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How to achieve the RIGOR expected in the CCSS
AAEA Susan A Gendron
Senior FellowInternational Center for Leadership in Education
September 26, 2012
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Rigor/Relevance Rigor/Relevance For For
All StudentsAll Students
2
A B
DC
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1.1. AwarenessAwareness2.2. Comprehension Comprehension 3.3. ApplicationApplication4.4. AnalysisAnalysis5.5. Synthesis Synthesis 6.6. EvaluationEvaluation
Knowledge TaxonomyKnowledge Taxonomy
3
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Application ModelApplication Model1.1. Knowledge in one disciplineKnowledge in one discipline
2. Application within one 2. Application within one disciplinediscipline
3. Application across disciplines3. Application across disciplines
4. Application to real-world 4. Application to real-world predictable situationspredictable situations
5. Application to real-world 5. Application to real-world unpredictable situationsunpredictable situations
4
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510811 22 33 44 55
Action/ApplicationAction/Application
Thinking /KnowledgeThinking /Knowledge
11
22
33
44
55
66
Rigor/Relevance FrameworkRigor/Relevance Framework
RelevanceRelevance
RigorRigor
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LevelsLevels
CC DD
AA BB 1 2 3 4 5
456
321
Bloom’sBloom’s
ApplicationApplication 6
Kn
ow
led
ge
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Awareness 1
Comprehension 2
Application 3
1
Knowledge in one
discipline
2
Apply knowledge
in one discipline
A
Acquisition
Students gather and store bits of knowledge/information and are expected to remember or understand this acquired knowledge.
Low-level Knowledge
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A Quadrant
• name• label• define• select• identify• list• memorize• recite• locate• record
• definition• worksheet• list• quiz• test• workbook• true-false• reproduction• recitation
Verbs Products
8
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Awareness 1
Comprehension 2
Application 3
B
Application
3
Apply knowledge
across disciplines
4
Apply to real-world
predictable situation
5
Apply to real-world
unpredictable situation
Students use acquired knowledge to solve problems, design solutions, and complete work.
Low-level Application
9
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B Quadrant
• apply• sequence• demonstrate• interview• construct• solve• calculate• dramatize• interpret• illustrate
• scrapbook• summary• interpretation• collection• annotation• explanation• solution• demonstration• outline
Verbs Products
10
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Application 3
Analysis 4
Synthesis 5
Evaluation 6
1
Knowledge in one
discipline
2
Apply knowledge
in one discipline
C
Assimilation
Students extend and refine their knowledge so that they can use it automatically and routinely to analyze and solve problems and create solutions.
High-level Knowledge
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C Quadrant
• sequence• annotate• examine• report• criticize• paraphras
e• calculate• expand• summarize• classify• diagram
Verbs Productsessayabstractblueprintinventoryreportplanchartquestionnaireclassificationdiagramdiscussioncollectionannotation 12
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3
Apply knowledge
across disciplines
4
Apply to real-world
predictable situation
5
Apply to real-world
unpredictable situation
Application 3
Analysis 4
Synthesis 5
Evaluation 6
D
Adaptation
Students think in complex ways and apply acquired knowledge and skills, even when confronted with perplexing unknowns, to find creative solutions and take action that further develops their skills and knowledge.
High-level Application
13
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D Quadrant
• evaluate• validate• justify• rate• referee• infer• rank• dramatize• argue• conclude
• evaluation• newspaper• estimation• trial• editorial• radio program• play• collage• machine• adaptation• poem• debate• new game• invention
Verbs Products
14
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1514
RIGOR
RELEVANCE
A B
DC
Rigor/Relevance FrameworkRigor/Relevance Framework
RoutineMemorization
Four Quadrants of Learning
ComplexAnalytical
ChallengingReal World
PracticalHands On
High
HighLow
Low Acquisition
A
Application
B
AdaptationD
Assimilation
C
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Rigor/Relevance FrameworkHistory - High School
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RIGOR
RELEVANCE
A B
DCHigh
HighLow
LowIdentify nations involved and reasons for WWII
Analyze original documents and summarize reasons for US opposition to entering WWII
Summarize global impacts of WWII and project impacts of Iraq war
Interview local WWII veterans and describe impacts from their perspective.
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International Center for Leadership in Education
A Use color counters to solve simple computational problems
B Sort quantities to discover fractions of the whole
C Find values in number sentences when represented by unknowns
D Develop formula for determining a large quantity without counting, such as beans in a jar.
Domain: Operational Thinking for Algebra
R/R Quadrant Student Performance
•Example Multiple Performances for Single StandardMath – K-5 Level
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RIGOR
RELEVANCE
AA BB
DDCC
Rigor/Relevance FrameworkRigor/Relevance Framework
TeacherTeacherWorkWork
Teacher/Student RolesTeacher/Student Roles
StudentStudentThinkThink
StudentStudentThink & WorkThink & Work
StudentStudentWorkWork
High
HighLow
Low
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RIGOR
RELEVANCE
AA BB
DDCC
Rigor/Relevance FrameworkRigor/Relevance Framework
RightRightAnswerAnswer
Did Students Get it Right?Did Students Get it Right?
RationalRationalAnswerAnswer
RightRightQuestionsQuestions
RightRightProcedureProcedure
High
HighLow
Low
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Instructional Instructional Strategies: Strategies:
How to How to Teach for Teach for Rigor and Rigor and RelevanceRelevance
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KNOWLEDGE
A P P L I C A T I O N
AA BB
DDCC
Rigor/Relevance Rigor/Relevance FrameworkFramework
ActivitiesActivities
ProjectsProjects
ProblemsProblems
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International Center for Leadership in Education
Selection Selection of of StrategieStrategies Based s Based on on Rigor/Rigor/Relevance Relevance FrameworFrameworkk
Page 1Page 1
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International Center for Leadership in Education
Selection Selection of of StrategieStrategies Based s Based on on Rigor/Rigor/Relevance Relevance FrameworFrameworkk
Page 2Page 2
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Rigor/ RelevanceHandbook
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Relevance makes rigor possible!
