Multiple ways of knowing - an inquiry into conflict resolution

I couldn't resist sharing the progression of this inquiry as it unfolds among our grade three students here at BHA. The UOI that our three Grade Three classes are currently exploring falls under the TDTheme of 'Sharing the planet' and the central idea is: Effective communication can resolve conflict. The focus on this post will be on the important role that our single subject teachers have played in this inquiry so far.

The students were prompted to consider the last time, or worst time, they were involved in a conflict with friends or siblings. They were asked to think of this as a story with a beginning, middle and end.

Beginning - what happened to give rise to a conflict situation?

Middle - what happened during the communication process to try and solve the conflict situation?

End - how was the conflict resolved and how did it move into peace?

In small groups they then chose one story to represent in a drawing. The students were given long sheets of paper and asked to think about the kinds of colours, shapes, lines, forms and patterns that would best describe what was happening in the three different parts of the conflict story. The drawings below show the conflict stories and their 3 parts; conflict, communication, resolution/peace. The next step is for the students to add emphasis and further structure to the drawings using collage shapes. They will then transition over to our music teacher and consider similar concepts such as dynamics and rhythm that represent the ideas of conflict and peace. To synthesise everything, the students will cut-out and re-arrange their designs as they compose an original score to reflect their stories.

This process clearly offers a tremendous insight into the students' understanding of the process of conflict resolution. Conflict starts out as a range of different opinions and ideas all jostling for the front position. Sometimes it's messier than what it started out like before it gets better. There's usually a breakout moment that occurs prior to the solution. When you get to a stage of finding common ground it is like the pieces fit together. Peace and love may not always be the outcome - sometime we try to cover up a conflict with a resolution. These are all big ideas that are worthy of inquiry into peace and conflict at any age.

So it teaches us two very important lessons about inquiry. (1) Students of any age are able to think conceptually and (2) Teachers must be open to providing multiple pathways for their students to express their understandings.

It is highly unlikely that the students at our school would have been able to articulate these ideas in written form alone. Yes, the teachers helped to tease out the verbal responses from the students (with translation required for some), but that's their role - to listen, not to tell. The point is that those responses were constructed by the students themselves and they may not have seen the light of day if this opportunity had not be available to them. This is succinctly summarised by any Reggio-inspired educator when they talk about the hundred languages of children.

The other beautiful thing about this connection to the UOI is that it was completely unplanned in terms of collaboration between the homeroom teachers and specialists. The idea started as a conversation between our Music and Visual Art teachers and they thought they'd give it a shot. There was no pressure to ensure that they fit in with what was happening in class* so there was a lot of freedom to test out different approaches. When the connections began to appear as significant and highly relevant for the learning that was also happening in the classroom, a lot of discussion between all teachers followed. Although making a strong connection with the unit of inquiry may not have been the first priority for music and art, creating an authentic learning experience certainly was. This idea grew legs because of the teachers' commitment to genuine learning and the lens of the unit of inquiry provided this without being forced.




* To clarify this, at this stage in our school's journey we ask that subject specialists meaningfully collaborate on at least one UOI with each grade throughout the year. They can certainly contribute to more than that, but one is the minimum requirement.

Seeing is not believing

Over the past three days my school has hosted Mark Church, of Making Thinking Visible fame. He visited us to hold preliminary discussions about us developing a culture of thinking and hopefully the faculty will decide that this is something worthwhile continuing so we can begin to delve into some different perspectives on teaching and learning.

I was lucky enough to be involved with several of the breakout sessions and one idea that was raised was that the students we teach don't necessarily believe what they see. Instead they see that which they already believe. This refers to the notion that a teacher could deliver a lesson in which they think that something has been taught, yet the student still harbours preconceived ideas. The example that we discussed regarding this was of the ideas of two students explaining that in a completely dark room your eyes would adjust to be able to see an object. Despite prolonged questioning and a carefully arranged experiment that allowed the teacher and student to sit in a room with absolutely no light, the student still maintained that her eyes would adjust to be able to see the object. Her original prediction was 2-3 minutes, then 5-6 minutes, then an hour or two and in the end she still maintained that her eyes would adjust - but it might take a year or two! This example showed that, even though the student was willing to shift her perspective slightly, she still did not believe or understand that the eye cannot see anything unless there is a light source. The lesson here for teachers is to recognise that its not necessarily the evidence that is presented that will cause a shift in conceptual understanding, but the ideas and opinions that students have around it that matters. The power is in the hands of the learner.

The acknowledgment that students have ideas and opinions has significant implications for teachers. Discovery learning, project learning, problem-based learning and the variety of other pedagogies fall short of the mark if they are enacted in a way that doesn't listen to or value the voice of the student. They need to be embedded in inquiry. If the impetus for learning is coming solely from the teacher then they will only produce the same results as behaviourist approaches to teaching.

