FEA/PSA - Judith T. Brendel - Spring 2014

FEA/PSA - Judith T. Brendel - Spring 2014
The PARCC Institute – High School Math: Preparing for PARCC! NJ’s Next Generation Standardized Assessment System FEA/PSA - Judith T. Brendel - Spring 2014

Welcome…

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. Common Core State Standards Partnership for Assessment of Readiness for College and Career

What should teaching and learning in the 21st century look like?”
“…revolutionary transformation rather than evolutionary tinkering.” US DOE, NETP 2010 CONSIDER USING POLL EVERYWHERE – (1-word responses) Revolutionary transformation rather than evolutionary tinkering. 4 4

Preparing a Globally Competent and Innovative Workforce
Education for a Contemporary Age Preparing a Globally Competent and Innovative Workforce 6 6

(What Work Requires of Schools)
A Changing World… A growing need for a paradigm shift in the way we teach and learn… A Nation at Risk (1983) SCANS Report and America (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) Both links work 11/18/13 NATION at RISK: see FINDINGS: Schools in US diff. grades, graduation requirements, college admissions, difficulty subject matter, amt. hw (2/3 say < 1hr/ nt. In HS) SCANS REPT: see What work requires of schools (p.18) … The educational side of work (p.19) US gr.11 stu. Puts in ½ of the 60 hrs a week that a Japanese peer devotes to schoolwork. …. What’s work like today (5 scenarios begin. P. 22) …. 5 competencies (p.26) … 3-part foundation (basic skills, thinking, interpersonal) … implications for learning (p.32 - ) 7 7

A Changing Student… (recommended resources)
Digital Natives, Digital Immigrants – Parts I and II – Do They Really Think Differently? (Prensky, 2001) Marc Prensky’s Essential 21st Century Skills “Different kinds of experiences lead to different brain structures.” Dr. Bruce D. Perry, Baylor College of Medicine LINKS NOT WORKING: Marc is a motivation education speaker … both a visionary and practical 8 8

A Changing Student… (recommended resources)
Authentic Intellectual Work and Standardized Tests: Conflict or Coexistence (2001) How People Learn: Brain, Mind, Experience and School (1999, 2003) 9 9

Listen to our students! “I am a 21st Century Learner!” 10 10 10 10

… through innovative pedagogy and ubiquitous technology.
How? Fostering essential skills… Global competence Content knowledge Entrepreneurship Adaptability Interpersonal Communication Collaborative problem solving Critical thinking Creativity Innovation … through innovative pedagogy and ubiquitous technology. 11 11

What conditions will foster these skills?
“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 : 12 12 12

21st learning… …what should it look like? Dr. BRIAN Chinni’s ‘ANIMOTO’
13

21st learning… 14 14

Common standards,… …common (online) assessments, and common instruction that promote the essential skills. 15 15

Reflection… …what are your thoughts?
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?

Let’s take a (quick) break!

Let’s get to work…

Let’s take our… (page-3)
PARCC Pre-Assessment! Activity 1 – page 2 Do alone (8 questions starting w/ What grade level … ) EXAMPLE 9 require understanding of slope from graph and table …. May skip and do easier examples in lower grades later on Item 9: grade-7 level math w/new CCSS (What’s different?) ADD H.S. EXAMPLE 19 19

A (Quick) Walk through the PARCC!

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 ACHIEVE was selected through a competitive bid process, by PARCC to be the Project Manager.

Race to the Top Assessment Grants:
New Jersey is PARCC Governing Board State: Will administer the assessment system statewide 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.

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)

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

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

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

PARCC Assessment Consortium

K-2 3-8 High School ONGOING STUDENT SUPPORTS/INTERVENTIONS
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 College readiness score to identify who is ready for college-level coursework Targeted interventions & supports: 12th-grade bridge courses PD for educators K-2 3-8 High School SUCCESS IN FIRST-YEAR, CREDIT-BEARING, POSTSECONDARY COURSEWORK ONGOING STUDENT SUPPORTS/INTERVENTIONS

