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A Purposeful Ice-Breaker, Hopefully…

A Purposeful Ice-Breaker, Hopefully…. Kentaro Iwasaki, Associate Director for Pathway & Curriculum Development ConnectEd: The California Center for College and Career . Ice Breaker for Norm Building. Goals: 1. Use an Ice Breaker to Get to Know Other People (and Ourselves) Better

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A Purposeful Ice-Breaker, Hopefully…

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  1. A Purposeful Ice-Breaker, Hopefully… Kentaro Iwasaki, Associate Director for Pathway & Curriculum Development ConnectEd: The California Center for College and Career

  2. Ice Breaker for Norm Building • Goals: • 1. Use an Ice Breaker to Get to Know Other People (and Ourselves) Better • Build Norms—an Essential Element in any Social Setting, Especially the Classroom

  3. Norm Building • Marshmallow Challenge • EACH TEAM BUILDS A FREE-STANDING STRUCTURE (NO TAPE ON TABLE) IN 15 MINUTES WITH THE INTACT MARSHMALLOW REACHING THE HIGHEST POINT POSSIBLE • 20 sticks of spaghetti + one yard tape + one yard string + one intact marshmallow

  4. Norm Building • Marshmallow Challenge Debrief Discuss what your group found out about: • the Marshmallow Challenge itself • members in your group (who did what?) • how your group worked together (what went well and what could be done better?) • anything else interesting

  5. Norm Building • Marshmallow Challenge Video • Think about: • 1. Debrief the video. • 2. What is your experience with norms in and out of the classroom ? • 3. What norms would be helpful to make the Marshmallow Challenge better?

  6. Norm Building • Students will not automatically know how to work collaboratively without explicit directions, norms, and “ground rules.” • My Personal Examples

  7. Norm Building • Norms for this PD: • Stay together on agreed-upon topic • Work to maintain equity of voice (“Step Up, Step Back”)

  8. Norm Building • Teachers themselves also need to abide by norms when they ask students to work collaboratively. • Which of these teacher roles is most challenging for teachers and why? • How can we help teachers with these roles and help them establish and maintain group norms?

  9. Frame of Reference • Please participate during this PD as a learner and as a teacher leader who will lead others in the formative assessment lesson process. • Jot down the names or people you will have in mind during the PD with whom you will share the formative assessment lessons and strategies.

  10. Agenda • Norm Building Task and Debrief • Background and Components of a Formative Assessment Lesson • Model, Participate In, and Analyze a Formative Assessment Lesson • CCSS-M Standards and Practices • Formative Feedback and Questioning • Formative Assessment Lesson #2 • Homework: Email Reflection Questions from Day 1

  11. OK, Who is this Guy?

  12. Formative Assessment and 5 Strategies • Please first read the “Big Idea of Formative Assessment” and then “Five Strategies of Formative Assessment,” and answer the questions individually (5 minutes) and then think-pair-share your reflections (5 minutes). • Please be ready to share out!

  13. Classroom Specific Strategies • Avoid cold-calling by giving opportunities for think-pair-share or think-group-share • Record the discussion thread with names and contribution

  14. Formative Assessment Lessons (FALs) • Part 1: Pre-Assessment : Give Students Feedbackand Teachers a QualitativeSense of Students’ Grasp of Targeted Mathematics (15 minutes) • Part 2: Brief Class Discussion (10 minutes) andCollaborativeActivity : Focus on Guided Inquiry to Address Student Misconceptions (45-90 minutes) • Part 3: Post Assessment and Revision: Give Students a Chance to Reflect on Their Learning and Offer Teachers Perspective on Next Steps and TheirTeaching Effectiveness

  15. “Interpreting Algebraic Expressions” Formative Assessment Lesson Math Goal: Translate between words, symbols, tables, and area representations of algebraic expressions. • Recognize the order of algebraic operations. • Recognize equivalent expressions. • Understand the distributive laws of multiplication and division over addition

  16. “Interpreting Algebraic Expressions” Formative Assessment Lesson COMMON CORE STATE STANDARDS A-SSE: Interpret the structure of expressions. A-APR: Rewrite rational expressions. Math Practices: 2. Reason abstractly and quantitatively. 7. Look for and make use of structure.

  17. “Interpreting Algebraic Expressions” Formative Assessment Lesson • Part 1: Individual Pre-Assessment • Please read through or do the pre-assessment individually. • What areas of student understanding or misconceptions can you gather from this?

  18. Part 2: Brief Classroom Discussion Class questions based on pre-assessment 2. Not intended to address every misconception 3. For example, write an algebraic expression that means a. Multiply n by n, and then multiply your answer by 5. b. Multiply n by 5, and then square your answer.

  19. Part 3: Collaborative Activity • Take out the pink andgreencards. Match the corresponding pinkcard to the greencard. Leave these cards out. • Take out the bluecards next and place the bluecards next to the corresponding pinkandgreencards. • Do the same with the yellowcards. • Please fill in any blanks on the cards. • How you might make extensions and/or modifications to this task if needed. • How does this task address student misconceptions and further student understanding?

  20. Part 4: Revision and Post-Assessment Pre-Assessment and a New Sheet are given back to students for revision. Students might respond to a prompt such as, “What did you learn from this lesson that helps you improve your work?”

  21. Part 5: Teacher Decisions about Next Steps Based on revisions and post-assessment, a teacher decides what next steps are best to address existing misconceptions. The Formative Assessment Lesson, if taught 2/3 of the way through a unit, allows time in the unit for a teacher to direct where he/she will lead the class.

