Big Ideas in Mathematics

Hello! And welcome to my new blog. It is here, in a series of posts on planning in mathematics that I hope to reach out to young teachers in an attempt to provide them with a behind the scenes view of mathematics planning in general. Hopefully I’ll be able to answer some of the questions new teachers might have about the concept of big ideas; the most effective ways to plan a unit and/or lesson; and the benefits of cross-curricular planning. As most of you know, members of the general public often hold the belief that math is “boring” or not applicable to real-life scenarios. I’ll do my best in this blog to refute such claims by posting fun and engaging videos and links that support the information. Now, without further ado, here is my first post:

The concept of “Big Ideas” in Mathematics has been floating around Ontario schools for at least a decade now (see for example, this article) and is a theoretical expression of the idea that teachers should focus on over-arching themes in their lesson planning rather than on each particular curriculum point. In other words, according to Charles (2005), “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” (10). While at first teaching using the big ideas concept can seem overwhelming, with practice it becomes routine. Ultimately, it helps both teachers and students to see the interconnectedness of curriculum concepts, rather than seeing them as isolated pieces that need to be taught one by one. Charles’ article lists several big ideas concepts, but one example is: “BIG IDEA #2 THE BASE TEN NUMERATION SYSTEM — The base ten numeration system is a scheme for recording numbers using digits 0-9, groups of ten, and place value” (p. 13). As you can see, for each grade, there are a large number of curriculum objectives that fall under this big idea. In my classroom, I like to group units according to “big ideas” concepts, rather than following the curriculum guide verbatim. While this takes some reorganization, I believe that it leads to a stronger theoretical understanding among students.

One of the biggest proponents of “Big Ideas” in Mathematics (especially in Ontario) has been Marian Small (http://www.onetwoinfinity.ca/). Check out this great series of webinars in which she explores and provides examples of the Big Ideas in all math strands, grades K-3: https://erlc.wikispaces.com/Big+Ideas+in+Math+K-3

References:

Charles, R.I. (2005). Big Ideas and understandings as the foundation for elementary and middle school mathematics. Journal of Mathematics Education Leadership, 7(3), pp. 9-24.