As I began to implement concept circles in my practice for vocabulary development in mathematics, a central idea in Math Expressions, I realized I wasn’t using this graphic organizer to its full potential. Yes, I did believe that it deepened students’ understanding of mathematical language (and I continue to use it in this way for vocabulary development in mathematics), but I was taken by its shape and wondered if I could use it beyond written words and images. What would happen if I enlarged the concept circle and used it to model mathematical concepts and mathematical relationships in a concrete way? I decided to explore the use of concept circles with math manipulatives. This was exciting! I found that by inviting students to engage in tasks in which they placed manipulatives directly on the concept circles the process helped them to develop math skills such as problem solving, mathematical discourse, spatial skills, modelling/representation, proportional reasoning (and the list goes on) all at the same time. I continued to explore this idea with a group of field-test teachers and found that concept circles provided

- rich opportunities for discussion, debate, and argumentation
- rich opportunities for discussion, debate, and argumentation
- targeted assessment, giving us insight into student thinking and helping us to identify potential misunderstandings at particular points of learning.

So, based on Nashville and other conferences, I’d like to share how I’ve used concept circles in my work with teachers and also share some wonderful samples/ideas that teachers have shared with me.

Marks Krpan, C. (2018). Teaching math with meaning: Cultivating self-efficacy through learning competencies. Toronto, Pearson Education Canada

Marks Krpan, C. (2012). Math expressions; Developing thinking and problem solving through communication. Toronto, Pearson Education Canada.

Vacca, J. L., Vacca, R. T., & Gove, M. K. (1987). Reading and learning. Glenview, IL: Scott, Foresman and Company.

Vacca, R.T., & Vacca, J. L. (1999). Content Area Reading: Literacy and Learning Across the Curriculum. Boston, MA: Longman.