The book I am reading has me in a contemplative mood.  My question is; how do you visualize inquiry?  When you think of inquiry, what image comes to mind?  What is the organization of that image?  What are the implications of that image on teaching, learning, and knowing?  Here are three possible images (among a sea of endless ones):

Image #1 – The linear graph

This image brings to mind an input/output system.  The teacher inputs the information into the student and the student outputs it back in the form of knowing.  We then increase along the line, building knowledge in a straight linear fashion.  It assumes that the previous knowledge has been acquired, and it therefore is known.  Think of how prevalent this is in school; linear curriculum, direct instruction, and top-down management (not to mention schedule blocks, standing in line, desks in rows; if you really wanted to tease apart all of the linear metaphors we use in education, it would take forever).  This type of model also assumes that there is a desired destination at the end of the journey.  Perhaps the line can continue to infinity, but it always going along a straight trajectory.  This type of view is problematic.  Think of a group of students, and each student is expected to travel on the line, and learn the same things in the same way.  Or, perhaps each student has their own line, and each student builds their own knowledge upwards, one piece of information at a time.  My biggest problem with a model like this (and I have many) is that it assumes there is only way path to follow, and one way to know.  That is, the way of the line.  That is the only possibility.

Image #2 – The spiral

This image is a variation on the line.  It curls back over itself (review and relearning and rediscovering) and gradually gets bigger and wider.  Near the bottom of the spiral the partial circle is small, but as the learner grows the circle and the space in-between the edges of the boundary grow, suggesting their is more room to build.  Again, this line could theoretically continue off to infinity, with the space in between ever widening, and the students perspective of the world ever increasing.  Many curriculums are built on this model, as each year there is a gradual increase in the level of difficulty after a brief review of what was studied last year.  Assessment takes on this form as we build formative tasks that finish off in a culminating activity that is designed to widen the circle and encompass all that came before it.

Yet, it is still a line.  It still suggests growth towards a known goal (knowledge?).  It makes the assumption that there is only one possibility, and that possibility moves in this shape.  It is still, at its core, a simple model and simple view of how we know.

Image #3 – The fractal tree

This image is taken from fractal geometry.  It starts with a simple seed, in this case a Y.  There is only one rule to build this image; at the end of every branch of the Y, build another Y.  If the rule is allowed to iterate, we get a picture that looks very much like a tree (using this seed, other seeds may cause other images).  What is the seed?  The person, the idea, the curriculum, the content?  How this relates to inquiry is obvious; as you travel along the branches of inquiry, you are faced with an extraordinary amount of choice. Do I go this way, or that way?  The branches you travel along will bring you to different points, with different perspectives.  Students, and teachers, are free to choose a path that is interesting to them, based on their own perspective of what they are learning and how they are knowing.  This image too can continue into infinity.  Also, in the other two diagrams, what happens if you were to go backwards on the line or the spiral?  Well, it would result you going back on your learning, or your circle getting smaller.  In this case, going backwards should be encouraged, because it opens up more possibilities, and presents different paths and ways of knowing.  Then, if we accept this image as a metaphor for inquiry and learning; what is the role of the teacher?  To help their students see as much of the tree as possible?  To orient students to a particular branch?  To create an environment where there are endless possibilities?

Any other images or interpretations come to your mind?

Quad blogging, which has been called the most interesting development in the last 20 years of education, is basically a group of four classes with blogs.  Each week one of the classes is a focus for the others – to visit their blogs and to leave comments for the students.  Recently I was contacted by Silvia Tolisano who wanted to use quad blogging to investigate the benefits of blogging on 3 different levels: for the students, the teachers and the curriculum – of course I was keen to join in with the inquiry.  Our quad is made up of four schools in four different countries:  the USA, the Czech Republic, Thailand and Switzerland.

