“Think of this as a path,” I said to my students.  “It’s here to help you see where to go.”

I was referring to a rubric that I created for our recent unit on geometry, architecture, and machines.  I had deconstructed each of the standards we’d be working on to scaffold the experience for them.  I find that rubrics, while linear, help ground my lessons, the students, and even myself, when things become complex and the purpose becomes unclear.  It gives us a common language, a place to which we can go back, and most importantly, a common vision of where we’re trying to go.  But I’ve started to think lately that maybe “vision” isn’t necessarily the right word; instead, perhaps it’s just the general direction in which we’re going instead of the actual destination itself.

This idea, though, of having direction without destination may be somewhat challenging for educators.  I know that, when I began as an educator, I fell into the trap of making my teaching too linear.  I made some grand assumptions, partially drawing upon my own experiences as a learner in elementary school, about the way teaching and learning should be.  I assumed the process was a straight line, with skills building upon subsequent skills.  This assumption wasn’t necessarily incorrect, as there were and will continue to be many times when a linear approach is helpful.

But there are also times when it isn’t.

Last week, I had the pleasure of meeting with one of our external resource providers, who consults with us on students with learning differences. We ended up having a conversation about teaching, in general, and this very conundrum of the balance between linear and non-linear processes in teaching.  Specifically, she called these two seemingly opposing paradigms “linear” and “simultaneous processing,” and while I don’t believe it’s necessary to label teachers as one or the other, I do think it’s important to recognize the pieces of ourselves — and of our craft — that are linear and non-linear.

Screen Shot 2015-04-21 at 6.17.25 PMLinear Thinking

Linearity is an essential part of what we do.  Knowing how skills build upon one another, and developing an understanding of how to deconstruct outcomes is essential when learning how to scaffold.  Further, being able to model sequence, both implicitly and explicitly, will not only teach students academic skills in reading and math, but it will also teach them the soft skills (i.e., executive functioning, planning, and perseverance).  However, confining students to unidirectional linearity may hinder creativity and problem-solving.

In fact, I sat in the Teachers’ College Workshop (@TCRWP) yesterday, pondering this linear/non-linear divide, while listening to our presenter speak about Webb’s Depth of Knowledge.  She discussed, specifically, how Webb’s depth of knowledge, while parsed into four discrete levels, was anything but linear. But in a way, I still saw it as such.  I wondered how a child could reach a deep level of knowledge without understanding the shallow levels first.  But then I thought of some of my brightest thinkers, and how non-linear their thinking is.  And even though it may seem like they’re jumping levels, I don’t actually believe this is the case.  Instead, I wonder if it simply speaks to their demonstration of this depth of knowledge, and an inability to discretely demonstrate the lower levels of knowledge… even though they are there.  Perhaps that’s where simultaneous processing comes in.

Screen Shot 2015-04-21 at 6.23.00 PMSimultaneous Processing

I imagine simultaneous processing somewhat like a web.  Clusters of dots come together, and lines begin to connect each of these dots, creating multiple pathways and corners within the web.  I find this especially helpful to think of when hoping students will construct knowledge on their own.  By giving students a linear process by which to acquire new knowledge, they lose resilience as well as the ability to think critically about process.  On the other hand, by taking a simultaneous approach — one where students are encouraged to uncover facts and make connections independently — students learn to be flexible, responsive, and adaptive.  As a result, kids learn that it’s not always going to turn out how they’ve expected and that they’ll have to change.

“It’s about collecting and connecting dots,” I always say, “not about just doing what your teacher told you to do.”

However, even within this simultaneous approach to research, teaching, and learning, we find elements of linearity and remnants of patterns formed over time, much like the synapses in our brain.  While our brains are also an interconnected web of dots, lines, angles, and vertices, this interconnected web would be impossible if not for the linear movements between synapses — if not for the fact that our synapses fire from point A to point B.

Leonardo_polyhedraThinking in 3D

But lately I’ve started to think, what might happen if we combine these two seemingly discrete ways of thinking?  Is it, in fact, possible to break free of this dichotomy and to actually identify both types of thinking within one setting or experience?

I think it might be, if we add a third dimension.

The first two types of thinking, when examined independently map most effectively in one- or two-dimensional spaces.  A line consists of only one dimension, while a web has both length and width, but perhaps by combining these two thinking modes, we create a third dimension of thinking that entails an intricate balance of both.  In this three-dimensional way of thinking, dots of knowledge create lines of understanding that form three-dimensional webs of synthesis, much like a human brain, with synapses linearly firing on a microscopic level to create volumes of knowledge and understanding macroscopically.

Reflections and Conclusions

We cannot confine ourselves to one paradigm of thinking.  Teaching, learning, and thinking exist in three-dimensional space, with sometimes very clear patterns that emerge, and other times, unclear puzzles that need to be solved.  By operating in this three-dimensional space we allow ourselves the structure and flexibility to be thoughtful when responding to student needs and helping to build a resilience in our students.  What’s most important, in my opinion, is that we find the times and places that individual students benefit from each of these ways of thinking, so that we can maximize each of them and, in turn, maximize student learning.

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