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The PARCC Institute – High School Math: Preparing for PARCC! NJ’s Next Generation Standardized Assessment System FEA/NJPSA - Judith T. Brendel - Spring 2014 Welcome… 2 Let’s take our… (pages 1-2) PARCC Pre-Assessment! Activity #1 : FAQs Pre-Test 3 3 HOW MANY math tests are required for HS students? • Three: Algebra-I, Geometry and Algebra II (or Math-I, Math-II and Math-III) • PBA Performance Based Assessment >75% of instruction • EOY End of Year Assessment > 90% of instruction HOW ARE the PBAs and EOYs ALIKE? • • • • • • 4 taken online divided into 2 sessions align with CCSS variety of question formats regular-ed and special-ed accommodations 4-week (20-day) window to take each test How do I know what CONTENT is included on each test? PARCC Blueprints: Algebra 1: PBA and EOY Geometry: PBA and EOY Algebra 2: PBA and EOY How many TOTAL POINTS on each test? PBA – 18-20 points EOY – 34-35 points = 52-55 What is a PROFICIENT SCORE? highly proficient score? To be determined after field tests are scored. How do I know the FORMAT of PARCC questions? Activity #2 – workbook pages 3-6 (to do soon) How many TYPES of tasks are on these tests? Activity – 3 separate packets for Type I, II and III tasks 5 What about calculator use? Is one session calculator active and the other not calculator active? What calculator will be available? (handout page-14A) ALG.1 NO Calculato r YES Calculato r Item Specific Calculato r Neutral PBA 1 18 7 6 EOY 3 9 15 11 NO Calculato r YES Calculato r Item Specific Calculato r Neutral PBA 16 1 7 EOY 16 6 22 NO Calculato r YES Calculato r Item Specific Calculato r Neutral PBA 3 28 4 3 EOY 4 9 19 9 GEOM. ALG.2 6 Ti-84 type graphing calculator HOW ARE PBAs and EOYs DIFFERENT from each other? PBA EOY Hand and Machine scored Machine scored only CCSS after 75% of instruction completed CCSS after 90% of instruction completed Type I, II and III questions Type I questions only 7 SA MS/HS– PD Session 3| April 4., 2011 HS Assessment Items Points Alg.1 Geom Alg2 BLUEPRINTS Type 1 pt. 21 19 19 EOY 1 2 pt. 11 12 12 for 4 pt. 3 3 3 MATHEMATICS EOY TOTAL ALGEBRA-I GEOMETRY ALGEBRA-II (page 22) 8 PBA/MYA/ MOY Type 1 Type 2 Type 1 P/M totals Type by course 2 Type 3 PBA/MYA TOTALS 1 pt. 2 pt. 3 pt. 4 pt. 3 pt. 6 pt. 35 10 2 2 2 2 10 34 10 2 2 2 2 10 34 10 2 2 2 3 10 4 4 5 4 4 5 18 18 20 Math Item Counts Per Form Integrated Math I, II, II HS Blueprints Assessment Item Points Math-I Math-II for Type 1 1 pt. 19 19 Mathematics EOY MATH I MATH II MATH III 9 Type 1 Type 2 PBA/MYA TOTALS (page 22) 2 pt. 4 pt. 12 3 34 12 3 34 19 14 2 35 1 pt. 2 pt. 3 pt. 4 pt. 3 pt 6 pt. 10 2 2 2 2 10 10 2 2 2 2 10 10 2 3 2 3 10 4 4 18 4 4 18 5 5 20 EOY TOTAL PBA/MYA Type 1 Type 2 Type 3 PBA/MYA TOTALS Math-III TODAY’S PLAN: •Understand the overall substance, design and technical aspects of next generation PARCC assessments •Experience PARCC assessment tasks and related resources •Align scope-and-sequence to PARCC assessment schedule •Share effective strategies to lead the transition to CCSS and PARCC assessments. 10 What should teaching and learning in the 21st century look like?” “…revolutionary transformation rather than evolutionary tinkering.” US DOE, NETP 2010 11 11 12 “The best time to plant a tree is twenty years ago; the second best time is today.” (Ancient Chinese Proverb) 13 13 Listen to our students! “I am a 21st Century Learner!” 14 14 How? Fostering essential skills… • • • • • Communication Collaborative problem solving Critical thinking Creativity Innovation • • • • • Global competence Content knowledge Entrepreneurship Adaptability Interpersonal … through innovative pedagogy and ubiquitous technology. 