Last week we had a Skype conference call where we talked through the form our action research will take.  We talked about the fact that good blogging starts with reading other blogs and so it would be necessary to set aside time during the four weeks of the quad blogging to focus on reading each others’ blogs.  We discussed different ways we could do this, for example have a Drop Everything And Read a Blog time each day.  We decided that it is important to set up a routine for reading the blogs, before we start to think about how to reply by writing comments and we all felt that this should be part of the normal reading and writing lessons not an add-on.  We discussed the way that students read blog posts now and about the fact that some students don’t really read a post in depth but just jump around in it.  To encourage students to read in more depth, we thought it might be valuable for us to set aside time for student to talk about and share what they have read.

Our quad is made up of students from three different grades – one class of Grade 3s, two clases of Grade 4s and one of Grade 5s.  In addition there are students who are learning English as an additional language in all these classes, and in one school the students are bilingual English/Hebrew speakers.  We felt it important to let the students know that we don’t expect all the writing and commenting to be at the same level.

We talked about the fact that we should make sure that each student in the class is assigned one student to post a comment on, but that after that we can encourage them to respond to as many others as they like.  We think it could be a good learning activity to reflect on why some students’ posts get more comments than others.  Perhaps if a student only gets one comment this might provide us with an opportunity to teach about improving the quality of their writing or how students can increase the amount of comments they receive – for example they might need to network more and perhaps leave more comments on other students’ blog posts asking students to get back to them.  We can teach students how to add a link back to their blog post into their comments.  Above all we thought it really important to ensure that in the week that is focused on their blog, the students reply to the comments they have received.

In order to know if quad blogging can improve student writing we need to do a pre-assessment so we know what level the students are already writing at.  Silvia developed rubrics for writing and for commenting.  We decided we would ask each student to choose a blog post that they have already published this year so that as teachers we could use this to pre-assess the writing using the rubric.  Then we will ask them to choose a comment that they have written on someone else’s post and self-assess their comment based on the comments rubric.  This way we will have both a teacher- and a self-assessment before we start the quad.  At the end of the quad blogging we will use the same rubrics to see if they have improved on the posts and comments they are making.

Our action research is focused on 3 main areas:

• Students – how can they improve blog comments and posts?
• Teachers – how can we become better writing teachers using blogging as the genre of writing?
• Coaches – how can we best support teachers?

I was a facilitator by means of my membership on the elementary Learning Council; a group of teachers and administrators responsible for instructional leadership in the PYP at LCS. We were all responsible for helping facilitate one of the lines of inquiry or contexts: Language Arts, Technology, PYP Induction and Concepts (as chosen by learners). To start off, we set up provocations to tune teachers into the contexts and ultimately refine their questions and goals for the process.

The following is my reflection during and after the tuning in phase as shared in an email to our elementary principal:

I’ve been thinking about last week and the “launch” of inquiry groups in the ES. Personally, I think it went as well as can be expected- we are asking teachers to get out of their comfort zones and be active agents of learning in their own PD -learning is uncomfortable!!!

I think understanding of this approach to PD will develop -I have faith in the inquiry process. Teachers will understand that they can use this time to inquire in their own or in a small group’s way into something relevant to them within one of the contexts build on their own goals.

As a Learning Council we need to continue to support the “immersion” and tuning in to the contexts as we work to formulate questions based on goals. Throughout the process we sponsor learning, directing to resources, trying to keep the inquiry process on track, asking guiding questions, supporting development of inquiry plan, attending to differences/challenges… 

Our summative reflection or evidence log will help teachers understand the inquiry process explicitly and hold us all accountable for our learning at the different stages of the inquiry. This will also help us measure the success of this inquiry based approach to PD. 

The Learning Council met weekly to discuss the successes of the current phase of the inquiry and to support each other in planning for the next phase. There was often some hesitation and confusion on the part of some of the learners and even for ourselves as facilitators –we were all charting new ground. There was some trepidation about the direction we should go next and how we should get there. Another challenge for the Learning Council members was that we all had our own questions we too wanted to investigate. Figuring out how to manage our own learning and facilitating for others was stressful. I tried my best to keep us focused on the Central Idea, the concepts and the guiding questions so we were all on the same page and understood where we were going.