I'm currently reading a book by Marcia Behrenbruch called 'Dancing in the Light'. In this she identifies two approaches to planning in inquiry classrooms. The first she terms 'planning for purpose'. This refers to the teachers' role in planning. It leaves less room for student-initiated inquiries but answers questions such as: 'What are the significant, relevant, challenging and engaging conceptual ideas that should be addressed? What knowledge and skills could be developed through these ideas?' This sort of planning in progressive curricula is based on the 'Backwards by Design' framework. The second approach to planning is referred to as 'planning for possibilities' - a term that I was immediately drawn to. This process supports the development of student inquiries around the identified conceptual understandings. A variety of frameworks exist and all encourage student questioning at the classroom activity stage. When these two frameworks support each other, a teacher achieves what Behrenbruch refers to as an 'integrative inquiry approach'. This is student-centered yet also allows for state, national or school requirements to be met within the curriculum. The craft of the teacher is dedicated to managing the interplay between the two frameworks, guiding the development of knowledge and skills identified in their 'planning for purpose', whilst also reflecting on the direction that student inquiries are taking. This is managed by formative assessment and focused through the conceptual lens(es) for understanding.

Mark also highlighted three types of data typically gathered by schools. That which we can count, that which we can see, and that which we can hear. He talked about filling up data buckets and that a great number of schools have a very large 'counting data' bucket, but much smaller 'seeing' and 'hearing' buckets. He referred to the analogy of a 4 year old visiting the doctor. If the doctor weighs the child, measures their height and takes their temperature then they may easily conclude that there is nothing wrong and they're perfectly fine. However, a thorough doctor would also, for example,  listen to the child's breathing and heartbeat, look for any abnormalities in or outside of the body. These may point to something else and give reason to further exploration. The point is that all three types of data tell a part of the story but none tell the full story alone. Schools must ask themselves how they are filling and scrutinising their three buckets of data. If we acknowledge that students come to our classrooms with ideas, opinions and preconceptions then we must ask ourselves how we are finding out about these? How are we getting our students' thinking into our heads, instead of the other way around?

Photo Credit: built4love.hain via Compfight cc

Reimagining our Early Years program

This year at BHA we have several professional learning communities operating in unison. I'd like to touch on one of those in this post. The team of five teachers in the kindergarten, plus any other teachers interested in learning about the early years, are currently in the beginning stages of redeveloping their approach to teaching and learning. They're working through the valuable and collaborative process of developing a shared image of child. I was lucky enough to be able to be part of a group that went through a similar process in my previous school and found the conversations both challenging and rewarding.

So far this group has examined their own personal opinions and ideas about children. They were asked to share what they thought a child was and these responses were collated and discussed. Teachers were given the opportunity to highlight which elements of everyone's statements they agreed with and which parts they still had questions or other wonderings about. This required further discussion to unpack and will be useful to re-visit later in the year once everyone has had the opportunity to reflect on their own and others' ideas.

This graphic was created to help make visible the key words about image of child that the group valued as a collective.

The session today was spent looking at these words and talking about what they meant. There were some comments about similarities between words, about which words were by-products of our images, and which words were useful to help support the creation of our image.

The next steps for this group will be to narrow down the words to a smaller selection - we're thinking between 5 and 10 - that truly sum up our thoughts about our image of child. From this list they will map out what it is that they believe they should be doing in order to foster the growth of this image of child in their classrooms (and across the school).

It promises to be an exciting year for this group of teachers (along with the rest of the faculty of course!). We're lucky to be hosting a regional IB conference in November and all of these teachers will have the opportunity to attend workshops that will help grow their understanding of a play-based curriculum. We'll also be looking to connect with like-minded schools in order to share ideas, practices and strategies. I'm very much looking forward to being part of this process.

Why inquiry isn't cyclical

I just watched a fabulous video that summarises a lot of key ideas about inquiry. Although this is specific to scientific inquiry, I think the lessons are transferable to all other areas of inquiry.

What I like most about this video is the analogy of the cycle of inquiry being similar to a game of pinball. You do not progress through an inquiry in a linear manner. Instead you revisit, revise and retest ideas, questions and theories. The visual design of many inquiry cycles has lead to these sorts of questions being posted in social media forums:

 

In fact, last year Kath blogged about her own inquiry cycle in order to bust some myths relating to it.
 

The visual produced in the video includes some nice animation that hasn't been captured on the screen shot. Essentially its the grey arrows that play such a big role in this model. They rotate back and forth, in and out of the green circle. It aides to highlight the notion that when we inquire into something we're continually gathering and interpreting data, analysing outcomes, gathering feedback, exploring and discovering.
 

