Summer Academy Planning and Teaching Mathematics Through Problem Solving Day 1 Facilitator: Rebeka Matthews Sousa Mathematics Specialist Teacher, Ministry of Education 1

2 Try the Facebook Challenge

 Two full-days  Module 1 and 2 of Mathematics Teacher Endorsement Programme  Participation and Assignment completion  Certificates and PD hours  Save the Date – September 23 4:30-5:30 3 An Overview of the Two-Day Course

During this session, Teachers will:  Share their math story  Unpack the National Math Strategy - Reviewing the five key strategies  Create a vision for Mathematics Education  Discuss our values and beliefs about Mathematics Education and what it means to teach through problem solving  Observe a lesson – analyzing the use of the framework, linking to the vision of mathematics instruction Assignment: Reading, Focus on Instructional Practice, Reflection Key Understandings 4

 I grew up thinking that mathematics was just about numbers and I thought that people who were “good” at math because they were able to memorize and recall math facts. I didn’t realize that it was so much more until I reached university and wondered why I struggled in my first year applied mathematics and structural engineering programme” ~RMS  Reflect: Think about your experiences with mathematics. What was your math identity? How was it taught to you? Why did you excel or not? How do you rate you overall experience through the years? 5 What was your math story?

Instructional Approaches Teacher Directed Student Practice Problem Solving - Application Problem Solving Scenario or Task Student Discovery Teacher Facilitated Sharing The Traditional Approach Teacher Centred The Three-Part Model Student Centred

Identify attributes of an effective math lesson. A Vision for Learning Mathematics 7

 Engaging all students in mathematics for understanding, ensuring a balance of conceptual understanding and procedural fluency  Mathematics as something one participates in and does, seas, hears, and touches in meaningful ways  Student expectations for doing mathematics include the following mathematical processes: Problem solving, Reasoning and Proof, Communication, Connections, and Representation, which all highlight ways of acquiring content knowledge Mathematics Reform Who should learn mathematics? How should we learn mathematics? What should we learn about mathematics? “It is important for students to build on their prior learning and knowledge of key math concepts and make connections to their own world. Inquiry, problem solving, discussion and question posing are all important parts of mathematics learning” (loc 227) 8

How does this lesson speak to the vision we created? Observing a Mathematics Classroom 9

…where students are confidently engaged in doing mathematics, problem solving, reasoning, critical thinking, collaboration and inquiry. This classroom will feature teachers who intentionally facilitate a community of students with rigorous and relevant tasks, building on student understanding and strategies to develop procedural and conceptual knowledge. - National Mathematics Strategy A Vision of Mathematics Education 10

National Mathematics Strategy Ensure common framework for teaching emphasizing problem solving Ensure access to effective, proven interventions Ensure opportunities for rigorous, relevant tasks Establish standards for use of high quality texts and resources Provide professional development for coaching, content and instruction 11

Bermuda Framework for Teaching Mathematics ENGAGE PHASE Activate student thinking (~20% of time in lesson DOING MATHEMATICS PHASE Students work on the task (~50% of time in lesson) REFLECT & CONNECT PHASE Students share understandings and strategies Teacher facilitates discussion (~20% of time in lesson) BUILDING SKILLS PHASE Mental Math/Skill Building (~10% of time in lesson) 12

 Read or re-read chapter 2 “Teaching through Problem-Solving” 13 Break

Teaching Through Problem Solving What is Teaching Through Problem Solving?

Teaching Through Problem Solving What do you foresee to be some opportunities to implementing problem-based mathematics tasks effectively in your classroom?

Teaching Through Problem Solving What do you foresee to be some challenges to implementing problem-based mathematics tasks effectively in your classroom?