15 15 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 : http://www.edlabgroup.org/tl/resources/InnovativeTeachers2006.pdf 17 17 21st learning… 18 …what should it look like? 21st learning… 19 http://www.pascack.k12.nj.us/cms/lib5/NJ01000238/Centricity/Domain/87 /Writing%20Equations%202.swf 19 Dan Meyer: Math Class Needs a Makeover 20 PARCC: Partnership for Assessment of Readiness for College and Career What does it mean? “Students are on-track or ready for college and careers.” 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 Use the modeling practice to solve real world problems 21 Express mathematical reasoning by constructing mathematical arguments and critiques Demonstrate fluency in areas set forth in the Standards for Content in grades 3-6 Standards of Mathematical Practices (MP) 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct Constructviable viablearguments argumentsand andcritique critiquethe thereasoning reasoningofof others. others 4. Modelwith withmathematics. mathematics. Model 5. Use appropriate tools strategically. 6. Attend to precision. 7. precision Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. 22 Activity #2 : Create different question formats Algebra, Algebra-II or Geometry (pages 3-8) 2y = 4x - 6 MC- one right answer (traditional format) MC – more than one right answer (at least A-D) MC – yes/no true/false listed questions; multiplestandards SCR – fill-in-the blank OE – compare/contrast; explain/defend; how do you know? 23 SA MS/HS– PD Session 3| April 4., 2011 A (Quick) Walk through the PARCC! 24 PARCC Assessment Consortium PBA MATH 25 EOY MATH Assessment Transition Timeline NJTransition ASK Assessment Timeline “Transitional Assessments” Spring 2012 Aligned to NJCCCS Aligned to the Spring 2014 CCSS & NJCCCS Aligned to the Full admin. of PARCC (Except Gr. 6-8 Math) CCSS assessment Spring 2013 2014-15 26 26 Understanding the Common Core State Standards …is to understand PARCC 27 PVRSD Math TF – Work Session 1 | November 18, 2010 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” 28 Principles of the CCSS… • • • 29 FEWER - CLEARER - HIGHER Aligned to requirements for College and Career Readiness Based on evidence Honest about time The CCSS Difference: Grade 8 Mathematics (2004) Before NJCCCS: 1. Understand and apply the Pythagorean Theorem. (2010) After CCSS 1. Explain a proof of the Pythagorean Theorem and its converse. 1. Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. 1. Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. 30 a 2 + b2 = c2 5 5 25 a=4 c=? 4 16 a 4 c b 3 9 3 b=3 31 Implications of the CCSS on WHAT and HOW to teach… What are the Critical Shifts to Consider? 32 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. 33 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. 34 Three (3) Significant Shifts in Mathematics: 1. Focus: Focus strongly where the Standards focus. 2. Coherence: Think across grades, and link to major topics within grades. 3. Rigor: In major topics, pursue: • conceptual understanding; • procedural skill and fluency; and 36 • application with equal intensity. Three (3) Significant Shifts in Mathematics: 1. Focus: Focus strongly where the Standards focus. 2. Coherence: Think across grades, and link to major topics within grades. 3. Rigor: In major topics, pursue: • conceptual understanding; • procedural skill and fluency; and 37 • application with equal intensity. Traditional U.S. Approach… K 12 Number and Operations Measurement and Geometry Algebra and Functions Statistics and 38 Probability 38 Focusing attention within Number and Operations Operations and Algebraic Thinking Number and Operations—Base Ten K 1 2 3 4 Algebra The Number System Number and Operations— Fractions 39 Expressions and Equations 5 6 7 8 High School Focus Areas in Mathematics (CCSS) Grade 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 7 40 Focus Areas in Support of Rich Instruction and Expectations of Fluency and Conceptual Understanding 8 Ratios and proportional reasoning; early expressions and equations Ratios and proportional reasoning; arithmetic of rational numbers Linear algebra, linear functions 40 Focus Areas in Mathematics (CCSS)- MS/HS ALG. - 1 41 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 41 Focus Areas in Mathematics (CCSS) - HS GEOMETRY 42 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 42 Focus Areas 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 Inferences and Conclusions from Data UNIT-4 43 43 FOCUS AREAS: High School 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. •F.IF.7/9 supporting Graph functions by hand (in simple cases) and with technology …. •A.REI.5, A.REI.6 additional Solve systems of linear equations in two variables … •A.REI.10, 11 major 44 Dec. 2, 2013 J.Brendel Three (3) Significant Shifts in Mathematics: 1. Focus: Focus strongly where the Standards focus. 2. Coherence: Think across grades, and link to major topics within grades. 3. Rigor: In major topics, pursue: • conceptual understanding; • procedural skill and fluency; and 45 • application with equal intensity. 45 COHERENCE Integrative tasks draw on multiple standards to ensure students are making important connections. The Standards are not treated as a checklist. 46 Coherence: Link to Major Topics Across Grades Gr.6- Apply properties One of several staircases to algebra designed in the OA domain. • Gr.5-expressions Gr.3- multiply … divide Gr.1- add … subtract 47 47 Coherence: Link to Major Topics Across Grades One of several staircases to algebra designed in the OA domain. ALGEBRA-I ALGEBRA- II 48 48 Coherence and NEW multiple-choice questions. Activity 3: Circle all that are true. Given: All squares A. are parallelograms and rectangles B. have 4 acute angles 25 5 C. have only 2 diagonals 3 5 D. Area = ½ base x height 21 7 E. Sum of consecutive angles = 180˚ F. Perimeter = 2 x Side length G. Area > area with the same perimeter. 49 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. a. Write an equation for the total number of gallons of fuel …. a. How much fuel is in the tanks after the pump … 8 minutes? b. Graph the equation … on the coordinate plane … label …. 50 Algebra-I Unit-1 50 Three (3) Significant Shifts in Mathematics: 1. Focus: Focus strongly where the Standards focus. 2. Coherence: Think across grades, and link to major topics within grades. 3. Rigor: In major topics, pursue: • conceptual understanding; • procedural skill and fluency; and 51 • application with equal intensity. 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. 52 Guess the grade level! See the Rigor in Grade-3 Fractions on a Number Line * a BIG change * a move away from the circular pie to understanding fractions on a number line. http://www.illustrativemathematics.org/standards/hs 53 See Rigor in Grade 6: Ratios * a BIG change * Students will have online tools to use that simulate hands-on tools PARCC - Grade-6 Slider Ruler: type-I http://www.parcconline.org/ samples/mathematics/grade6-slider-ruler 54 See the Rigor in Middle Grades Understanding of Fractions Write a number that is greater than 1 5 and less than Hint: Find equivalent fractions for denominators of 40 or 100. 1 5 and 1 4 1 4 with Why wasn’t it helpful to use 20 as a denominator? (JB) 55 See the Rigor – High School Part A 56 Part B Describe Write Compare 57 Required Fluencies in K-6 Grade Standard K K.OA.5 Add/subtract within 5 1 1.OA.6 Add/subtract within 10 2.OA.2 Add/subtract within 20 (know single-digit sums from memory) 2.NBT.5 Add/subtract within 100 Multiply/divide within 100 (know single-digit products from memory) 2 3 58 3.OA.7 3.NBT.2 Required Fluency 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 58 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. 59 59 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. 60 60 See what online looks like! Real world application – Grade ? 