(Photo courtesy of Flickr user: .michael.newman.)

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:

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.**plan**

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?

Hey Paul. Great post and I applaud your efforts to plan to “be less helpful”. I’ve been doing some learning around assessment lately and your post made me reflect on how assessment for and as learning fits into math inquiry. A fantastic book that I’m reading is Embedded Formative Assessment by Dylan Wiliam and he argues that while most teachers may plan problem based and engaging lessons for students, they may not spend as much time planning how they will assess their students. So some questions that I have been pondering around math and assessment are:

How can learning goals and success criteria be incorporated in a math inquiry so that students aren’t funnelled into a narrow path of learning without room for flexibility and divergent thinking?

How can descriptive feedback be delivered to students that moves their math learning and thinking forward (a Dylan Wiliam term) rather than shut down the learning?

How can students as a math community become active partners and engaged in the assessment process in a math inquiry?

Looking forward to reading more of your reflections.

Hi Thomas. Thanks for sharing the learning you have been doing around assessment. All the questions you raise are some of the very things I have been thinking about too. I am currently trying to learn more about how to make better use of “assessment as learning” practices in the classroom. The William book you shared is going to be my next purchase.

As for success criteria, I have found that it is useful to students to start generating them around the middle of their inquiry learning arc. At the start, it blinkers the thinking, and at the end the students don’t get a chance to use it, to check their work. I am thinking the middle to end portion fits with the learning community I am trying to build. Initially, students get a chance to develop their own intuitive math sense and strategies. Then, they share, reflect and add on to peers’ thinking. Later, the teacher highlights student thinking. Then we co-construct success criteria. After that, students get a chance to solve other problems and use the success criteria to assess their understanding and work. Just thoughts.

Thanks for the questions, I think you have given me a few more topics to blog about. Also, thanks for letting me source some of your work.