Big Ideas in Math – Focus on the Early Years

So what is all this hype about “BIG IDEAS” and is the hype worth it?

Let’s start by talking about what Big Ideas are.  Different researchers have different names for Big Ideas – they can also be called enduring understandings, key concepts or key ideas.  In the NCSM Journal in 2005 Randall I. Charles defines Big Ideas:

A Big Idea is a statement of an idea that is central to the learning of mathematics, one that links numerous mathematical understandings into a coherent whole.

You may need to read this quote a few times for it to really make sense.  At first the concept may seem like it is trying to make things more confusing but the heart of it is that it is trying to make thinking more succinct, more concise and easier to relate.  Think about all those specific expectations in a math curriculum.  When starting a school year it can seem very daunting when looking through everything.  Many new teachers wondering how they are ever going to get through it all!  Sometimes when we plan based on these specific expectations we can get very ‘hung up’ on the little details.  We worry that are students may not be meeting one very small specific expectation and that we are failing as a teacher.  Big Ideas help us take a step back and focus on the important understandings that we are in essence teaching our students.

Marian Small writes that by

Focusing the learning of each strand in mathematics around a few big ideas makes it easier for students to relate new knowledge to previously learned ideas.  In addition, it simplifies the teacher’s job of prioritizing what is usually a fairly lengthy list of specific curriculum expectations/outcomes by organizing them around a relatively small number of big ideas.

Making Math Meaningful to Canadian Students, K-8 pg. 18

OK did you catch that “simplifies the teacher’s job”!!!  Big Ideas are not only useful for building student understanding but make a teacher’s job easier.

I was sold, now the next step was to figure out – What are these Big Ideas?  That task proved to me a bit more difficult.  I started by looking in the 2010-11 Full-Day Early Learning – Kindergarten Program.

In the mathematics section it lists the Big Idea as:

Young children have a conceptual understanding of mathematics and of mathematical thinking and reasoning.

To me this is very broad and very big – it isn’t going to help me or my students.  I decided I needed to look a little further.  When looking at Small’s writing it didn’t clear anything up as she started by saying that different researchers look at big ideas in different ways.  Some big ideas sound like overall curriculum expectations while others are more specific.  If you can get a copy of Marian Small’s Making Math Meaningful to Canadian Students (2013) she has an excellent overview of different approaches to Big Ideas on page 18 to 24.  Personally I was starting to get a bit better understanding but not yet sure I had found something that was going to help be directly in my classroom so I turned to another source – the internet.

After a bit of searching I found the perfect resource for helping me in my Kindergarten classroom in Ontario.  It is was a resource called “Kindergarten Unit Plans Linked to the Big Ideas” and published by the Lambton Kent District School Board. Here are the reasons this resource jumped out at me:

1.  This is a school board in Ontario so they are using the same curriculum/program document that I am using in my class.
2. It connects with the Big Ideas in A Guide to Effective Instruction in Mathematics.
3. It makes sense in language I can relate to and connect with my youngest learners!  For example under the idea of Quantity it outlines the big idea as: ” the “howmuchness” of a number and is a crucial concept in developing number sense.”

This is an idea I can use in my planning, I can use with my students, and I can use when explaining learning to the parents of my students.  We can all understanding this language and help move everyone forward in their understanding.

So in short I have personally reached the conclusion that Big Ideas can be extremely valuable in mathematics planning.  The exact wording of those big ideas may be a bit different for different educators but the important thing is that they are valuable for you and your students.