Teaching Through Problem Solving Describe in your own words what is meant by “teaching mathematics through problem solving”. What do you foresee to be some opportunities and challenges to implementing problem-based mathematics tasks effectively in your classroom? What is Teaching Through Problem Solving What are some opportunities for Teaching Through Problem Solving What are some challenges for Teaching Through Problems BLUEYELLOWPURPLE

Identifying Teacher Practices in Exemplary Mathematics Classrooms An effective mathematics learning environment Promotes positive beliefs and attitudes toward mathematics Values prior knowledge Makes connections between that knowledge, the world of the child, and the strands and actions of mathematics Encourages the establishment of a community of mathematics learns Focuses on important mathematical concepts or big ideas Explores concepts though problem solving Includes a variety of learning resources, tools, and manipulatives Is supported by strong roles of teacher, principal, and senior administrator Is supported at home 18 Rubric

Students in a P4 class were given the following task: Add 86 and 47 Use two different strategies to solve this problem. Show all working. Operational Strategies and Mathematical Discussions Cambridge Objectives: 1Nc18 Begin to add single and two-digit numbers; 1Pt1 Choose appropriate strategies to carry out calculations, explaining working out 2Nc12 Add pairs of two-digit numbers; 2Pt2 Explain methods and reasoning orally 3Nc14 Add and subtract pairs of two-digit numbers; 3Ps2 Explain a choice of calculation strategy and show how the answer was worked out 4Nc9 Add any pair of two-digit numbers, choosing an appropriate strategy; 4Ps3 Choose strategies to find answers to addition or subtraction problem, explain and show working 5Nc10 Use appropriate strategies to add or subtract pairs of two- and three-digit numbers and number with one decimal place, using jottings where necessary; 5Ps2 Choose an appropriate strategy for a calculation and explain how they worked out the answer 6Nc11 Add two- and three-digit numbers with the same or different numbers of digits/decimal places; 6Ps1 Explain why they chose a particular method to perform a calculation and show working

 Which attributes of an effective mathematics lesson did you observe?  Which elements of the Bermuda Framework for Teaching Mathematics did you notice?  Identify an instructional practice that you wish to be your focus 20 Observing a Lesson

21 Lunch Break

Observing a Lesson  Lower Primary – Shape Sort Shape Sort  Upper Primary – Area Area  Middle –  Volume 1 and 2 Volume2

Observing a Lesson FrameworkTasks/Assessment Teacher SayingTeacher Doing Students SayingStudents Doing Task Teacher Student

 Which attributes of an effective mathematics lesson did you observe?  Which elements of the Bermuda Framework for Teaching Mathematics did you notice? How was the lesson ‘taught through Problem Solving’? 24 Observing a Lesson

Example (What it is) Non-Example (What it isn’t) Sort the descriptions as Example or Non-examples Are there statements missing? Use the blank pieces to create your own statement. ENGAGE PHASE DOING MATHEMATICS PHASE REFLECT & CONNECT PHASE The Framework for Teaching Mathematics

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Planning an Effective Math Lesson QUICK WRITE: You have 1 minute to consider effective planning. In order to execute an exemplary math lesson, what do you need to plan for?

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

Checklist for Planning Effective Mathematics Tasks 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.

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

Focus the closure around a specific goal Select task(s) Anticipate student thinking and address the misconceptions QuestioningAssessment Planning (Starting with the end in view) Outcomes Students need to know Students need to be able to do Examples

 Reading Chapter 1 – Teaching for Understanding  Review curriculum horizontally and vertically (numbers)  Bring a lesson plan 32 Homework

 Cambridge International Examinations (2011). Primary Maths Teacher Guide. Retrieved September 2012, from Cambridge International Examinations - Teacher Resources:  Guskey, T.R. (2002). Professional development and teacher change. Teachers and Teaching: Theory and Practice, 8,  National Council of Teachers of Mathematics (NCTM). Process Standards of Mathematics. Retrieved September 2012, from  Ontario Principals’ Council. (2009). The Principal As Mathematics Leader (Leading Student Achievement Series). Thousand Oaks, CA: Corwin Press.  Van de Walle, J., Karp, K. S., & Bay-Williams, J. M. (2014). Elementary and Middle School Mathematics: Teaching Developmentally: The Professional Development Edition for Mathematics Coaches and Other Teacher Leaders. Boston: Pearson Education Inc. References 33

34 Resources