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The concept circle graphic organizer was introduced through Vacca and Vacca’s (2001)  work as a way to support student vocabulary development in language arts. A circle is divided into four sections with each section containing a word or phrase.

When I observe effective teachers of mathematics, there is one characteristic that they all have in common. It is the space they provide for their students to voice their ideas, reflect on their thinking and explore mathematical concepts. This may seem simplistic. But I argue that it is not. Space is time. It is the precious real estate in the classroom schedule of which we never have enough.

I am sitting at the back of the class, unnoticed. You instruct us at the front of the class, unnoticed. Patterns and the rich meaning of mathematics pass us by, unnoticed.

Students often hold misconceptions about effective thinkers. They may believe that these people never struggle; that they never second-guess their ideas; that “they get it right” immediately. Think alouds can help dispel these misconceptions by opening up discussions about self-talk and enabling all students to access mathematical thinking.

As teachers we continually strive to explain to our students how they will use the mathematics they are learning in their daily lives. Many resources provide examples of laying tile for area, building fences for perimeter, and eating pizzas for the division of fractions as real-life applications of mathematical concepts.