Post 1 - Counting Circles

Up until MTH229, I had no idea what a counting circle was. 

To those unfamiliar like I was, a counting circle can best be described as a game to teach math students arithmetic and critical thinking, among other things. Before the game starts, students form a circle. The circle aspect is important, but we'll get to that in a bit. A random student is picked in the circle and given a number; the number depends on the level of the students as a whole, and should be non-threatening for the first few times the game is played. Next, an operation is defined to the class. Typically, the operation is addition; however, subtraction can be obtained by adding a negative number. The first student applies the operation to the initial number given. Regardless of whether or not the student applies the operation correctly, the number the student states is recorded on the board. The next student in the sequence applies the operation to the number the student before them presented. Rinse. Repeat. This continues for at least a full circle until the teacher pauses the class. At this point, the teacher prompts the students to solve for a number further in the sequence. After each student signals to the teacher they have solved it, the teacher then prompts the students to share ways in which they found the answer. This, in whole, is a counting circle. 

There are a number of different things I enjoy about counting circles, both as someone who participates and someone who hopes to be a math teacher one day. One of the more important aspects, I believe, to a counting circle is well, the fact that it is a circle! It can be symbolic for how math builds upon itself or even demonstrate how patterns can be 

e n  d   l    e     s      s       , 

such as with the operation the students preform. Working within in the circle also builds a sense of a team within the student community and familiarizes the students with one another. Because there is no pressure on whether or not the student preforms the operation correctly, students feel less fearful of mistakes. When students feel less frightened, they are more likely to participate in class and put forth genuine effort because there is nothing at stake. When the teacher prompts the students to solve for a number later in the sequence, it allows the students to practice pattern-seeking skills. It helps students transition to higher thinking in math, and gives them a greater understanding of both patterns and seeking out patterns. 

What I believe to be the most important part, though, is when the students share the ways in which they solved for the later number in the sequence. This allows students to practice two very important skills - communication and critical thinking. As a student explains their method, they are practicing communicating their thoughts in a way that is accessible to others. I personally find explaining a concept to someone else helps me grasp the concept better as well. It also may help students develop a more advanced math vocabulary ("subtract" as opposed to "minus", as an example). 

Through this sharing process, students are exposed to the many different ways a solution can be obtained, and even the individuality of each student. Many teachers, intentionally or unintentionally, convey the idea that there is one "right way" to solve a problem. To this day, I recall my 7th grade math teacher who would not allow me to solve a problem any other way than her own. Somehow, she developed the idea in me that math was not discovery, but resuscitation. In the process of her teaching, critical thinking was completely lost. My mother, who taught middle school math, and I would argue because I wanted her to "show me how to do the problem!", whereas she wanted to help me form new ways to solve it. Try as she might, I did not rework the way I viewed math until my senior year of high school. I believe counting circles are a good way to combat this idea in students and develop their critical thinking skills. 

In all, I believe counting circles are a very engaging way to involve students in class and build important lifelong skills. They are useful in many ways - from building a sense of a team, to practicing communication, to creating an accepting classroom environment. As someone who was initially taught to avoid thinking critically, I think counting circles are a great way to both introduce critical thinking to math, and develop it further. Counting circles are quite amazing things because they develop many important concepts and ideas within students without the negative connotation of the word "math". Because it is viewed as a game, students are likely to be excited to participate! For many students, math is something they find difficult to be excited about, and this is a cleverly disguised math activity. Although it may not be practical to use counting circles daily, I believe semi-regular use of it would have a positive impact on any classroom.