1. Teaching Through Problem Solving Part 2 – Bermuda Framework for Teaching Mathematics Gilbert Institute Ongoing PD commencing the week of March 3, 2014 Rebeka Matthews Sousa Instructional Facilitator for Mathematics rsousa@moed.bm Resources from PD available here: www.myteacherpages.com/webpages/mathscience www.myteacherpages.com/webpages/mathscience

2. In this Session, teachers will: O Consider the shifts in classroom teaching O Reflect on the previous Mathematics Lesson (Triangle/Shape sort) which demonstrated the Framework for Teaching Mathematics O Discuss and Reflect on the Framework (Three-Part Lesson)

3. Review of the Reflections 1. What were some of the components of this lesson? O A task is presented. Students worked together to explore/find out the solution. Students given time to share, explain how they got the answer or explain their thinking for the strategy they used. O Problem solving; group work (making it engaging); share O Work with a partner to solve a problem/complete a task; evaluate other group’s results; share and discuss lesson on terminology O Intro/Group/Independent O Engaging/Working on it/Reflect(Share ideas) O Student friendly; hands on O Identifying and organizing shapes into categories O Introduction of lesson using visual aids; Independent selection and work; Group collaboration O Intro, students involved in solving a problem, conclusion

4. Review of the Reflections 2. Consider the Rubric for Quality Teaching in Mathematics, which components of the rubric were met during this lesson? O All key teacher actions for instruction were met, several learner actions were done, environment was set up for group work and sharing O Encourage interactions and communication amongst student; connects the big idea; rigorous; appropriately varied for students to demonstrate understanding of knowledge O Several materials were used; shared a balance of skills; engaging; utilizes a variety of questions, assesses student knowledge, students justify their answers O Aligned with curriculum; engaging and relevant to students interest clear directions and expectations; work collaboratively with peers O All students motivated; provided clear directions; utilizes a variety of questions; encourage interactions O Rigorous, reflected and deepened understanding O Clear directions; share and explore O Manageable and measureable O Encourage interaction and communication amongst students

5. Reading from Chapter 2 Teaching Through Problem Solving O Introductory Paragraphs – p13-17 Text & ISBNTitleAuthors Year Level recommended ISBN-13: 978-0132824828 Teaching Student- Centered Mathematics: Developmentally Appropriate Instruction for Grades Pre K-2 (Volume I) (2nd Edition) John A. Van de WalleJohn A. Van de Walle, Lou Ann H. Lovin, Karen H Karp, Jennifer M. Bay WilliamsLou Ann H. LovinKaren H KarpJennifer M. Bay Williams P1-P3 ISBN-13: 978-0132824873 Teaching Student- Centered Mathematics: Developmentally Appropriate Instruction for Grades 3-5 (Volume II) (2nd Edition) John A. Van de WalleJohn A. Van de Walle, Karen S. Karp, Lou Ann H. Lovin, Jennifer M. Bay-Williams Karen S. KarpLou Ann H. LovinJennifer M. Bay-Williams P4-P6 *P3 may choose this book instead of Volume 1

6. What is Teaching through Problem Solving? “By inviting young children to solve problems in their own ways, we are initiating them into the community of mathematicians who engage in structuring and modeling their ‘lived worlds’ mathematically” Discussion Questions: O Was the lesson you experienced last week “Teaching Through Problem Solving”? Explain why or why not. O What did you think about “Teaching through Problem Solving” prior to reading the text? O How has the reading changed your view of what “Teaching through Problem Solving” really means?

7. Reflection - Teaching Through Problem Solving – Part 2 (Three-Part Lesson) 1. Explain in your own words, the phases of the three-part lesson. 2. Explain the three-parts based on the lesson you experienced last week. 3. Referring to the Shifts in Classroom Practices: How does the three-part model for teaching support these shifts in classroom practices?