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PARCC Assessment DesignEnglish Language Arts/Literacy and Mathematics, Grades 3-11
End-of-Year Assessment
•Innovative, computer-based items•Required
Performance-BasedAssessment (PBA)
•Extended tasks•Applications of concepts and skills•Required
Diagnostic Assessment• Early indicator of student knowledge and skills to inform instruction, supports, and PD•Non-summative
Speaking And ListeningAssessment
•Locally scored•Non-summative, required
2 Optional Assessments/Flexible Administration
Mid-Year Assessment•Performance-based•Emphasis on hard-to-measure standards•Potentially summative
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Claims Driving Design: ELA/Literacy
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Claims Driving Design: Mathematics
Students are on-track or ready for college and careers
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Advances in the PARCC ELA/Literacy Assessment
August 2012
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I. PARCC Core Commitments, Key Shifts in the Standards, and the Corresponding
Advances in PARCC
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PARCC is designed to reward quality instruction aligned to the Standards, so the assessment is worthy of preparation rather than a distraction from good work.
PARCC’s Fundamental Advance
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• Texts Worth Reading: The assessments will use authentic texts worthy of study instead of artificially produced or commissioned passages.
• Questions Worth Answering: Sequences of questions that draw students into deeper encounters with texts will be the norm (as in an excellent classroom), rather than sets of random questions of varying quality.
• Better Standards Demand Better Questions: Instead of reusing existing items, PARCC will develop custom items to the Standards.
• Fidelity to the Standards (now in Teachers’ hands): PARCC evidences are rooted in the language of the Standards so that expectations remain the same in both instructional and assessment settings.
PARCC’s Core Commitments to ELA/Literacy Assessment Quality
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• PARCC states first developed the Model Content Frameworks to provide guidance on key elements of excellent instruction aligned with the Standards.
• Then, those Frameworks informed the assessment blueprint design.
So, for the first time. . .
• PARCC is communicating in the same voice to teachers as it is to assessment developers!
• PARCC is designing the assessments around exactly the same critical content the standards expect of teachers and students.
What is Different About PARCC’s Development Process?
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1. Complexity: Regular practice with complex text and its academic language.
2. Evidence: Reading and writing grounded in evidence from text, literary and informational.
3. Knowledge: Building knowledge through content rich nonfiction.
What Are the Shifts at the Heart of PARCC Design (and the Standards)?
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The CCSS Shifts Build Toward College and Career Readiness for All Students
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Staircasing Texts
Text at Low End of Grade Band
Text Between Low End and Middle of
Grade Band
Text Near Middle of Grade Band
Text Between Middle and High End of Grade Band
Text at High End of Grade Band
Beginning of Year
End of Year
Toward CCR
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Overview of Text Complexity
Reading Standards include over exemplar texts (stories and literature, poetry, and informational texts) that illustrate appropriate level of complexity by grade
Text complexity is defined by:
Qua
litat
ive
1. Qualitative measures – levels of meaning, structure, language conventionality and clarity, and knowledge demands Q
uantitative
2. Quantitative measures – readability and other scores of text complexity
Reader and Task
3. Reader and Task – background knowledge of reader, motivation, interests, and complexity generated by tasks assigned
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Step 1: Qualitative Measures
Measures such as:• Levels of meaning• Levels of purpose• Structure• Organization• Language conventionality• Language clarity• Prior knowledge demands
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SMARTER Balanced Assessment Consortia
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Measures such as:• Word length• Word frequency• Word difficulty• Sentence length• Text length• Text cohesion
Step 2: Quantitative Measures
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Quantitative: Using Formulas
Lexile®sentence length + word
frequency
Spache sentence length + unfamiliar words
Dale-Chall sentence length + unfamiliar words
Flesch-Kincaid sentence length + word length in syllables
Fry sentence length + word length in syllables
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Text Complexity Grade Bands and Associated Lexile Ranges
Text Complexity Grade Band in the
Standards
Old Lexile Ranges Lexile Ranges Aligned to CCR
expectations
K-1 N/A N/A
2-3 450-725 450-790
4-5 645-845 770-980
6-8 860-1010 955-1155
9-10 960-1115 1080-1305
11-CCR 1070-1220 1215-1355
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Lexile Analyzerhttp://www.lexile.com/analyzer/
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Step 3: Reader and Task
Considerations such as:•Motivation•Knowledge and experience•Purpose for reading•Complexity of task assigned regarding text•Complexity of questions asked regarding text
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Step 4: Recommended Placement
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Step 4: Recommended Placement
After reflecting upon all three legs of the text complexity model we can make a final recommendation of placement within a text and begin to document our thinking for future reference.
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The CCSS Shifts Build Toward College and Career Readiness for All Students
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Grade 4 Informational
Integration of Knowledge and Ideas 8 Explain how an author uses reasons and evidence to support particular points in a text.
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Performance Task
Students explain how Melvin Berger uses reasons and evidence in his book Discovering Mars: The Amazing Story of the Red Planet to support particular points regarding the topology of the planet. [RI.4.8]
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Key Ideas and Details
RI.7.1. Cite several pieces of textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text. RI.7.2. Determine two or more central ideas in a text and analyze their development over the course of the text; provide an objective summary of the text. RI.7.3. Analyze the interactions between individuals, events, and ideas in a text (e.g., how ideas influence individuals or events, or how individuals influence ideas or events).
Craft and Structure
RI.7.4. Determine the meaning of words and phrases as they are used in a text, including figurative, connotative, and technical meanings; analyze the impact of a specific word choice on meaning and tone. RI.7.5. Analyze the structure an author uses to organize a text, including how the major sections contribute to the whole and to the development of the ideas. RI.7.6. Determine an author’s point of view or purpose in a text and analyze how the author distinguishes his or her position from that of others.
Integration of Knowledge and Ideas
RI.7.7. Compare and contrast a text to an audio, video, or multimedia version of the text, analyzing each medium’s portrayal of the subject (e.g., how the delivery of a speech affects the impact of the words). RI.7.8. Trace and evaluate the argument and specific claims in a text, assessing whether the reasoning is sound and the evidence is relevant and sufficient to support the claims. RI.7.9. Analyze how two or more authors writing about the same topic shape their presentations of key information by emphasizing different evidence or advancing different interpretations of facts.
