Fellows Meeting 4 APRIL 21, 2015 ESD 105 Fellows Meeting #4 A candy jar contains 5 Jolly Ranchers (squares) and 13 Jawbreakers (circles). Suppose you had a new candy jar with the same ratio of Jolly Ranchers to Jawbreakers, but it contained 100 Jolly Ranchers. How many Jawbreakers would you have? Explain how you know. ◦ Please try to do this problem in as many ways as you can. ◦ If done, share your work with a neighbor. Road Map of Our Day 8:30-10:00 Principles to Action Book Study 10:00-10:15 Break 10:15-11:30 CSTP- Fellows Groups Together 11:30-12:30 Lunch 12:30-1:30 Discourse and English Language Learners 1:30-1:45 Break 1:45-2:45 SBAC Claims and Depth of Knowledge 2:45-3:30 Next Steps-Evaluations Best Math Lesson Ever Turn and Talk What made it so successful? What was the math teacher doing? What were the students doing? What mathematics was being learned? Teaching Practices that Support Common Core Implementation • Establish Mathematics Goals to Focus Learning • Implementing Tasks that Promote Reasoning and Problem Solving • Use and Connect Mathematical Representations • Facilitate Meaningful Mathematical Discourse • Pose Purposeful Questions • Build Procedural Fluency from Conceptual Understanding • Support Productive Struggle in Learning Mathematics • Elicit and Use Evidence of Student Thinking Turn and Talk How has the book study around the 8 teaching practices deepened your understanding around your vision of mathematics reform efforts? How has the study impacted your work with your building/district? Facilitate Meaningful Mathematical Discourse Purposeful Questioning Math Practices Effective teaching of mathematics facilitates discourse among students to build shared understanding of mathematical ideas by analyzing and comparing student approaches and arguments. Review pages 29-41… What was one thought that resonated with you from either practice? Share out your thoughts in a small group. Facilitating Discourse Simply having students talk does not necessarily advance the mathematical goals of a lesson. oHow can the Five Practices identified on page 30, as described by Smith and Stein (2011), support and facilitate the purposeful exchange of ideas in the mathematics classroom? oNow consider Mr. Donnelly’s lesson and how he incorporated the Five Practices to facilitate classroom discussion. (p. 34) Five Practices to Support Facilitating Discourse 1. Anticipating student response prior to the lesson 2. Monitoring students’ work on and engagement with the tasks 3. Selecting particular students to present their mathematical work 4. Sequencing students’ responses in a specific order for discussion 5. Connecting different students’ responses and connecting the responses to key mathematical ideas Facilitating Meaningful Discourse Considering the Levels of Student Discourse: oWhich of these practices are under utilized in classrooms? oHow can we help teachers become more intentional incorporating these practices? Mathematics Teaching Practice Pose Purposeful Questions oGathering Information oProbing Thinking oMaking the Mathematics Visible oEncouraging Reflection and Justification Pose Purposeful Questions Consider the math task for your Grade Band from Digging for Dinosaurs 1. Review the standards associated with the task you chose 2. Do the math 3. Anticipate likely student responses and misconceptions (see Smith & Stein’s practice 1, p. 30) 4. Create a list of related questions using the framework in figure 14 (pp. 36–37) 5. Create a poster with your questions Review Levels of Discourse Review Chart from Principles to Actions (p. 32) oWhat do you see as next steps to see you move along the continuum? oHow does this continuum help you think about your work with teachers? Break- The Center for Strengthening the Teaching Profession (CSTP) Module 4 – Case Story Discussion Objectives Apply your developing understanding of the Teacher Leadership Framework and your skills as a Teacher Leader to Case Stories. Reflect on your growth as a teacher leader in your role as a Fellow this year. Pre-flection Review your results from the Teacher Leadership Framework Self-Assessment: ◦ Do these results reflect where you are now? Why or why not? ◦ What has gotten more challenging? What has gotten easier? ◦ How do you deal with dilemmas that come up and still focus on building capacity? Learning Through Case Stories Read the Case Story “Overwhelmed and Underappreciated” As you read, consider what you know from the Teacher Leadership Framework that might connect to the Case Story – either in evidence provided or lack thereof. Annotate your thoughts within the article or on scratch paper. Learning Through Case Stories How do you and don’t you see yourself in this dilemma? Where does this dilemma ‘live’ in terms of the five areas in the Teacher Leadership Framework (could be multiple areas)? Where do you see evidence of the teacher leader employing specific knowledge, skills and dispositions from the Teacher Leadership Framework? What from the Teacher Leadership Framework might assist this teacher leader in managing this dilemma? Set-Up: Circle of Viewpoints Brainstorm a list of players in this dilemma – in other words, who is part of the system described in the Case Story? Each person in your group takes on the role of one of the players identified in your brainstorm Circle of Viewpoints Use the Circle of Viewpoints Routine to re-examine and discuss the Case Story. Going one at a time, each group member contributes to the following three prompts: ◦ I am thinking of this Case Story from the point of view of… ◦ I think… ◦ A question I have is… Repeat with the next group member until you’ve gone all the way around the whole group. Reflections & Next Steps After using the Circle of Viewpoints routine, what new ideas do you have that you didn’t have before? What implications or realizations did you have for your own work as a fellow in reading this Case Story? What are your next steps? I used to think…Now I think… Fellows 2015-16 Applications are now open.. Returning Fellows New Fellows Lunch-Meet back with your fellows group at 12:30 Math Fellows Next Steps… Fellows Student Task Data SurveyFellows Self-Assessment Pre/PostSubmit Fellows Plans Video Questions- OPSI Clock Hours/Evaluations Date: April 21, 2015 Title: Washington State Math Fellows Professional Development Hours: 6 The Language of Mathematics for All Children (CCSS to ELP and Beyond) Helping all students communicate mathematical understanding. Session Goals… Promote student engagement through interactive math tasks Provide strategies and tools to support student discourse Updates/Assessment Resources What do you know about English Language Learners in Washington State? Languages Spoken in Washington State Schools 219 Different Home Languages Most identified language is Spanish, spoken by 67.4% of students Next were Russian, Vietnamese, Somali, Chinese, Ukrainian, Arabic, Tagalog, Korean, Marshallese, spoken by 19% of Students ELL’s in Washington State 2013-14 Around 110,000 Bilingual Student a 5.3% increase from the previous year Comprises 9.7% of the statewide student population - 0.6% points higher than the previous year Since 2005–06, the number of ELLs served by TBIP in the state has increased by 32.6% ELL’s in Washington State 2013-14 Twenty-seven districts had an ELL headcount of at least 25% of their total student population. Thirty districts enrolled more than 1,000 ELLs. These districts collectively served 72% of all ELL’s statewide. Forty-seven districts enrolled 500 or more ELL students. Thirteen districts reported an increase of 10– 15%. ELL’s in Washington State 2013-14 Fifty-six districts enrolled fewer than 50 ELL students. Fifteen districts reported fewer than 10 ELLs. 55.9% served by the TBIP were enrolled in grades K–3. 25% are newly eligible students ELL’s in Washington State 2013-14 42 districts have more than 20 languages 19 of these districts had more than 50 languages. Of the 219 languages, 103 of these languages have less than 10 students The largest language increase is in Spanish The greatest decrease is in Korean Classroom Level Discuss the language supports in your district/classroom…. Focused Mathematical Discourse… “In linguistically diverse classrooms, unstructured small group and partnering activities continually fail to produce substantive L2 oral language growth. Merely increasing student interaction without explicit, coached language instruction and accountability for application leads to discussions with minimal cognitive or linguistic challenge and negligible academic content.” Gersten & Baker, 2001 Saunders and Goldenberg, 2010 Preparing ELL’s To meet both content and language standards Talk Build on prior knowledge about new ideas Read Introduce new content Talk Integrate new content into schema Write Informally show what you know and ask questions you still have Talk Refine thinking and deepen learning “Reading and writing float on a sea of talk.” James Britton Graphic Organizers… What do you know about races? A Race Amy and Rebecca are running in a road race. The map, drawn to scale, shows the route of the race: It takes Amy 8 minutes to run a mile. Rebecca takes 12 minutes to run a mile. The race consists of four laps of the route and Amy and Rebecca run clockwise along the route at a constant speed. Sharing Individual Solutions 1. Take turns to share your individual work with your partner(s). 2. Share the notes you made on how you might improve your work. 3. Listen carefully to each other, asking questions if you don’t understand. 4. Use the Present an Idea Card and Pose a Question to guide your conversation. P-47 Joint Solution: Making Posters-Talk Through 1. In your group, agree on the best method for completing the problem. 2. Produce a poster that shows a joint solution to the A Race task, that is better than your individual work. 3. State on your poster any assumptions you have made. 4. Give clear reasons for your choice of method. P-48 Sharing Posters- Talk Through 1. One person from each group get up and visit a different group. 2. If you are staying with your poster, explain your work to the visitor, giving reasons for your choice of method. 3. If you are the visitor, look carefully at the work, asking clarifying questions to help you to understand the method used. 4. Discuss whether or not the method described on the poster is similar to the visitor’s method. 5. The visitor is to write on a post-it note, suggestions on how the work could be improved. P-49 Sample Responses to Discuss: Sally P-50 Sample Responses to Discuss 1. Read each piece of sample student work carefully. 2. Use the E.L. Achieve Discussion Cards (Build on and Idea and Challenge and Idea) to understand what Sally, Diane and George’s mathematical thinking. 3. Take turns explaining your thinking to your partner. 4. Listen carefully and ask clarifying questions. Use the Pose a Question Card to frame your questions. 