PARCC Mathematics PARCC Partnership for Assessment of Readiness

PARCC Mathematics PARCC: Partnership for Assessment of Readiness for College and Career What’s New in SY 2015 -16 & Review of Important Facts Ronda Davis, davis_r@aps. edu Member of the NM PARCC Educator Leader Cadre Member of PARCC Consortium Math Operational Working Group APS Math Specialist for Assessment

Which One Doesn’t Belong http: //wodb. ca/

Mathematical Flexibility

4 2016 Testing Window - ONE window

New Math Design Testing Times PARCC Math Assessment Unit Testing Times 5 4 4 4 3 2 1. 5 1. 33 1 0 Unit 1 Unit 2 Unit 3 Unit 4 Total 1 1 Grades 3 -5 1 1 4 Unit 1 Grades 6 -8 1. 33 A 1, Geo, A 2 EOC Tests 1. 5 4 Unit 2 Unit 3 4. 5 Unit 4 Total 5

Test Design Changes – Fewer Test Units With the changes, students in all grades will participate in fewer test units. The redesigned ELA/L tests are composed of 3 units. The math tests are composed of 3 or 4 units.

Comparison of 2015 and New Math Design Grades 3 -5/6 -8 Short Items Reasoning Items Modeling Items Total Points Units Total Time Algebra I, Short Items Geometry, Reasoning Items Algebra II Modeling Items Total Points Units Total Time New Single Window 56 pts 40 pts 14 pts 12 pts 82 pts 66 pts 4 @ varies 4@ 60 min/3 @ 80 min 5 hrs. 4 hrs. 65 pts 14 pts 18 pts 97/107 pts 4 @ varies 5. 3 – 5. 5 hrs. 49 pts 14 pts 18 pts 81 pts 3 @ 90 min. 4. 5 hrs. 7 2015 2 Windows

http: //www. parcconline. org/assessments/test-design/mathematics/math-testspecifications-documents

PARCC’s Core Commitment to Assessment Quality • Focus (Math): where the Standards focus, more time to master concepts at a deeper level (CCSS, MCF, ES Tables) • Problems Worth Doing (Math): multistep problems, conceptual questions, applications, and substantial procedures

PARCC Accessibility Policies Built into the test Available to All Students Features for All Students Accessibility Features Example: magnification, highlighting, eliminate answer choices, line reader Available to All Students Must be turned on in Advance Example: answer masking, text-to-speech for mathematics, background/font color Identified in advance Accommodations Available with IEP/504 Must be identified in Advance Example: Word to word dictionary, small group testing, extended time http: //parcconline. org/parcc-accessibility-features-and-accommodations-manual

Features Built Into The Test • Bookmark • Eliminate Answer Choices • Highlighter Tool • Line Reader Tool • Magnifier (Tool or Keyboard Shortcut) • Notepad • Redirect Student • Spell Check

Accessibility Features Identified in Advance (ALL students) • Answer Masking AND/OR General Masking • Background/Font Color (Color Contrast) • Text-to-Speech • Headphone will be needed • NOTE: Headphones can be used as noise buffers • Human Reader • Small group testing • Frequent breaks • Time of day • Separate or alternate location • Specified area or seating

Additionally. . . Students with IEP’s or ELL Students Accommodations for Special Ed • Calculators on Noncalc Section • Math Manipulatives • Extended Time Accomodations for ELL • Word to Word Dictionary • Extended Time • Spanish/English Version of Test (CBT or PBT) • Human Reader in Spanish • Text to Speech in Spanish

• Which accessibility features and/or accommodations would benefit students during instruction and assessments? • Which new accessibility features and/or accommodations, if any, would increase the student’s access to instruction and assessment by addressing the student’s learning needs?