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Performance Task• Students determine the figurative and
connotative meanings of words such as wayfaring, laconic, and taciturnity as well as of phrases such as hold his peace in John Steinbeck’s Travels with Charley: In Search of America. They analyze how Steinbeck’s specific word choices and diction impact the meaning and tone of his writing and the characterization of the individuals and places he describes. [RI.7.4]
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The CCSS Shifts Build Toward College and Career Readiness for All Students
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Text Dependent Questions
• Step One: Identify the Core Understandings and Key Ideas of the Text– Design Backwards– What are the major points– Essential to designing good questions
and a culminating assignment–
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Text Dependent Questions
• Step Two: Start Small to Build Confidence– Opening questions should be ones that
help orientate students to the text– Be sufficiently specific enough for them
to answer – Confidence to tackle more difficult
questions later on. –
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Text Dependent Questions
• Step Three: Target Vocabulary and Text Structure– Key text structures– Academic words in the text that are
connected to the key ideas and understandings, and
– Craft questions that illuminate these connections
–
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Text Dependent Questions
• Step Four: Tackle Tough Sections Head-on– Find the sections of the text that will present
the greatest difficulty and craft questions that support students in mastering these sections (these could be sections with difficult syntax, particularly dense information, and tricky transitions or places that offer a variety of possible inferences).
–
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Text Dependent Questions
• Step Five: Create Coherent Sequences of Text Dependent Questions – Questions should not be random but
should build toward more coherent understanding and analysis to ensure that students learn to stay focused on the text to bring them to a gradual understanding of its meaning.
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Text Dependent Questions• Step Six: Identify the Standards That
Are Being Addressed • Step Seven: Create the Culminating
Assessment– (a) mastery of one or more of the standards– (b) involves writing, and– (c) is structured to be completed by
students independently.
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A Close Reading of Lincoln’s Gettysburg Address
• SECTION 1 What’s at stake: a nation as a place and an idea
• (1–2 days)• Section 1 Activities • Students first read Lincoln’s Gettysburg Address silently. • Teacher reads out loud, student follow along• Students re-read the first paragraph and translate it into their
own words.• Teacher asks the class a small set of guiding questions about
the first paragraph of Lincoln’s speech.• After the discussion, students rewrite their translation of
Lincoln’s paragraph.• The teacher guides discussion of first line of second paragraph. • Wrap up.
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A Close Reading of Lincoln’s Gettysburg Address
• SECTION 1 What’s at stake: a nation as a place and an idea
• (1–2 days)• Section 1 Activities • Students first read Lincoln’s Gettysburg Address silently. • Teacher reads out loud, student follow along• Students re-read the first paragraph and translate it into their
own words.• Teacher asks the class a small set of guiding questions about
the first paragraph of Lincoln’s speech.• After the discussion, students rewrite their translation of
Lincoln’s paragraph.• The teacher guides discussion of first line of second paragraph. • Wrap up.
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A Close Reading of Lincoln’s Gettysburg Address
• In the first sentence, what does Lincoln tell us about this new nation?
•“Four score and seven years ago our fathers brought forth on this continent, a new nation, conceived in Liberty, and dedicated to the proposition that all men are created equal.”
•
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Creating Text Based Questions
In small groups develop several questions that require close reading of the passage.
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A Close Reading of Lincoln’s Gettysburg Address
• Guiding Questions:
– What does Lincoln mean by “four score and seven years ago”? Who are “our fathers”?
– What does conceived mean? – What does proposition mean? – What is he saying is significant about
America? Is he saying that no one has been free or equal before? So what is new?
– Sum up and gather what students have learned so far: have students summarize the three ways in which the nation is new.
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Text Dependent Questions
• Close analytic reading of Lincoln’s “Gettysburg Address,” the following would not be text dependent questions:
• Why did the North fight the civil war?• Have you ever been to a funeral or gravesite?• Lincoln says that the nation is dedicated to
the proposition that “all men are created equal.” Why is equality an important value to promote?
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Why Literacy in History/Social Studies, Science and Technical?
Students are consistently unable to meet the demands of reading text within a particular discipline.
Reading within a discipline is different than reading literature.
The ability to read within the discipline is important to citizenship.
Being literate across a broad range of disciplines is required to be considered College and Career Ready.
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How is reading history/social studies different from other types of reading?
• History is interpretive.• History is an argument in favor of a
particular narrative.• Who the author is matters.
(sourcing)• The author’s purpose matters. (bias
and perspective)• A single text is problematic.
(corroboration)
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How is reading science and technical reading different from other types of reading?
• Focus is on claims and counter claims• Precise details, complex details and
processes• Analyze results by comparing• Determining what question is being
raised• Navigate text, graphs, tables, charts• Evaluate basis for claims
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Teaching ChannelSarah Brown Wessiling
http://www.teachingchannel.org/videos/pinwheel-discussions-texts-in-conversation
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What is your focus?1. Examine your data2. Gap Analysis3. Identify 1-2 focus areas4. Build from strengths5. Define measurable criteria6. Monitor, Monitor, Monitor7. Support teachers! (Coaching,
Professional development)76
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Solid Implementation • Focus
• Fidelity of Implementation
• Leading and Lagging Indicators
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Proportions of students scoring in each decile of the MCAS 8th grade ELA distribution
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Proportions of students scoring in each decile of the MCAS 8th grade Math distribution
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MCAS Math gains 8th to 10th grade, compared to others from the same 8th grade decile
(School Rank Percentile)
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MCAS ELA gains 8th to 10th grade, compared to others from the same 8th grade decile
(School rank percentile/100)
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OPEN RESPONSE STEPS TO FOLLOW
1. READ QUESTION CAREFULLY. 2. CIRCLE OR UNDERLINE KEY WORDS. 3. RESTATE QUESTION AS THESIS (LEAVING BLANKS). 4. READ PASSAGE CAREFULLY. 5. TAKE NOTES THAT RESPOND TO THE QUESTION. BRAINSTORM & MAP OUT YOUR ANSWER. 6. COMPLETE YOUR THESIS. 7. WRITE YOUR RESPONSE CAREFULLY, USING YOUR
MAP AS A GUIDE. 8. STATEGICALLY REPEAT KEY WORDS FROM THESIS IN YOUR BODY AND IN YOUR END SENTENCE. 9. PARAGRAPH YOUR RESPONSE. 10. REREAD AND EDIT YOUR RESPONSE.
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As a follow up to this activity, I am requiring Department Heads to collect from each teacher at least one student sample from each of the teachers’ classes. The student samples should include:
Student NameTeacher NameDateCourse Name and LevelPeriodA copy of the reading selection and questionEvidence of the student’s active readingAll pre-writing work that the student has done, e.g.
websA copy of the written open response The new scoring rubric and completed assessment
After you have collected the samples from each teacher and have had the opportunity to review them for quality and completeness, please send them to me in a department folder with a checklist of your teachers. Again, please be sure that your teachers clearly label their student samples.