61 Real world application – Grade 4 62 MORE THAN one choice See what online looks like! Linking to major topics – Grade 7 (page-26-27) 63 Part B 64 See what online looks like! HS Teachers outside of math use grade-level-appropriate math 65 Part B 66 Part C 67 Part D 68 Activity No. 3: Shifts Happen - Mathematics What is this shift? Why this shift? Opportunities Focus: Focus strongly where the Standards focus. Coherence: Think across grades, and link to major topics within grades. 69 Rigor: In major topics, pursue conceptual understanding, procedural skill and fluency, and application with equal intensity. Handout page-25 Challenges What do you mean 3 TYPES of TASKS? No, not differently formatted No, not different levels-of-difficulty 70 TASK TYPES – PARCC (x – 2)2 + 6 = 75 solve for c: (x + c)/z = 2c(w-y) Explain how you can use the graphs to find solutions. Estimate …. Compare the 3 sets of data (graph, chart, and equation) and defend the argument that …. 71 Let’s take a quick break! 72 TASK TYPES – PARCC I – Computation, Skills, Process (x – 2)2 + 6 = 75 solve for c: (x + c)/z = 2c(w-y) II – Mathematical Reasoning Explain how you can use the graphs to find solutions. Estimate …. III – Modeling, Combined Standards, Applications Compare the 3 sets of data (graph, chart, and equation) and defend the argument that …. 73 TASK TYPE-I Tasks assess 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, computerbased formats. -will appear on the Performance Based and End-of-Year Assessments 74 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. 75 December 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. 76 December 2, 2013 TYPE-I PARCC TASKS Tasks assess concepts, skills and procedures. All are machine score-able. 77 Mathematics online Sample Item/Prototypes: (separate packets) PARCC TYPE-I TASKS (1, 2, or 4 point questions) HS – FunctionsS HS – Seeing Structure in Quadratic Equation HS – Picture Frame (Algebra-I/Math 2) http://www.parcconline.org/sites/parcc/files/HS-Alg1Math2PictureFrame.pdf HS – Myla’s Swimming Poole (Algebra-I) HS – Green Tea Observation Study (Algebra-2/Math 3) 78 Functions http://www.parcconline.org/samples/mathematics/high-schoolfunctions (first page of Type-I Task package; see graph and table) Given f(x) as a graphed parabola and g(x) as table of values 1. Compare y-intercepts 1. Compare f(3) and g(3) DIFFICULTY? 1. Compare maximum values of each w/in range -5 ≤ x ≤ 5 1. Compare f (5)- f (2) g(5)- g(2) and 5- 2 5- 2 STANDARDS? A Type-I PARCC task 79 J. Brendel 12.3.2013 Seeing Structure in a Quadratic Equations http://www.parcconline.org/samples/mathematics/high-school-seeingstructure-quadratic-equation (second page in Type-I packet) (3x - 2)2 = 6x – 4 STANDARDS? 80 J. Brendel 12.3.2013 a Type-I PARCC task Seeing Structure in Equations http://www.parcconline.org/samples/mathematics/high-school-seeing-structure-equation (see third page in Type-I packet) 24 + 10x – x2 = p – (x – 5)2 Solve for p STANDARDS? 81 J. Brendel 12.3.2013 a Type I PARCC task PICTURE FRAME http://www.parcconline.org/sites/parcc/files/HS-Alg1Math2PictureFrame.pdf (See pages 4-6 of Type-I packet; see Details for Teacher width X in. X + 2 in. length STANDARDS? 82 J. Brendel 12.3.2013 a Type I PARCC task GREEN TEA TYPE http://www.parcconline.org/sites/parcc/files/PARCC_SampleItems_Mathematics_HS AlgIIMathIIIGreenTeaStudy_081913_Final_0.pdf STANDARDS? a Type I PARCC task 83 J. Brendel 12.3.2013 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. 84 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 http://www.parcconline.org/sites/parcc/files/HighSchoolAlg2Math3-GraphsofFunctions.pdf • HS – Michelle’s Conjectures (Algebra-II/Math III) http://www.parcconline.org/sites/parcc/files/PARCC_SampleItems_Mathematics_HSAlgIMathIIMichelle Conjecture_081913_Final_0.pdf • HS – Geometric Construction Connection (Geometry/Math III) PARCC_SampleItems_Mathematics_HSGeoMathIIIGeometricConnection_081913_Final_0.pdf http://www.parcconline.org/sites/parcc/files 85 Dec. 2, 2013 GRAPH of FUNCTIONS (posted November 2013) (See first 3 pages of Type-II packet See two-page details for teacher) http://www.parcconline.org/sites/parcc/files/HighSchoolAlg2Math3GraphsofFunctions.pdf STANDARDS? 