Middle Mathematics Teacher Endorsement Programme Planning and Teaching Mathematics Through Problem Solving Session 3 Facilitator: Rebeka Matthews Sousa Mathematics Specialist Teacher, Ministry of Education 1

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? ENGAGE: Reflection Questions Who should learn mathematics? How should we learn mathematics? What should we learn about mathematics? 2

During this session, Teachers will:  Investigate the attributes of a “good” mathematics task  Analyse tasks using Levels of Cognitive Demands Assignment: Reading – Chapter 2 Teaching Through Problem Solving Review documents in folder for future sessions Key Understandings 3

4 Using the rubric for Teaching Through Problem Solving

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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7 Math Tasks – Levels of Cognitive Demand

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9 Examples of Math Tasks

10 Examples of Math Tasks

 Identify the Level of Cognitive Demand for your assigned task.  Be prepared to justify your answer 11 Analysing Stein’s Tasks

Aspects of a Worthwhile Task 1.Mathematics is grade-level appropriate (aligned to Cambridge Curriculum). 2.Makes connections between concepts and procedures 3.Makes connections between different mathematical topics. 4.Requires reasoning (non-algorithmic thinking). 5.Connects to real situations that are familiar and relevant to them. 6.Provides entry points that make it accessible to the diverse students in your classroom. 7.Is appropriately challenging (engages students’ interest and intellect). 8.Provides multiple ways to demonstrate understanding of the mathematics concepts and procedures. 9.Requires students to illustrate or explain mathematical ideas. 10.Has potential to develop perseverance and positive student dispositions to do mathematics. 12 What make a task, a “good” task? Mathematics Coaching: Resources and Tools for Coaches and Leaders, k-12 by Bay-Williams, McGatha, Kobett, and Wray

Students were asked to model the “Perfect Purple Paint” Students were shown a worked example and asked to complete the following problems 13 Compare these two tasks

 Describe your overall evaluation of whether your task/lesson has the potential to engage students in higher-level thinking 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

Reading Assignment – Chapter 2 Teaching Through Problem Solving Van de Walle, J. et al. Teaching Student Centered Mathematics (Vol 3) 15 Reflection Who should learn mathematics? How should we learn mathematics? What should we learn about mathematics? Selecting, Creating and Sharing Great Tasks Changed to January CBA – CST office (by Ruth Seaton James

16 Observing a Mathematics Classroom

 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 17

18 Resources