org/samples/item-task-prototypesGrade-3 Fractions on a Number Line: type- I http://www.parcconline.org/samples/mathematics/grade-3-mathematics-number-line
Grade-4 Fraction model: type-II http://www.parcconline.org/sites/parcc/files/PARCC_SampleItems_Mathematics_G4FractionModel_081913_Final.pdf
Grade-6 Slider Ruler: type-I http://www.parcconline.org/samples/mathematics/grade-6-slider-ruler
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See the Rigor in High School Math
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Linking to major topics – High School Part A
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Part B
Describe
Compare
Write
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REQUIRED FLUENCIES
SA MS/HS– PD Session 3| April 4., 2011
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Required Fluencies in K-6
Grade Standard Required Fluency
K K.OA.5 Add/subtract within 5
1 1.OA.6 Add/subtract within 10
22.OA.2
2.NBT.5
Add/subtract within 20 (know single-digit sums from memory)
Add/subtract within 100
33.OA.7
3.NBT.2
Multiply/divide within 100 (know single-digit products from memory)
Add/subtract within 1000
4 4.NBT.4 Add/subtract within 1,000,000
5 5.NBT.5 Multi-digit multiplication
6 6.NS.2,3Multi-digit division
Multi-digit decimal operations
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HS EXPECTATIONSALGEBRA-I: Unit 2 – LINEAR RELATIONSHIPS
• Find approximate solutions to linear equations by making a table of values, using technology to graph and successive approximations.
• Graph functions by hand (in simple cases) and with technology ….
• Solve systems of linear equations in two variables …
Dec. 2, 2013 J.Brendel
A.REI.5, A.REI.6 additional
A.REI.10, 11 major
F.IF.7/9 supporting
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•
One of several staircases to algebra designed in the OA domain.
Coherence: Link to Major Topics Across Grades
120
1. add … subtract
3. multiply … divide
5. expressions
6. Apply properties
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One of several staircases to algebra designed in the OA domain.
Coherence: Link to Major Topics Across Grades
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ALGEBRA-I
ALGEBRA- II
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Application
• Students can use appropriate concepts and procedures for application even when not prompted to do so.
• Teachers provide opportunities at all grade levels for students to apply math concepts in “real world” situations, recognizing this means different things in K-5, 6-8, and HS.
• Teachers in content areas outside of math, particularly science, ensure that students are using grade-level-appropriate math to make meaning of and access science content.
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Fluency
FLUENCY and new type of MC question
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HS Teachers outside of math use grade-level-appropriate math
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Part B
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Part C
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Part D
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Standards of Mathematical Practices1. 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.
Construct viable arguments and critique the reasoning of othersModel with mathematics.
Attend to precision
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Analysis of the PARCC Mathematics Assessment:
Design Shifts(Activity No. 4)
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Shift No. 1…Focus where Standards Focus
Advance: PARCC assessments will focus strongly where the Standards focus (70% or more on the major work in grades 3-8).
Focus allows for a variety of problem types to get at concept in multiple ways.Students will have more time to master concepts at a deeper level.
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Shift No. 2…Coherence across/within grades
Advance: The assessment design is informed by multi-grade progressions in the Standards and the Model Content Frameworks.Key beginnings are stressed:
e.g., ratio concepts in grade 6, e.g., fluency with the multiplication table in
grade 3Become key endpoints and takeaway skills
133
Shift No. 2…Coherence across/within grades
Advance: Integrative tasks draw on multiple standards to ensure students are making important connections.The Standards are not treated as a checklist.
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Shift No. 3…Rigor
Advance: PARCC assessments will reach the rigor in the Standards through innovations in technology and item design.
135 December 2, 2013
SAMPLE ALGEBRA-1 UNIT-I ASSESSMENT
and High School Reference Sheet(separate packet)
• Solution Guide
• With notes to teachers
• Sample responses and scoring
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The Mathematics Common Core ToolboxMathematics Sample Item/Prototypes:
PARCC online at the Dana Center•Grade 4 (Deer in the Park) p. 23
•Grade 6 (Gasoline Consumption)
•High School (Isabella’s Credit Card) *p. 24-25)
•High School (Popcorn Inventory) new Nov. 2013 http://www.parcconline.org/sites/parcc/files HSAlg1Math1PopcornInventory.pdf
Activity: grade-2 (p. 26-27) *What makes it unique? ….
