Commentary 2: Noticing Student Thinking: A Commentary on Civil’s Case

I have been involved in mathematics education as a teacher and teacher educator for close to two decades. I have worked as a high school teacher, a graduate assistant, a middle-school math coach, a professional developer, and a professor of mathematics education. Throughout my experiences, I have reflected upon the ideas in Civil’s case many times in many different contexts. Broadly speaking, whose mathematics matters and who gets to decide?

Most recently, I have had the opportunity to teach mathematics content courses for prospective elementary teachers. In these courses, we spend a great deal of time discussing algorithms. While discussing operations, I work to illustrate many different algorithms and provide examples of students’ clinical interviews illustrating various ways of thinking. In class, my students and I then discuss the “traditional” algorithm versus alternate algorithms. We consider the shortcomings of different algorithms and how certain ones might make more sense to a particular child. However, I have not incorporated more culturally based ways of doing mathematics, nor do I explicitly connect various algorithms to cultural origins. After reading Civil’s case, I see the value (and necessity) of adding this component to my courses as a way to challenge prospective teachers’ beliefs about mathematics and students.