The Open Response calendar of implementation is as follows:
Nov 2-6: Social Science, Social Sci Biling.Nov 30-Dec 4: Wellness, JROTC Dec 14-18: Science, Science BilingualJan 11-15: Business, Tech, & Career Ed.Jan 25-29: Math, Math BilingualFeb 22-26: Foreign Lang, Special EdMar. 7-11: English, ESLMar 20-24 Family &Cons. Sci, ProjGradsApr 5-9: Music, Art
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981/999
Brockton High School 2012
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Nine Specific Advances in the PARCC ELA/Literacy Assessment Demanded by the
Three Core Shifts. . .
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1. PARCC builds a staircase of text complexity to ensure students are on track each year for college and career reading.
2. PARCC rewards careful, close reading rather than racing through passages.
3. PARCC systematically focuses on the words that matter most—not obscure vocabulary, but the academic language that pervades complex texts.
Shift 1: Regular practice with complex text and its academic language
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4. PARCC focuses on students rigorously citing evidence from texts throughout the assessment (including selected-response items).
5. PARCC includes questions with more than one right answer to allow students to generate a range of rich insights that are substantiated by evidence from text(s).
6. PARCC requires writing to sources rather than writing to de-contextualized expository prompts.
7. PARCC also includes rigorous expectations for narrative writing, including accuracy and precision in writing in later grades.
Shift 2: Reading and writing grounded in evidence from text, literary and informational
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8. PARCC assesses not just ELA but a full range of reading and writing across the disciplines of science and social studies.
9. PARCC simulates research on the assessment, including the comparison and synthesis of ideas across a range of informational sources.
Shift 3: Building knowledge through content rich nonfiction
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II. Sample Items Illustrating Some of the Advances
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SO. . .
Two standards are always in play—whether they be reading or writing items, selected-response or constructed-response items on any one of the four components of PARCC. They are:
– Reading Standard One (Use of Evidence) – Reading Standard Ten (Complex Texts)
Students’ Command of Evidence with Complex Texts is at the Core of Every Part of the Assessment!
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•Evidence-Based Selected Response (EBSR)—Combines a traditional selected-response question with a second selected-response question that asks students to show evidence from the text that supports the answer they provided to the first question. Underscores the importance of Reading Anchor Standard 1 for implementation of the CCSS.
Three Innovative Item Types That Showcase Students’ Command of Evidence with Complex Texts
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•Technology-Enhanced Constructed Response (TECR)—Uses technology to capture student comprehension of texts in authentic ways that have been difficult to score by machine for large scale assessments (e.g., drag and drop, cut and paste, shade text, move items to show relationships).
Three Innovative Item Types That Showcase Students’ Command of Evidence with Complex Texts
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Technology
New Purchases (as of April 2012)– Hardware – 1GHz processor, 1 GB RAM, 9.5 inch screen size (10
inch class), screen resolution of 1024 x 768o Must have tools to temporarily disable features ( i.e.. web
browser, Bluetooth connections, application switching)– Operating Systems – Windows 7, Mac 10.7, Linux (Ubuntu
11.10, Fedora 16), Chrome, iOS, Android 4.0o Will consider older versions and Linux after survey data and
cognitive labs– Network – Must be able to connect to the Internet
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Technology
New Purchases (as of April 2012)– Form Factors –Desktops, laptops, netbooks, thin-client, and
tablets ) iPad, Windows and Android) that meet the above specifications
– Additional Accessories –o Headphones may be required for audio supporto Physical keyboards (as opposed to virtual) and/or mice may be
required for use with tablets
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•Range of Prose Constructed Responses (PCR)—Elicits evidence that students have understood a text or texts they have read and can communicate that understanding well both in terms of written expression and knowledge of language and conventions. There are four of these items of varying types on each annual performance-based assessment.
Three Innovative Item Types That Showcase Students’ Command of Evidence with Complex Texts
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PARCC Summative Assessment with EBSR, TECR, and PCR Items
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Literary Analysis Task (Grade 10):Ovid’s “Daedalus and Icarus” and
Sexton’s “To a Friend Whose Work Has Come to Triumph”
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•Students carefully consider two literary texts worthy of close study.•They are asked to answer a few EBSR and TECR questions about each text to demonstrate their ability to do close analytic reading and to compare and synthesize ideas. •Students write a literary analysis about the two texts.
Understanding the Literary Analysis Task
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• Range: Example of assessing literature and helping to satisfy the 70%-30% split of informational text to literature at the high school grade band.
• Quality: The story of Daedalus and Icarus from Ovid's Metamorphoses is a classic of the genre and has proven to be inspirational to painters and poets alike, and no poet’s version is more striking than that of Anne Sexton. Her “To a Friend Whose Work Has Come to Triumph” refashions the themes of the myth in dramatic fashion, providing a powerful counterpoint for students to explore.
• Complexity: Quantitatively and qualitatively, the passages have been validated and deemed suitable for use at grade 10.
Texts Worth Reading?
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On the following pages, there are two Evidence-Based Selected-Response Items and one Prose Constructed Response Item that challenge students’ command of evidence with complex texts.
Questions Worth Answering?
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Use what you have learned from reading “Daedalus and Icarus” by Ovid and “To a Friend Whose Work Has Come to Triumph” by Anne Sexton to write an essay that provides an analysis of how Sexton transforms Daedalus and Icarus.
As a starting point, you may want to consider what is emphasized, absent, or different in the two texts, but feel free to develop your own focus for analysis.
Develop your essay by providing textual evidence from both texts. Be sure to follow the conventions of standard English.
Grade 10 Prose Constructed-Response Item
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• Specific CCSS alignment to:– RL.10.1 (use of evidence); RI.10.9 (comparison of authors’ presentation); RL.10.10
(complex texts). – W.10.2 (writing to inform and explain); W.10.4 (writing coherently); W.10.9
(drawing evidence from texts).– L10.1-3 (grammar and conventions).
• Measures the ability to explain how one text transforms ideas from another text by focusing on a specific concept presented in the texts (the transformation of ideas with regard to the experience of flying).
• Asks students to write to sources rather than write to a de-contextualized prompt.
• Focuses on students’ rigorously citing evidence for their answer.• Requires students to demonstrate they can apply the knowledge of
language and conventions when writing.
Aligns to the Standards and Reflects Good Practice
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Part A
Which of the following sentences best states an important theme about human behavior as described in Ovid’s “Daedalus and Icarus”?
a.Striving to achieve one’s dreams is a worthwhile endeavor.
b.The thoughtlessness of youth can have tragic results.*
c.Imagination and creativity bring their own rewards.
d.Everyone should learn from his or her mistakes.