Use the modeling practice to solve real world problems
What does it mean? “Students are on-track or ready for college and careers” (Math) Solve problems involving the major content for their grade level with connections to practices Solve problems involving the additional and supporting content for their grade level with connections to practices Express mathematical reasoning by constructing mathematical arguments and critiques Use the modeling practice to solve real world problems Demonstrate fluency in areas set forth in the Standards for Content in grades 3-6

Assessment Transition Timeline
Spring 2012 NJ ASK Aligned to NJCCCS Spring 2013 NJ ASK Aligned to the CCSS and NJCCCS (Except Gr Math) Spring 2014 Aligned to the CCSS SY Full administration of PARCC assessments “Transitional Assessments”

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! 31

Understanding the Common Core State Standards …is to understand PARCC
PVRSD Math TF – Work Session 1 | November 18, 2010 32

Why Common Core State Standards?
"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. 33 33

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” 34

Principles of the CCSS…
FEWER CLEARER HIGHER Aligned to requirements for College and Career Readiness Based on evidence Honest about time 35

The CCSS Difference: Grade 8 Mathematics
Before: NJCCCS (2004) Understand and apply the Pythagorean Theorem. After: CCSS (2010) Explain a proof of the Pythagorean Theorem and its converse. 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. 36

a2 + b2 = c2 a = 4 b = 3 c = ? 5 25 a b c 3 9 4 16

Implications of the CCSS on WHAT and HOW to teach…
What are the Critical Shifts to Consider? 38

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.

CC SHIFTS in ASSESSMENTS continued ….
Shift 4: Deep Understanding Each 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.

PARCC sample prototypes with Task Type
PVRSD Math TF – Work Session 1 | November 18, 2010 41

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 …. Whole group discuss … Ask what is being assessed I, how is II different from I? …

Tasks assessing concepts, skills and procedures.
TASK TYPE-I Tasks 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.* December 2, 2013

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) HS – Myla’s Swimming Poole (Algebra-I) HS – Green Tea Observation Study (Algebra-2/Math 3) As of Nov. 14, 2013 December 2, 2013

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. December 2, 2013

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 rubric HS – Michelle’s Conjectures (Algebra-II/Math III) HS – Geometric Construction Connection (Geometry/Math III) PARCC_SampleItems_Mathematics_HSGeoMathIIIGeometricConnection_081913_Final_0.pdf As of Nov. 14, 2013 Dec. 2, 2013

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. December 2, 2013

PARCC Model Content Frameworks for Mathematics.*
TYPE-I PARCC TASKS include 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.* SA MS/HS– PD Session 3| April 4., 2011

Functions http://www. parcconline
Given f(x) as a graphed parabola and g(x) as table of values Compare y-intercepts Compare f(3) and g(3) Compare maximum values of each w/in range -5 ≤ x ≤ 5 Compare DIFFICULTY? POINTS? Solutions: What course? Alg.II Level of difficulty? Low … medium … high (1, 2, 3, 4) No Points: 4? What standards: A.REI.D What is different? COURSE ? STANDARDS? A type I PARCC task J. Brendel

Seeing Structure in a Quadratic Equations
(3x - 2)2 = 6x – 4 DIFFICULTY? COURSE ? POINTS? Solutions: What course? Alg.II Level of difficulty? Low … medium … high (1, 2, 3, 4) No Points: 1 What standards: What is different? STANDARDS? a Type-I PARCC task J. Brendel

24 + 10x – x2 = p – (x – 5)2 Solve for p
Seeing Structure in Equations x – x2 = p – (x – 5)2 Solve for p COURSE ? DIFFICULTY? POINTS? Course: Algebra-I/Math I Points: 1 Standards: STANDARDS? a Type I PARCC task J. Brendel

PICTURE FRAME DIFFICULTY? COURSE ? POINTS? STANDARDS?
DIFFICULTY? COURSE ? POINTS? STANDARDS? Algebra-I/Math-II Standard: ASSE 1-2 Points: 2 Length of picture alone in inches = X + 2 Length of frame in inches = X + 4 Area of picture alone = x (x+2) … they don’t ask student to solve ... could be x2 + 2x Area of picture and frame together = (x+4) ( x+2) … “ ‘ …. Could be x2 + 12x + 8 Scoring: all 4 parts correct = 2 points, 3 parts correct = 1 point a Type I PARCC task J. Brendel

GREEN TEA TYPE COURSE ? DIFFICULTY? POINTS? STANDARDS?
COURSE ? DIFFICULTY? POINTS? Algebra II/Math II Standard: S.IC.3-1,3 MP.4 (S.IC.3) Scoring: 2 points 1-point: Part A – “is associated with,” and “the women in the study only.” 1-point: Part B = “be asked to drink green tee;” “be asked not to drink green tea,” and “at random.” STANDARDS? a Type I PARCC task J. Brendel

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.