In my own group, teachers were off and running in different directions and at different speeds. It was becoming more exciting as we delved deeper into our context by reading on the subject, trying different things out in our classes and working to plan with the concepts in mind. From one of our sessions and specifically related to one group member’s inquiry looking at explicitly organizing engagements according to the focus concepts, together, we came up with a planning tool/table (Conceptual Engagement Organizer (Celebrations KG). We all agreed to try out the tool. The buy in and enthusiasm was picking up. We flew through the sorting out and attempted to go further by really affecting our practice. All whilst documenting the types of things we were doing and learning at each phase of the inquiry for our summative reflection. We planned to share our learning in my group through a poster presentation including our questions, the evolution of our new planning tool and how we used it, my survey results from my own inquiry into how experienced PYP teachers at LCS understand and are using the PYP key and related concepts and our reflections on the process. We felt quite proud of our group’s accomplishments and excited about our learning.

I think, the sentiment was shared, as we set about sharing our learning last week. We were walked through personal reflections from the Language Arts context, the PYP induction group gave us a great refresher of the 5 essential elements of the PYP, the tech group organized a gallery exploration of the tools they’d discovered and experimented with and of course my group had a cruise by poster board set up for perusal. I was moved to tears at how engaged all staff were as different groups presented their learning but also by the appreciation colleagues had of one another’s learning. It was meaningful, it was collaborative and it will no doubt have an impact on teaching practice and our collective understanding of inquiry at LCS.

Of course there were a few teachers who put less effort into the process and resultantly got less out of it. You can’t please everyone…My next dream though is to align this process with a Learner Profile reflection and have it tie even more closely into supervision and evaluation and maybe that will help inspire those who are on the fence about being inquirers themselves to take more responsibility for their own PD. That said, having been an initiator of this approach to PD at the school and having worked hard to coral colleagues as learners and facilitators to follow our set framework, I am very satisfied with the overall results.

You can check out the PYP Planner charting the whole process in the attached word document: Inquiry_Groups.

As part of the Technology Inquiry Group, I looked into how iPads can be used to support struggling and reluctant readers. Enthusiastic about the topic, I jumped right into the Finding Out phase, reading how iPads were used by other schools and libraries and what apps they recommended. But then I had my first important lesson: while I was discovering excellent resources around iPads in education in general, I suddenly realized that I had lost sight of my main inquiry and found myself completely confused. Fortunately, my facilitator Sarah Pickles and the guiding questions for each phase of the inquiry model helped me to get back on track. It made me realize what an important role the teacher/facilitator plays during inquiry, helping the learner to stay on track by constantly reconnecting to the Central Idea.

I felt very much back on track as I was sorting out what I had discovered and made sense of what I was learning at the same time. I realized that most probably the most powerful element in the use of iPads with struggling readers is that they turn reading from a task into a fun activity. Of course, there are several features within the apps that support the reader in various ways, e.g. reading the text or individual words out loud. I began to wonder how I could best put my learning into practice.

These new tensions and wonderings provided the basis for the Going Further phase during which I tried to find additional answers and put some of my new knowledge into practice. However, I had to make a change to my original plan since the first opportunity I got to use the iPad with readers was with a group of confident KG students for whom this would provide an extension of their reading experience. The idea came from their teacher Miranda Rose (she is one of the facilitators of this PD inquiry and her reflections are available on this blog under “Teachers as Inquirers – Reflections from a Facilitator”). Until this point, I had never considered that iPads could be as beneficial to high-performing readers as well as to those struggling.

While Drawing Conclusions, I not only summarized my findings regarding the use of iPads with readers but also my experiences in going through an inquiry cycle as a learner. I think these were the really powerful outcomes of this learning experience for me, gaining a better understanding of my role as a facilitator while experiencing the challenges the learner is faced with. I therefore want to share all of them with you as I recorded them on my wiki page (by the way, the wiki page also represents my summative assessment):

• There never seems to be enough time to get everything done, that we would like to do.
• Answers always create new questions and it’s okay that the inquiry somehow never ends.
• It’s important to keep the fluidity of the inquiry cycle in mind, there are no strict boundaries between the individual stages (I have experienced that sometimes I am finding it challenging to say exactly on what phase I am, e.g. is it already Sorting out or still Finding out etc.).
• The role of the facilitator is extremely important in keeping the learner on track/on task and re-connecting to the Central Idea constantly.
• No matter how big or small the initial question or wondering, the inquiry process can always be applied. Often we go through the process without being aware of it.
• Inquiry requires personal initiative and engagement – you can’t expect that everything gets done in the allocated time. Thinking about students, wouldn’t the ideal be that they follow up in their own time too?