Grade 10 Evidence-Based Selected-Response Item
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Part B
Select three pieces of evidence from Ovid’s “Daedalus and Icarus” that support the answer to Part A.
a.“and by his playfulness retard the work/his anxious father planned” (lines 310-311)*
b.“But when at last/the father finished it, he poised himself” (lines 312-313)
c.“he fitted on his son the plumed wings/ with trembling hands, while down his withered cheeks/the tears were falling” (lines 327-329)
d.“Proud of his success/the foolish Icarus forsook his guide” (lines 348-349)*
e.“and, bold in vanity, began to soar/rising above his wings to touch the skies” (lines 350-351)*
f.“and as the years went by the gifted youth/began to rival his instructor’s art” (lines 376-377)
g.“Wherefore Daedalus/enraged and envious, sought to slay the youth” (lines 384-385)
h.“The Partridge hides/in shaded places by the leafy trees…for it is mindful of its former fall” (lines 395-396, 399)
Grade 10 Evidence-Based Selected-Response Item
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• Specific CCSS alignment to:– RL.10.1 (evidence).– RL.10.2 (theme). – RL.10.10 (complex text).
• This item helps students gather information and details for use on the Prose Constructed Response; it requires close analytical reading to answer both parts correctly (e.g., Part A of this item is challenging because it requires synthesis of several parts of the myth to determine the answer).
• Requires students in Part B to provide evidence for the accuracy of their answer in Part A.
• PARCC assessment gives students the opportunity to gain partial credit if their answers reflect genuine comprehension on their part (e.g., they identify the theme correctly and are able to identify at least 2 details).
Aligns to the Standards and Reflects Good Practice
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Part AWhat does the word vanity mean in these lines from the text “Daedalus and Icarus”?
“Proud of his success, the foolish Icarus forsook his guide, and, bold in vanity, began to soar” (lines 345-349)a.arrogance*b.fearc.heroismd.enthusiasm
Part BWhich word from the lines from the text in Part A best helps the reader understand the meaning of vanity?
a.proud*b.successc.foolishd.soar
Grade 10 Evidence-Based Selected-Response Item
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• Specific CCSS alignment to:– RL.10.1 (use of evidence).– RL.10.4 (meaning of words and phrases).– RL.10.10 (complex texts).
• Reflects a key advance, namely focusing on the words that matter most, not obscure vocabulary, but the academic language that pervades complex texts.
• Rewards careful, close reading rather than requiring students to race through the passage to determine the meaning (by using the context of the text) of an academic word that is important to one of the main characters and to the central themes. Again, this item helps students gather details for use on the Prose Constructed Response.
• Credit for Part B (evidence) is given only if Part A is correct, signaling the importance of the connection between the claim and the evidence.
Aligns to the Standards and Reflects Good Practice
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Research Simulation Task (Grade 7): Amelia Earhart’s Disappearance
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• Session 1:– Students begin by reading an anchor text that introduces the topic.
EBSR and TECR items ask students to gather key details about the passage to support their understanding.
– Then, they write a summary or short analysis of the piece.• Session 2:
– Students read two additional sources (may include a multimedia text) and answer a few questions about each text to learn more about the topic so they are ready to write the final essay and to show their reading comprehension.
– Finally, students mirror the research process by synthesizing their understandings into an analytic essay using textual evidence from several of the sources.
Understanding the Research Simulation Task
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• Range: Example of assessing reading across the disciplines and helping to satisfy the 55%-45% split of informational text to literature at the 6-8 grade band.
• Quality: The texts on Amelia Earhart represent content-rich nonfiction on a topic that is historically significant.
• Complexity: Quantitatively and qualitatively, the passages have been validated and deemed suitable for use at grade 7.
Texts Worth Reading?
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On the following pages there are two Prose Constructed Response Items and one Technology Enhanced Constructed-Response Item that challenge students’ command of evidence with complex texts.
Questions Worth Answering?
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Based on the information in the text “Biography of Amelia Earhart,” write an essay that summarizes and explains the challenges Earhart faced throughout her life. Remember to use textual evidence to support your ideas.
Grade 7 Analytical Prose Constructed-Response Item #1
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• Specific CCSS alignment to: – RI.7.1 (use of evidence); RI.7.2 (summary of text); RI.7.10 (complex texts).– W.7.2 (writing to explain or inform); W.7.4 (writing coherently); W.7.9 (drawing evidence
from texts).– L.7.1-3 (grammar and conventions).
• Requires writing to sources rather than to a de-contextualized or generalized prompt (e.g., asks about a specific aspect of Earhart’s life).
• Requires students to draw evidence from the text and cite this evidence clearly.
• Requires students to apply the knowledge of language and conventions when writing.
• Purposely designed to help students gather information for writing the final analytic essay that asks students to evaluate the arguments made in three texts about Earhart’s bravery (i.e., her bravery can be expressed as her ability to face the many challenges).
Aligns to the Standards and Reflects Good Practice
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You have read three texts describing Amelia Earhart. All three include the claim that Earhart was a brave, courageous person. The three texts are:
•“Biography of Amelia Earhart”
•“Earhart's Final Resting Place Believed Found”
•“Amelia Earhart’s Life and Disappearance”
Consider the argument each author uses to demonstrate Earhart’s bravery.
Write an essay that analyzes the strength of the arguments about Earhart’s bravery in at least two of the texts. Remember to use textual evidence to support your ideas.
Final Grade 7 Prose Constructed-Response Item #2
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• Specific CCSS alignment to:– RI.7.1 (use of evidence); RI.7.8 (evaluate claims in a text); RI.7.9 (comparison of authors’
presentation); RI.7.10 (complex texts).– W.7.2 (writing to inform and explain); W.7.4 (writing coherently); W.7.7 (conduct short
research projects); W.7.8 (gather relevant information from multiple sources); W.7.9 (drawing evidence from texts).
– L.7.1-3 (grammar and conventions).
• Measures the ability to compare and synthesize ideas across multiple texts and the ability to analyze the strength of various arguments.
• Asks students to write to sources rather than write to a de-contextualized prompt.
• Focuses on students rigorously citing evidence for their answer.• Requires students to delve deeply into multiple texts to gather evidence to
analyze a given claim, simulating the research process.• Requires students to demonstrate they can apply the knowledge of language
and conventions when writing.