GRAPH of FUNCTIONS COURSE ? DIFFICULTY? POINTS ? STANDARDS?
GRAPH of FUNCTIONS (posted November 2013) COURSE ? DIFFICULTY? POINTS ? STANDARDS? POINTS: 2- 4? Algebra-II/Math 3? Standards: A.REI.D a Type-II PARCC Task

GEOMETRY CONSTRUCTION CONNECTION
GEOMETRY CONSTRUCTION CONNECTION POINTS ? STANDARDS? DIFFICULTY? Points 3 Geometry//Math 3 Task type 2 Standards G-CO.D a Type-II PARCC Task

MICHELLE’S CONJECTURES
(Aug.19, 2013) DIFFICULTY? COURSE ? POINTS ? Points 3 Algebra-II//Math 3 Points STANDARDS? a Type-II PARCC Task

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.

MINI GOLF PRICES COURSE ? DIFFICULTY? POINTS ? STANDARDS?
MINI GOLF PRICES (November, 2013) COURSE ? DIFFICULTY? POINTS ? ALGEBRA-I/Math-II Points: 6 Standards: FBF-I STANDARDS? a Type-III PARCC Task

BRETT’S RACE DIFFICULTY? COURSE ? POINTS ? STANDARDS? (November, 2013)
BRETT’S RACE (November, 2013) COURSE ? DIFFICULTY? POINTS ? ALGEBRA-I Level-3 Standards D.205, A.CED, A.CED.A Problem-Based Task assessment only Points: 3 Part A . 1 pt. – formulate mode y = 81/3x + 20 … or y = 100/12 = 20 x= 9.6; Olympian y = 100, 100 = 10x, 10 = xOlympian’s distance is related to time y = 10x Points: Part B. 1 pt – correct winner …and … correct margin of victory … Brett = 0.4 seconds STANDARDS? a Type-III PARCC Task

POPCORN INVENTORY DIFFICULTY? COURSE ? POINTS ? a Type-III PARCC Task
(NOVEMBER 2013) COURSE ? DIFFICULTY? POINTS ? COURSE: ALGEBRA-I LEVEL III Points: 6 Standards HS Di-I 7.RP.2,3 a Type-III PARCC Task

TEMPERATURE CHANGES COURSE ? DIFFICULTY? POINTS ?
COURSE ? DIFFICULTY? POINTS ? COURSE: Algebra-II/Math III Level III Points 3 (can be scored 0, 1, 2, or 3) Standards: F.BF.A, F.IF.4 a Type-III PARCC Task

As of 12/4/2013

PARCC RELEASED TASKS include elsewhere? Use this slide to ‘hold’ sites
file://localhost/Users/jbrendel/Desktop/PARCC%20HS%20Functions.html (November/December 2013)

Statistical analysis to rank baseball players GRADES 11-12
min lesson “fly quadcopters” math/science/engineering … a 4-month project … Ms. Brookins and Mr. James GRADE-11 How/if .. .include here? Statistical analysis to rank baseball players GRADES 11-12 CCSS Standards: Math SID. 1, 2 and 3 SA MS/HS– PD Session 3| April 4., 2011

What you SHOULD NOT see !

x y > (3,6) (3,2) Z N Slope = < slope =

What should teachers NOT be doing?
BRAINSTORM in GROUPS What should teachers NOT be doing? SA MS/HS– PD Session 3| April 4., 2011

READING CCSS and Mathematics

Not Text-Dependent in ELA Text-Dependent in ELA
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 According to Lincoln’s speech, why is this year significant to the events described in the speech? Examples of questions that take students outside and inside the text. Text-dependent questions require students to pay attention to the text at hand and to draw evidence from that text. What does this look like in the classroom? Teachers insist that classroom experiences stay deeply connected to the text on the page and that students develop habits for making evidentiary argument both in conversation, as well as in writing to assess comprehension of a text. Students have rich and rigorous conversations and develop writing that are dependent on a common text.

