Creating Classroom Cultures of Mathematical Thinking (Inquiry)

Last fall, I posted “Resources for Creating Dynamic Mathematics Learning Environments” that included a variety of resources and tools to create learner-centered environments, but that post mostly concentrated on teacher actions.  This post aims to set a vision for student actions in the mathematics classroom.  (Sorry teachers, you are not off the hook for this one. Your actions make this vision possible for students!)  Once again, the goal is to continuously reflect on these questions: Who is carrying the cognitive load in your classroom during mathematics lessons?  Who is doing the mathematics?  Who is doing the thinking and talking?

(1) The role of student-driven questions.  Teacher questioning is important in facilitating classroom discourse and making important connections, yet we oftentimes leave students out of the question posing process.  Fostering Student Questions: Strategies for Inquiry-Based Learning and Creating a Culture of Inquiry offer some ideas and protocols on how to develop a culture of student-driven inquiry based on questions, justification, and choice.  Of course, good questions come from good tasks and learning experiences crafted by teachers.  This is where the distinction between problems and exercises is important (see “Rethinking Mathematics Homework” post for the difference between the two). Good questions come from good problems where the mathematics needed to solve isn’t readily apparent.  Exercises can generate questions, too, but the nature of those questions is generally more procedural and structural in nature.  (Note that exercises can be turned into problems given the right context and perhaps some tweaking/editing.)  Yet, none of this will happen without classroom norms that challenge the established and status quo culture of many mathematics classrooms, which is a culture of correct answers.  To transform classrooms into a culture of questions, Jo Boaler offers some Positive Norms to Encourage in Math Class that challenge many of the preconceived notions of mathematics that permeate throughout the United States and our own experiences as learners of mathematics.

(2) Intentional Focus on the Standards for Mathematical Practice.  While all eight Standards for Mathematical Practice are important in terms of establishing habits of mind for emerging mathematicians K-12, particular emphasis should be made on two of them if we wish to transform our mathematics learning environments:

  • SMP #1: Make sense of problems and persevere in solving them.
  • SMP #3: Construct viable arguments and critique the reasoning of others.

If we make strides with these specific practices, our mathematics classrooms will feel and look very different.  In addition, the role of student questions fits perfectly with these specific practices.  But let’s not just limit these to the mathematics classroom, as these specific practices transcend all content areas and are good habits of mind for everyone within an organization.  As a school department/faculty, when was the last time the team made sense of a school problem and persevered in finding a solution?  When was the last time adult discourse occurred at a department/faculty meeting around critiquing reasoning and arguments (and not the people making those arguments)?  When was the last time a meeting was driven by questions posed by the participants?

If we want students to carry the cognitive load and do the mathematical thinking in our classrooms, then we have to model these actions.  As teachers, do we model posing questions around a problem?  Do we model perseverance in solving problems, even when a solution strategy might lead to a dead end?  Do we model complete mathematical arguments using proper academic vocabulary?  If students never see their teachers perform these actions, it’s a tough ask to demand of them without some frame of reference.

Still not sure what this is all about or what the vision looks like?  Mark Chubb (Instructional Coach in Niagara) offers some ideas in his blog post “Quick fixes and silver bullets…” that illustrates common practices that suppress mathematical thinking.