86 a Type-II PARCC Task GEOMETRY CONSTRUCTION CONNECTION (See 4th-6th page in Type-II packet; see details for teacher.) http://www.parcconline.org/sites/parcc/files/PARCC_SampleItems_Mathematics_HS GeoMathIIIGeometricConnection_081913_Final_0.pdf STANDARDS? 87 a Type-II PARCC Task MICHELLE’S CONJECTURES (Aug.19, 2013) (See last 3-pages in Type-II packet; see details for teacher) http://www.parcconline.org/sites/parcc/files/PARCC_SampleItems_Mathematics_HSAlgIMat hIIMichelleConjecture_081913_Final_0.pdf Investigate the effect on the vertex of the graph f(x) = x2 + 6 when f(x) is replaced by f(x + k) POINTS ? 88 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. 89 MINI GOLF PRICES (November, 2013) (See first four pages in Type-III packet) http://www.parcconline.org/sites/parcc/files/HSAlg1Math2MiniGolfPrices.pdf Part A: … write a liner function to model … Part B: … write a quadratic function for … Part C: … maximum possible weekly revenue is what percent greater than the weekly revenue … STANDARDS? 90 a Type-III PARCC Task BRETT’S RACE (November, 2013) (See pages 5-8 in Type-III packet) http://www.parcconline.org/sites/parcc/files/BRHSSampleItem.pdf Part A: … write an equation for each person that …. Part B: Based on your equation … who will win ... ? Justify your answer. STANDARDS? 91 a Type-III PARCC Task POPCORN INVENTORY (NOVEMBER 2013) http://www.parcconline.org/sites/parcc/files/HSAlg1Math1 PopcornInventory.pdf Read scenario, understand table, read additional facts … Estimate the amount of popcorn … Show or explain the reasoning you used to determine your estimate. POINTS ? 92 a Type-III PARCC Task TEMPERATURE CHANGES (See last 4 pages in Type-II packet) http://www.parcconline.org/sites/parcc/files/PARCC_SampleItems_M athematics_HSAlgIIMathIIITemperatureChange_081913_Final_0.pdf Part A: Which model is linear? Which model is best for the range … ? Explain why the other model … Part B: Construct a function …. POINTS ? 93 a Type-III PARCC Task Task Type 1 1 1 PARCC PROTOTYPE SAMPLE TASKS As of 12/5/2013 Algebra-I/Math I Geometry/Math II Algebra-II / Math III Seeing Structure in Equations (1 point) Picture Frame (2 points) Myla’s Swimming Pool (2 points) 2 Michele’s Conjectures 3 Popcorn Inventory (6 points) 3 Brett’s Race (3 points) Golf Prices (6 points) 3 94 Seeing Structure in Functions Quadratic Equation (1 point) Green Tea (2 points) Geometry Construction (3 points) Graph function (4 points) Temperature Changes (3 points) Help Students and Teachers Prepare for the Change 95 READING CCSS and Mathematics 96 Regular Practice with Complex Text and its Academic Language 97 Not 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 98value to promote? 98 Text-Dependent in ELA What makes Casey’s experiences at bat humorous? What can you infer from King’s letter about the letter that he received? “The Gettysburg Address” mentions the year 1776. According to Lincoln’s speech, why is this year significant to the events described in the speech? Text-Dependent in mathematics TOSHIE’S SISTER CHIE 6) · Circle the floors in the building Chie is learning about odd and that have laundry rooms. even numbers in school. Help her do the two problems in 1 2 3 4 5 6 7 8 9 example 6). Remember, the laundry rooms are on floors with even numbers. The parking garages are on floors with odd numbers. 99 December 2, 2013 author: J. Brendel Material not to be duplicated. 10 · 11 12 13 14 15 16 Circle the floors in the building that have parking garages. 1 10 2 11 3 4 5 6 12 13 14 7 8 15 9 16 Regular Practice with Complex Text and Its “Academic Language” Basic constructions w/triangles using protractors, compasses or online with simulation tools: Students construct, do proofs and solve problems involving: Medians, vertex angle, balancing point, centroid Altitudes, acute triangles, obtuse triangles, right triangles, orthocenter, interior, exterior or …. Perpendicular Bisectors, concurrent lines, point of concurrency, circumcenter of a triangle Angle Bisectors, incenter, equidistant, …. 