Calculator Use • Grades 3 – 5 – No Calculators • Grades 6 – 7: Four Function with Sq Rt & % • Grade 8: Scientific Calculator v. Middle School ~ 75% of exam w calc • Algebra 1, Geometry, Algebra 2: Graphing Calculator (~85% of exam w calc) PARCC Calculator Policy

Math Tools • On-Line Grades 3 - 8: • Rulers available as on-line tools • Grade 3: ¼ inch • Grades 4 – 8: 1/8 inch • On-Line Grades 4 – 7: • Protractors as shown to the right • 8 th Grade, Geometry & Integrated Math: • Not Provided as On-Line Tools, but. . . Ø Schools or Students May Provide: tracing paper, reflection tools, straight edge and compass – think Transformational Geometry Tools Math Tool Policy

Scratch Paper • Test Administrators Must Provide: ØScratch paper – Blank, Lined &/or Graph (At Least 1 sheet) ØScratch paper is NOT limited

Reference Sheets – Only Provided in Grade 5 • Think about how to incorporate these into your instruction • Will be provided as a dropdown ØHard copies may be provided by schools Grades 5 - 8 Reference Sheet High School Reference

4 th Grade: No Reference Sheet • Students in grade 4 will be required to know relative sizes of measurement units within one system of units. • 1 meter = 100 centimeters • 1 kilometer = 1000 meters • 1 kilogram = 1000 grams • 1 liter = 1000 milliliters • 1 minute = 60 seconds • 1 hour = 60 minutes • The area and perimeter formulas for rectangles are also considered requisite knowledge for Grade 4. Math Informational Guide

5 th Grade Requisite Knowledge – Not on Reference Sheet • Think about how to incorporate these into your instruction NOT on reference sheet, but requisite knowledge for 5 th grade (in addition to the 4 th grade on previous slide) • 1 foot = 12 inches • 1 yard = 3 feet • 1 day = 24 hours • 1 meter = 1000 millimeters • Area of a Rectangle: A = lw or A= bh Math Informational Guide

Evidence Tables Have Useful Clarifications (unpack the standards)

Securely Held Knowledge

C & D Claims are NOT explicitly found in the CCSSM document

Securely Held Knowledge in D Claims

Brain Research on Math, Jo Boaler • https: //www. youcubed. org/wim-day-1/ • NOTE: you must register for this site before you will have access to the video.

• Turn to your neighbor. . . • How does what you just heard impact instructional decisions?

Practice Tests – Mimic the Actual Test • Assessments should be worthy of instructional imitation • Released items and sample tasks are a nice starting place • PARCC’S view: Some final thoughts… – Content, practices, and balance – Cognitive complexity (1/3 high + 1/3 medium + 1/3 low) – PLDs

Sub-Claim C: Highlighted Practices MP. 3, 6 with Connections to Content (expressing mathematical reasoning) The student expresses grade/courselevel appropriate mathematical Claims reasoning by constructing viable arguments, critiquing the reasoning of others, and/or attending to precision when making mathematical statements.

Analyzing Reasoning Tasks – Content, Practices, Balance Intro • Overview of standards and PARCC • Discussion of mathematics content and practices worth enacting c 1 Inc. ’s Item Analysis Flow Chart • Read annotate the first item • Discuss with partner what makes this item worthwhile 2 3 • Review the standards/evidences for the grade level • What standard/evidence is being measured? • What content do students need to know (on grade level and securely held knowledge) to be able to answer the item? • What practice(s) do students need to know to be able to answer the item? • How are conceptual understanding, procedure, and/or modeling/application emphasized? • Consider instructional decisions • Consider how the standards and evidences for content and practice could be demonstrated in student work • How can teachers structure instruction to ensure that students know/can do what is being asked of them in light of this item, but in a classroom setting? • What links, if any, are there to formative assessment practices? Ultimately, what are the implications/adjustments to curriculum, instruction, and assessment