Text-Dependent in mathematics
Use a high school EXAMPLE not grade-2 December 2, author: J. Brendel Material not to be duplicated.

Regular Practice with Complex Text and
its Academic Language Attendees make a list of 10 Vocab words specific to hs math 72

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 73

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 Or “base salary” plus “commission” – similar vocab. students rarely know 74

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 Teacher (mid Nov in cp Geometry) … students had hands-on construction practice w/compass & protractor … for 3 different special line segments … and they never used the terminology. Not discovery-based … followed teacher step-by-step … (The could have done wax-paper folding as informal discovery … and will do Geometer’s Sketchpad constructions following week). May have been more effective to do more w/’medians’ first and include applications and real-life problem scenarios. 75

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. Kappan article re elementary mathematics and ‘habits to change.’ OTHER PROBLEMS: focus on interesting students/getting them moving/ motivated … but … improper math habits and language! Relate TV video Excellent Teaching (saw Nov. 28, 2013) … model classroom experiences … mid school … students survey time classmates spent each day (1-week) using diff. forms of technology, reading, etc. … Teacher ‘told them’ just put minutes over 60 and get decimal number … then she read decimal number as “point 45” … no discussion of estimated and comparing to ‘half,’ … no discussion of what “point 45” really meant … Students mimicked the teacher’s terminology. 76

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. 77

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 78

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 79

Texts Worth Reading…and Questions Worth Answering!
It all boils down to… Texts Worth Reading…and Questions Worth Answering! 80

Let’s take a quick break!
1 minute stretch 81

Understanding the Common Core Math Standards …is to understand PARCC Math!
Processing the CC Math Shifts Activity Here! PVRSD Math TF – Work Session 1 | November 18, 2010 82

The Common Core Standards: Classroom Video Illustration
High School School Click to link to online video … NYC Hillcrest HS Queens NY … see applications / hear CCSS HS concepts outlined …

The Standards are NOT new names for old ways of doing things…

NOT … 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 85 85

Dan Meyer: Math Class Needs a Makeover
Dan Meyer’s is a high school math teacher. I believe this video is helpful in showing WHAT this learning looks like in the classroom. He does not address content/curriculum development specifically, but I believe models high student engagement, critical thinking in authentic learning situations. He also shares how disciplines can work collaboratively.

From.... To…. 856 = ___ hundreds, ___ tens, ___ ones 1 hundredth = ___ tenths x2 + 10x + 21 = 0 ¾ c(c –1) = c 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. NOT 87

Three (3) Significant Shifts in Mathematics:
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. Processing the CC Math Shifts Activity Here 88

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. NO Handout page- Processing the CC Math Shifts Activity Here 89

 Students will have more time to master concepts at a deeper level.
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.

The shape of math in A+ countries…
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 1 Schmidt, Houang, & Cogan, “A Coherent Curriculum: The Case of Mathematics.” (2002). 92

Traditional U.S. Approach…
K Number and Operations Measurement and Geometry Algebra and Functions Statistics and Probability 1 minute stretch 93 93

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 1 minute stretch 94

Priorities in Mathematics (CCSS)
Grade Focus Areas in Support of Rich Instruction and Expectations of Fluency and Conceptual Understanding K–2 Addition and subtraction - concepts, skills, and problem solving and place value 3–5 Multiplication and division of whole numbers and fractions – concepts, skills, and problem solving 6 Ratios and proportional reasoning; early expressions and equations 7 Ratios and proportional reasoning; arithmetic of rational numbers 8 Linear algebra, linear functions 1 minute stretch 95 95

Priorities in Mathematics (CCSS)- MS/HS
ALG. - 1 Focus 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 Model Curriculum – print out from our district 96 96

Priorities in Mathematics (CCSS) - HS
GEOMETRY Focus 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-6 Applications of Probability Model Curriculum – print out from our dist. 97 97

Priorities in Mathematics (CCSS) – HS
ALG. - 2 Focus 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 Model Curriculum – print out from our dist. 98 98

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. Processing the CC Math Shifts Activity Here 99 99

COHERENCE Integrative tasks draw on multiple standards to ensure students are making important connections.  The Standards are not treated as a checklist.

