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Summer AcademyPlanning and Teaching Mathematics

Through Problem SolvingDay 1

Facilitator: Rebeka Matthews SousaMathematics Specialist Teacher, Ministry of

Education

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Try the Facebook Challenge

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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

An Overview of the Two-Day Course

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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

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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?

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

TH

E F

LIPPED

CLA

SSRO

OM

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Identify attributes of an effective math lesson.

A Vision for Learning Mathematics

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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)

9How does this lesson speak to the vision we

created?

Observing a Mathematics Classroom

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…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

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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

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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)

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

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

BLUE YELLOW PURPLE

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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

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 out2Nc12 Add pairs of two-digit numbers; 2Pt2 Explain methods and reasoning orally3Nc14 Add and subtract pairs of two-digit numbers; 3Ps2 Explain a choice of calculation strategy and show how the answer was worked out4Nc9 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 working5Nc10 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 answer6Nc11 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

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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

Observing a Lesson

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Lunch Break

Observing a Lesson

Lower Primary – Shape Sort

Upper Primary – Area

Middle – Volume 1 and 2

Observing a Lesson

Framework Tasks/Assessment

Teacher Saying Teacher Doing

Students Saying Students 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’?

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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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Break

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 TasksThe 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)DifferentiatedRequires decision making above and beyond the choosing of a

mathematical operation.May encourage collaboration in seeking solutions.Resources, materials, manipulatives prepared in advanced.AssessmentVariety of assessment tools to access students throughout the

lessonQuestioningQuestions 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

Focus the closure around a specific

goal

Select task(s)

Anticipate student thinking and address the misconceptions

Questioning

Assessment

Planning(Starting with the end in view)

Outcomes

Students need to know

Students need to be able to do

Examples

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Reading Chapter 1 – Teaching for Understanding

Review curriculum horizontally and vertically (numbers)

Bring a lesson plan

Homework

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Cambridge International Examinations (2011). Primary Maths Teacher Guide. Retrieved September 2012, from Cambridge International Examinations - Teacher Resources: www.cie.org.uk

Guskey, T.R. (2002). Professional development and teacher change. Teachers and Teaching: Theory and Practice, 8, 381-391

National Council of Teachers of Mathematics (NCTM). Process Standards of Mathematics. Retrieved September 2012, from http://www.nctm.org/standards/content.aspx?id=322

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

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ResourcesText & I SBN Title Authors 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 Walle, Lou Ann H. Lovin, Karen H Karp, Jennifer 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 Walle, Karen S. Karp, Lou Ann H. Lovin, Jennifer M. Bay-Williams

P4-P6 *P3 may choose this book instead of Volume 1

ISBN-13: 978-0132824866

Teaching Student-Centered Mathematics: Developmentally Appropriate Instruction for Grades 6-8 (Volume III) (2nd Edition)

John A. Van de Walle, Jennifer M. Bay Williams, Lou Ann H. Lovin, Karen H. Karp

M1-M3 *P6 and S1 teachers may select this book

ISBN-13: 978-0133007008

Mathematics Coaching: Resources and Tools for Coaches and Leaders, K-12

Jennifer M. Bay-Williams, Maggie McGatha, Beth M. McCord Kobett, Jonathan A. Wray (Author)

All levels

ISBN-13: 978-0133006469

Elementary and Middle School Mathematics: Teaching Developmentally: The Professional Development Edition for Mathematics Coaches and Other Teacher ... Student-Centered Mathematics Series)

John A. Van de Walle, Karen S. Karp, Jennifer M. Bay-Williams

P1-M3