When I was a student, and early in my teaching career, the teacher was expected to tell students how to solve problems. Classrooms were structured in a traditional setting— the students sitting in individual desks in rows, and the teacher at the front giving students the methods that they would need to solve the problems. The textbook was the sole driver of the content, and students were told a procedure, required to memorize that procedure, and made to use that procedure on similar problem types.
Within my first few years of teaching, the idea of teaching mathematics for depth began to enter the conversation. But, besides having students sit in small groups rather than rows, the classroom environment was still the same, with students memorizing procedures and using those procedures on subsequent problems. Though the goal was to teach fewer topics but go more into more depth with each one, how to do that effectively was a problem that remained unsolved.
Throughout my teaching career, I have noticed that classrooms have started to shift from ones that foster memorization to ones that emphasize reasoning. Students are becoming more active participants in the classroom rather than passive listeners. This means that they do most of the reasoning and sense making, with the teacher's role transitioning into that of a facilitator and not someone simply telling students how to solve a problem. Students are required to think about each problem, find a solution process that works for them, and be able to explain the process they chose as well as someone else's.
Students are situated at tables so that they can have an opportunity to talk about ideas and learn from one another; they are then given the opportunity to share their strategies with the whole class.
At the start of my teaching career in 2003, I rarely used student thinking to drive my instruction, and I found myself following the order of topics and teaching the methods that were presented in the curriculum. Within a few years, classroom structure was coming into the conversation, which also happened to be right around the time that the Common Core State Standards (NGA Center and CCSSO 2010) came out. Changing from teaching in a more traditional setting to a more student-centered approach was not an easy or quick transition to make. It took me approximately a year and a half to adjust to having students explain and justify, which subsequently changed my beliefs about teaching. But as a teacher, it gave me greater insight into how my students are thinking when afforded me the opportunity to have a better understanding of how students think differently so that I could then tailor instruction to meet their needs.
Throughout my career, I have been fortunate to have the opportunity to observe classroom teachers already using student-centered methods and to co-teach with them. I have been able to collaboratively plan lessons and to discuss with colleagues how to find and create problems that would lead to good discussions and multiple answers, as well as how to ask questions to elicit student thinking. These experiences are what has shaped me as a teacher, and my hope is that all teachers will be given the opportunity to have similar ones of their own. (For a personal introduction to this article, see video 1.)
Though I was not introduced to this method of teaching until a few years into my career, I have found that the key is to have conversations with colleagues and to collaboratively plan with one another. The conversations I have with classroom teachers, administrators, and district-level supervisors today are focused on ways to develop student-centered classrooms. I foresee these conversations continuing within districts, becoming more widespread, and directly influencing how classroom structure evolves in the future.
National Governors Association Center for Best Practices (NGA Center) and Council of Chief State School Officers (CCSSO). 2010. Common Core State Standards for Mathematics. Washington, DC: NGA Center and CCSSO. http://www.corestandards.org.
Jennifer M. Tobias is a professor of mathematics education at Illinois State University in Normal, Illinois. Her research interests include deepening prospective teachers' understanding of rational number concepts and operations. She is also interested in the professional development of teachers.