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Performance Based Assessment (PBA)
•Type I items (machine-scorable)
•Type II items (Mathematical Reasoning/hand-scored)
•Type III items (Mathematical Modeling/hand scored and/or machine-scored
End-of-Year Assessment (EOA)•Type I items only (All machine-scorable)
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Sample Online Performance TasksMathematics Sample online Item/Prototypes:
Smarter Balanced: link on next slide
•Grade 3 - Lemonade Sale•Grade 4 - Family Trip to the Zoo•Grade 6 - Cereal Box (vol., surf.area, min s.a.)•Grade 7 - Food Basket (calories, grams, protein)•Grade 8 - Heartbeats (scatter plot ….)•Grade 11- Speeding Ticket (graph, what is fair? ….)
•Grade 2 hardcopy-Trip to Zoo (gr. 4 modified; J. Brendel Barron’s)(page 27-28)
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EXPERIENCE an ASSESSMENTActivity 6
• https://sbacpt.tds.airast.org/student/login.aspx?c=SBAC_PT
• Sample online Smarter Balanced Assessments. Select from grades 3, 4, 5, 6, 7, 8 or 11
• Select Examples or Performance Tasks J.Brendel 11/2013
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J. Brendel 11/2013
CIRCLEShttp://sampleitems.smarterbalanced.org/itempreview/
ModernShell.aspx?config=SBAC%5CContent%5CCircle1.json
MATH II - WALLShttp://sampleitems.smarterbalanced.org/itempreview/
ModernShell.aspx?config=SBAC%5CContent%5CRoomWall.json
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The Specs, Accountability, and Resources:
What We Know Now!
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PARCC Assessment Consortium
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Dynamic Learning Maps (DLM) Alternate Assessment Consortium
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Performance Based Assessment
ELA/Literacy Math TOTAL
Grade Literacy Analysis
Research Narrative Session 1
Session 2
9-10Alg I/
Math IGeo/
Math II
Estimated Time on
Task(minutes)
80 85 50 50 50 315
Estimated Time on Task: Grade 9-10
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End-of-Year (EOY) Assessment
ELA/Literacy Math TOTAL
Grade Session 1
Session 2
Session 1
Session 2
9-10Alg I/ Math IGeo/ Math II
Estimated Time on
Task(minutes)
70 70 65 65 270
Estimated Time on Task: Grade 9-10
Grade 9-10 Summative Total: 9 Hours, 45 minutes
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Performance Based Assessment
ELA/Literacy Math TOTAL
Grade Literacy Analysis
Research Narrative
Session 1
Session 2
11Alg II/
Math III
Estimated Time on
Task(minutes)
80 85 50 65 65 345
Estimated Time on Task: Grade 11
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End-of-Year (EOY) Assessment
ELA/Literacy Math TOTAL
Grade Session 1
Session 2
Session 1
Session 2
11Alg II/
Math III
Estimated Time on
Task(minutes)
70 70 55 55 250
Estimated Time on Task: Grade 11
Grade 11 Summative Total: 9 Hours, 55 minutes
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~ 1/3 total points = PBA
End-of-Year machine scored
149
~ 1/3 total points =
PBA
End-of-Year machine scored
150
What Else… 20 Day Window…for both the PBA and EOY
summative assessments (performance based and end-of-year) Summative Assessments Retest Opportunities
Grades 3-8 - 1 retest opportunity/year HS - up to 3 retest opps/year for each assessment
Computer-based (w/paper version available in rare circumstances), contingency back-up
PBA delay? No…
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What Else…Accessibility Features for ALL students•Audio Amplification•Blank Paper (provided by test administrator)
•Eliminate Answer Choices•Flag Items to Review•General Administration Directions (provided by test administrator)
•General Administration Directions Read Aloud and Repeated (provided by test administrator)
Accommodations / Modifications for Special Education students (55 page manual)
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What Else…Accessibility Features for ALL students continued•Highlight tool•Headphones•Magnification/Enlargement Device•Notepad•Pop-Up Glossary•Redirect Student to Test (provided by test administrator)
•Spell Checker•Writing Tool
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What Else…Accommodations / Modifications for Special Education Students (from the 55-page PARCC Accessibility manual)
Accessibility Features Identified in Advance• Answer Masking• Background/Font Color (Color Contrast)• General Masking• Line Reader Tool• Text-to-Speech for the Mathematics Assessments
http://parcconline.org/parcc-accessibility-accommodations-and-fairness
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Modifications Accommodations NOT permittedModifications involve changes in the conditions under which a student takes an assessment that result in unacceptable changes to the test itself, or what the test measures (e.g., reducing or changing expectations for students) and are therefore not permitted on PARCC assessments.