Aligns to the Standards and Reflects Good Practice
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Below are three claims that one could make based on the article “Earhart’s Final Resting Place Believed Found.”
Part A•Highlight the claim that is supported by the most relevant and sufficient facts within “Earhart’s Final Resting Place Believed Found.”
Part B•Click on two facts within the article that best provide evidence to support the claim selected in Part A.
Grade 7 Technology-Enhanced Constructed-Response Item
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• Specific CCSS alignment to: – RI.7.1 (use of evidence).– RI.7.8 (author’s claims and evidence).– RI.7.10 (complex texts).
• This item helps students gather information and details for use on the first and second Prose Constructed Response.
• Requires students to employ reasoning skills, since all of the claims listed could be made, but only one is supported by the most relevant and sufficient facts.
• Reflects the key shift of reading closely and weighing evidence by offering credit for Part B only if Part A is correct.
• Technology enables students to highlight evidence that supports their understanding.
Aligns to Standards and Reflects Good Practice
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Narrative Task (Grade 6):Jean Craighead George’s
Excerpt from Julie of the Wolves
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• Students read one or two brief texts and answer a few questions to help clarify their understanding of the text(s).
• Students then write either a narrative story or a narrative description (e.g., writing a historical account of important figures; detailing a scientific process; describing an account of events, scenes, or objects).
Understanding the Narrative Writing Task
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• Range: Example of assessing literature and helping to satisfy the 55%-45% split of informational text to literature at the 6-8 grade-band.
• Quality: Julie of the Wolves was a winner of the Newbery Medal in 1973. This text about a young Eskimo girl surviving on her own in the tundra by communicating with wolves offers a story rich with characterization and imagery that will appeal to a diverse student population.
• Complexity: Quantitatively and qualitatively, the passages have been validated and deemed suitable for use at grade 6.
Texts Worth Reading?
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On the following pages there is one Evidence-Based Selected-Response Item, one Technology Enhanced Constructed-Response Item, and one Prose Constructed Response Item that challenge students’ command of evidence with complex texts.
Questions Worth Answering?
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In the passage, the author developed a strong character named Miyax. Think about Miyax and the details the author used to create that character. The passage ends with Miyax waiting for the black wolf to look at her.
Write an original story to continue where the passage ended. In your story, be sure to use what you have learned about the character Miyax as you tell what happens to her next.
Grade 6 Prose Constructed-Response Item
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• Specific CCSS alignment to:– RL.6.1 (use of evidence); RL.6.3 (describe how characters respond to changes); RL.6.10 (complex
text).– W.6.3 (narrative writing); W.6.4 (writing coherently).– L.6.1-3 (grammar and conventions).
• Includes rigorous expectations for narrative writing, including weaving details from the source text accurately into an original narrative story (students must draw evidence from the text—character traits and the events of the story—and apply that understanding to create a story).
• For students who struggle to create original stories, the source text provides ideas from which to begin; for those students who readily create imaginative experiences, the source provides a means to “jump off” and innovate.
• Focuses on students applying their knowledge of language and conventions when writing (an expectation for both college and careers).
Aligns to the the Standards and Reflects Good Practice
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Part AWhat does the word “regal” mean as it is used in the passage?a.generousb.threateningc.kingly*d.uninterested
Grade 6 Evidence-Based Selected-Response Item #1
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Part BWhich of the phrases from the passage best helps the reader understand the meaning of “regal?”a.“wagging their tales as they awoke”b.“the wolves, who were shy”c.“their sounds and movements expressed goodwill”d.“with his head high and his chest out”*
Grade 6 Evidence-Based Selected-Response Item #1
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• Specific CCSS alignment to:
– RL.6.1 (use of evidence).
– RL.6.4 (meaning of words and phrases).
– RL.6.10 (complex texts).• Reflects a key shift, namely focusing on the words that matter most, not
obscure vocabulary, but the academic language that pervades complex texts.
• Rewards careful, close reading rather than requiring the students to race through the passage to determine the meaning of an academic word by showing the context within the passage that helped them determine the meaning of the word.
Aligns to the Standards and Reflects Good Practice
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Part ABased on the passage from Julie of the Wolves, how does Miyax feel about her father?a.She is angry that he left her alone.b.She blames him for her difficult childhood.c.She appreciates him for his knowledge of nature.*d.She is grateful that he planned out her future.
Grade 6 Evidence-Based Selected-Response Item #2
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Part BWhich sentence from the passage best shows Miyax’s feelings for her father?a.“She had been lost without food for many sleeps on the North Slope of Alaska.”b.“This could be done she knew, for her father, an Eskimo hunter, had done so.”*c.“Unfortunately, Miyax’s father never explained to her how he had told the wolf of his needs.”d.“And not long afterward he paddled his kayak into the Bering Sea to hunt for seal, and he never returned.”
Grade 6 Evidence-Based Selected-Response Item #2
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• Specific CCSS alignment to:
– RL.6.1 (use of evidence).
– RL.6.3 (how characters respond).
– RL.6.10 (complex texts).• Rewards careful, close reading to find specific information and applying
understanding of a text.• Focuses students on rigorously citing evidence for their answer; students
must provide the context used to establish the accuracy of their answer or they don’t receive credit for the item.
• Asks students to delve deeply into how the main character is feeling as she reflects on her predicament, helping students gather information and details for use on the Prose Constructed Response.
Aligns to the Standards and Reflects Good Practice
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Part AChoose one word that describes Miyax based on evidence from the text. There is more than one correct choice listed below.A.recklessB.livelyC.imaginative*D.observant*E.impatientF.Confident
Grade 6 Technology-Enhanced Selected-Response Item
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Part BFind a sentence in the passage with details that support your response to Part A. Click on that sentence and drag and drop it into the box below.
Part CFind a second sentence in the passage with details that support your response to Part A. Click on that sentence and drag and drop it into the box below.
Grade 6 Technology-Enhanced Selected-Response Item
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• Specific CCSS alignment to:– RL.6.1 (use of evidence).– RL.6.3 (how characters respond).– RL.6.10 (complex texts).
• Rather than a single right answer, this item allows students to explore different solutions and generate varying insights about a multi-dimensional character, choosing the word they most strongly feel they can defend.
• The item also insists on students rigorously substantiating their conclusions/insights about the character of Miyax with two details drawn from the text, helping students gather information and details for use on the Prose Constructed Response.
• Technology enables students to “drag and drop” evidence that supports their understanding.
