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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 • 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! CCSS - Equity for ALL Students http://www.portlandoregon.gov/oehr/ 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 21st century. OSPI Math Webinar_Part 3_ 3-26-2014 4 Class of 2011: Bridgeport High School Classroom Impact of CCSS Content Culture Practices OSPI Math Webinar_Part 3_ 3-26-2014 5 OSPI Math Webinar_Part 3_ 3-26-2014 6 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 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 Shift One: Focus strongly where the Standards focus • 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. Less topic coverage can be associated with higher scores on those topics covered because students have more time to master the content that is taught.” – Ginsburg et al., 20059 WaToToM – March 7th-9th, 2014 Attaining Focus in early grades 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 WaToToM – March 7th-9th, 2014 10 Traditional K-12 U.S. Approach K Number and Operations Measurement and Geometry Algebra and Functions Statistics and Probability 12 Focus by Grade Level Pre-K-8 Domains Progression Domains Counting and Cardinality Operations and Algebraic Thinking Number and Operations in Base Ten Number and Operations - Fractions Ratios and Proportional Relationships The Number System Expressions and Equations Functions Geometry Measurement and Data Statistics and Probability PK K 1 2 3 4 5 6 7 8 Grade Level Focus 13 WaToToM – March 7th-9th, 2014 Shift Two: Coherence Think 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. 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/ Progression of Learning Grade 3 Grade 4 Grade 5 WaToToM – March 7th-9th, 2014 17 K-5 – NBT Progression Document WaToToM – March 7th-9th, 2014 18 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 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. 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.OA.2 Add/subtract within 20 (know single-digit sums from memory) 2 3 2.NBT.5 3.OA.7 Add/subtract within 100 Multiply/divide within 100 (know single-digit products from memory) 3.NBT.2 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 WaToToM – March 7th-9th, 2014 21 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. Procedural Fluency is not all about Timed Tests Find the number that goes into each box: A) + = □ B) 5 + □ = 8 C) □ - 2 = 6 D) 9 - □ = 5 E) □ + □ = 10 “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 Applications should be motivating for students What is the relationship between the height you drop a ball and it’s corresponding bounce height? Standards for Mathematical Practice 1. Make sense of problems and persevere in solving them 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others 4. Model with mathematics 5. Use appropriate tools strategically 6. Attend to precision 7. Look for and make use of structure 8. Look for and express regularity in repeated reasoning The practices live within the content. WaToToM – March 7th-9th, 2014 25 Describes mathematical “habits of mind” that students at ALL grade levels should develop. STATE-WIDE NETWORK Ongoing: Statewide Coordination and Collaboration to Support Implementation (Professional Learning Providers and Partners Across WA ) Washington Including: • School Districts (CCSS District Implementation Network) • Higher Education • Education and Educator Content Associations • Business Partners 28 OSPI Math Webinar_Part 3_ 3-26-2014 • I will send another slide about signing up for movers and shakers—how to stay connected. RESOURCES CCSS Implementation Resources Top Resources – Big Picture Achieve The Core www.achievethecore.org Resources included annotated tasks, practice guides, assessment guides, instructional materials toolkit Assessment System Resources www.smarterbalanced.org Smarter Balanced Released Sample Items / Performance. Tasks Smarter Balanced Practice & Training Tests http://www.smarterbalanced.org/practice-test/ Achieve www.achieve.org Multiple array of resources to support implementation of CCSS NWMC 10/11/13 31 Top Resources - Math Illustrative Mathematics Project www.illustrativemathematics.org Takes available aligned to the CCSS that illustrate the standards. These tasks have been vetted by leaders in the nation for alignment and quality. Progression Documents http://ime.math.arizona.edu/progressions/ These documents give the narrative or story of how the domains progress both in a particular grade and through several grades. Engage NY http://www.engageny.org/ Engage NY is building out units in ELA and mathematics that are aligned to the CCSS Inside Mathematics http://www.insidemathematics.org/ Video excerpts of mathematics lessons correlated with the practice standards, resources on content standards alignment, and videos of exemplary lessons in both elementary and secondary settings. Publishers Criteria http://www.achievethecore.org/downloads/Math_Publishers_Criteria_K8_Summer_2012.pdf Provides criteria for aligned materials to CCSS. Based on the two major evidencebased design principles of the CCSSM, focus and coherence, the document intends to guide the work of publishers and curriculum developers, as well as states and school districts, as they design, evaluate, and select materials or revise existing materials. NWMC 10/11/13 32 CCSS-M Implementation Resources Top Resources – Big Picture Achieve The Core www.achievethecore.org Resources included annotated tasks, practice guides, assessment guides, instructional materials toolkit Illustrative Mathematics Project www.illustrativemathematics.org Takes available aligned to the CCSS that illustrate the standards. These tasks have been vetted by leaders in the nation for alignment and quality. Achieve www.achieve.org Multiple array of resources to support implementation of CCSS Assessment System Resources www.smarterbalanced.org Smarter Balanced Practice Test/Released Sample Items & Performance Tasks CCSS-M Implementation Resources Top Resources - Math Progression Documents http://ime.math.arizona.edu/progressions/ These documents give the narrative or story of how the domains progress both in a particular grade and through several grades. Engage NY http://www.engageny.org/ Engage NY is building out units in ELA and mathematics that are aligned to the CCSS Inside Mathematics http://www.insidemathematics.org/index.php/home Classroom examples and tools for innovative instruction, and videos of instructional practices aligned to the CCSS Mathematics Assessment Project http://map.mathshell.org/materials/index.php The Mathematics Assessment Program (MAP) aims to bring to life the Common Core State Standards (CCSSM and exemplify CCSSM in engaging tasks, performance assessments and lessons grounded in formative assessment. 