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Goals

Because You Can’t Memorize Understanding! Supporting ELL Students in Common Core Mathematics Presented by: Katy Absten, K-12 Mathematics Specialist, OSPI Teaching and Learning Washington Association for Bilingual Educators April 12, 2014 . Goals.

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Goals

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  1. Because You Can’t Memorize Understanding! Supporting ELL Students inCommon Core MathematicsPresented by: Katy Absten, K-12 Mathematics Specialist, OSPI Teaching and LearningWashington Association for Bilingual EducatorsApril 12, 2014

  2. Goals • Understand the 3 shifts and 8 math practices in the Common Core Mathematics Standards and how they can support English Language Learners’ mathematical achievement. • Learn about research-based resources available to support teachers of English Language Learners. • Engage in a math task using these resources!

  3. CCSS - Equity for ALL Students http://www.portlandoregon.gov/oehr/

  4. Washington’s Vision for Education Every Washington public school student will graduate from high school globally competitive for work and postsecondary education and prepared for life in the 21stcentury. OSPI Math Webinar_Part 3_ 3-26-2014 Class of 2011: Bridgeport High School

  5. Classroom Impact of CCSS OSPI Math Webinar_Part 3_ 3-26-2014

  6. OSPI Math Webinar_Part 3_ 3-26-2014

  7. The Three Shifts in Mathematics • Focus: Strongly where the standards focus • Coherence: Think across grades and link to major topics within grades • Rigor: In major topics, pursue with equal intensity: • Conceptual understanding • Procedural skill and fluency • Application

  8. Shift One: Focus Strongly Where the Standards Focus • Significantly narrow the scope of content and deepen how time and energy is spent in the math classroom • Focus deeply only on what is emphasized in the standards, so that students gain strong foundations

  9. Shift One: Focusstrongly where the Standards focus Less topic coverage can be associated withhigher scores on those topics covered becausestudents have more time to master thecontent that is taught.” – Ginsburg et al., 2005 WaToToM – March 7th-9th, 2014 • Move away from "mile wide, inch deep" curricula identified in TIMSS. • Spend more time on foundational concepts to deepen understanding • Focus is necessary in order to achieve the rigor set forth in the standards • Teach less, learn more.

  10. Attaining Focus in early grades WaToToM – March 7th-9th, 2014 K-2 is a deep focus on number, place value, and operation (addition and subtraction) - concepts, skills and problem solving 3-5 builds on these foundational concepts and focuses on multiplication and division of whole numbers and fractions - concepts, skills and problems solving There is very little data work in K-5, and what’s there is tightly connected with core progressions in number systems, the number line, and problem solving using the four operations Concentration on arithmetic and the aspects of measurement that support it

  11. Traditional K-12 U.S. Approach

  12. Focus by Grade Level

  13. Grade Level Focus WaToToM – March 7th-9th, 2014

  14. Shift Two: CoherenceThink across grades, and link to major topics within grades • Carefully connect the learning within and across grades so that students can build new understanding onto foundations built in previous years. • Begin to count on solid conceptual understanding of core content and build on it. Each standard is not a new event, but an extension of previous learning.

  15. Coherence “The Standards are not so much built from topics as they are woven out of progressions.” Structure is the Standards, Publishers’ Criteria for Mathematics, Appendix http://ime.math.arizona.edu/progressions/

  16. Progression of Learning

  17. WaToToM – March 7th-9th, 2014

  18. K-5 – NBT Progression Document WaToToM – March 7th-9th, 2014

  19. Coherence Within Grades 3.OA.B 3.MD.C.7 Relate area to the operations of multiplication & addition. Understand properties of multiplication … 3.G.A Reason with shapes and their attributes. The standards make explicit connections at a single grade

  20. Shift Three: Rigor Equal intensity in conceptual understanding, procedural skill/fluency, and application • The CCSSM require: • Solid conceptual understanding • Procedural skill and fluency • Application of mathematics to problem solving situations • In the major work of the grade, this requires equal intensity in time, activities, and resources in pursuit of all three.

  21. Required Fluencies in K-6 WaToToM – March 7th-9th, 2014

  22. Conceptual Understanding is more than explaining What are two different equations with the same solution as 3(y – 1) = 8? Asking students to show work and explain can be informative, but it isn’t the only way to assess conceptual understanding and can become tiring for students.

  23. Procedural Fluency is not all about Timed Tests “Reasoning and pattern searching are never facilitated by restricted time….strategy development and general number sense are the best contributors to fact mastery.” --Van de Walle Find the number that goes into each box: A) B) 5 + = 8 C) - 2 = 6 D) 9 - = 5 E) + = 10

  24. Applications should be motivating for students What is the relationship between the height you drop a ball and it’s corresponding bounce height?