COHERENCE Need to include h.s. task(s) that incorporate multiple standards to show connections.

Circle all that are true. Given: All squares
Coherence and NEW multiple-choice questions. Circle all that are true. Given: All squares are parallelograms and rectangles have 4 acute angles have only 2 diagonals Area = ½ base x height Sum of consecutive angles = 180˚ Perimeter = 2 x Side length Area > area with the same perimeter. 5 3 7 25 21 SAMPLE NEW MC TYPE (multiple standards)

*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 Work in groups … give enough time and workspace

Coherence: Link to major topics within grades
Example: HIGH SCHOOL performance task; 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. Write an equation for the total number of gallons of fuel …. How much fuel is in the tanks after the pump … 8 minutes? Graph the equation … on the coordinate plane … label …. Algebra-I Unit-1 104 104

RIGOR Need to include h.s. task(s) that incorporate multiple standards to show connections.

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. Processing the CC Math Shifts Activity Here Guess the grade level! 107

See the Rigor in Grade-3 Fractions on a Number Line
A major topic focus in 3rd grade is fractions. This problem causes students to truly understand fractions and not just memorize patterns.

See the Rigor in Middle Grades
Understanding 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) Processing the CC Math Shifts Activity Here 109

See Rigor in Grade 6: Ratios
Ratios is one of the major topics of focus for 6th grade. This is not your typical ratio problem. Students must build upon their solid knowledge of fractions, established primarily in 3rd grade, and apply it to what they have learned about ratios. This problem not only demonstrates Shift 1, focus where the standards focus, but also Shift 2 – Coherence within and across grade levels. PARCC - Grade-6 Slider Ruler: type-I

ONLINE http://www.parcconline.org/samples/item-task-prototypes
Grade-3 Fractions on a Number Line: type- I Grade-4 Fraction model: type-II Grade-6 Slider Ruler: type-I SHOW ONLINE: Easiest to go to main site and then to each grade … otherwise returns to this ‘create’ screen between links GR.3 fractions on number line type-I (slide points to number line … can correct before submit) Gr.6 slider ruler type-I Gr.4 fraction model type-II (if time … you can’t actually type here)

See the Rigor in High School Math

Linking to major topics – Grade 7
This two-part problem illustrates coherence within and across grade levels. You see major topics covered previously as well as multiple grade level concepts being connected to each other..

Part B Are these the types of questions we are asking in our classrooms or are we just leading our children through rote practice applying memorized algorithms with little or no conceptual understanding?

Linking to major topics – High School Part A
A high school example, again demonstrating coherence within and across grade bands.

Part B Describe Write Compare
Students must be able to apply the skills used to solve Part A to create a new example and must be able to explain. General note: Students are expected to recognize and compare functions seen within a scenario, as an algebraic equation, a table, or graph. (Relate to how do you compare fractions with different denominators … or numbers seen as decimals, percents, and fractions.)

REQUIRED FLUENCIES SA MS/HS– PD Session 3| April 4., 2011

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 2 2.OA.2 2.NBT.5 Add/subtract within 20 (know single-digit sums from memory) Add/subtract within 100 3 3.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.2,3 Multi-digit division Multi-digit decimal operations Processing the CC Math Shifts Activity Here 118 118

HS EXPECTATIONS ALGEBRA-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 … A.REI.10, 11 major F.IF.7/9 supporting Color codes used in Model Curriculum: Green – major Turquoise = supporting Yellow = additional A.REI.5, A.REI.6 additional Dec. 2, 2013 J.Brendel

Coherence: Link to Major Topics Across Grades
6. Apply properties One of several staircases to algebra designed in the OA domain. 5. expressions Algebra begins in 6.EE.3 in its cleanest sense. Here is a beautiful illustration of the design of the standards. {read slide} 3. multiply … divide 1. add … subtract 120

Coherence: Link to Major Topics Across Grades
One of several staircases to algebra designed in the OA domain. ALGEBRA- II ALGEBRA-I Algebra-I to II ( begins in 6.EE.3 – see progression at HS level) {read slide} 121