Perhaps the title of this post is a little misleading. There is still a cyclical process involved with inquiry, but it is important for us to remember that no inquiry (or writing) cycle was designed to be a linear, hierarchical process. It's messy, unpredictable and continuous. Check out the video for a more detailed explanation and some links to further reading.

 

The Giant of Jeju - an inquiry into patterns

I'd like to share another teaching engagement that my colleagues and I introduced yesterday. We called it the Giant of Jeju and it is adapted from a lesson that the Maths Coach at one of my previous schools introduced to us.

I love the premise of this task. Its shrouded in mystery from the beginning and that seems to hook the students in. It also give them very little concrete information to work with so there is a lot of scope for inquiry and divergent thinking. We begin by showing the students a picture of a hand, telling them that a group of archeologists discovered this fossil imprinted into the Jeju terrain. Their role, as genetic researchers, is to predict as accurately as possible how tall the Giant would have been when it was alive. We aligned the learning targets with our mathematics central idea and provided guidance through key questions that were related directly to the task. Here's the summary that we provided the students with:

The Giant of Jeju by Dave Secomb

In Making the PYP Happen, inquiry in practice is characterised by a series of actions that could include: exploring, wondering and questioning; experimenting and playing with possibilities; making connections between previous learning and current learning; making predictions and acting purposefully to see what happens; collecting data and reporting findings; clarifying existing ideas and reappraising perceptions of events; deepening understanding through application of a concept; making and testing theories; researching and seeking information; taking and defending a position; solving problems in a variety of ways. This task requires students to perform many of these roles in order to solve it.

One of the best things about this task is that there is no single accurate answer. So even if two groups arrived at a solution that was similar, they still had to defend their findings and explain why their predication was more accurate than another. Several groups worked off premises that were based on flawed logic or showed no pattern. They arrived at answers that were vastly different from the majority and were found out when they had to prove their accuracy with reason. Some of these students were able to recognise this as it became clear to them while they were trying to explain their answers to the rest of the class. Those that still managed to arrive at solutions that were similar to others had their theories tested by questions from their peers asking them how they knew that they were accurate. Two or three groups had very similar (and accurate) answers but were unable to prove why their solution was correct. Many times throughout the year we've talked about the importance of process over product and this is a difficult idea for a lot of our girls to grasp because they have come from systems of education that value the opposite approach. This task helped to clarify to them why the process is so important.

Some solutions and reasons:

• 2.8m due to a ratio of 1:1.97. This is because we measured the length of our hand and our height from one of our group members. Then we applied that calculation to the Giant.
• 3.02m due to a ratio of 1:2. This is because the Giant's hand is twice the size of one of our hands.
• 2.66m because 9.5 of our hands make up our total height so we multiplied the length of the Giant's hand by 9.5.
• Arm length = hand length x 7. Arm + head + legs = height. So the total height is 4.86m.

Agreement/Disagreement

Our current UOI in Grade Five is using the central idea 'A balanced lifestyle contributes to well-being'. Although our hope is that they never truly end, we're coming towards the scheduled end of this inquiry. Over the past five weeks the students have explored the different body systems, how they function and interact; the different elements of lifestyle and how they influence each other; and the effect of reflection on achievement. Yesterday my teaching partner and I introduced a forum for discussion about some aspects of our learning. We presented the students with a series of statements and they were all required to take a stance in relation to their level of agreement. They could choose one of the following four options:

• Completely 100% agree
• More agree than disagree
• More disagree than agree
• Completely disagree

This was a great formative assessment opportunity for us as teachers because it required the students to make a decision and then justify it to everyone else. The strength of their justification provided an insight into their understandings about the UOI.

Philip Cam, in his book 20 Thinking Tools, states:

"In collaborative inquiry, agreement and disagreement represent patterns of convergence and divergence in thought that enable us to tack back and forth into the wind, and give our inquiry its forward movement"

We were lucky to have three teachers in the room during this task so while one of us was moderating the discussion, the other two could take notes on specific students and their responses. Later on we caught up to read over and discuss these. One example of a statement we posed to the students was this:

It is ok to spend a lot of time on your work if its something that you are passionate about.

This statement infers that if you are spending a lot of time working on something then your lifestyle is not balanced. It helped the students to test their understanding of balance, how lifestyle and elicited a variety of responses. One of our students said that she completely 100% agreed with this statement. When we asked her to explain why, she said that even though you're spending more time on your work, because its something that you're passionate about it means that your mental and emotional well-being will be strong. And you'll also be able to develop your social well-being because you'll be around people that are interested in the same thing as you. Wow. This showed us that she had a very strong understanding of the elements of well-being and how they can connect with our lifestyle choices.

