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PK-5 Math Forum

PK-5 Math Forum. October 4, 2012. I need exactly 4 quarts of water to make a punch for the class party. I have a 5 qt. bucket and a 3 qt. bucket. How can I measure exactly 4 qt. of water using just these two buckets?. How would you model this problem to help you think it through ?

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PK-5 Math Forum

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  1. PK-5 Math Forum October 4, 2012

  2. I need exactly 4 quarts of water to make a punch for the class party. I have a 5 qt. bucket and a 3 qt. bucket. How can I measure exactly 4 qt. of water using just these two buckets? How would you model this problem to help you think it through? How would you record your steps to communicate what you did? How many different solutions?

  3. http://e2math.weebly.com/ • Explain “why” • Important Updates • Models to Support Thinking • Promote collaboration and communication • Blog format • Support your work as teacher leaders in your districts • PK-5 Implementation • PK-5 Forum

  4. Advances in the PARCC Mathematics Assessment http://parcconline.org/samples/item-task-prototypes August 2012

  5. PARCC’s Fundamental Advance PARCC is designed to reward quality instruction aligned to the Standards, so the assessment is worthy of preparation rather than a distraction from good work.

  6. PARCC’s Core Commitments to Mathematics Assessment Quality • Focus: PARCC assessments will focus strongly on where the Standards focus. Students will have more time to master concepts at a deeper level. • Problems worth doing: Multi-step problems, conceptual questions, applications, and substantial procedures will be common, as in an excellent classroom. • Better Standards Demand Better Questions: Instead of reusing existing items, PARCC will develop custom items to the Standards. • Fidelity to the Standards (now in Teacher’s hands): PARCC evidences are rooted in the language of the Standards so that expectations remain the same in both instructional and assessment settings.

  7. What is Different About PARCC’s Development Process? • PARCC states first developed the Model Content Frameworks to provide guidance to key elements of excellent instruction aligned with the Standards. • The Model Content Frameworks were then used to provide guidance in the content emphasis for the mathematics assessment. So, for the first time. . . • PARCC is communicating in the same voice to teachers as it is to assessment developers!  • PARCC is designing the assessments around exactly the same SHIFTS the standards expect of teachers and students.

  8. What Are the Shifts in the Math Standards at the Heart of PARCC Design? • Focus: The PARCC Assessment will 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.

  9. Advances in Assessment Specificadvances in the PARCC mathematics assessments demanded by the three shifts…

  10. Advances in Assessment Demanded by the Shifts Shift #1 – Focus: The PARCC assessments will focusstrongly where the Standards focus Advance: PARCC assessments will focus strongly where the Standards focus (70% or more on the major work in grades 3-8). • Focus allows for a variety of problem types to get at concept in multiple ways. • Students will have more time to master concepts at a deeper level.

  11. Advances in Assessment Demanded by the Shifts Shift #2- Coherence: Think across grades, and link to major topics 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), as are key endpoints and takeaway skills (e.g., fluency with the multiplication table in grade 3).

  12. Advances in Assessment Demanded by the Shifts Shift #2 - Coherence: Think across grades, and link to major topics within grades Advance: Integrative tasks draw on multiple standards to ensure students are making important connections. • The Standards are not treated as a checklist.

  13. Advances in assessment demanded by the shifts Shift #3- Rigor: In major topics, pursue conceptual understanding, procedural skill and fluency, and application Advance: PARCC assessments will reach the rigor in the Standards through innovations in technology and item design…

  14. Using Technology to Advance Assessment and the Shifts • Technology enhancements supporting accessibility (e.g., the ability to hover over a word to see and/or hear its definition, etc.) • Transformative formats making possible what can not be done with traditional paper-pencil assessments (e.g., simulations to improve a model, game-like environments, drawing/constructing diagrams or visual models, etc.) • Getting beyond the bubble and avoiding drawbacks of traditional selected response such as guessing or choice elimination.

  15. Using Technology to Advance Assessment and the Shifts • Capturing complex student responses through a device interface (e.g., using drawing tools, symbol palettes, etc.) • Machine scorable multi-step tasks are more efficient to administer and score.

  16. Sample Items Illustrating the Advances in Assessment The next section of this presentation is comprised of sample items that illustrate some of the advances called for by the three shifts.

  17. Overview of Mathematics Task Types PARCC mathematics assessments will include three types of tasks. For more information see PARCC Item Development ITN Appendix D.

  18. Fluency To support mathematical thinking

  19. Erin Wheeler, IES Erie 2 BOCES, 8-26-2012 Counting Fluency

  20. Erin Wheeler, IES Erie 2 BOCES, 8-26-2012 Sprints Bill Davidson http://www.youtube.com/watch?v=G_y9gGnd68M

  21. Erin Wheeler, IES Erie 2 BOCES, 8-26-2012 Application Problem solving requires studentsto apply the 8 Mathematical Practices Bill McCallum – “Structuring the Mathematical Practices” http://commoncoretools.me

  22. Erin Wheeler, IES Erie 2 BOCES, 8-26-2012 Table I and 2

  23. Erin Wheeler, IES Erie 2 BOCES, 8-26-2012 Making the Connection 9 + 6= 15

  24. Erin Wheeler, IES Erie 2 BOCES, 8-26-2012 Multipurpose Models • Number path • Number stairs • Number bond • Place Value Models • Ten frames, bundles, base ten blocks, money, number disks • Bar Model • Area Model • Number line • Array • Rekenrek- physical model of an array

  25. Erin Wheeler, IES Erie 2 BOCES, 8-26-2012 Second Grade 8 children are swimming in the pool. 5 more children jump in. How many children are in the pool now? ? 8 children 5 more 8 + 5 = 13 13 children are in the pool.

  26. Erin Wheeler, IES Erie 2 BOCES, 8-26-2012 Marcus has 12 pencils. Sergio has 3 more pencils than Marcus. How many pencils does Sergio have?

  27. Erin Wheeler, IES Erie 2 BOCES, 8-26-2012 Jerry has 12 eggs. He gave 3 to Kevin. How many eggs does Jerry have now?

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