Teaching As Inquiry: mid-year reflection 2018

What steps have I taken to change my practice in the first half of 2018?  My practice has inevitably changed with the transition from levelled-group teaching to the Developing Mathematical Inquiry in a Learning Community (DMIC) problem-solving approach to Maths with in-class mentoring provided by Dr Bobbie Hunter’s team at the University of Waikato.

An important focus during the first half of the year has been setting up the norms and expectations for learners when working together in a small group to solve a Maths problem. It is easy to forget that this change in approach to learning Maths is also new for the learners and vastly different from how they have historically learnt Maths at school. Unpacking and exploring the key competencies of managing self and relating to others has been crucial throughout this period so that students feel empowered to embrace this new way of Maths learning. It is beautiful to hear something as simple as a learner politely asking a presenter to speak up so everyone can hear significant Maths thinking.

Consequently, Learn Create Share has taken on a different emphasis during these early days of DMiC problem-solving:

• Learn: learning to work with others to be able to solve a Maths problem
• Create: creating Maths learning collaboratively with others in a small group while being thoughtful of others, respectful of their ideas and empathetic to their feelings
• Share: sharing Maths thinking orally as a cohesive group for the benefit of others

Naturally, opportunities for students to learn together in small collaborative groups have been provided across all learning areas to build positive relationships and encourage a sense of community responsibility.  Not only does this support the DMiC approach to learning Maths but is helping Room 11 make headway in its "waka".

As for my target learners, there are positive and observable shifts in their attitude towards Maths. I no longer hear talk of “I don’t like Maths”, “I suck at Maths”, “I’m dumb at Maths”. Maths is now viewed as a time when you work with others to talk about a problem and how it can be solved. Within the small social groupings, everyone brings different perspectives and knowledge about how to solve a problem. It is still very much a work-in-progress but collaboration is replacing suspicion and competitiveness now that people realise that there really is no top Maths group! It is noticeable that everyone is more confident to share their Maths thinking in front of others and, equally as important, most are much more confident to ask questions if they don’t fully understand what someone else is talking about.

As far as possible, Maths problems have been created to integrate number and strand, while balancing curriculum demands with student prior knowledge. Interestingly, a problem was posed recently to explore number flexibility and explicitly begin the transition from additive to multiplicative thinking (as many learners rely on skip-counting to solve multiplication problems).

This context with blocks of wood was chosen as real blocks of wood have been available for building bases in the playground recently. These objects have been the source of great enjoyment and frustration as groups of students build and knock down each other’s bases. Much talk at our first exploration of this problem centred around the fairness of the problem: Why can’t they put all the blocks together and make one big base? Why do they have different amounts? It would be fair if all the blocks were added together and then shared equally so there won’t be any arguments.

Rich oral language and the key competencies were clearly on display while the Maths in this problem was explored further on a second occasion. There are the beginnings of understanding that numbers can be broken up and recombined in different ways - and that some numbers are more flexible than others. Some connections have been made that using your times tables is more efficient for solving some problems than skip-counting - based on the arrays that were drawn to show how the flexible number 24 can be broken up in a range of different ways.