This engagement also has benefits for other areas of the classroom community. First of all, it is inclusive. If someone doesn't have a solid understanding of the question or statement posed then they are able to discuss it with their peers while they arrive at a decision. They also have the ability to listen to other people's perspectives when they are giving reasons for their choices, and can change their position on something if their thinking shifts during the process. We have a lot of students with English language needs at our school and they were able to join in this activity without the fear of being put 'on the spot' in front of their peers. This activity also helps students to learn about and deal with instances where there are differences of opinion, clashing of ideas and debate over perceived truths. These are vitally important skills to develop and we were impressed to see the way that our girls handled themselves when challenged by their peers and teachers. 

Here are the statements that we used.

Lifestyle Agree:Disagree Statements by Dave Secomb

This video shows a discussion with Professor Cam and his views on teaching philosophy in schools.

Why inquiry?

Part of the learning process is something that is referred to as internalisation. This occurs when individual thinking transfers from an external social plane to become part of a person's mental function. Ratner states that these functions are formed as 'individuals engage in practical social activities and can then be applied in different contexts'. A simple example if this is addition. As someone internalises each of the different processes of addition then they can use these in a variety of contexts (e.g. adding decimals when using money, weight and length).

Simon Davidson says that in any high quality teaching approach students should leave with skills, knowledge and conceptual understandings. These can be achieved in most approaches to teaching. Students will be able to read, write and add. They will be able to use maps, glossaries, rulers. They will have a knowledge of social studies and science. To many people this is enough - 'as long as my child can do these things then I don't care how they learn it'. It is also what many people have experienced from their own education, which is why some people - most typically parents - question approaches such as inquiry learning. Its probably inaccurate to say that they don't support this approach or that they're anti-inquiry (well, maybe some are), more that they've got little experience with this way of teaching and are eager to make sure that they're children are taken care of. A lot of the time inquiry is a messy process and there aren't specific tests that can measure results and show parents how much their child has learned that day. This can worry parents and might lead them to request for a 'back-to-basics' approach (more about this later). Ultimately though, they are simply concerned for the well-being of their children.

The big differences between beliefs about learning reveal themselves when we compare models of teaching. Two of the most common found in schools around the world are the aforementioned inquiry and didactic. Inquiry is underpinned by a constructivist theory of learning, where understanding is crafted by each individual learner, usually in a social context. A didactic approach is typified by a stimulus-response way of learning that is initiated by the teacher (i.e. teacher says, student does). It is important to note that both have benefits.

When we focus on the initial topic of this post - internalisation - the importance of an inquiry approach is unveiled. As I mentioned before, if either of the two approaches - inquiry or didactic - are well executed then the results for the students can be positive. However, inquiry learning offers something to support internalisation that a didactic approach doesn't - a social plane. I'd like to try and use a sporting example as a metaphor here - team sports to be more specific.

A sportsman or woman trains hard to learn the skills of their game. They can become experts in kicking, passing, shooting, running, blocking, tackling, whatever is required of them to participate effectively. They can also learn the rules that define their sport plus the strategies that their team hopes will help them achieve their goal. However, none of these play out perfectly to plan once a competition starts and there is an element of social interaction. Social engagement brings new perspectives, different challenges and fresh ideas. Suddenly they cannot pass the ball to a specific position like they did in the training drill because there is a defender standing in their way. They have to re-evaluate and make a different decision. The effectiveness of their choice will be reflected in how much they have practiced the skills, how well they know the game and their level of understanding about how the strategy connects to the bigger picture. They can have a solid grasp of the skills, knowledge and understandings, but if they don't know how to apply these in a social setting then they're not of much use to anyone. The same applies to something concrete in schools around the world: reading. Through the internalisation of the processes involved with learning how to read, one not only acquires the skills of reading, they also become part of a community of readers & interact around books.

A more didactic approach to learning is sometimes requested by parents if they feel that inquiry isn't meeting the needs of their children. As Bambi Betts says, 'everyone is an expert in education because they had one once… unlike technology, or medicine, or telecommunications, parents have been to school.  They have been primary ‘users’ of the place called school and the thinking goes… ‘I turned out pretty much ok, didn’t I’ (they think) – so just keep doing what you did when I was in school.’   Familiarity as a design principle for schooling actually breeds complacency'.  The challenge when following a solely didactic approach is that if something is learned by rote, then there is no exploration of the association or relationships that is shares with other concepts. The result of this is a poor level of understanding and that it is difficult to remember. That's not to say that there are never any moments where direct instruction might be beneficial for a student. But educators should be mindful of how their beliefs about education are being put into practice.

Humans are not independent and autonomous. We do not live in separate spaces all of the time or experience the world in separate subjects. We live and work with each other & use our learning as part of a community. Didactic teaching separates social organisation and content. It diminishes context, which has implications for understanding. Inquiry learning creates a community of learners dedicated to understanding, not just following a curriculum. This is a vital part of learning for our students as they grow into the world.

