Counting Circles More than Answers

I have really enjoyed the counting circle game that we have participated in.  The game entails a group of students standing in a horseshoe in front of the teacher.  The teacher presents an original number like 288, then asks the first student to give the next number in the sequence when adding or subtracting some number x.

For example, 288 subtracting 13

The sequence would go 288, 275, 262, 249, 236, 223, 210,197,184, 171, 158

Then the teacher would ask the students what would the 12th student from the student who said 158 says for the correct number in the sequence?

The whole class proceeds to find out who the 12th student is, and answers the question through a variety of mathematical computations which are not necessarily the same from student to student.  This portion emphasizes to students that there are a number of different ways to solve a math problem, and no one way is the only way.

One student may say, I tried to think of 12×13 and came up with 156.  Then I subtracted that number from 158.

So the 158-( 12 students x 13 subtracted each time){1}

158-(156)= 2 {2}

Another may say I did

13×10=130 and 13×2=26

Then added the two together to obtain 156, so I subtracted this value from 158 to obtain 2.

These are just two of the numerous ways to approach this problem.

From this activity I have learned that teachers often make mistakes, are not necessarily the best at doing mental math, and knowing a variety of ways to solve problems can be very useful for improving your problem solving efficiency and understanding.  It was incredible to watch future teacher, after future teacher make mistakes in a seemingly simple counting game.  I was reminded that teaching does not require perfect computation, but a willingness to learn from your mistakes, and understand the problem solving process.

Additionally,  I have been really struggling with the math major at GVSU as I am struggling with proofs at all levels.  This activity reminded me that teaching math is more simplistic than proofs, and great teachers approach problems in a variety of ways.  I am excited to help my future students learn from their mistakes and have a blast teaching and improving as a teacher.


One comment

  1. So glad the counting circles have been good.

    To make this an exemplar, you want to show 1-2 hours of work (complete). You could work through an example of a counting circle, or read up and share info from some of Sadie’s counting circle resources linked on the course page.

    Your conclusion seems important, too, and could be expanded, or the subject of a whole post. What connections and disconnects do you see between math courses and math teacher preparation. Or how does this experience change your ideas about teaching?


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