I come across interesting material when I checking out a variety of topics on teaching the big mathematical idea because it is easier for students to relate to connected concepts.
If you think you know what they mean by big idea, you might be surprised by its definition. I was. Think of the big mathematical idea in this way.
The big mathematical idea is a statement or idea central to learning mathematics. It links several mathematical concepts into a coherent whole. It turns out there are several components to the big idea.
1. It is a statement.
2. It is an idea that is central to learning mathematics.
3. It links everything together so it makes sense.
For instance, if you stated that all numbers, fractions, decimals, numerical expressions and algebraic equations can be represented in so many different ways that have the same value. This is a big idea because you can find equivalents which have the same value. 2 + 4 has the same value as 5 + 1, or one more than 2.5 + 2.5.
Big ideas apply across all strands of mathematics rather than applying to only one strand. Ideas such as "Geometric figures have attributes that can be classified and described" or "Numbers represent sets of items that can be composed or decomposed." Furthermore, these ideas can be applied across grade levels which makes it more vertically aligned.
Each big mathematical idea connects learning together under an umbrella. They build a better foundation because the connectivity in inherent in the ideas which leads to deeper understanding. Yesterday my Algebra I class started rewriting literal equations for one term. One of the students noted they were solving them just like they did their algebraic equations. He saw the connection.
Using big ideas helps students become more flexible, generalize knowledge, improve problem solving, makes mastering new facts and procedures while and allows for better transfer.
I am from a generation who learned math by focusing on processes but for me trying to figure out the big idea is difficult. I did find some help in this presentation for the big ideas in math. Although the presentation is for elementary school, it gives me a starting point so I have ideas to use as umbrellas in class next year.
Let me know what you think. I always love hearing from people.