Mia’s Fraction

• Review the standards/evidences for the grade level • What standard/evidence is being measured? • What content do students need to know (on grade level and securely held knowledge) to be able to answer the item? • What practice(s) do students need to know to be able to answer the item? • How are conceptual understanding, procedure, and/or modeling/application emphasized PARCC Reasoning Task Analysis 2

Mia’s Fraction – Sample Student Response & Alignment Sample Student Response: Point P is at 5/6 on the number line. The denominator represents the total number of equal parts between 0 and 1. There are six equal segments between 0 and 1 so each segment is 1/6. The numerator represents the number of segments that the number is to the right of 0. So, if you count 5 segments of 1/6, you end up at 5/6. 3. C. 6 -1: Base explanations/reasoning on a number line diagram (whether provided in the prompt or constructed by the student in her response). Content Scope: Knowledge and skills articulated in 3. NF. 2. In this item, the focus is on 3. NF. 2 b: Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.

• Consider instructional decisions • Consider how the standards and evidences for content and practice could be demonstrated in student work • How can teachers structure instruction to ensure that students know/can do what is being asked of them in light of this item, but in a classroom setting? • What links, if any, are there to formative assessment practices? PARCC Reasoning Task 3 Analysis

Intro 1 • Overview of standards and PARCC • Discussion of mathematics content and practices worth enacting • Read annotate the first item • Discuss with partner what makes this item worthwhile In small groups (20 min): 2 3 • Review the standards/evidences for the grade level • What standard/evidence is being measured? • What content do students need to know (on grade level and securely held knowledge) to be able to answer the item? • What practice(s) do students need to know to be able to answer the item? • How are conceptual understanding, procedure, and/or modeling/application emphasized? • Consider instructional decisions • Consider how the standards and evidences for content and practice could be demonstrated in student work • How can teachers structure instruction to ensure that students know/can do what is being asked of them in light of this item, but in a classroom setting? • What links, if any, are there to formative assessment practices?

Reflect. . . • How can you use what we’ve just done as you are designing tasks to elicit evidence of reasoning? Reasoning Reflection • What are some implications and adjustments we might want to consider to our curriculum, instruction and assessment?

Sub-Claim D: Highlighted Practice MP. 4 with Connections to Content (modeling/application) The student solves real-world problems with a degree of difficulty appropriate to the grade/course by applying knowledge and skills articulated in the standards for the current grade/course (or for more complex problems, knowledge and skills articulated in the standards for previous grades/courses), engaging particularly in the Modeling practice, and where helpful making sense of problems and persevering to solve them (MP. 1), reasoning abstractly and quantitatively (MP. 2), using appropriate tools strategically (MP. 5), looking for and making use of structure (MP. 7), and/or looking for and expressing regularity in repeated reasoning (MP. 8).

Modeling Claim 1. Identifying variables in the situation and selecting well; 2. Formulating a model by creating and selecting representations that describe relationships between the variables 3. Analyzing and performing operations to draw conclusions 4. Interpreting results in terms of original situation 5. Validating conclusions – improve model if necessary 6. Reporting conclusions

Analyzing a Modeling Task Intro 1 • Overview of standards and PARCC • Discussion of mathematics content and practices worth enacting • Read annotate the first item • Discuss with partner what makes this item worthwhile In small groups (20 min): 2 3 • Review the standards/evidences for the grade level • What standard/evidence is being measured? • What content do students need to know (on grade level and securely held knowledge) to be able to answer the item? • What practice(s) do students need to know to be able to answer the item? • How are conceptual understanding, procedure, and/or modeling/application emphasized? • Consider instructional decisions • Consider how the standards and evidences for content and practice could be demonstrated in student work • How can teachers structure instruction to ensure that students know/can do what is being asked of them in light of this item, but in a classroom setting? • What links, if any, are there to formative assessment practices?

Reflect. . . • How can you use what we’ve just done as you are designing modeling tasks? Reasoning Reflection • What are some implications and adjustments we might want to consider to our curriculum, instruction and assessment?