Photo credit

Outdoor Learning

This year in Grade Three, my colleague and I decided that we wanted to head outside to engage in some activities, problems and inquiries. We took the inspiration from our Early Years department who have embraced outdoor learning as a daily part of their program. Recent educational research has indicated that outdoor learning programs can increase student achievement by almost 50% over the course of a year. One of our Vice-Principals is an authority on all things Early Years and she gave us some good ideas to start with. We were also aware that many schools in the UK already have outdoor learning programs. So we thought we'd give it a crack ourselves.

During the this first semester that we've held outdoor learning the students have:

• Practiced their navigation skills to find their way around the school and crack codes.
• Explored the pond area and made some fascinating discoveries.
• Developed teamwork and communication skills by working together to solve problems.
• Tested and re-tested theories in order to make conclusions.
• Explored ways of building knowledge in group environments.
• Reflected on shifts in thinking and understanding.
• Created Andy Goldsworthy inspired art.
• Predicted, collected, analysed and explained mathematical data.

We've been lucky to have some parent helpers each week and this has allowed us teachers to document the learning. This is another thing that has come from the Reggio-inspired program of our Early Years team. Individually, us two teachers have noticed some interesting things about each student during outdoor learning. But I report on my class and she reports on hers, so we need to find time to meet and discuss our findings. Plus the real power of documentation comes in the discussions held by the observers. It is the combination of these different viewpoints that helps build a complete picture about each child.

Being a new initiative, we're still perfecting the setup. We started off very open - playing in the sand and documenting research skills. Each week, however, we seemed to become a bit more focused with the tasks - measuring the perimeter of a playground area, for example. This may be because at our school we need to report on outcomes so we need to provide opportunities for the students to engage in tasks that allow us the chance to assess their understanding. Perhaps our mind has subconsciously been tracking back to this. 

A few weeks ago we gathered some feedback from the students about how they felt outdoor learning was going. From the start we wanted this to be about the student's learning so we felt it was important for them to be involved in the planning process. Some said that they felt everything was going fine. To our surprise, though, quite a few said they were becoming less interested in outdoor learning because they felt the tasks were becoming too regimented and organised. They preferred the freedom of greater choice and exploration. I'm glad the students felt comfortable enough to share these opinions - it really helped us. The teachers also shared their concerns about the students behaviour during outdoor learning. We felt that some were forgetting about the second word in the title. This feedback encouraged us to make a few changes to our setup. So far they've been well-received.

Some students just flourish outdoors. Maybe they find the classroom walls restrictive - I'm sure there's a number of reasons. It's been great to see these students come more alive with their learning. Others are equally as comfortable in the classroom and outside. Some only prefer the indoors. At least this way we're opening up the scope of access to more students and differentiating our approaches to the learning profile of our students. Most importantly, the students are participating in some interesting learning engagements. And I reckon they're having a bit of fun too.

The Question Quadrant - ideas into practice

Last year I blogged about the Question Quadrant as a way to develop the inquiry skills of my students. The aim was to make them better problem posers and this will have an obvious impact on their inquiries. Having read Phil Cam's book - 20 Thinking Tools - I decided that the Question Quadrant really was something that I wanted to have a go at in my classroom.

Last week I introduced it to my students and we explored what each section of the quadrant meant. I explained that we would use this tools to help us become better inquirers. We used the book 'Me and You', by Anthony Brown, as a way of introducing the tool. This fantastic book also served as a way to elaborate on one of our key concepts for this UOI - Perspective. I had previously developed some questions:

• Who is dressed more colourfully?
• Who wrote the story?
• What is the main colour of the bear's furniture?
• What are the names of the characters?
• Where are the bears going on their walk?
• Why isn't the girl dressed in more pretty clothes?
• Is it ever ok to use someone else's things without their permission?

After first describing each of the sections, we discussed each question one by one and decided where they should be placed. 

I was happy to see that the students were able to recognise where each closed question should fit. The difficulties came for the students when they had to consider that there might be more than one answer. Open, textual questions took a little while to flesh out, but we arrived at a conclusion for where it should be placed reasonably quickly. The open, intellectual question took a lot longer to discuss. The majority of the children thought that there was a black and white answer to this and it took the opinions of two students in order to let the rest of the class see that there might be other possibilities - 'What if you're being chased by something dangerous and you need to use something that belongs to someone else to defend yourself?'

We got there in the end and then it was time for the big understanding to be revealed. What sorts of questions should we be asking if we want to be good inquirers? 

Their answer? Closed, intellectual questions.