8. What are some elements of the teaching through problem-solving/inquiry based framework? Three-partsTeacher could…Student Role BEFORE Engage “Activate thinking” Launch Task. Model manipulatives Solve a similar/simpler problem with the students Think about the problem. Ask questions for clarification. DURING “Working on it” Students “doing” Mathematics Using questioning and prompting to guide students, but not giving solution. Ask about the strategies they are using and why they have selected them? Working through the problem. Using manipulatives and various strategies. AFTER Reflect and Connect “Share time” Addresses misconceptions and facilitates discussion based on student responses. Direct instruction. Student shares ideas, through process

9. Review of the Reflections 3. Why use the three-part lesson or teaching through problem solving framework to teach math? O So that students are more involved in the lesson, they are doing/working on a task, discussing with group members, finding out, discovering answers themselves as opposed to the teacher at the front doing all the work and giving the answer O It is an evaluation (assessment) of the students knowledge about the topic. It allows all students to be engaged and it is student centered. O To get students more engaged and used to problem solving. O Students discover and become the authority rather than the teacher O Allows students to think and problem solve and prove their theories O Allows students to explore and think about what they do O Allows the students to explore and actively engage in their learning through problem solving

10. Why Problem-Solving/Inquiry based Lessons? It’s a comprehensive learning/teaching structure that: O Supports the delivery of curriculum O Is based on the problem solving model O Promotes conceptual mathematical understandings O Promotes 21 st Century Learning Skills O Allows for differentiated instruction O Is consistent with independent skills being demonstrated in the mathematics processes (e.g. problem solving, reasoning and proving, reflecting, tool and strategy selection, making connections, representing understanding and communication) O Allows students to get the “BIG IDEAS” or the fundamental principles of mathematics that link the specifics O Promotes collaboration

11. …The Three-Part Lesson

12. A Mathematics Framework Based on the Balance Math Program DO NOW / Math Review Three Part Lesson 1. Activate 2. Working On it 3. Reflect and Connect Mental Math

13. Review of the Reflections 4. How do I plan to make this part of my everyday math lesson? Or how do I find resources to continue teaching this way? O Make it a lesson structure routine. O First, I need to shift my mindset of best practice. Discover the big idea and lead them to it (baby steps). Have my lessons more student centered O Use resources such as: Teaching Students Centered Mathematics, or website O Try it! Some of the resources we presently have (Hodder ‘Ready to Go Lessons’)

14. Key to planning How will you know that your students know it?

15. Planning Learning Tasks Asking yourself the following questions will help you plan effective learning tasks: O What are the concepts I want my students to learn from the task I plan? O What is it that students need to know and be able to do? O How will I determine my students’ prior knowledge? O What tasks will I present to students? O How will I design a lesson (learning tasks) to help students explore and learn these concepts and engage my students in mathematical thinking? O How will I assess student learning and check for understanding? O Planning Template Planning Template

16. Criteria for Effective Mathematics Tasks A good instructional task captures students’ interest and imagination and satisfies the following criteria: The solution is not immediately obvious The problem provides a learning situation related to a key concept or big idea The task is aligned with the Cambridge Objective(s) The context of the problem is meaningful to students. There may be more than one solution. The problem promotes the use of one or more problem solving strategies The situation requires decision making above and beyond the choosing of a mathematical operation. The solution time is reasonable. The situation may encourage collaboration in seeking solutions.

18. Checklist for Planning Effective Mathematics Tasks The Lesson  Has a balance of skills: mental math, conceptual understanding, problem solving, and computational skills  May include the Three-Part Lesson as a vehicle to Teach Through Problem-solving: (Activate Thinking, Working on it, Reflect and Connect)  A good instructional task captures students’ interests and imagination and also satisfies the following criteria. The Task(s)  Are aligned with the Cambridge Objective(s).  Provides a learning situation related to key concept or big ideas.  Or problem is meaningful relevant and interesting to students.  Cognitively demanding (solution is not immediately obvious) and there may be more than one solution)  Or problem promotes the use of one or more problem solving strategies (multiple entry or exit points)  Differentiated  Requires decision making above and beyond the choosing of a mathematical operation.  May encourage collaboration in seeking solutions.  Resources, materials, manipulatives prepared in advanced. Assessment  Variety of assessment tools to access students throughout the lesson Questioning  Questions are prepared in advance to encourage mathematical thinking and communication of mathematical reasoning.

19. Some Points of Discussion What do you see as the benefits of teaching this way? What additional questions do you have with regards to the Mathematics Framework for Teaching (Three-Part Lesson) What can you do in your lessons to encourage mathematical thinking and reasoning? How can the three-part framework assist in structuring such lessons? Next Phase: Planning and Implementation Teacher Inventory #1, 2, 3, 11, In-class support -