The Big Ideas

Making math meaningful for our students is one of my priorities as a teacher, and by concentrating on the Big Ideas I can better do that. 

What are the '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."

For example, the big ideas in Number Sense and Numeration in the Elementary grades are as follows:

• counting (grades K - 3)
• quantity (grades K - 6)
• operational sense (grades K - 6)
• relationships (grades K - 6)
• representation (grades K - 6)
• proportional reasoning (grades 4 - 6)

Why should I plan for Math using the Big Ideas?

• As per the guide on ‘Number Sense and Numeration, Grades 4-6’ on page 11, “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. An emphasis on big ideas contributes to the main goal of mathematics instruction – to help students gain a deeper understanding of mathematical concepts.” Rather than skimming through all of the specific curriculum expectations, briefly touching on these detailed concepts, providing students with the opportunity to delve deeply into the big ideas and gain true understanding of them is a far more worthy goal.

• A key way to create meaning is to create connections in our learning. “Children are better able to see the connections in mathematics and thus to learn mathematics when it is organized in big, coherent “chunks”.” (Guide to Effective Instruction in Mathematics, Kindergarten to Grade 3 - Number Sense and Numeration, p. viii). Creating connections so often lies at the heart of those a-ha moments that we experience as learners. These connections create relevance and meaning.

• Tapping into our students’ prior knowledge, learning styles and current skill level is key to differentiating our teaching within the classroom. “Focusing on the big ideas provides teachers with a global view of the concepts represented in the strand.” (‘Number Sense and Numeration, Grades 4-6’, p. 12). Gaining this personal view of our students is better achieved through the Big Ideas, and will then allow us to better plan for each child.

Teaching math through the lens of the Big Ideas provides greater context for learning. Planning with the Big Ideas in mind supports students in understanding mathematical concepts more deeply, and facilitates the making of connections, thus bringing greater meaning to math.


Resources

A Guide to Effective Instruction in Mathematics, Kindergarten to Grade 3, Number Sense and Numeration. Ontario Early Math Strategy. Ministry of Education: Queen's Printer for Ontario, 2003.  

A Guide to Effective Instruction in Mathematics, Kindergarten to Grade 6, Number Sense and Numeration Grades 4 to 6, Volume One, The Big Ideas. Ministry of Education: The Queen's Printer for Ontario, 2006. 

The Ontario Curriculum Grades 1-8: Mathematics. The Ministry of Education: Queen's Printer for Ontario, 2005 (revised).