1. Teaching Through Problem Solving – Bermuda Framework for Teaching Mathematics
Gilbert Institute
Ongoing PD commencing the week of March 3, 2014
Rebeka Matthews Sousa
Instructional Facilitator for Mathematics

2. In this Session, teachers will:
Consider the shifts in classroom teaching
Engage in Mathematics Lesson, which demonstrates the Framework for Teaching Mathematics
Discuss and Reflect on the Framework (Three-Part Lesson)

3. Shifts in Classroom Practice
In the Mathematics Education world, we have undergone huge paradigm shifts.
The classroom in which we were students of is no longer what is consider exceptional teaching
Why the shift? – we don’t just want our students to be good at school math, but we want them to be able to apply what they know to real world examples and context. This requires many skills as mention previously (our process skills)
You will now have a moment to reflect the shifts needed in the classroom.
The types of learners may or may not have changed – that is up for debate, however, what we expect of them as learners has changed.

4. Mathematics Education Reform
Problem Solving, 
Reasoning and Proof, 
Communication, 
Connections, and 
Representation
All highlight ways of acquiring content knowledge
Student Expectations for doing Mathematics
Shifts in Classroom Practice
Teaching Skills
require
Its not just about reading and arithmetic anymore.
Major mathematics education reform have considered that our students do not just need to be good in school mathematics, but there are other skills that they require. Our students must be able to collaborate and discuss, communicate reasoning, problem solving and ultimately THINK
This requires shifts in classroom practice, which includes new teaching skills.
The mathematics classroom today looks very different than the mathematics classroom we experienced as students. Math is not just about the right answer or one procedure to determine a computation, but about a balance of skils including computation and mental math skills as well as communication, justification and reasoning and problem solving.
In the Cambridge Curriculum and Planning documents it specifies that the problem solving it not to be taught in isolation, but taught throughout the curriculum strands. So do we make this happen?
Which problem solving strands would apply to the Fixed volume task.
includes

5. Cambridge Objectives Mathematicians 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
Materials needed: chart paper, triangles, rulers, compasses, protractor,

6. Triangles Triangle Sort
Sort the entire collection into three groups so that no triangle belongs to two groups.
Give a description or name to each of the groups and record on chart paper.
Once you have found one criterion for sorting. Determine a second.
In groups of 2-4

7. Cooperative Learning Groups & ResponsibilitiesLS P6
Group Leader
Materials Manager
Task Manager
Recorder
Liaison between group and teacher
Group speaker
Collects and returns all materials for group
Ensure all members are participating, on task, and keeps track of time.
Records all information necessary on chart paper to reflect participants thoughts and ideas

8. Reflection How did you sort the triangles?
Which categories or descriptions did you use?

9. Summarizing Triangles
The following shows how triangles can be classified according to some of their features: ANGLES, SIDES, SIZE
Chart description on separate paper:
Angles, Size, Length

10. Summarizing Triangles
The following shows how triangles can be classified according to some of their features: ANGLES, SIDES, SIZE
Chart description on separate paper:
Angles, Size, Length

11. Exit Card
In your own words, write your own description of each of these types of triangles.
Draw a diagram of each – using a ruler!
Triangle
Description
Diagram
Scalene
Isosceles
Equilateral

12. Extension Sketch a triangle in each of the nine cells.
Of the nine cells in the chart, two of them are impossible to fill. Can you tell which ones and why?
“Triangle sort” results in definitions of the six different types of triangles without having to list these definitions and have you memorize them.

13. Teacher Reflection What were some of the components of this lesson?
Consider the Rubric for Quality Teaching in Mathematics, which components of the rubric were met during this lesson?
Why use the three-part lesson or teaching through problem solving framework to teach mathematics?
How do I make this part of my everyday math lesson? Or how do I find resources to continue teaching this way?
Strategies
Critical Thinking
Justification and evaluation
Communication

14. Triangle Sort Lesson Plan

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

16. What are some elements of the teaching through problem-solving/inquiry based framework?
Three-parts
Teacher could…
Student Role
BEFORE
Engage
“Activate thinking”
Launch Task.
Model manipulatives Solve a similar/simpler problem with the students
Think about the problem.
Ask questions for clarification.
DURING
Teaching 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.
AFTER
Reflect and Connect “Share time”
Addresses misconceptions and facilitates discussion based on student responses.
Direct instruction.
Student shares ideas, through process
Reflect on the lesson 5 mins
What do you think is the most challenging part for teachers?
“letting go”
What task do I choose?
What are the types of questions do I ask? – Give questions cards

17. Reading from Chapter 2 Teaching Through Problem Solving
Introductory Paragraphs – p13-17
Text & ISBN
Title
Authors
Year Level recommended
ISBN-13: 
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  
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

18. Reflection (Three-Part Lesson)
Explain in your own words, the phases of the three-part lesson.
Explain the three-parts based on the lesson you experienced last week.
Which

19. 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?
Jot down on sticky
Place on board

20. Why Problem-Solving/Inquiry based Lessons?
It’s a comprehensive learning/teaching structure that:
Supports the delivery of curriculum
Is based on the problem solving model
Promotes conceptual mathematical understandings
Promotes 21st Century Learning Skills
Allows for differentiated instruction
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)
Allows students to get the “BIG IDEAS” or the fundamental principles of mathematics that link the specifics
Promotes collaboration

21. A Mathematics Framework Based on the Balance Math Program
DO NOW
/ Math Review
Three Part Lesson
1. Activate
2. Working On it
3. Reflect and Connect
Mental Math

22. Reflection (Three-Part Lesson)
What do you see as the benefits of teaching this way?
What additional questions do you have with regards to the Mathematics Framework for Teaching (Three-Part Lesson)
What can you do in your lessons to encourage mathematical thinking and reasoning? How can the three-part framework assist in structuring such lessons?

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