100 Geometry Regular Practice with Complex Text and its “Academic Language” Cramer’s Rule for solving systems of equations uses determinants to solve for each variable. D is the determinant of the coefficient matrix. Dy is the determinant formed by replacing the coefficients of y in D with the constant terms. Algebra-II Sample academic language in a basic statistics task: measure of central tendency, skewed, mean, median, mode, outlier, bimodal, quartiles, box-and-whisker plot, percentile, random sample, … 101 New to Pre-Algebra, Algebra I or II Regular Practice with Complex Text and its Academic Language (“Adult Language”) Example: Phone company ‘A’ charges an initiation fee plus a charge per minute. The cost of using 300 minutes (plus initiation fee) is $25 and the cost of 700 minutes (plus initiation fee) is $33. • • • • • 102 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 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. (2)(2) is equivalent to √16 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. (-4) + (-5) 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. (-4) - (-8) 103 Regular Practice With Complex Text and its Academic Language: Why? 104 • 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. What are the Features of Complex Text? 105 • • • • • Subtle and/or frequent transitions • Complex sentences 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 What are the Features of Complex Text? (cont.) 106 • • Uncommon vocabulary • • Longer paragraphs Lack of words, sentences or paragraphs that review or pull things together for the student Any text structure which is less narrative and/or mixes structures What you SHOULD NOT see ! 109 y m = y1 - y 6-2 4 = = x1 - x2 3- 3 0 (3,6) N Z 0 slope = 4 110 Slope = (3,2) > 4 0 x < The Mathematics Common Core Toolbox K. I. S. S. Mathematics Sample Item/Prototypes: PARCC online at the Dana Center •Grade 4 (Deer in the Park) p. 23 CHANGE PROCESS •Grade 6 (Gasoline Consumption) •High School (Isabella’s Credit Card) *p. 24-25) Keep content SIMPLE •High School (Popcorn Inventory) new Nov. 2013 http://www.parcconline.org/sites/parcc/files HSAlg1Math1PopcornInventory.pdf 111 The Mathematics Common Core Toolbox Mathematics Sample Item/Prototypes: PARCC online at the Dana Center • Grade 4 (Deer in the Park) • Grade 6 (Gasoline Consumption) • High School (Isabella’s Credit Card) (page-21) • High School (Popcorn Inventory) new Nov. 2013 http://www.parcconline.org/sites/parcc/files HSAlg1Math1PopcornInventory.pdf 112 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., surface area, minimum surface area) •Grade 7 - Food Basket (calories, grams, protein) •Grade 8 - Heartbeats (scatter plot ….) •Grade 11- Speeding Ticket (graph, what is fair? ….) 113 EXPERIENCE an ONLINE ASSESSMENT *Smarter Balanced Online Activities • Sample online Smarter Balanced Assessments. *Select from grades 3, 4, 5, 6, 7, 8 or 11 • https://sbacpt.tds.airast.org/student/login.aspx?c=S BAC_PT J.Brendel 11/2013 114 EXPERIENCE ONLINE TASKS just released; similar to testing environment *PARCC Online Activities http://practice.parcc.testnav.com/# * difficulty levels vary item types vary users are encouraged to work w/items across grades additional online functionality … in coming weeks. J.Brendel 3/8/14 115 PRACTICE ONLINE w/earlier grade resources • • • • • • 116 Order Juice (grade-4) – Dana Center (p.28-29) Spicy Veggies (grade-7) – Dana Center (p.26-27) Drag and Drop (Smarter-Balanced sample) Circle; explain (Smarter-Balanced sample) Noise Level (Smarter-Balanced sample) Scatter Plot (Smarter-Balanced) SAMPLE ASSESSMENT examples 1-12 from Smarter Balanced site separate hardcopy-packet pages 15-20 and High School Reference Sheet page-13 117 December 2, 2013 Activity: BRAINSTORM in GROUPS How should high school math teaching change from the traditional teaching? What non-math type skills are essential? 