After I picked myself up from the floor from the shock of their answer, I tried to regain my composure. After such a lively discussion I was sure that the students had realised that open, intellectual questions were best suited to inquiry. There were obvious lessons for me out of this experience. First and foremost is the fact that this tool needs to be built upon and revisited throughout the year in order for my students to develop their understanding and skills in questioning. Secondly, I found it very interesting to see that nearly all of the students think that knowing clear cut answers is the best indicator of successful inquiry. The uncomfortable feeling of being in the 'area of unknown' when investigating something clearly doesn't sit well with them yet and they prefer to be able to reach the end point of something efficiently and accurately and then be done with it.

So I see my role now as being one of helping the students to feel safe and comfortable in the murky waters of not having quite reached an indisputable answer. I need to help them be risk-takers to explore new and unknown things and also develop persistence so when they do reach an answer they can consider alternatives and dig deeper. These are broad habits that will apply across the entire curriculum.  In terms of the Question Quadrant, we'll be relating our thinking back to this whenever we get the opportunity and use the chart to refine our questions as we come up with them.

As is usually the case with anything worth doing - there's no quick fix.

Moving Forward

People who know me well know that I'm a big fan of Australian Football - AFL. My suffering wife is, thankfully, supportive of the must-see 6 to 7 games per week that I usually try and watch. It works well for us at the moment that we live in Switzerland because the games are usually started and finished by mid-morning so we still have the rest of the day to devote to 'regular' weekend activities. Anyway, the team that I support has had a recent surge up the ladder and is looking like having a successful year. This has come after 3 years of dismal performances that made me glad to be away from Australia! There was a lot of pressure on the coach to resign during these dark years but he stuck to his beliefs and the results are now beginning to show. He is regularly questioned about the (relatively) quick improvement that his team has made over the past year (they went from dead last to 3rd last season). As they are sitting second on the ladder halfway through this season, the questions arise about how the coach is now guiding the team. The general feeling is that there should be some period of 'resting on one's laurels' seeing as they've put in a lot of hard work risen so quickly. The answer that the coach has been giving throughout this year is that he is always looking for continual improvement from himself and his players.

This got me thinking about my own improvement. Over the past two years at my school here in Switzerland I think I've improved in a lot of areas in a relatively short period of time. This has been due to my own initiative and being involved in as many development projects as possible, and also due to the support of my Principal and colleagues. During my first year I developed a much better understanding of curriculum and worked on improving my leadership skills. This is has served me well in my role as Team Leader as I am regularly called upon to chair grade and subject specialist meetings that involve discussions about all aspects of the curriculum. This has been an interesting area to explore and I find that the more I delve into it the more there is to discover.

This year I have been extremely lucky to have the guidance of one of the best mentors I've ever had. While I was never really a slouch at IT, our IT Co-ordinator has helped me to discover the real power behind the ways that we can use technology today and I feel like my teaching has improved dramatically as a result. Part of this rapid improvement has been due to the fact that I knew she would be leaving our school early on this year so wanted to make as best use of the remaining time as I could. I feel very lucky to have had the chance to teach with Maggie and am sure that I'll be contacting her next year at her new school with many more questions!

Recently I have been thinking about my improvement focus for next year. I have a couple of things in mind that I will address and am narrowing these down as I prepare to write my goals for next year. Earlier on this year I blogged about inquiry and analysed the facets in relation to my own teaching. Encouraging my students to problem-pose was an element that I felt I needed to improve at. With that in mind, I was happy to discover a nice graphic organiser about questioning not so long ago. I think this will be a great tool for me to enhance the questioning skills of my students next year and my prediction is that it will lead to greater problem-posing. I discovered the Question Quadrant through Twitter and also found that the author - Phil Cam - has written some books that look interesting. I created an adapted version of the Question Quadrant to trial with my current students this year and so far the results have been positive. I need to use it more in order to help the students guide, improve and answer their thinking about each type of question they pose. I'm looking forward to seeing how this will work out next year.

A dividing inquiry

This morning my students tackled a problem that required them to use a variety of skills and processes they have recently been working with. You might be able to see in the picture below that they had to find a way to split up some distances of a relay race. The race was 26km long and they could choose as many runners as they want as long as it was between 3 and 10 (including those numbers).


I encouraged them to start off by using one of their problem solving strategies - identifying the key words. 

It was decided that the key information was: 

• The total distance was 26km.
• There had to be between 3 - 10 runners.
• Each runner had to run an equal distance.
• We had to be as accurate as possible with our answer.

The students then set to work with a partner in order to find out a possible answer for this problem. Although we have recently been investigating division, fractions and decimals, I didn't give any indication to the students that they might need to use these skills for this problem. I was interested to hear the some of the questions and comments that arose during their discussions:

- "How are we going to break them up?"