Examples of modifications that will result in invalidated results on PARCC include:•Requiring a student to be assessed on less content matter than other students because he has been taught less material;•Reducing the scope of assessments so a student needs to complete only a limited number of problems or items;
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• Modifying the complexity of assessments to make them easier (e.g., deleting half of the response choices on a multiple-choice test so that a student selects from two options instead of four);
• Giving hints, clues, or other coaching that directs the student to correct
responses on assignments and tests; • Adults defining vocabulary on the test or explaining test items; • Allowing the student to complete an assessment of English language arts
in a language other than English; and • Using dictionaries that provide definitions (rather than an acceptable
word-to-word dual-language dictionary).
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Accountability:What We Know Now!
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Results Types…
Performance Level Description
Level 5* Distinguished Command
Level 4* Strong Command
Level 3 Moderate Command
Level 2 Partial Command
Level 1 Minimal Command
Proficiency (PLDs) On-Track-to-College and
Career Readiness (CCRDs) Growth Data
Performance Level Descriptors (PLDs)
*Achieved CCR Performance Threshold
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What does “distinguished” (Level 5) mean?“Students performing at this level demonstrate a distinguished command of the knowledge, skills, and practices embodied by the Common Core State Standards for English language arts/literacy assessed at grade 11.
They are academically well prepared to engage successfully in entry-level, credit-bearing courses in College English Composition, Literature, and technical courses requiring college-level reading and writing.
Students performing at this level are exempt from having to take and pass placement tests in two- and four-year public institutions of higher education designed to determine whether they are academically prepared for such courses without need for remediation.”
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What does it mean to be CCR? (Level-4)
“Students who earn a PARCC College- and Career-Ready
Determination by performing at Level 4 in mathematics
and enroll in College Algebra, Introductory College
Statistics, and technical courses requiring an equivalent
level of mathematics have approximately a 0.75
probability of earning college credit by attaining at least a
grade of C or its equivalent in those courses.”
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What does it mean to be CCR? (cont.)Will be used as a benchmark against which the CCR cut score on the PARCC assessments will be validated through empirical research.
•WHY - a “C” is the minimum grade needed to earn credit for a course
•WHY - a reasonably high standard but not unattainable.
•WHY - similar to the criteria used by ACT,
•WHY - other important CCR skills will not be measured by PARCC assessments.
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What are the cut scores for each level?
As/PARCC, “the vendor selected through the RFP will
also work with state leaders, educators and eternal
experts to determine the cut scores to establish the five
PARCC Performance levels for each grade-level
assessment.
RFP for “Operational Assessment”
Vendor proposals are due by Dec. 11, 2013.
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Timelines and Resources:What We Know Now!
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PARCC Timeline…
Jan – Aug 2013
• Release of 2nd set of prototype assessment and instructional tasks (spring 2013)
• Release of online professional learning modules (spring 2013) (update: expected June 2014)
• Item tryouts (spring 2013) – see next slide
2013-2014
• Full-scale pilot/field testing (spring 2014)• Partnership Resource Center launches (spring 2013)• Optional performance tasks for K-2 available (February 2014)• College readiness tools available (spring 2014)
2014-2015
• Diagnostic assessments release (September 2014)• Full operational administration of PARCC assessments (spring 2015)• Setting of achievement levels, including college-ready performance
levels (late spring 2015 (post-administration)
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PARCC Timeline…
*Over the next year, PARCC will develop five online training modules for teachers, school leaders, and school site testing coordinators – each with a unique purpose.
