“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

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

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.”

“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.

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

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

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)

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

Problem Solving

Think About the Problem

Select a Plan after Reviewing options

Execute the Strategy

Check your Answer

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

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

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

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