On Saturday 30th April, I and two others from SLMP attended the MANSW Primary and Middle School Conference. The theme appealed to me as soon as the advertising began to roll out.
With speakers like Dr Paul Swan and Katherin Cartwright, I was hooked. What I wanted most was the language to speak, promote and lead the unpacking of reasoning back at school.
What is reasoning?
From the rationale of the NSW Syllabus…(emphasis added)
“Mathematics is a reasoning and creative activity employing abstraction and generalisation to identify, describe and apply patterns and relationships. The symbolic nature of mathematics provides a powerful, precise and concise means of communication. “
From the Mathematical proficiencies, found in the Australian Curriculum, again emphasis added…
“Students develop an increasingly sophisticated capacity for logical thought and actions, such as analysing, proving, evaluating, explaining, inferring, justifying and generalising. Students are reasoning mathematically when they explain their thinking, when they deduce and justify strategies used and conclusions reached, when they adapt the known to the unknown, when they transfer learning from one context to another, when they prove that something is true or false, and when they compare and contrast related ideas and explain their choices.”
A generated word cloud allows one to see the core skills behind what it means to reason.
Through the power of nifty visuals, it is neat to see that the term reasoning is at the centre alongside the word students. But are our students actually reasoning? Do we recognise their moments? Are we even creating the environment for reasoning to occur? From here on, I am going to discuss how to promote dialogue as a means of reasoning. I acknowledge that there are a number of other areas, such as classroom culture and learning environment design, and planning challenging tasks (all of which are interrelated with dialogue) that also help engage reasoning skills, but for the purpose of this post, reasoning through communication will be explored.
Planning for reasoning through communication
During the planning phase, teachers make decisions that affect instruction dramatically. They decide what to teach, how they are going to teach, how to organise the classroom, what routines to use, and how to adapt instruction for individualsFennema, E., and M.L Franke. “Teachers Knowledge and Its Impact.” In Handbook of Research on Mathematics Teacher and Learning, edited by D. Grouws, pp. 147-64, Reston, Va: National Council of Teachers of Mathematics, 1992.
It makes sense to view the planning stage as the field in which to sow the reasoning seeds. However, this comes with a rather large caveat…don’t expect children to reason if you’re doing all the communicating or you are restricting the ways in which the students can communicate their understanding. You could even go so far to say that communicating is the channel in which reasoning can occur.
It is known that teachers ask many questions in the ebb and flow of the day, and I dare say that we probably think we are asking ‘good questions’, but are they really the right kind of questions? Are these questions that encourage high-level thinking? One of the most powerful instructional shifts an educator can make to increase the amount of reasoning occurring in their classroom is to specifically plan to ask questions are “discussion-generating questions, probing questions, and questions that make the mathematics visible” (5 Practices for Orchestrating Productive Mathematics Discussion, 2nd Edition, Margaret Schwan Smith and Mary Kay Stein, 2018, p.89). Using a framework such as the revised edition of Bloom’s Taxonomy to craft question styles will be helpful to scaffold and promote hard thinking. Further thinking about questioning will lead to the understanding that asking questions serves different purposes as this link from the University of New South Wales demonstrates. In short, knowing which questions to ask is an important skill set to be continually honing as a teacher. Some of my favourite questions to generate discussion and probe understanding are:
- Tell me more about this;
- I’m interested to know more about what you’re telling me; and
- Convince me that this is the only possible answer.
My goal when asking questions such as these is to understand what the student knows how they are doing it and why. I want the student to do more of the talking, and I in turn, more listening so that the instructional shifts I make are precise for that particular student. Here is an example of a template that I may use in the planning stages to help articulate questions or prompts to promote reasoning through dialogue. Click the image for a copy of the planning template.
Asking questions is a large part of the generation and cultivating of mathematical discourse in the classroom. Shifting the dialogue in the classroom however, must focus not simply on asking questions, but truly listening when students are talking. Marilyn Burns describes the critical nature of listening in an interview on her blog, Math Solutions. She notes,
“I’m always listening, not for what they don’t know; I’m not looking for their deficits. I’m looking for where they are, so I can have something to build on, so it can inform my number talks, so I know what kind of questions I might ask that could be developing understanding for some kids, while it’s cementing for other students, and while it’s extending for even others. Listen, listen, listen! I learn, and then I get to be a better teacher.”
Marilyn’s words sent me into a deep spiral of reflection, especially in regards to my own practice. What if we respond by asking questions that we think we should be asking and missing the opportunities to ask the questions that the student needs us to ask to help drive their learning forward? Someone once said to me that if you value something, you make time for it. I wonder do we actually value listening to students when they are talking about their learning. Granted, it can be near impossible to make the time to listen to every student for everything across the day, but being strategic about who to listen to and when is important. Consequently, I believe it is as powerful to plan for listening moments as it is to plan for questioning. Listening purposefully and responding accordingly is perhaps the truest sense of formative assessment- noticing, listening and acting.
In our diocese, many teachers encourage and promote dialogue through a framework called ‘Talk Moves’. Talk Moves help facilitate student discourse by placing the teacher as the conductor of powerful discussion by supporting and modelling mathematical discussion. The Talk Moves are explained in the image below and can be easily planned for, but even harder to implement. I have walked into many classrooms and have seen the teacher have a small printed version of this image on the side of their workstation or whiteboard.
In summary, for students to be able to reason they need to be given the opportunities to talk about their learning and experiences. Perhaps in future posts I will add further to the conditions that help promote reasoning, but I hope for now I have been able to place the spotlight on dialogue and purposeful listening as necessary platform for students to be able to reason.