5. Provide feedback to each of the three responses using the discussion cards. P-51 E.L. Achieve Discussion Cards Support Your Thinking-Secondary Math Simple Academic Language •The solution is reasonable because… •Look at the pattern. I see… •My method for solving this problem can also work for … E.L. Achieve Discussion Cards Support Your Thinking-Secondary Math Solid Academic Language The solution demonstrates that … because … Based on the data, I see that… My strategy for solving this problem can also be used for …. E.L. Achieve Discussion Cards Support Your Thinking-Secondary Math Sophisticated Academic Language Although I estimated …., my solution is reasonable because… Based on the rule … I can justify that … because… Because …, I can generalize the that the strategy for solving this problem applies to … Rich Math Tasks Rich Math Tasks: Digging for Dinosaurs Exploration and Extensions… Having quality Math Task leads to discussion. How did the use of the E.L. Achieve Cards an other graphic organizers help support critiquing the reasoning of others? How might you utilize a teaching tool such as the E.L. Achieve Cards and graphic organizers? Break… Smarter Balanced Assessment Consortium Mathematics Content Specifications How do we ensure that our student can understand standards? Structure of the Smarter Balanced Assessment Consortium Mathematics Content Specifications Introduction and Background • • • • General Considerations Claims and Assessment Targets Rationale and Evidence for Each Claim Cognitive Rigor Matrix / Depth of Knowledge 4 Claims for Mathematics (a/o Round 1 – released 8/29/11) Concepts and Procedures “Students can explain and apply mathematical concepts and carry out mathematical procedures with precision and fluency.” Problem Solving “Students can frame and solve a range of complex problems in pure and applied mathematics.” Communicating Reasoning “Students can clearly and precisely construct viable arguments to support their own reasoning and to critique the reasoning of others.” Data Analysis and Modeling “Students can analyze complex, real-world scenarios and can use mathematical models to interpret and solve problems.” Mathematics Claim #1 Concepts and Procedures “This claim addresses procedural skills and the conceptual understanding on which developing skills depend.” ◦ Selected Response ◦ Short Constructed Response ◦ Highly Scaffolded Tasks ◦ Extended Response Claim #2 Problem Solving “Assessment items and task focused on this claim include well-posed problems in pure mathematics and problems set in context.” Single Step/Multistep Problems Balanced types of problems that could include… ◦ Problems in Pure Math ◦ Design Problems ◦ Planning Problems Claim #2 Problem Solving Draw from knowledge and skills within many standards May draw on knowledge and skills from lower grades Provide evidence for many assessment targets Relevant verbs include: Understand Solve Apply Describe Illustrate Interpret Analyze Claim #3 Communicating Reasoning “This claim refers to a recurring theme in the CCSSM content and practice standards: the ability to construct and present a clear, logical convincing argument.” Relevant Verbs Include: ◦ Understand ◦ Explain ◦ Justify ◦ Prove ◦ Derive ◦ Assess ◦ Illustrate ◦ Analyze Claim #4 Modeling and Data Analysis “Modeling is the process of choosing and using appropriate mathematics and statistics to analyze empirical situations, to understand them better, and to improve decision-making.” Math Practices in the Claims Claim 1 – MP 5, 6, 7, 8 Claim 2 – MP 1, 5, 7, 8 Claim 3 – MP 3, 6 Claim 4 – MP 2, 4, 5 SBAC Cognitive Rigor Foundation The Common Core State Standards require high-level cognitive demand, such as requiring students to demonstrate deeper conceptual understanding through the application of content knowledge and skills to new situations and sustained tasks. SBAC Cognitive Rigor Foundation For each Assessment Target in English language arts and mathematics, the depth(s) of knowledge (DOK) that the student needs to bring to the item/task has been identified. Content Specification Documents Math Content Specifications, p. 41 Webb’s Depth of Knowledge (DOK) Depth of Knowledge measures the degree to which the knowledge elicited from students on an assessment matches the complexity of what students must know and do as part of the standards. http://vimeo.com/42788913 Cognitive Rigor and Depth of Knowledge The level of complexity of the cognitive demand. Level 1: Recall and Reproduction Requires eliciting information such as a fact, definition, term, or a simple procedure, as well as performing a simple algorithm or applying a formula. Level 2: Basic Skills and Concepts Requires the engagement of some mental processing beyond a recall of information. Level 3: Strategic Thinking and Reasoning Requires reasoning, planning, using evidence, and explanations of thinking. Level 4: Extended Thinking Requires complex reasoning, planning, developing, and thinking most likely over an extended period of time. Hess Cognitive Rigor Matrix BLOOM’S What type of thinking (verbs) is needed to complete a task? WEBB’S How deeply do you have to understand the content to successfully interact with it? How complex or abstract is the content? Hess Depth of knowledge… (DOK) Assessing your understanding of the Mathematical Claims and DOK Work in Small Groups or Partners • Choose a grade band of Sample Test Items • Decide on a Mathematical Claim for the Sample Item • Decide on the DOK for the Sample Item • Provide evidence for your answers • Check answers with Answer Sheets Fellows Next Steps… Student Data Survey… Teacher Survey… Turn in Fellows Plans… Fellows Application… Application Topics for Next Year Meeting Dates

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