You can read more about my journey through this inquiry cycle on Tanja’s Page of our Technology wiki.

• Leander: Here is so many!
• Nikhil: Yeah, one hundred!
• Leander: I think one thousand.
• Nikhil: No, it’s more. It’s ten hundred. And even a hundred hundred.
• Hal: A thousand hundred.
• Trenton: A million.
• Hal: A billion.
• Leander: A million hundred.
• Nikhil: No, because million is the biggest.
• Trenton: But nothing is biggest because numbers never stop. They always not stop counting because always more
• Nikhil: But not more than a million.
• Leander: I think two hundred 0r one hundred
• Hal: But we can’t count because there is too many.
• Nikhil: But we can’t count.  How we can count?  Too many.
• Trenton: But we can still count.

As I listend to the conversation it occurred to me that there were several possibilities for further exploration: the infinite nature of numbers; place value; estimation; counting large numbers. I have observed that recently quite a few of the children have shown a particular interest in counting large numbers so I decided to follow that line of inquiry.

At our next meeting, I told the children that I had noticed that many of them seemed interested in counting big numbers, and I wondered if we should make some time to explore this more.  The children responded enthusiastically.  ”I LOVE to count!”, said Rika. “Me too!”, rang out a chorus from other children. For this engagement I had decided that I would group the children, rather than having them choose their own partners.  I paired some children with partners of a similar ability and paired others in mixed ability groups, depending on the children’s social and developmental needs.  I decided not to give the children much direction at this stage, and to observe carefully to see what they did.  I was particularly interested to see what counting strategies the children would use when faced with a large number of objects (between 100 and 1000).  In math circle times, we have been skip counting in twos and tens. I wondered if any of the children would transfer those skills to a hands-on counting task.

Throughout their inquiries the children were engaged and focused.  There was a purposeful hum of activity as the children went about their business, trying out strategies, encountering logistical problems and coming up with new strategies to overcome those problems.  This will be an ongoing inquiry. The adults in the team have been engaged in conversations about how we can best support the children in their inquiries. We wondered at what point we should intervene and model the strategy of grouping in tens. For now, the children are engaged and motivated and are clearly learning so I see no need to intervene. Finding out for oneself is so much more powerful than being told.

We were working on area of a circle and the class was trying to get their heads around all the different parts of the various equations.  I tried to make it interactive earlier in the week by having them rotate pencils, where the pencil could be either the radius or the diameter.  This would lead to two very different circles.  Once we had the radius or the diameter, we could plug it in and find the area, or the circumference.  This series of lessons was created by ME, the teacher, and given to THEM, the students.  For some, they go it.  For others, it wasn’t sticking.  I had to try again.

Next time, I thought I would do the same lesson, but the kids who got it would teach the kids who didn’t (Aside: I realize that I sorted and classified my students into two camps, whose that get it and those that don’t, and I have singled them out from the group.  That is on purpose.  As a community and a team, it is imperative that we tell each other when we are unsure of something, so those that do understand can help those that don’t.  There is no shame in not understanding and asking someone who does for help.  If all work together, we all go further. End Aside)  This however, wasn’t working either.  Until, one boy got down on the floor and started spinning.  I immediately got everyone involved and watching this odd display.

Everyone watched as I grabbed this student and spun him around his center point.

He is the diameter, one child said.

What would happen if he was the radius?  another asked.

As soon as I said that, the kids were off, rotating around on the floor, trying to be the radius or the diameter of a circle.  I asked them to draw a picture (or use Pages on a MacBook) to find as many values of a circle as they could and be as specific as possible.

This was a great learning experience, but it was one that I could have never planned.  If I did come up with this idea, and tell the kids to do it, would it have been the same?  Instead of coming from ME, and going to THEM; this activity evolved from THEM and stayed withTHEM.

