Summer Academy Planning and Teaching Mathematics Through Problem Solving Day 2 Facilitator: Rebeka Matthews Sousa Mathematics Specialist Teacher, Ministry of Education 1

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During this session, Teachers will:  Investigate the attributes of a “good” mathematics task  Analyse tasks using Levels of Cognitive Demands  Create and share mathematics tasks and exemplary mathematics lessons Assignment: Submit your instructional focus, Upload a lesson plan, Complete reflection on Teaching Through Problem Solving Key Understandings 4

1.What is Mathematics? How do my beliefs about mathematics impact my teaching and student learning? 2.What is teaching through problem solving and why is it important to teach this way? 3.What do we need to plan for to teach effective math lessons? Reflection Questions Who should learn mathematics? How should we learn mathematics? What should we learn about mathematics? 5

Teaching Mathematics  Most of time in our math classes is spent practicing mathematical procedures and reteaching  The key feature of success is that students engage in active struggle with mathematics concepts and procedures.

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8 Math Tasks – Levels of Cognitive Demand

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10 Examples of Math Tasks

11 Examples of Math Tasks

 Identify the Level of Cognitive Demand for your assigned task.  Be prepared to justify your answer 12 Analysing Stein’s Tasks

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Working in pairs (same year level)–  Describe your overall evaluation of whether your task/lesson has the potential to engage students in higher-level thinking You may use the Worthwhile Task Analysis Tool to further evaluate the lesson  What adaptations can you make to the task or lesson to increase its cognitive demand potential? 14 Analysing Tasks

Working in pairs (same year level)–  Use the Planning Questions to design your own task/lesson  Select or create “good” math tasks/lessons for September.  Resources/Unit Plan/Computer 15 Creating Tasks

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

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

Year LevelTask/Lesson NameCIE objectives P1One Up and One Down Crooked Paths Using Data to Answer a Question Shape Sorts 1Nc6, 1Nc8, 1Nc11, 1Pt1 1Ml1, 1Ml3 1Dh1 1Gs1 P2Crooked Paths Using Data to Answer a Question Shape Sorts 2Ml1, 2Ml2, 2Pt2 2Dh1, 2Pt11 2Gs1 P3Exploring Subtracting Strategies Close, Far, and In Between 3Nc14, 3Ps2 3Nn8-12, 3Pt12 P4Fixed Areas Exploring Subtracting Strategies 4Ma3, 4Ma2, 4Ps5, 4Ps8 4Nc10, 4Pt1 P5Fixed Areas If You Didn’t Know Odd or Even? High or Low 5Ma1-3 5Nc3, 5Nc13, 5Ps2, 5Ps4 5Nn14, 5Ps4, 5Ps8 5Nc21, 5Nc12, 5Pt6, 6Pt7 P6Multiplication and Division6Nc15, 6Pt1 MiddleFind the zero Zoom 7Ni1 7Nf3, 7Nf3, 7Pt7 19 Lesson Examples

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 Look back at the chapter and identify any ideas that make you uncomfortable or that challenge your current thinking about mathematics or about teaching and learning mathematics.  Try to determine why these ideas challenge you or make you uncomfortable. 21 Teaching for Understanding

1.What is Mathematics? How do my beliefs about mathematics impact my teaching and student learning? 2.What is teaching through problem solving and why is it important to teach this way? 3.What do we need to plan for to teach effective math lessons? Reflection Questions Who should learn mathematics? How should we learn mathematics? What should we learn about mathematics? 22

 Name:  School  Year Level  What instructional practice will you focus on?  What additional support or professional development would you like to see in September? 23 Reflect and Connect

 Rate your overall workshop experience  I have a better understanding of what teaching through problem solving is and how to plan for it  The workshop met my needs for teaching mathematics this year  Any additional comments or feedback 24 Workshop Feedback

Complete the following online: 1.Design a task 2.Complete the workshop feedback form 3.Upload a lesson plan 4.Complete reflection on Teaching Through Problem Solving s.cfm 25 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 26

27 Resources