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. Using mathematics in problem solving contexts is the third leg of the stool supporting the learning that is going on in the math classroom. This is the “why we learn math” piece, right? We learn it so we can apply it in situations that require mathematical knowledge. There are requirements for application all the way throughout the grades in the CCSS. {read slide} But again, we can’t just focus solely on application—we need also to give students opportunities to gain deep insight into the mathematical concepts they are using and also develop fluency with the procedures that will be applied in these situations. The problem-solving aspect of application is what’s at stake here—if we attempt this with a lack of conceptual knowledge and procedural fluency, the problem just becomes three times harder. At the same time, we don’t want to save all the application for the end of the learning progression. Application can be motivational and interesting, and there is a need for students at all levels to connect the mathematics they are learning to the world around them.

FLUENCY and new type of MC question
3rd grade PARCC Fluency Sample. Students must be able to move with ease through basic multiplication and division facts to recognize which of these equations are true.

Real world application – Grade 4
Relatable, real-world problems will engage students and demand they apply their conceptual understandings in new and rigorous ways.

HS Teachers outside of math use grade-level-appropriate math
This is a high school prototype, which asks students to connect math and science, demonstrates beautifully the application component of Shift 3. This problem has 4 parts, the last of which asks students to explain their thinking in detail and connect it to prior learning.

Part B In Part B of the same problem, students must move the tiles to write a recursive definition using the chart at the top.

Part C In Part C, students must recognize statements that are true after applying the formula.

Part D We must not teach students to take tests but rather prepare them to solve problems creating and explaining their own solutions. FROM Kimberley Harrington, Director of Standards, NJ Department of Education

Standards of Mathematical Practices
Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning. Construct viable arguments and critique the reasoning of others Model with mathematics. Attend to precision 129

Mathematics Assessment:
Analysis of the PARCC Mathematics Assessment: Design Shifts (Activity No. 4) 130

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. 131

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 3 Become key endpoints and takeaway skills 132

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. 133

Shift No. 3…Rigor Advance: PARCC assessments will reach the rigor in the Standards through innovations in technology and item design. 134

and High School Reference Sheet
SAMPLE ALGEBRA-1 UNIT-I ASSESSMENT and High School Reference Sheet (separate packet) Solution Guide With notes to teachers Sample responses and scoring Distribute sample Algebra-I Unit-I test w/rubric … and HS Reference sheet December 2, 2013

The Mathematics Common Core Toolbox
Mathematics 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 ) High School (Popcorn Inventory) new Nov. 2013 HSAlg1Math1PopcornInventory.pdf Activity: grade-2 (p ) *What makes it unique? …. Online to see all … hardcopy of Grade-4 and HS in packet Look at Popcorn Inventory … discuss …. What skills students’ need … how to transition to these types of problems? 136

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)

Sample Online Performance Tasks
Mathematics 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) Do one … then see grade-2 hardcopy …. Students CAN PRACTICE off-line, too. Have HS students begin w/MS resources (KISS) new process/easy content. 138

EXPERIENCE an ASSESSMENT Activity 6
Sample online Smarter Balanced Assessments. Select from grades 3, 4, 5, 6, 7, 8 or 11 Select Examples or Performance Tasks Link to Smarter Balanced site to experience Performance Task … Discuss skills and experiences students need to develop … PARCC expected to make sample assessments available late spring 2014. J.Brendel 11/2013

CIRCLES MATH II - WALLS J. Brendel 11/2013

The Specs, Accountability,
and Resources: What We Know Now! 141

PARCC Assessment Consortium

Dynamic Learning Maps (DLM) Alternate Assessment Consortium

Estimated Time on Task: Grade 9-10 Performance Based Assessment
ELA/Literacy Math TOTAL Grade Literacy Analysis Research Narrative Session 1 2 9-10 Alg I/ Math I Geo/ Math II Estimated Time on Task (minutes) 80 85 50 315

Estimated Time on Task: Grade 9-10 End-of-Year (EOY) Assessment
ELA/Literacy Math TOTAL Grade Session 1 2 9-10 Alg I/ Math I Geo/ Math II Estimated Time on Task (minutes) 70 65 270 Grade 9-10 Summative Total: 9 Hours, 45 minutes