In this scenario, what was my role?  Where do I fit into this system?

I guess my question now it this; in a decentralized classroom where the ideas are evolving from the collective, what is the role of the teacher?  Are we a part of the collective?  An agent in the system?  Or do we have a bigger role to play? Perhaps, we serve as the consciousness? (This is an idea put forward by Brent Davis at the University of Calgary, you can download the article here, it is called Teacher as Consciousness of the Collective).

I don’t know (and never will!).

To teach well, I have to be able to learn from others. Teaching is a conversation with a learner. This means accepting learners as whole people and genuinely listening to their thoughts.

I think of all the times in class where I have short-circuited an avenue of inquiry by bringing a student’s wandering curiosity back to the immediate syllabus and the requirements of the approaching high-stakes test. “That’s an interesting question, but let’s stay focused on the topic at hand” is a refrain that I am all too guilty of overusing in my own teaching. Stable programs and a culture where curriculum is locked in are not the hallmarks of good pedagogy.

Each student departs a lesson with their own personal interpretation of what was taught. The teaching and learning process is an interaction with the environment, a mutual, reciprocal interaction which is experienced differently by each developing person. In the classroom this is rarely a one on one interaction. It is a tenuously forged group learning that weaves together the different understandings of each disparate individual. Rather than being a one-way transmission of information from the teacher to the students, it is a dynamically interactive relationship. Just as students learn from teachers, in the process of teaching, teachers also learn from students. Teaching is a process of permanent inquiry, perhaps best conceived of as a reflective conversation.

I had made an entirely different plan for the morning but Carl’s plan seemed more important. I abandoned my plans to follow this initiative, intrigued to see what the other children would make of the math inquiry. As the children came in, they read the message and discussed the content with each other.

Jenny Hmmmm. Well I dont think that Carl is the boss.
Saku Because we are all the boss of us.
Eileen But its not boss, only idea.
Lisa I think it’s a good idea.
Aika I think its a good idea because we can learn in inquiry
Lars I agree with Aika, I like it.
Anish Me too, like it.

The children began to explore the equipment that Carl and Eileen had set out on the tables. For the next hour, the children were deeply engaged, experimenting, hypothesizing, testing, comparing and discussing. Some children spent the whole time involved in one inquiry. Other children moved from table to table. As the adults observed the children at work, we remarked on how independent and motivated the children were and reflected on the power of children following their own interests and having an input into what and how they learn.

A Math Inquiry on PhotoPeach

http://photopeach.com/public/swf/story.swf

The children’s interest in measuring continued. A few mornings later, Aika suggested we have “a measuring inquiry”. I asked the children what the inquiry would be about.

• So that we can find out stuff about measuring.
• So we do inquiry so we know how to measure.
• I know already.  You need stick.
• A long stick with lots of numbers on.
• You can just have short stick and you can stick together.
• No need numbers.  Stick.
• Yes!  Need numbers.
• The numbers tell you how big it is.
• But you can do it with no numbers if you count.  Then you dont need numbers, you just have to count.
• You need a short stick for measuring short stuff and a long stick for measuring long stuff.
• If there is no numbers on the stick you have to write them on.
• Kilometers is for measuring.
• Kilometers is for measuring roads.
• And houses.  And there’s 100 kilometeres.
• You have to measure because if you want to make a house it has to be the proper size.
• More than one kilometer.
• Otherwise it will be a funny shape.  Like a octagon.
• Not a funny shape, the wrong size.

The children spent the morning inquiring. That afternoon, I read them The Fabric of Measurement. This beautiful, hard-backed book documents a measuring project carried out by some of the KC children when they were in the ELC. In the days that followed, the children eagerly continued with their personal inquiries into measurement of length.

http://photopeach.com/public/swf/story.swf

A few mornings later, in response to the children’s ongoing interest in measuring, I asked the children if they would be interested in measuring each other. Saku clapped his hands with delight. “That’s an excellent idea!” proclaimed Lisa. “Let’ measure who is the biggest” suggested Aika. “Carl! Carl is biggest” cried Issey.

