We are about to begin a unit involving Dance where shape and spacial awareness is key. What better way to prepare students' minds than through Mathematics. That got me thinking to create a series of spacial visualisation challenges that called for students to use the Problem Solving Steps and required me to use of Problem Solving Talk.

The challenges involve constructing a 3-dimensional grid "stage" to create or recreate 3-dimensional shapes. I tried it out on my PYP Coordinator and colleagues first. This gave me practice in being receptive and using questions to focus on process and thinking rather than on results and being directive. Then I presented the first challenge to my class - Space Map A. I found that to use effective types of questions which cause students to think I needed to hold back. I had to think quick to recall, formulate or use questions from the support poster. (See my blog Math IS How We Organise Ourselves.) The mind gymnastics on my part was well worth it. I began to see students thinking for themselves, reflecting, concluding and proving their solutions. I also had to allow for possibilities I hadn't thought of or reasonable but unique interpretations such as negative space seen as positive space. I needed to read facial expressions and body language rapidly to inform my action choices. I also had to insist that students respect the value of the problem solving process and what it provides them, rather than jump straight into Step 3 Act. 

With my "Be More Receptive" hat on, I also noticed for the first time the signs that my students' beliefs about Math were being challenged. For example, one conversation went: 
    "Ms Hutchins but that isn't a 3-D shape!" 
    Instead of stating, "Yes it is." Followed by my explanation as to why. Instead I tried, "What to you believe a 3-D shape is?" 
    To which was replied with a circling hand motion, "A shape that goes all the way around like a cylinder , pyramid or cube." 
   "Ok, does that explanation connect to this situation?" I had shown myself that through questioning students can build on their own knowledge and apply it to unfamiliar contexts creating their own new and accurate knowledge.

The most important point I learned was to distinguish between the two reasons why I may reframe a Math question. Firstly, reframing a question I formulated with good intentions but one that needs clarity is necessary. I try my best but often my questioning is only better with age - at least one use. That is why I like trialling things on colleagues first. Secondly, and the more dangerous pitfall to avoid is, reframing a question that makes the pathway to solving a good question easier or quicker. In doing so, and unbeknownst to my students, this immediately robs them of independently solving worthwhile Math.

The best part was the genuine confusion in their faces turn into a quiet smirk of pride when they got it. Also it was great watching chairs being pushed aside so as to get down and see the actual view at eye-level. I knew they had it when, as if an optical allusion was revealed like a magic trick, I heard, "Wow! Look at it - it really works." 

Last year I found myself running two planners, one for the UOI theme How We Express Ourselves and another for my Math both sharing the central idea: Talents, attitudes and skills help organisations to achieve their goals. The basis of the UOI was for students to experience how they organize themselves by running an art competition based on their collective interest in a type of Visual Art. This worked well but we did have many other opportunities within our other UOIs to include The Arts in a major way. For example you can check out Dare To Dance? 

What was a challenge when reviewing our POI (Program of Inquiry) was the opportunities within the year where Math was the star. So I felt at least I could run a Math unit alongside our main UOI, where the basis would be an idea I found about Inquiry Teapots by Craig Dwyer (@dwyerteacher). You can also check out what inspired Craig at Geometric Teapot Packages. So there we embarked on our first Teapot Inquiry! 

During post-unit reflection on our main UOI and my Math UOI, it did not take long for an A-HA! moment. I realized that Math was a excellent fit within this UOI and should be the main act. Maybe our central idea was truly supportive of transdisciplinary learning as it could be applied to Visual Art or Math and possibly other areas. I enjoyed reading a straight forward explanation on Transdisciplinary Learning from Greenwich Public Schools. 

This year the UOI was a thrill. To live inside Math everyday where students are learning about it and applying it together to solve problems felt like we had successfully achieved a planner and UOI that was true to the transdisciplinary theme and didn't compromise on Math which is often stand-alone.

The transdisciplinary theme says, How We Organize Ourselves is an inquiry into the interconnectedness of human-made systems and communities; the structure and function of organizations; societal decision-making; economic activities and their impact on humankind and the environment.

The heart of this UOI is an inquiry into the structure and function of organizations and societal decision-making. This unit focusses on Thinking, Self-Management and Social Skills by learning how to effectively work towards a goal within a group by organising ourselves to solve mathematical problems involving Measurement and Shape and Space. It requires students to develop their Interactions within Physical, Personal and Social Education.

I found a few great resources that helped us understand how to best approach problem solving in Mathematics. K-5 Teaching Resources have created fantastic e-books for Math Journals, Vocabulary and Projects. If you purchase a very affordable downloadable file, the explanation about Math Journals is straight forward and informative.

Another key factor was having students cycle through a problem-solving inquiry process as many times as possible within the UOI. This meant that students would be able to reflect on their skills, concepts, understandings and knowledge while giving them the opportunity to take action by applying what they have learned within the next inquiry cycle. It also meant that differentiation was imbedded as each "problem-solving organisation" or small group would be able to work at their own learning pace and level of understanding. 

It was important for each student to select their group based on what the task or "goal" and the skills that he or she were bringing to the table as well as considering the skills that he or she needed from others. Rather than relying on random groupings or on a friendship basis. This meant that both students and myself had to be consistently aware of their skills state-of-play, through formative assessment, reflection and discussion. It also meant that before diving into a task, an extended moment of pause was needed to consider and apply thinking skills to ascertain what the goal actually was. This would ensure students practice good habits of thinking and avoid assumptions or racing ahead unaware of where they need to go (which was also up to themselves). This experience reaffirmed my love for open-ended Mathematics - its so rich and truly enjoyable!

In addition to the group tasks, I also ran individual Math Journals using the same process to allow for alone-time with Math and mathematical thinking.

I've been trying out and thinking of authentic and effective ways to centre Student Voice within our inquiry planning. So when we were about to embark on our Summative Assessment during our first Unit of Inquiry this year I thought, "Aha! This is the perfect opportunity for you Natasha to put this into action." I'm not sure about you, but uncharted waters are where you dive in and have to figure out where your going, how your going, while your going "there" wherever that actually is. But not being one to balk at a challenge, I dived in. A good place to start is by visualizing, asking yourself, "When all my students responses are piled on my desk, what evidence do I want to find within them?"

The overall result was a crisp Summative Assessment which each student owned and was fully engaged in, as well as, clarity for the teacher from the initial question through to how the student's response is connected to the curriculum.