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 35 Resources to support English Language Learners in Mathematics OSPI Math Webinar_Part 3_ 3-26-2014 37 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). 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 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. 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. 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 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. 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 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. http://mathandlanguage.edc.org/ Mathematical Thinking: Supports for English Language Learners A website 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. 5 types of support tools accompany each task. Printable PDFs are of sets of tasks and tools available for free download. • Warm-ups help give teachers an idea of students' prior knowledge, provide scaffolding, and reinforce some of the academic language used in the task. • Sentence starters & frames help reinforce some of the mathematical sentence structures useful in solving the problem and facilitate the development of academic language. • Word charts break down key words and phrases in the task, identifying cognates, related terms, and meanings in Common English versus Academic English. • Support notes help make teachers aware of the nuances and other potential points of confusion in the language used in the task. • Spanish translation of the task Communications Campaign • Ready Washington is a coalition of state and local education agencies, associations and advocacy organizations that support college- and career-ready learning standards. Their audience is public (parents, community, educators, lawmakers) to build awareness and support for CCSS, prepare for initial decline in test scores in transition to more rigorous assessments and counter misinformation/myths. * www.ReadyWA.org CCR Systems Webinar Pt.1.9-16-13 52 Current Resources for Communities and Families • Website designed to provide accurate information on the CCSS: • http://thecommoncore.com/ • The Common Core State Standards: An Introduction for Families and Other Stakeholders (from the Aspen Institute) http://www.aspeninstitute.org/publications/common-core-state-standardsintroduction-families-other-stakeholders – Flyers in Spanish and English for download • OSPI’s CCSS Web Site: http://www.k12.wa.us/CoreStandards/Families/default.aspx • National PTA Parent Guides • Parent Roadmaps to the CCSS – from the Council for Great City Schools CCR Systems Webinar Pt.1.9-16-13 53 SMARTER BALANCED ASSESSMENT SYSTEM Improving Teaching & Learning Common Core State Standards specify K-12 expectations for college and career readiness Summative: College and career readiness assessments for accountability Teachers and schools have information and tools they need to improve teaching and learning Formative Interim: resources: Flexible and open Digital Library with assessments, used instructional and for actionable professional learning feedback resources for educators to improve instructionOSPI Math Webinar_Part 3_ 3-26-2014 All students leave high school college and career ready Page 55 ✔ Balanced Assessment Summative Assessments for Accountability ✔ ✔ •Coverage of full breadth/depth of Common Core •Computer Adaptive Testing (CAT) • Precise assessment of all students • More engaging assessment experience •Performance Tasks – real world problems Interim Assessments to Signal Improvement Formative Tools and Resources for Improved Instruction •Optional for district, school or classroom use •Fully aligned with Common Core – same item pool •Focus on set of standards or mirror summative test •Teachers can review and score responses •Digital library gives access to high-quality resources •Tools/materials for classroom-based assessments •Professional social networking (Web-based PLCs) •Useful for in-service and pre-service development OSPI Math Webinar_Part 3_ 3-26-2014 56 Resources in the Digital Library Assessment Literacy Modules Exemplar Instructional Modules • Commissioned professional development modules • Resources for students and families • Frame formative assessment within a balanced assessment system • Articulate the formative assessment process • Highlight formative assessment practices and tools • Commissioned professional development modules • Instructional materials for educators • Instructional materials for students • Demonstrate/support effective implementation of the formative process • Focus on key content and practice from the Common Core State Standards for Mathematics and English Language Arts • High-quality vetted instructional resources and tools for educators • High-quality vetted resources and tools for students and families Education Resources • Reflect and support the formative process • Reflect and support the Common Core State Standards for Mathematics and English Language Arts • Create Professional Learning Communities * Resources include the following file types: Video, HTML5, Audio, PPT,Math Excel,Webinar_Part Word, and PDF. 3_ OSPI 3-26-2014 Page 57