- "We should find an equation that goes into six. Nine goes better."

- "You have to halve it. I did five and a half and I'm left over with five."

- "Argghh....we've got leftovers! What if we try four?"

- "Four doesn't work, does two?" "Two is below three so we can't use it"

- "Something has to divide into 26"

- "We need to do fours." "But 26 isn't into the four times table"

- "I tried seven, its impossible"

- "Let's go through the tables and see which works. It has to be equal. If we use the fours then we have two left over."

The students used a variety of strategies to organise their thinking. Some created tables, some glued their work to their page so they could keep track of them and others cut out their sheet to group the kms together.

From here, some students became stuck and needed some thinking time in order to go any further. A popular strategy was to try and add more kms onto the race in order to make the groups fit exactly with their chosen number of runners. Others started to make some connections between what they had learned previously and  where they could go next:

- "We can change the numbers. The numbers can be parts of kms too."

- "You could break one km into three and then the other one into three."

- "We can split a km in half and make it meters."

- "We can use some from this one and some from the other one."

- "Can we use numbers like 4.5? Can we use decimals?"

These statements kicked the investigation up a level. Students realised that it didn't have to divide by 26 equally in order to work and began exploring the possibilities. Before too long we had solutions using 3, 4 and 6 runners. These groups organised their leftovers into fractions and distributed them accordingly so that each runner ran the same distance each. In order to achieve the accuracy component of the lesson, I challenged some of the groups to explore ways that they could convert their fractions into decimals so that the runners would know exactly how far they would have to run.

We finished up by discussing why each group could calculate a different answer. One of the understanding goals for this unit of work is that students can see that all numbers can be broken up into smaller amounts, and that this can be done through many different strategies. Today allowed them to use their knowledge of fractions, decimals and/or division strategies. It was good to see that the students are well on their way down the track with this. It was also a good opportunity to see the students bring their problem solving strategies into play and gain more experience working collaboratively with their peers.

Unpacking a maths program

Currently at my school we are in the process of revising our maths curriculum. Schools are typically in a cycle of curriculum revision and ours is no different. It's been an interesting process so far and we still have a way to go. To put things in context, last year we created a K-12 continuum of learning outcomes for Maths, Language, Science, Humanities, PSHE, German, Music and PE - I think that's all (phew!). This was obviously a lot to achieve within the timeline of one year and our Curriculum Director has indicated that these will need tweaking as we work through them. 


Our Maths Coach (a new appointment this year) is settling into his role and has brought with him a new approach to the design of our maths units. In previous years we have focused on a core resource for informing our mathematics practice and supplemented this with other resources where required. Along with our newly created outcomes we revised this resource and decided that it wasn't the best fit for our program. We recently received our new core resource and are now familiarising ourselves with this. 


Through the self-analysis of our program in the Elementary School, one of our main criticisms of our work was that we don't revisit mathematical concepts throughout the year. This is referred to as 'spiraling', as concepts are visited and re-visited throughout the course of the year. The belief behind this is that students are able to build on their knowledge throughout the year and develop deeper understandings. This also aligns with the constructivist approach to learning that the PYP values. Conversely, a curriculum based on 'mastery' places emphasis on mastering specific concepts of mathematics before moving onto the next one. Mastery is the end goal for all mathematical concepts, spiraling is one way of achieving that. Some educators achieve a spiraling curriculum by addressing concepts during each year of a students' school life. In this example the students learn certain parts of concepts (eg. fractions) in grades 1, 2, 3 etc, with each part becoming developmentally more challenging. Spiraling can also occur within a grade level and this would involve students re-visiting the concept at different times of the year. This is what we are looking towards in our school.


To encourage this approach our maths program has been re-designed around five units: Counting, Partitioning and Calculating; Securing Number Facts and Understanding Shapes; Handling Data and Measures; Calculating, Measuring and Understanding Shapes; and Securing Facts, Calculating and Identifying. I believe that these are similar to (or the same as) those used in the National Curriculum for the UK. Each unit has multiple mathematical concepts within it, for example, Algebra, Measurement and Number, and our outcomes have been placed accordingly. In order to spiral these we visit each unit twice - once in the first semester and again in the second semester. In this structure we spend around 3-4 weeks on each unit per visit and in the second visit are able to build upon the outcomes that we initially addressed in the first half of the year. Because the units are structured like this, we can choose to place them at any time of the year that we wish. This lets us link our maths units more authentically with our Units of Inquiry. For example, in our recent unit on Forces and Motion for How the World Works, we decided to run the Data Handling and Measures unit alongside it as it provided a natural trans-disciplinary link.


