Teaching Through Problem Solving

– Bermuda Framework for Teaching Mathematics

Gilbert InstituteOngoing PD commencing the week of March 3, 2014

Rebeka Matthews SousaInstructional Facilitator for Mathematics

rsousa@moed.bm

In this Session, teachers will:

OConsider the shifts in classroom teaching

OEngage in Mathematics Lesson, which demonstrates the Framework for Teaching Mathematics

ODiscuss and Reflect on the Framework (Three-Part Lesson)

Shifts in Classroom Practice

Mathematics Education Reform

Student Expectations

for doing Mathematics

Shifts in Classroom Practice

Teaching Skills

require

includes

O Problem Solving, O Reasoning and Proof, O Communication, O Connections, and O RepresentationAll highlight ways of acquiring content knowledge

Cambridge ObjectivesMathematicians will:5Gs1 Identify and describe properties of triangles and classify as isosceles, equilateral or scalene.

5Ps7 Identify simple relationships between shapes, e.g. these triangles are all isosceles because …5Ps9 Explain methods and justify reasoning orally and in writing; make hypotheses and test them out

Triangle Sort1. Sort the entire collection into three

groups so that no triangle belongs to two groups.

2. Give a description or name to each of the groups and record on chart paper.

3. Once you have found one criterion for sorting. Determine a second.

Triangles

Reflection

OHow did you sort the triangles?OWhich categories or descriptions

did you use?

The following shows how triangles can be classified according to some of their features: ANGLES, SIDES, SIZE

Summarizing Triangles

The following shows how triangles can be classified according to some of their features: ANGLES, SIDES, SIZE

Summarizing Triangles

Exit CardO In your own words, write your own

description of each of these types of triangles.

ODraw a diagram of each – using a ruler!Triangle Description Diagram

Scalene

Isosceles

Equilateral

OSketch a triangle in each of the nine cells.

OOf the nine cells in the chart, two of them are impossible to fill. Can you tell which ones and why?

Extension

Teacher Reflection1. What were some of the components of this

lesson?2. Consider the

Rubric for Quality Teaching in Mathematics, which components of the rubric were met during this lesson?

3. Why use the three-part lesson or teaching through problem solving framework to teach mathematics?

4. How do I make this part of my everyday math lesson? Or how do I find resources to continue teaching this way?

Triangle Sort Lesson Plan

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

What are some elements of the teaching through problem-solving/inquiry based

framework?Three-parts Teacher could… Student Role

BEFOREEngage “Activate thinking”

Launch Task.Model manipulatives Solve a similar/simpler problem with the students

Think about the problem.Ask questions for clarification.

DURINGTeaching through Problem Solving 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.

AFTERReflect and Connect “Share time”

Addresses misconceptions and facilitates discussion based on student responses. Direct instruction.

Student shares ideas, through process

Reading from Chapter 2Teaching Through Problem Solving

O Introductory Paragraphs – p13-17Text & ISBN 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

Reflection (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.

Teaching Through Problem Solving

Referring to the Shifts in Classroom Practices

How does the three-part model for teaching support these shifts in classroom practices?

Why Problem-Solving/Inquiry based Lessons?

It’s a comprehensive learning/teaching structure that:O Supports the delivery of curriculumO Is based on the problem solving modelO Promotes conceptual mathematical understandingsO Promotes 21st Century Learning SkillsO Allows for differentiated instructionO 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

A Mathematics FrameworkBased on the Balance Math Program

DO NOW/ Math Review

Three Part Lesson1. Activate

2. Working On it3. Reflect and

Connect

Mental Math

Reflection (Three-Part Lesson)

3. What do you see as the benefits of teaching this way?

4. What additional questions do you have with regards to the Mathematics Framework for Teaching (Three-Part Lesson)

5. What can you do in your lessons to encourage mathematical thinking and reasoning? How can the three-part framework assist in structuring such lessons?

ReflectionOHow do I make this part of my everyday math lesson? Or how do I find resources to continue teaching this way?