118 Other Resources CIRCLES http://sampleitems.smarterbalanced.org/itempreview/ModernShell.asp x?config=SBAC%5CContent%5CCircle1.json MATH II - WALLS http://sampleitems.smarterbalanced.org/itempreview/ModernShell.asp x?config=SBAC%5CContent%5CRoomWall.json J. Brendel 11/2013 119 PARCC RELEASED TASKS include elsewhere? file://localhost/Users/jbrendel/Desktop/PARCC%20HS%20Functi ons.html (November/December 2013) https://www.teachingchannel.org/videos/laws-of-sines-cosineslesson# 14-min lesson “fly quadcopters” math/science/engineering … a 4-month project … Ms. Brookins and Mr. James GRADE-11 https://www.teachingchannel.org/videos/statistical-analysis-lesson Statistical analysis to rank baseball players GRADES 11-12 CCSS Standards: Math SID. 1, 2 and 3 120 The Specs, Accountability, and Resources: What We Know Now! 121 FIELD TESTING this SPRING (2014) >1 million students across PARCC states and Washington DC >10,000 students / 1,276 schools / 445 districts in NJ PBA – anytime between March 24 – April 11 EOY – anytime between May 5 – June 6 Results: not individual student or school results Sample online test available “spring” 2014 Field Test questions: Dr. Jeffrey B. Hauger [email protected] 122 Estimated Time on Task: Grade 9-10 Performance Based Assessment ELA/Literacy Grade 9-10 Alg I/ Math I Geo/ Math II 123 Estimated Time on Task (minutes) Math Literacy Analysis Research Narrative 80 85 50 Session 1 50 TOTAL Session 2 50 315 Estimated Time on Task: Grade 9-10 End-of-Year (EOY) Assessment ELA/Literacy Grade 9-10 Alg I/ Math I Geo/ Math II Estimated Time on Task (minutes) Session 1 Session 2 70 70 Math Session 1 65 Grade 9-10 Summative Total: 124 TOTAL Session 2 65 270 9 Hours, 45 minutes Estimated Time on Task: Grade 11 Performance Based Assessment ELA/Literacy Grade 11 Alg II/ Math III 125 Estimated Time on Task (minutes) Math Literacy Analysis Research Narrativ e 80 85 50 Session 1 65 TOTAL Session 2 65 345 Estimated Time on Task: Grade 11 End-of-Year (EOY) Assessment ELA/Literacy Grade 11 Alg II/ Math III Estimated Time on Task (minutes) Session 1 Session 2 70 70 Math Session 1 55 TOTAL Session 2 55 250 Grade 11 Summative Total: 126 9 Hours, 55 minutes HOW will I know what should be ‘learned’ before the PBA? before the EOY? (Activity) ALGEBRA-I PBA and EOY (2 packets) GEOMETRY PBA and EOY (2 packets) ALGEBRA-2 PBA and EOY (2 packets) ALGEBRA-I PBA vs EOY (packet) 127 What Else… 128 • 20 Day Window…for both the PBA and EOY summative assessments (performance based and end-of-year) • Summative Assessments Retest Opportunities Grades 3-8 - 1 retest opportunity/year HS - up to 3 retest opps/year for each assessment • Computer-based (w/paper version available in rare circumstances), contingency back-up • PBA delay? No… 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) 129 What Else… Accessibility Features for ALL students continued • • • • • • • • 130 Highlight tool Headphones Magnification/Enlargement Device Notepad Pop-Up Glossary Redirect Student to Test (provided by test administrator) Spell Checker Writing Tool What Else… • Accommodations / Modifications for Special Education Students (from the 55-page PARCC Accessibility manual) • Accessibility Features Identified in Advance • Answer Masking • Background/Font Color (Color Contrast) • General Masking • Line Reader Tool • Text-to-Speech for the Mathematics Assessments http://parcconline.org/parcc-accessibility-accommodations-and-fairness 131 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; 132 • 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). 133 Accountability: What We Know Now! 134 Results Types… Proficiency (PLDs) On-Track-to-College and Career Readiness (CCRDs) Growth Data Performance Level Descriptors Performance Level (PLDs) 135 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 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.” 