An Overview of Math Circles

What are Math Circles?
Math Circles provide students with opportunities to develop and practice problem-solving skills through communication and connections.  Like literature circles, Math Circles are small intimate groups (approximately 4 students) that meet weekly with the head teacher.  It is a time for collaboration and meaningful conversation and exchange of thinking as well as explanation of the process of problem solving.  At the start, these groups are teacher facilitated, and then over time become run by the students.  Like Literature Circles, there are four jobs (or steps) that help students break down problem solving into manageable components.  These are Detective, Illustrator, Calculator, and Editor.  The teacher and student volunteers model the task for each of the four roles, and then students practice the strategies. The process demonstrates the different roles and allows students to practice the techniques before they are responsible for completing the tasks on their own. After this introduction, students are ready to use the strategies independently.

When do Math Circles occur?
Each student participates in a Math Circle at least one time a week.  Groupings may vary (be flexible) to be both heterogeneous as well needs based.  When I first started using this method, Math Circles took place during the middle 20 minutes of math time 3 x week (in a 50-60 minute math block), coming after a 20 minute whole group lesson and before a 10-20 minute whole group closing.

What does the Math Circle look like?
While the rest of the group is working independently or with Assistant's help, the math circle group is sitting in a specific area of the classroom (a round table, surrounded by math resources, manipulatives,etc.) with the head teacher, looking at pre-created math problems (taken from your math curriculum, state tests, etc.) and practicing problem solving strategies, guided by the teacher. Pre-selected problems cover a range, including both challenge and reinforcement.  Specific strategies are initially modeled by the teacher.

Teachers first introduce and model these different roles in problem solving with the whole group:

Detective: identifying math vocabulary words/concepts that need to be used to solve the problem.  The EM Student Reference Book would be used with this role as a support

Illustrator: drawing the picture to go with the word problem (visualizing)

Calculator: writing a number sentence and doing the computation

Editor – making sure that the answer is clearly marked and labeled with units.  Also, that the answer really answers the question.

** Eventually the role of Summarizer would be introduced.  This would involve listing and explaining the specific steps that were necessary to solve the problem (this is critical on state testing open response)

Then students use a math circle recording sheet to practice recording and explaining their approaches. At the end of math time, the whole group comes together to share new math vocabulary to add to a class math word wall or to share what math vocabulary they used to solve problems.  This whole group time becomes an important opportunity for sharing and review/reinforcement.
This approach is easy to implement in your classroom.

What are some of the immediate benefits?

The power of observation:

In math circles, teachers can observe students as they problem solve, even using student mistakes as insight into why students make errors in the first place.  For example, a student may understand how to do straight computation but due to a reading weakness, might not be able to infer what concept to apply when reading a word problem.  This was particularly true with some students in my class one year.  They were comfortable with computation, but felt less capable when solving word problems that required them to infer.

The power of communication:

I have seen how students enjoy communicating their solutions/strategies to their peers and teachers.  Math circles helps to create these opportunities in the classroom.  The classroom becomes a place where the language of math is continuously explored and discussed

I hear and I forget. I see and I remember. 
I do and I understand.- 
Chinese Proverb