  22. DEBRIEF What aspects of the formative assessment lesson allow for deeper student engagement and learning? What challenges arise around the formative assessment lessons for teachers and students? How will you address these challenges?

  23. VIDEO Please observe the video and be ready to share out thoughts or observations.

  24. QUALITATIVE FEEDBACK Based on a study by Ruth Butler (1988), which type of feedback improves student work quality the mostfrom a first lesson to a similar second lesson? Why? Numerical score/grade only Written feedback only Numerical score/grade and written feedback No feedback

  25. QUALITATIVE FEEDBACK What type of feedback did you or other math teachers typically give to students? How did you (or others) provide feedback? How effective did you find your feedback to be? Why? How would you think the feedback could be more effective? Why?

  26. QUALITATIVE FEEDBACK Evaluate the feedback suggestions given. How effective do you find them to be? How might you make them more effective?

  27. QUALITATIVE FEEDBACK Read the sheet on qualitative feedback. Discuss in a small group. How can we improve the feedback we and other teachers give to students?

  28. Concept Development Lessons and Problem Solving Lessons Concept Developmentlessons are intended to assess and develop students’ understanding of fundamental concepts through activities that engage them in classifying and defining, representing concepts in multiple ways/representations, testing and challenging common misconceptions, and exploring the structure of a problem.

  29. Concept Development Lessons and Problem Solving Lessons Problem Solvinglessons are intended to assess and develop students’ capacity to select and deploy their mathematical knowledge in non-routine contexts and typically involve students in comparing and critiquing alternative approaches to solving a problem.

  30. Problem Solving Lessons’ Structure Students individually work on a “less structured” task (pre-assessment) Brief Class Lesson Drawing Out Misconceptions Students Collaborate on the Task Students Examine sample student work and asked to critique and improve these Students then revise their initial attempts and/or try an alternative approach.

  31. Security Cameras • Mathematical goals • This lesson unit is intended to help you assess how well students are able to: • Analyze a realistic situation mathematically. • Construct sight lines to decide which areas of a room are visible or hidden from a camera. • Find and compare areas of triangles and quadrilaterals. • Calculate and compare percentages and/or fractions of areas.

  32. Security Cameras Mathematical Content 6.RP:Understand ratio concepts and use ratio reasoning to solve problems. 6.G:Solve real-world and mathematical problems involving area, surface area, and volume. Mathematical Practices MP1:Make sense of problems and persevere in solving them MP2:Reason abstractly and quantitatively MP3:Construct viable arguments and critique the reasoning of others MP4:Model with mathematics

  33. Security Cameras 1. What misconceptions do you think students will have? What questions would you ask for a BRIEF class discussion? What type of feedback would you give or be prepared to give?

  34. Making Matchsticks 1. What misconceptions do you think students will have? What questions would you ask for a BRIEF class discussion? What type of feedback would you give or be prepared to give?

  35. Agenda Feedback—thanks! Re-Norming Formative Assessment Lesson #3 with EL Support Questioning Feedback Formative Assessment #4 Planning/Next Steps, Evaluation

  36. Re-Norming Debrief the String Geometry Activity. Discuss how and when teachers would use re-norming

  37. Bruce Tuckman’s Stages of Group Development Form Storm Norm Perform Our addition—Re-Norm

  38. EL Support ell.stanford.edu Focus on students’ mathematical reasoning and not on their accuracy in using language Focus on mathematical practices and not on language as single words or definitions Treat everyday and home languages as resources and not as obstacles

  39. EL Support How would you scaffold this lesson for EL students? What would you add? What would you keep the same? Describe your rationale.

  40. EL Support--Instructions One suggestion is to change the instructions in the activity to be clear, direct, and concise. How would you suggest writing the instructions?

  41. EL Support--Instructions “Estimate how many matches can be made from the wood in this tree. Use the relevant information on the formula sheet. It will help you find some answers. Read the task, and show all your work. Showing your work helps me understand your reasoning (thinking). It is important that your work is organized and presented in a clear manner (way).”

  42. QUESTIONING Please spend a few minutes individually reflecting on these questions. Then we will share in small groups and in a large group.

  43. VIDEO 295 Students in a school. A bus holds 25 students. How many buses are needed to hold all the students?

  44. QUESTIONING Fill in the blanks: Based on large study of elementary school classrooms, Ted Wragg analyzed 1000 teacher questions. _____% Managerial Questions _____% Recall Questions _____% Questions that Require Students to Analyze, Make Inferences, Generalize __________________________________ Less than _____% resulted in new learning

  45. QUESTIONING Which questions do you find most effective? Why? Which questions can be improved? How so? What challenges around questioning do math teachers face? How do we support math teachers in asking good questions?

  46. Planning to Work With Teachers Local, Organic, Sustainable It’s a Long Road… Do Math Together in Your PLC/Dept/Team

  47. Planning to Work With Teachers Strategize with your district teachers or instructional specialists to determine what needs and next steps you have in working with teachers on the formative assessment lessons and strategies. What do you need? What do the teachers need? How will you work with the teachers on what they need?

  48. Planning to Work With Teachers 3 webinars throughout the school year to support your work with teachers: Norm Building FAL enactment FAL issues? EL Issues?

  49. Planning to Work With Teachers 3 webinars throughout the school year to support your work with teachers: Norm Building FAL enactment FAL issues? EL Issues?

  50. Math Design Collaborative (MDC) “Mathematically proficient students continually ask themselves, “Does this make sense?” and change course if necessary. They justify their conclusions, communicate them to others, and respond to the arguments of others. They can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. They continually evaluate the reasonableness of their intermediate results, realizing that these may need revision later.” —Common Core State Standards for mathematics

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