The children began to organize themselves into a line. This prove to be quite difficult. Everyone had different ideas and the children struggled to find a consensus. I wondered whether I should intervene or not. I observed for several minutes and finally stepped in when I felt the children were becoming frustrated. After a little input from me, the children came up with a common vision and I returned to the background as an observer.

The children organized themselves into a line and took turns to see if everyone was in the correct order. Once they were happy with the result they spent a few seconds enjoying their achievement till Jenny wondered, “But how will we still know? We can’t stay here all the time, like all night and for ever, don’t you know!” “We can do a list.” Eileen suggested and quickly got a clip-board and paper to record this data.

This morning, we looked again at the list. I pointed out that now we know that Carl is the tallest but we still dont know how tall he is. Lars asked Carl to stand up, and the measuring began.

How tall is Carl? on PhotoPeach

http://photopeach.com/public/swf/story.swf

This is an ongoing inquiry. It has raised questions which will help the children to understand the need for standard units and a degree of accuracy. I resist the temptation to give them answers and wonder instead where the children will take this next.

Why are schools so resistant to change?

Is it because of the entrenched patterns of institutionalised social relationships in schools? Is it due to the separate culture that grows within a school, binding personalities together and separating the school from the surrounding world? Is it because almost every aspect of our work lives reinforces conservatism? Is it because prior to taking up our first teaching post, we have already been encultured for sixteen years in traditional patterns of thought and practice via our own schooling experiences? To what extent does indifferent teacher education and the abrupt, isolated introduction to the classroom lead us to fall back on the long apprenticeship of observation that we undertook as school students?

Why do students accept the mass custody of the current system and view it as a rite of passage? Why is going to school an important democratic ritual? Why is there a contradiction between the structure of schools and the espoused purpose of schools? Why are schools so passive, and why do they protect the status quo? Has a mechanistic emphasis on reductionist science progressively developed schools into more and more unhealthy institutions? Is the obsession with attendance rates, dropout rates, test scores, and suspension rates an unpleasant parody of Vietnam War body counts? Are accountability, standardisation, and bureaucratisation the only means of controlling the unwieldy structure?

I’m a great fan of the Project Zero Visible Thinking program and its ‘thinking routines‘ which provide simple structures to support student thinking and questioning. If you start a unit of inquiry with a powerful provocation that hooks students into the big ideas, followed by an appropriate thinking routine, like ‘See Think, Wonder’ or ‘Connect, Extend, Challenge’, or ‘Question Starts‘ you’ll have kids asking great questions right from the start.

What do you do with student questions?

If you’re an inquiry teacher, you’ll know it’s not just about providing answers! We’ve spent some time recently exploring ways of analysing students’ questions. Here are some approaches that we have tried:

A range of student questions were gathered, printed off and cut into strips, one question on each. The ‘central idea‘ (enduring understanding), lines of inquiry and key concepts were printed on another sheet. In pairs, the teachers sorted the questions in any way they chose. Some assessed the questions’ relevance to the central idea. Others grouped them by concepts. Another group sorted them into deep and shallow questions, ones you could ‘google’ for a quick answer and ones that would lead to deeper inquiry. Irrespective, there was careful consideration of the questions and great conversation ensued as a result.

In another session, a group consisting of teachers from different grade levels analysed a set of questions from a Year 1 class, using the LAST protocol from Project Zero, which includes these steps: explaining the task,  describing the work,  speculating about students’ thinking, asking questions about the work and  discussing implications for teaching and learning. The Year 1 teacher (who didn’t participate till the fourth stage, as per the protocol guidelines) found the suggested directions and strategies for future teaching and learning really valuable.

In both sessions, the questions revealed where learners were in terms of their understanding, misconceptions which needed to be corrected and areas of interest, which could guide where the teacher might take the inquiry next… or where students might go with their own inquiries.

We’re planing on developing the process further next year. Really ‘listening to’ and analysing students’ thinking reveals a great deal about both the learners and the learning process. Documenting and tracking students’ thinking and questions over time would reveal even more about individual learners… but that’s another story for a future post.

Flickr image by Dom Dada.