This is a follow up to my preparing for math inquiry blog entry. In that post I explain that an important place to start, when preparing for math inquiry, is to focus on developing the math talk community. Or attending to the classroom culture, as the National Council of Teachers of Mathematics (NCTM) explain in a recent research brief (January, 2013). By extension this post focuses on what the teacher can do to help contribute to the healthy development of an inquiry or problem based learning environment, within a math context.
With the goal of implementing inquiry in the classroom, the first major and daunting change I made in my math practice was to REPOSITION the textbook in my planning framework from ‘program’ to ‘resource’. In other words, I placed more responsibility on myself – as the teacher – to make conscious decisions about where the math learning needed to go, based on the needs of my learners, and how I believe the curriculum could seamlessly link together. This was done in place of following a textbook from one unit to the next.
I have learned that as the textbook is repositioned from program to resource, so to the teacher must reposition themselves in the classroom from ‘math sage’ to ‘math guide and activator’. To paraphrase math researcher Fosnot, a math program should ‘not strive to fix math thinking, but instead work to develop the math thinker’.
I believe this idea tries to address what math researcher, Dan Meyer, suggests are 5 ways you know you are doing math reasoning wrong (Math class needs a makeover). Specifically, students demonstrate:
I have observed that when I made a few specific but small changes to my teaching practice, on the scale of my daily interactions with students and their learning, I have noted significant gains in addressing the 5 points listed above.
What did I do as a teacher?
In short, I planned to be less helpful.
What I mean by this is, I made a purposeful and strategic effort to:
- plan to present math topics as contextual problems;
- plan to let learners mull over these shared problems with partners then individually;
- plan to promote peer to peer discussion so as to push student thinking and not, rescue the student from thinking by ‘telling’ them the strategy to use; and
- plan to highlight student thinking during the “reflect and connect” stage of the 3-part lesson. This is something educator Thomas Ro has suggested is often an unfortunately overlooked process embedded within the 3-Part lesson.
An important change I needed to make as a teacher was to adjust how I interacted with students during the problem solving stage. What I mean by this is some teachers new to ‘inquiry’ often inadvertently project a sense of “sorry but I can’t tell you right now” or “just think about it some more and we will look at the answer later” to the student. My feeling is that this does not contribute to the spirit of inquiry we are trying to develop within our classrooms.
Instead I have found it useful to project a sense of “Let’s figure this out together” to the student. A strategy I employ to help promote the spirit of inquiry within the classroom learning community is to use ‘talk moves’ so as to avoid ‘tells’. Tells are general comments made by the teacher which essentially relieves the student from the duty of developing their own intuitive math thinking or strategy. An example of a tell might be a comment made by a teacher to a student like: “for this question you need to add the 3 apples in one basket and the 2 apples in the other”.
A ‘talk move’, on the other hand, elicits dialogue and quietly encourage students to ‘show’ their thinking. A talk move can be as simple as, “How does their thinking match with yours?” I have noticed that this question elicits much conversation, especially once students have become comfortable with the problem based or inquiry community. The work of Chapin, O’Connor, and Anderson (2003), Classroom Discussions: Using math talk to help students learn, have informed my practice. Here is an adapted version of their work, create by the YRDSB Math Team (Five Talk Moves), which explain 5 high yield talk move strategies. They are: revoicing, paraphrasing, agree or disagree & why?, prompting for further participation, and using wait time.
Are there any other important ways we might ‘plan’ to be less helpful for the benefit of our students?
What else should we consider when planning for inquiry or problem based learning?