The difficulties we are facing at the moment is that it is nearly impossible to create a central idea for a maths unit if it contains so many different mathematical concepts. The Data Handling unit is unique in this setup as it contains concepts that are only linked to data and probability, instead of many other concepts, but the others have many differing ideas all covered under the same umbrella.


This leads onto the next obstacle. With the many different concepts being grouped in each unit there is a lot to cover. It has been suggested to us as teachers that we should aim to cover some element of every single aspect of the unit during the first visit. The result is that teachers are rushing through the work in order to complete it within the given time frame. There is little time for genuine inquiry as the students are being pushed through the topics at a fast pace. One solution to this that is being trialled is the development of rich maths learning engagements that ask the students to connect their skills, knowledge and understanding of several areas in order to complete the task. The one we trialled in Grade Four (centered around 'volume') worked well and was more geared towards inquiry-based learning. It gave the students the opportunity to experiment with different arrangements (measurement outcomes) test out their own theories and construct a formula (algebra outcomes) that could be used to determine the volume of any cuboid.  They also had to calculate their answers along the way (number outcomes). It is envisaged that these tasks will then lead into inquiries in some of the areas of maths that were included in the task. Time will play an important role in this strategy as these tasks need to be developed for five units across six grade levels - and then again for the second visit for that year!


The irony of all this is that by developing a spiralled curriculum within each grade we run the risk of making the maths less meaningful for our students. I'm curious to know how other schools handle this paradox. If you do create units based on certain concepts, such as fractions, do you ensure that they are being re-visited again later in the year? If you don't, do the students have a thorough enough mastery of the concept to hit the ground running the next year or does time need to be spent on refreshing them at the beginning of the topic? If you do re-visit them, how do you make sure you've had enough time to give them their due course initially and are they addressed through the principles of inquiry?

The Negotiated Curriculum

At about this time every year I sit back and reflect on the year that is fast coming to a close. I think I have done many things right this year and learned a lot. Still, I know I have many areas to improve in and have been asking myself an important question over the past few weeks: Am I afraid to give up control of a learning experience?

By handing over the metaphorical reigns of learning to the students, teachers allow them to drive their own learning through their own curiosity. This usually results in genuine and significant inquires. This aspect of the curriculum - the role of students in decisions made about and for their learning - is valued by the IB, and particularly in the Primary Years Program:

Many different forms of inquiry are recognized, based on students’ curiosity and on their wanting and

needing to know more about the world. They are most successful when students’ questions and inquiries are

genuine and have real significance in helping them progress to new levels of knowledge and understanding.

The most insightful inquiries, ones most likely to move the students’ understanding further, come from

existing knowledge. (PYP Basis for Practice pp. 4)

It is also something that I don't find particularly easy to manage and one of my goals for next year is to really try and improve in this area.

Generally, I think I fall into one of two traps. I either expect (a) too much too early from my students and they aren't able to lead a learning experience (or don't yet know how) with their own curiosity, or (b) I don't give them enough of an opportunity.

These aren't done on purpose, of course. Sometimes I simply don't feel that I have enough time to let the students 'wonder and wander' for extended periods as I have to get through other mandated curriculum. Other times I haven't provided the students with enough opportunity to develop their knowledge of an inquiry before allowing them the chance to drive it. Then I feel worried that nothing is happening, the lesson is shallow and my reaction is to take more control.

Some strategies that I will be working on next year are:

Taking more time to really listen to my students - either as a class, in small groups or individually. Although I give my students plenty of my honest attention I am sure there must be some things that I'm not picking up. So I'm making a conscious effort next year to really look for indicators when the students are talking. I'm going to make a checklist of things to look out for during conversations so I can constantly remind myself. I'd also like to trial a few different ways of recording the information too, as this is something that I've found tricky to manage in other years.

I'm also thinking about the best ways to display student questions and inquiries as they arise. When I've attended PYP workshops in the past the facilitators have usually created a 'wonderwall' or something similar. Unfortunately these are not always re-addressed throughout the workshop but when they are I really like the way they work. It's not something I've successfully achieved in my own classes thus far so I want to try harder next year. I've tried using wallwisher before but I think I'd really like something that is up in the class and can be accessed at all times.

The next strategy I'm going to try and employ is to try and work opportunities for student input into my planning. I know that many student observations occur 'out of the blue' and can't be planned for, but I think I can facilitate these better by thinking about the type and structure of my lessons. What are my students revealing to me? How will this inform and alter future lessons?

I think it is also important that these experiences are developed around an environment that really encourages this type of behaviour. Some students may not be used to this level of freedom, opportunity or responsibility from other classes they've been in so I think it is important to model the sort of behaviour I want from my students. I must admit, I regularly fall into the trap of expecting that my students know what I want them to do without me really modeling it for them. It will also be helpful for me to provide routines and structures which they can follow - scaffolding, not controlling!