I am trying to hash out a couple of ideas in my head right now, so bear with me.

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?

I like both models 2 and 3 in terms of representing inquiry, but as you point out, going “backwards” or “moving” around the continuum of inquiry doesn’t seem to work. Although the MYP model for inquiry is by no means perfect. If you have access to “MYP: From Principles into Practice” take a look at page 21. I wish I had the graphic of the model to post in the comment, or even a web-link…but I can’t find one (only in .pdf form). Hope you have “From Principles into Practice” handy :-).

For the current inquiry model in the MYP, I like the way the arrows show that inquiry is a back-and-forth process. Where would you start the inquiry according to the MYP model? That is another great feature of the model, it has no direct starting point, it depends on the context of the inquiry. It could start at any of the three stages and proceed to either of the next two and then back again…(Reflection–Understanding & Awareness–Action).

Thank you for a thoughtful posting, Craig. It reminds me of a Ted Talk as well, about modeling scientific concepts through dance. http://www.ted.com/talks/john_bohannon_dance_vs_powerpoint_a_modest_proposal.html

Models help us understand!

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I love that TED talk. Have done something similar with science concepts…

No starting point is a great way to start thinking of inquiry…

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Another thought…what would a “helix” model of inquiry look like? Moving forward, but contracting and expanding on the way?

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I like the tree diagram. I love the idea of the multitude of possible ways the learning can grow. But where are the roots… The prior knowledge and experiences that influence the learning? 🙂

Thought provoking post -Thanks, Craig!

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I like the fractal tree -with no narrowly defined destination in mind, but a broader idea of the general direction (onwards and upwards). I like Edna’s idea of roots. I am not sure that inquiry is as regular as the fractal tree, though? I visualize it to be an irregularly shaped tree, with unpredictable sprouts and spurts. Great post! It has made me think about my image of inquiry and how that is reflected in my teaching.

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I think that is the strength of the fractal tree. It can be organized if you want it to, but in reality it will be messy, but with an emerging order.

Take a look at Benoit Mandelbrot talking Fractals on Ted:

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A double helix would be an interesting model; especially if there are small connections connecting the two spirals. It would suggest a lot of possibility and movement. Not as much as the fractal image, but it would be more suggestive than the the single spiral.

Something about me likes the idea of getting lost in the lines of the fractal tree. There is so much room for different paths and different ways of knowing. Edna had a question in her post a couple of days ago; why was Youtube invented? Immediately, it made me think of this. That question is such a great example of the multitude of possible explanations and ways of understanding. It is not because it is a difficult question, it is because it is a question with no answer. The answers are multifaceted and complex, and should be approached as such.

Also, I love what Tasha is saying. The fractal tree still suggests pattern and structure, yet inquiry sometimes doesn’t follow those rules. It is ever evolving and ever changing.

How does a teacher stay aware of the structure of the inquiry that is unfolding in their class? Do they need to be aware of it? Interesting questions with no simple answer. That is why I love this job.

Great responses. Thanks!

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The idea of spiraling back seems reflective, a way to loop prior knowledge into learning, and the tree can just keep growing as long as it gets nourishment. Teachers should expose students to many ideas. They can guide students, but should not direct them to a particular branch unless the student wants to grow in that direction. Today, more than ever, there are possibilities that we have not seen yet; therefore, as teachers we, too, need to visualize our own learning.

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The spiral does allow for looping back and reflection, but so does the tree. You travel back down branches and revisit prior concepts.

Of course these are all mental constructs meant as metaphor, it matters how we actually “do” it. This requires structure and intentionality.

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