When the BC ministry re-wrote their math curriculum, everyone (well maybe only like 90%!) complained and thought what’s the big idea?! But that’s just the point…it is all about big ideas! Mathematics has often been thought of as a skill-based subject (i.e. the old curriculum); it’s not. Mathematics is a set of connected, big ideas and the best way to design a curriculum is to make those ideas transparent.
“Teachers need to understand the big ideas of mathematics and be able to represent mathematics as a coherent and connected enterprise.” (NCTM, 2000, p. 17)
As we begin a new school year, I thought long and hard about what I would like teachers to keep in mind as they plan their year in math. I feel there are two things you should keep at the forefront of your mind: your approach and the big ideas. As you read more below, I hope it gets you thinking: hey, what is the big idea?!
A. Problem-solving and real-world connections should be embedded in all areas of mathematics. Problem-solving is not a separate strand, it is a method of teaching and learning that mimics the real-world.
B. A transdisciplinary approach should be taken so that concepts are connected to other strands of mathematics, as well as connected to other subjects, whenever possible.
C. Instruction should be differentiated. Not only do students’ needs vary and differ within a classroom, so too will an individual student’s needs change throughout the year. Providing opportunities for all students to engage in a “productive struggle” is key to personalizing learning.
D. Math is a creative subject. There is more than one way to tackle a problem and the different strategies should be celebrated, not ignored. Students are encouraged to show their thinking in a variety of ways. The way students reason, communicate and make connections mathematically, is more important than the final answer.
E. Teach and learn with a growth mindset. Research has now proven that brains can grow, adapt and change; even in mathematics.
The Big Ideas:
“Big Ideas provide curriculum coherence and articulate the important mathematical ideas that should be the focus of curriculum.” Randall Charles, 2005.
Last year, my school reevaluated their scope and sequence and I loved the process of figuring out what big ideas should drive our programme. I borrowed and researched from many sources: our own staff was the biggest resource, but I also pulled from the BC Ministry, IB PYP scope, Van de Walle books, Carole Fullerton resources, Marilyn Burns, Pearson’s Taking Shapes book, Jo Boaler and many, many more. Then we immersed the big ideas right into our curriculum. Well, I presented the scope in the first week back and a teacher actually came up and hugged me! She was so grateful to have a coherent curriculum that spelled out the important ideas, enriched her understanding of the curriculum, and will allow her to plan and teach better.
Randall Charles defines a big idea as a “statement of an idea that is central to the learning of mathematics, one that links numerous mathematical understandings into a coherent whole.” Randall Charles, 2005.
Here is an example of what that might look like in terms of defining each strand:
|Number Sense||Numbers describe quantities that can be represented in different ways.
Computational fluency involves recognizing and analyzing patterns and relations between the operations and flexible composing and decomposing of numbers and an understanding of place value.
|Financial Literacy||Money has value that can be measured and used to trade for objects or work. Financially literate citizens make thoughtful decisions about what they want and what they need. They set realistic goals, establish priorities, and make plans for earning, saving, spending or giving away money.|
|Patterns and Algebra||Patterns represent regularities; the repeating elements can be identified; we can use patterns to make generalizations.
Algebra is a way to represent and explain mathematical relationships and to describe and analyze change.
|Geometry||Objects have attributes that can be described, measured and compared.
|Measurement||Measurement involves a comparison of an attribute of an item with a unit that has the same attribute. Estimation and benchmarks help increase familiarity with units.
|Data and Probability||Statistics involves 4 steps: formulating questions, collecting data, analyzing data and interpreting results. How we represent data can impact how we understand it.
Categorizing events using terms such as likely, certain, impossible and unlikely is a way of describing probability. Probability helps us make predictions about future events.
“Because Big Ideas have connections to many other ideas, understanding big ideas develops a deep understanding of mathematics. When one understands big ideas, mathematics is no longer seen as a set of disconnected concepts, skills, and facts. Rather, mathematics becomes a coherent set of ideas.” Randall Charles, 2005.
If your school hasn’t given you the big ideas behind your math curriculum, you can come up with your own! Get together with your grade team, use the resources I mentioned above, or research other curricula. Think of how much richer your teaching and learning will become.
“When teachers work on identifying and discussing big ideas, they become attuned to the mathematics that is most important and that they may see in tasks; they also develop a greater appreciation of the connections that run between tasks and ideas.” Boaler, Munsen (2017): What is Mathematical Beauty?
So what’s the big idea? The big ideas are the big idea!
Have a great year!