  25. Standards for Mathematical Practice The practices live within the content. WaToToM – March 7th-9th, 2014 • 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

  26. Describes mathematical “habits of mind” that students at ALL grade levels should develop.

  27. State-wide Network

  28. Washington Ongoing: Statewide Coordination and Collaboration to Support Implementation (Professional Learning Providers and Partners Across WA ) • Including: • School Districts (CCSS District Implementation Network) • Higher Education • Education and Educator Content Associations • Business Partners OSPI Math Webinar_Part 3_ 3-26-2014

  29. I will send another slide about signing up for movers and shakers—how to stay connected.

  30. Resources

  31. CCSS Implementation Resources NWMC 10/11/13

  32. NWMC 10/11/13

  33. CCSS-M Implementation Resources

  34. CCSS-M Implementation Resources

  35. Opportunities to be involved Movers and Shakers http://k12.wa.us/Mathematics/default.aspx OSPI CCSS Webinar Series https://www.k12.wa.us/CoreStandards/updatesevents.aspx PD Offered through all 9 ESDs Check with your local ESD to determine what professional learning opportunities are available. OSPI Math Webinar_Part 3_ 3-26-2014

  36. Resources to support English Language Learners in Mathematics

  37. OSPI Math Webinar_Part 3_ 3-26-2014

  38. Goal of the Understanding Language materials Illustrate how mathematics tasks that are aligned with the Common Core State Standards (CCSS) for Math can be used to support mathematics instruction and the learning of English Language Learners (ELLs), at three grade spans (elementary, middle, and high school).

  39. ELLs develop mathematical proficiency as well as the linguistic resources to express that proficiency by actively participating in mathematical practices and rigorous mathematical reasoning that is well scaffolded by instruction. These resources are based on the premise that the eight Common Core Standards for Mathematical Practice focus on key aspects of mathematical expertise and set expectations for students to be engaged in mathematical activities that, over time, simultaneously build: • procedural fluency, • conceptual understanding, and • mathematical reasoning and sense making

  40. Although learning vocabulary may be necessary, it is not sufficient. • Learning to communicate mathematically and participate in mathematical discussions is not simply a matter of learning vocabulary. • During discussions in mathematics classrooms, students are learning to describe relationships, make generalizations, and use representations to support their claims.

  41. The question is not whether students who are ELLs should learn vocabulary but rather how instruction can best support students to learn vocabulary as they actively engage in mathematical reasoning about important mathematical topics. Therefore, these materials and recommendations stress the importance of creating (and supporting students in) engaging rich mathematical discussions.

  42. Key Principles • Focus on students’ mathematical reasoning, not accuracy in using language • Focus on mathematical practices, not language as single words or definitions • Recognize the complexity of language in mathematics classrooms & supports students in engaging in this complexity • Treat everyday and home languages as resources, not obstacles

  43. Sample Mathematics Tasks • We used or adapted tasks from two publicly accessible curriculum projects, Inside Mathematics and Mathematics Assessment Project. • The mathematics tasks with annotations (available on the UL web site) provide examples of how teachers can use a mathematics task that is aligned with the CCSS when working with ELLs.

  44. Language of Mathematics Tasks TASKS TO SUPPORT READING MATHEMATICS PROBLEM • Reading and Understanding a Mathematics Problem • Jigsaw Reading TASKS TO SUPPORT VOCABULARY FOR MATHEMATICAL COMMUNICATION • Vocabulary Review Jigsaw • Mathematically Speaking • Vocabulary Pieces, Roots, and Families

  45. READING AND UNDERSTANDING A MATHEMATICS PROBLEM • Step 1. Read the problem out loud to a peer. Try to answer this question: What’s the problem about? • Step 2. Read the problem again. Talk to your partner about these questions: What is the question in the problem? What are you looking for? (Hint: Look at the end of the problem for question.) • Step 3. Read the problem a third time. Talk to your partner about these questions. • What information do you need to solve the problem? (What do you want to know?) • What information do you have? (What do you know?) • What information are you missing? (What don’t you know?) • Draw a diagram of the problem and label all the information you know.

  46. http://mathandlanguage.edc.org/

  47. Mathematical Thinking: Supports for English Language Learners Awebsite born from the Fostering Mathematical Success for English Language Learners1(FMSELL) project carried out by the Education Development Center, Inc. in collaboration with Horizon Research, Inc. The site is primarily designed for math educators of English Learners in the middle grades. The site's content includes 14 mathematics tasks from The Fostering Geometric Thinking Toolkit2, as well as a set of support tools for each of the tasks.

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