Aligns to the Standards and Reflects Good Practice
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End-of-Year Assessment (Grade 3):“How Animals Live”
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• Students will be given several passages to read closely.• EBSR and TECR questions will be sequenced in a way that
they will draw students into deeper encounters with the texts and will result in thorough comprehension of the concepts to provide models for the regular course of instruction.
• Will draw on higher order skills such as critical reading and analysis, the comparison and synthesis of ideas within and across texts, and determining the meaning of words and phrases in context.
Understanding the End-of-Year Assessment
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• Range: Follows the requirements in the standards to make use of informational texts, including history, science, and technical passages (50% of the points in grades 3-5 are to come from informational texts).
• Quality: This is an example of a science passage from a third-grade textbook.
• Complexity: Quantitatively and qualitatively, the passages have been validated and deemed suitable for use at grade 3.
Texts Worth Reading?
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On the following pages there is one Evidence-Based Selected-Response Item and one Technology Enhanced Constructed-Response Item that challenge students’ command of evidence with complex texts.
Questions Worth Answering?
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Part A
What is one main idea of “How Animals Live?”
a.There are many types of animals on the planet.
b.Animals need water to live.
c.There are many ways to sort different animals.*
d.Animals begin their life cycles in different forms.
Grade 3 Evidence-Based Selected-Response Item #1
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Part B
Which sentence from the article best supports the answer to Part A?
a.“Animals get oxygen from air or water.”
b."Animals can be grouped by their traits.”*
c."Worms are invertebrates.”
d."All animals grow and change over time.”
e."Almost all animals need water, food, oxygen, and shelter to live."
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• Specific CCSS alignment to:– RI.3.1 (evidence).– RI.3.2 (main idea).– RI.3.10 (complex text).
• While this is an example of a less complex item—one where the main idea and details to support it are explicit and readily found—students must provide evidence for the accuracy of their answer in Part B, illustrating one of the key shifts: use of textual evidence.
Aligns to the Standards and Reflects Good Practice
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Drag the words from the word box into the correct locations on
the graphic to show the life cycle of a butterfly as described in
“How Animals Live.”
Words:
Grade 3 Technology-Enhanced Constructed-Response Item
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• Specific CCSS alignment to:– RI.3.1 (use of evidence).– RI.3.3 (relationship between events).– RI.3.10 (complex texts).
• Reflects the key shift of building knowledge from informational text: – students must apply their understanding of the text to complete the graphic.– requires explicit references to the text as the basis for the answers rather than
simply guessing.
• Whereas traditional items might have asked students to “fill in one blank” on a graphic (with three steps already provided), this technology enhanced item allows students to demonstrate understanding of the entire sequence of the life cycle because none of the steps are ordered for them.
Aligns to the Standards and Reflects Good Practice
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What’s different about CCSS?
These Standards are not intended to be new names for old ways of doing business. They are a call to take the next step. It is time for states to work together to build
on lessons learned from two decades of standards based reforms. It is time to recognize that standards are not
just promises to our children, but promises we intend to keep.
— CCSS (2010, p.5)
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Advances in the PARCC Mathematics Assessment
August 2012
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Focus: PARCC assessments will focus strongly on where the Standards focus. Students will have more time to master concepts at a deeper level.
Problems worth doing: Multi-step problems, conceptual questions, applications, and substantial procedures will be common, as in an excellent classroom.
Better Standards Demand Better Questions: Instead of reusing existing items, PARCC will develop custom items to the Standards.
Fidelity to the Standards (now in Teacher’s hands): PARCC evidences are rooted in the language of the Standards so that expectations remain the same in both instructional and assessment settings.
PARCC’s Core Commitments to Mathematics Assessment Quality
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What Are the Shifts in the Math Standards at the Heart of PARCC Design?
1. Focus: The PARCC Assessment will 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.
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What Are the Shifts in the Math Standards at the Heart of PARCC Design?
Focus
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•
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Shift #1: Focus Strongly where the
Standards Focus
Significantly narrow the scope of content and deepen how time and energy is spent in the math classroom.
• Focus deeply on what is emphasized in the standards, so that students gain strong foundations.
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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). 148
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K 12
Number 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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Grade 1
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Grade 2
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Grade 3
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Grade 4
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Grade 5
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Grade 6
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Fractions, Grades 3–6 3. Develop an understanding of fractions as numbers. 4. Extend understanding of fraction equivalence and ordering. 4. Build fractions from unit fractions by applying and
extending previous understandings of operations on whole numbers.
4. Understand decimal notation for fractions, and compare decimal fractions.
5. Use equivalent fractions as a strategy to add and subtract fractions.
5. Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
6. Apply and extend previous understandings of multiplication and division to divide fractions by fractions.
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Grade 7
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Grade 8
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PARCC High School Framework
•Course-specific analysis.
•General analysis
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HS Framework
• Individual end-of-course overviews.• For each course:
– Examples of key advances from previous grades or courses
– Discussion of Mathematical Practices in relation to course content
– Fluency recommendations
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HS Framework
• Pathway summary table. • Assessment limits table for
standards assessed on more than one end-of-course test.
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Algebra I
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Algebra I
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Geometry
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Algebra II
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Algebra II
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Algebra II
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What Are the Shifts in the Math Standards at the Heart of PARCC Design?
2. Coherence: Think across grades and link to major topics within grades
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Elbow Partner Discussion• Shift #2: Coherence: Think across grades, link to
major topics within grades
• Discuss what coherence in the math curriculum means to you. Be sure to address both elements—coherence within the grade and coherence across grades. Cite specific examples.
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•
One of several staircases to algebra designed in the OA domain.
Alignment in Context: Neighboring Grades and Progressions
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Coherence: Link to Major Topics Within Grades
Example: Data Representation
Standard 3.MD.3
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Example: Geometric Measurement
3.MD, third cluster
Coherence: Link to Major Topics Within Grades
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What Are the Shifts in the Math Standards at the Heart of PARCC Design?
3. Rigor: In major topics, pursue conceptual understanding, procedural skill and fluency, and application.
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•
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Shift #3: Rigor: In Major Topics, Pursue Conceptual Understanding, Procedural Skill and Fluency, and Application
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Rigor -Require fluency, application, and deep understanding
• Conceptual understanding – solving short conceptual problems, applying math in new situations, and speaking about their understanding
• Procedural skill and fluency - speed and accuracy in calculation.