PARCC will produce modules with the following foci:
1. PARCC Common Assessments Overview
2. Introduction to the PARCC Mid-Year Assessment
3. Introduction to the PARCC Diagnostic Assessment
4. Introduction to the PARCC Speaking/Listening Assessment
5. PARCC Accessibility System
*It is anticipated that modules will be available in June 2014.
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PARCC Timeline… NJ Spotlight (Nov. 20, 2013)
For the first time since 1989, New Jersey will next year suspend its requirement that high school graduates pass a state test in language arts and math to receive their diplomas. (No HSPA) But that doesn't mean there will be fewer tests, just that they'll be used for different purposes.
For instance, current eighth, ninth, and 10th graders will be tested in language arts and math now in three separate tests, and while passing the exams will not be required for graduation, the scores will be included in a student’s permanent transcript. (2014-15 school year)
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NJDOE Model Curricula(handouts Algebra-I, Geometry, Algebra-II)
PARCC Model Content Frameworks
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INITIAL QUESTIONS to CONSIDER
when choosing or developing a
Quality Math Assessment.
See handout page-31
JB modified from: http://www.state.nj.us/education/AchieveNJ/teacher/SGOGuidebook.pdf
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GENERAL TEST PREP:
What does this look like?
See handout pages 32-33
•Know the test in terms of the following:•10 Considerations for Success
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www.achievethecore.org
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Links to Model Math Curriculum Sites
Sample Assessments by grade:http://www.achievethecore.corg/
Common Core and Special Education Studentshttp://www.ode.state.or.us/search/page/?id=3741
Common Core Practice Testhttps://sbacot.tds.airast.org/student/login.aspz?c=SBAC.PThttp://sbac.portal.airast.org/practice-test/
Common Core Resources to use with studentshttp://www.illustrativemathematics.org
Dana Center Resources http://www.ccsstoolbox.org/http://ccsstoolbox.agilemind.com/pdf/DanaCenter_YAG_HS.pdf
171December 2013 J.Brendel
COMPANIES are developing new programs to assist districts:
ACUITY: a comprehensive K-12 assessment programTom Moellering from McGraw Hills as/DA/District Administration (30 minute video/conversation)
•pre-built assessments (diagnostic) – or item banks to create your own;
•can be delivered online or in print; scan in software …
•automatically scores and results to teacher quickly
•teacher can see individual/class(es)/school/district results
•teacher can assign specific tasks
•instruction resources in general (including Performance Tasks)
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COMPANIES are developing new programs to assist districts as they transition to technology-based assessments:
Pearson’s online Assessment Roadmap 2014www.Commoncore.pearsoned.com/index.cfm?locator=PS11Uz
Step-1: Conducting a Needs Analysis
Step-2: Developing a Transition Strategy
Step-3: Ensuring Interoperability
Step-4: Communicating Proactively
Step-5: Anticipating Ongoing Change
www.PearsonAssessments.com/NextGenRoadmapBryan Bleil (VP, online & tech), Ellen Stain Seymore
J. Brendel 11/2013
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TEXTBOOK PUBLISHERS are beginning to develop new programs to assist districts as they transition to technology-based assessments:
Many now have all resources online including assessment options.
Sample:http://www.connected.mcgraw-hill.com
•Teacher username and password
•Select Subject: [Algebra-I CC Standards National]
•Select Standards: [National] [Assess] [Algebra-I]
[Create a New Test]
J. Brendel 11/2013
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Two Activities
Self-Evaluation, Action Planning and Next Steps
Response Priority Comments Roadblocks (pages 28-29)
Action Planning/Next Steps (page 30)
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Questions?Concerns (silly question)?
Discussion/Debrief
176
SINCERE THANKS…
For your participation, collaboration and dedicated efforts!!!
Judy [email protected]