Big Ideas and Problem Solving in Math Instruction

1. “Big Ideas” and Problem Solving
in Junior Math Instruction
“At the heart of mathematics is the process of setting up
relationships and trying to prove those relationships
mathematically in order to communicate them to others.
Creativity is at the core of what mathematicians do.”
-Fosnot and Dolk, 2001

2. Learning Goals
+ To review the concepts of “Big Ideas” and Problem
Solving in Junior Math
+ To examine why the problem solving approach is
important to the development and understanding of
“Big Ideas”.
+ To discuss classroom structures that support
problem solving

3. What are Big Ideas?
The term “Big Ideas” is defined in the Grade 1-8
Ontario Mathematics curriculum as:
“the interrelated concepts that form a
framework for learning mathematics in a
coherent way.”

4. “Big Ideas” in Math
+ In a mathematical context “Big Ideas” refers to the
key principles of math.
+ For example, “big ideas” could include patterns or
relationships between ideas.

5. Math Strands and Big Ideas
Each Strand is divided into key principles or big
ideas. For example,
+ Number Sense and Numeration:
÷ Quantity Relationships
÷ Operational Sense
÷ Relationships
÷ Representation
÷ Proportional Reasoning

6. Problem Solving:
Is relevant in the real
world
Builds confidence in math
skills
Allows students to make
connections and build on
prior knowledge
Allows students to reason,
communicate ideas, and
apply knowledge in new
contexts
Increases interests in
math and promotes
collaboration

7. Problem Solving
Problem solving is a central part of learning math.
By learning to solve problems and by
learning through problem solving, students
are given numerous opportunities to
connect mathematical ideas and to develop
conceptual understanding.
(Ontario Grade 1-8 Math Curriculum)

8. Big Ideas and Problem
Solving
“In developing a mathematics program, it is
important to concentrate on the big ideas and
on the important knowledge and skills that
relate to those big ideas.”
A Guide to Effective Instruction in Mathematics, Kindergarten to Grade 6, Volume 1

9. Problem Solving
Think About the Problem
Select a Plan after Reviewing
options
Execute the Strategy
Check your Answer

10. In your Table Groups
• Discuss why the problem solving approach
is important to the development and
understanding of “Big Ideas”.
Programs that are organized around big ideas and focus
on problem solving provide cohesive learning opportunities
that allow students to explore mathematical concepts in
depth.
A Guide to Effective Instruction in Mathematics, Kindergarten to Grade 6, Volume 1

11. According to the Research …
“Mathematical communication is an
essential process for learning mathematics
because through communication, students
reflect upon, clarify and expand their ideas
and understanding of mathematical
relationships and mathematical
arguments.”
Ontario Ministry of Education, 2005

12. Criteria for Evaluating
The following are some criteria for evaluating
communication of mathematical ideas
÷ Precision
÷ Clarity
÷ Cohesion
÷ Elaboration
÷ Assumptions and Generalizations and,
÷ Using mathematical terminology, symbolic notation
and standard forms accurately

13. Some Helpful Resources
The following resources can be helpful for improving
students mathematical communication
• High Yield Strategies for Improving Mathematics
Instruction and Student Learning
• Engaging Students in Mathematics
• Honouring Student Voice in the Mathematics Classroom