Estimated Time on Task: Grade 11 Performance Based Assessment
ELA/Literacy Math TOTAL Grade Literacy Analysis Research Narrative Session 1 2 11 Alg II/ Math III Estimated Time on Task (minutes) 80 85 50 65 345

Estimated Time on Task: Grade 11 End-of-Year (EOY) Assessment
ELA/Literacy Math TOTAL Grade Session 1 2 11 Alg II/ Math III Estimated Time on Task (minutes) 70 55 250 Grade 11 Summative Total: 9 Hours, 55 minutes

End-of-Year machine scored
~ 1/3 total points = PBA EOY = End-of-Year (May?) – machine scored PBA/MYA = performance based assessment/mid-year assessment (Feb.?)

End-of-Year machine scored
Go to slide 124 ~ 1/3 total points = PBA

What Else… 20 Day Window…for both the PBA and EOY summative assessments (performance based and end-of-year) Summative Assessments Retest Opportunities Grades 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… 150

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) 151

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 152

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 153

Modifications Accommodations NOT permitted
Modifications 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;

Modifying the complexity of assessments to make them easier (e. g
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).

Accountability: What We Know Now! 156 156

Distinguished Command
Results Types… Proficiency (PLDs) On-Track-to-College and Career Readiness (CCRDs) Growth Data Performance Level Descriptors (PLDs) Performance Level Description Level 5* Distinguished Command Level 4* Strong Command Level 3 Moderate Command Level 2 Partial Command Level 1 Minimal Command *Achieved CCR Performance Threshold 157

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.” Acuplacer test (Typical Community College placement test) no need to be taken if student “passes” the PARCC test in h.s. 158

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 probability of earning college credit by attaining at least a grade of C or its equivalent in those courses.” 159

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. 160

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.

Timelines and Resources:
What We Know Now! 162 162

PARCC Timeline… Jan – Aug 2013
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 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) 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) “It is anticipated … that the PARCC ONLINE PD modules will be available in June as/site below 11/29/13. 163

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: PARCC Common Assessments Overview Introduction to the PARCC Mid-Year Assessment Introduction to the PARCC Diagnostic Assessment Introduction to the PARCC Speaking/Listening Assessment PARCC Accessibility System *It is anticipated that modules will be available in June 2014. (above on site as of 11/29/13)

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. ( school year) 165

NJDOE Model Curricula (handouts Algebra-I, Geometry, Algebra-II) PARCC Model Content Frameworks
distribute model curric. Our district Alg.I, Geom. Alg recommend adding PARCC and present SmarterBalanced online links to practice examples and performance tasks.

INITIAL QUESTIONS to CONSIDER
when choosing or developing a Quality Math Assessment. See handout page-31 JB modified from:

What does this look like?
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

Links to Model Math Curriculum Sites
Sample Assessments by grade: Common Core and Special Education Students Common Core Practice Test Common Core Resources to use with students Dana Center Resources

ACUITY: a comprehensive K-12 assessment program
COMPANIES are developing new programs to assist districts: ACUITY: a comprehensive K-12 assessment program Tom 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) NOT recommending any … just be aware of what will eventually be available …consider when creating budgets December J.Brendel

Pearson’s online Assessment Roadmap 2014
COMPANIES are developing new programs to assist districts as they transition to technology-based assessments: Pearson’s online Assessment Roadmap 2014 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 Bryan Bleil (VP, online & tech), Ellen Stain Seymore J. Brendel 11/2013

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: Teacher username and password Select Subject: [Algebra-I CC Standards National] Select Standards: [National] [Assess] [Algebra-I] [Create a New Test] User name: JUDITHB39 J. Brendel 11/2013

Two Activities Self-Evaluation, Action Planning and Next Steps
Response Priority Comments Roadblocks (pages 28-29) Action Planning/Next Steps (page 30)

Questions? Concerns (silly question)? Discussion/Debrief

For your participation, collaboration and dedicated efforts!!! Judy
SINCERE THANKS… For your participation, collaboration and dedicated efforts!!! Judy Brian

FEA/PSA - Judith T. Brendel - Spring 2014

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