136 What does it mean to be CCR? (Level-4) “Students who earn a PARCC College- and Career-Ready Determination by performing at Level 4 in mathematics and enroll in College Algebra, Introductory College Statistics, and technical courses requiring an equivalent level of mathematics have approximately a 0.75 probability of earning college credit by attaining at least a grade of C or its equivalent in those courses.” 137 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. 138 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. 139 RFP for “Operational Assessment” Vendor proposals were due by Dec. 11, 2013. Timelines and Resources: What We Know Now! 140 140 PARCC Timeline… • Jan – Aug 2013 2013-2014 2014-2015 141 • 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) • PARCC Timeline… *Over the next year, PARCC will develop five online training modules for teachers, school leaders, and school site testing coordinators – each with a unique purpose. PARCC will produce modules with the following foci: 1. PARCC Common Assessments Overview 2. Introduction to the PARCC Mid-Year Assessment 3. Introduction to the PARCC Diagnostic Assessment 4. Introduction to the PARCC Speaking/Listening Assessment 5. PARCC Accessibility System *It is anticipated that modules will be available in June 2014. 142 PARCC Timeline… NJ Spotlight (Nov. 20, 2013) For the first time since 1989, New Jersey will next year suspend its requirement that high school graduates pass a state test in language arts and math to receive their diplomas. (No HSPA) But that doesn't mean there will be fewer tests, just that they'll be used for different purposes. For instance, current eighth, ninth, and 10th graders will be tested in language arts and math now in three separate tests, and while passing the exams will not be required for graduation, the scores will be included in a student’s permanent transcript. (2014-15 school year) 143 HIGHER ED FOCUS June 16-17, 2014 convening The focus will be on policy associated with student scores that signal on track; that signal a student is ready for entry level, college-bearing credit classes. 144 www.achievethecore.org 145 Links to Model Math Curriculum Sites Sample Assessments by grade: http://www.achievethecore.corg/ Common Core and Special Education Students http://www.ode.state.or.us/search/page/?id=3741 Common Core Practice Test https://sbacot.tds.airast.org/student/login.aspz?c=SBAC.PT http://sbac.portal.airast.org/practice-test/ Common Core Resources to use with students http://www.illustrativemathematics.org Dana Center Resources http://www.ccsstoolbox.org/ http://ccsstoolbox.agilemind.com/pdf/DanaCenter_YAG_HS.pdf 146 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) December 2013 J.Brendel 147 COMPANIES are developing new programs to assist districts as they transition to technology-based assessments: Pearson’s online Assessment Roadmap 2014 www.Commoncore.pearsoned.com/index.cfm?locator=PS11Uz Step-1: Conducting a Needs Analysis Step-2: Developing a Transition Strategy Step-3: Ensuring Interoperability Step-4: Communicating Proactively Step-5: Anticipating Ongoing Change www.PearsonAssessments.com/NextGenRoadmap Bryan Bleil (VP, online & tech), Ellen Stain Seymore 148 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: http://www.connected.mcgraw-hill.com • Teacher username and password • Select Subject: [Algebra-I CC Standards National] • Select Standards: [National] [Assess] [Algebra-I] [Create a New Test] 149 J. Brendel 11/2013 Self-Evaluation, Action Planning and Next Steps Roadblocks Action Planning Next Steps 150 Let’s take our… (last page in packet) PARCC POST-Assessment! Activity : FAQs POST-Test 151 151 Questions? Concerns (silly question)? Discussion/Debrief 152 SINCERE THANKS… For your participation, collaboration and dedicated efforts!!! Judy [email protected] or contact NJPSA/FEA 153