• Application - “real world” situations
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Reasoning• Invite Exploration of important
mathematical concepts• Allow students to solidify and make
connections• Make connections and develop
coherent framework for mathematical ideas
• Problem formulation, problem solving and mathematical reasoning
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Reasoning
• More than one solution• Development of all students’
disposition to do math
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Mathematically proficient students
• Make conjectures• Build logical progressions to explore
the truth of their conjectures• Justify and communicate their
conclusions• Respond to arguments
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Which number does not belong? Why?
4 16 36 48 64 81
Instead of asking which numbers are odd?
From: Math for All: Differentiating Instruction, Grades 3-5, Dacey and Lynch
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Procedural Fluency
• Knowledgeable about procedures• Know when and how to use them• Skill in performing procedures
flexibly, accurately, efficiently and with understanding
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Advances in Assessment
Specific advances in the PARCC mathematics assessments demanded by the three shifts…
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Advances in Assessment Demanded by the Shifts
Shift #1 – Focus: The PARCC assessments will focus strongly where the 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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Grade FluencyK Add/subtract within 5
1 Add/subtract within 10 2 Add/subtract within 20
Add/subtract within 100 (pencil and paper) 3 Multiply/divide within 100
Add/subtract within 1000
4 Add/subtract within 1,000,000 5 Multi digit multiplication ‐
6 Multi digit division‐Multi digit decimal operations ‐
7 Multi digit division‐Multi digit decimal operations ‐
8 Solve simple 22 systems by inspection 184
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Advances in Assessment Demanded by the Shifts
Shift #2 - Coherence: Think across grades, and link to major topics within gradesAdvance: 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), as are key endpoints and takeaway skills (e.g., fluency with the multiplication table in grade 3).
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Advances in Assessment Demanded by the Shifts
Shift #2 - Coherence: Think across grades, and link to major topics within gradesAdvance: 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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Advances in assessment demanded by the shifts
Shift #3 - Rigor: In major topics, pursue conceptual understanding, procedural skill and fluency, and application
Advance: PARCC assessments will reach the rigor in the Standards through innovations in technology and item design…
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Using Technology to Advance Assessment and the Shifts
• Technology enhancements supporting accessibility (e.g., the ability to hover over a word to see and/or hear its definition, etc.)
• Transformative formats making possible what can not be done with traditional paper-pencil assessments (e.g., simulations to improve a model, game-like environments, drawing/constructing diagrams or visual models, etc.)
• Getting beyond the bubble and avoiding drawbacks of traditional selected response such as guessing or choice elimination.
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Using Technology to Advance Assessment and the Shifts
• Capturing complex student responses through a device interface (e.g., using drawing tools, symbol palettes, etc.)
• Machine scorable multi-step tasks are more efficient to administer and score.
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Sample Items Illustrating the Advances in Assessment
The next section of this presentation is comprised of sample items that illustrate some of the advances called for by the three shifts.
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Overview of Mathematics Task Types
PARCC mathematics assessments will include three types of tasks.
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Task Type Description of Task Type
I. Tasks assessing concepts, skills and procedures
• Balance of conceptual understanding, fluency, and application• Can involve any or all mathematical practice standards• Machine scorable including innovative, computer-based formats• Will appear on the End of Year and Performance Based Assessment
components
II. Tasks assessing expressing mathematical reasoning
• Each task calls for written arguments / justifications, critique of reasoning, or precision in mathematical statements (MP.3, 6).
• Can involve other mathematical practice standards• May include a mix of machine scored and hand scored responses• Included on the Performance Based Assessment component
III. Tasks assessing modeling / applications
• Each task calls for modeling/application in a real-world context or scenario (MP.4)
• Can involve other mathematical practice standards.• May include a mix of machine scored and hand scored responses• Included on the Performance Based Assessment component
For more information see PARCC Item Development ITN Appendix D.
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Grade 7 Illustrative Sample Item
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Aligns to the Standards and Reflects Good Practice
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Grade 7 Sample Illustrative Item: Speed
Task Type I: Tasks assessing concepts, skills and procedures Alignment: Most Relevant Content Standard(s)•7.RP.2b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. •In addition, see 7.RP.2d: Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate. (The “explain” portion is not required in the task, but the task involves some of the concepts detailed here.)Alignment: Most Relevant Mathematical Practice(s)•MP.2 enters (Reason abstractly and quantitatively), as students must relate the graphs and tables to each other via the unit rate and then to the context at hand.
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Aligns to the Standards and Reflects Good Practice
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Grade 7 Sample Illustrative Item Key Features and Assessment Advances•The PARCC assessment will seek to preserve the focus of the Standards by thoroughly exploring the major work of the grade. •In this case, a multi-point problem is devoted to a single standard about proportional relationships, which are a major focus in grades 6 and 7. •Unlike traditional multiple choice, it is difficult to guess the correct answer or use a choice elimination strategy. •Variants of the task could probe understanding of unit rates and representations of proportional relationships by showing different scales on the two graphs, and/or by presenting the data in tables C and D with the ordered pairs not equally spaced in time.
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High School Illustrative Sample Item
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Seeing Structure in a Quadratic Equation
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Aligns to the Standards and Reflects Good Practice
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High School Sample Illustrative Item: Seeing Structure in a Quadratic Equation
Task Type I: Tasks assessing concepts, skills and procedures Alignment: Most Relevant Content Standard(s)•A-REI.4. Solve quadratic equations in one variable.
a) Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)2 = q that has the same solutions. Derive the quadratic formula from this form.
b) Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula, and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a bi for real numbers a and b.
Alignment: Most Relevant Mathematical Practice(s)•Students taking a brute-force approach to this task will need considerable symbolic fluency to obtain the solutions. In this sense, the task rewards looking for and making use of structure (MP.7).
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Aligns to the Standards and Reflects Good Practice
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Resources
• PARCC Resources: http://parcconline.org
• Progressions & Common Core Tools
http://commoncoretools.wordpress.com \• Illustrative Mathematicshttp://www.illustrativemathematics.org/
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Resources
• National Council of Supervisors of Math: www.mathleadership.org/ccss
• Mathematics Assessment Project (MAP):
http://map.mathshell.org/materials/background.phpInside mathematics: http://insidemathematics.org
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Practical strategies to support school and district leaders:•Supporting teachers in changing instruction to meet the requirements of the Common Core State Standards and Next Generation Assessments •Approaching evaluation from the broader perspective of selection, support, and evaluation of all educators •Providing meaningful Teacher Evaluations even with limited time and resources
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[email protected] Route 146
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Phone (518) 399-2776
Fax (518) 399-7607
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