Non-linear learning techniques: Teaching by leaps and bounds
What if learning happened in equal intervals on level ground in fairly predictable ways and at a roughly estimable pace? Then most of our textbooks and educational methods and teacher training would be just right for the task. But learning doesn’t and, therefore, they aren’t. The learning curve really is a curve!
That might just be a rather big deal. I’m not claiming no one has ever recognized this disconnect. Many have and worked to do something about it, but our natural tendencies keep drawing us back into the organizational paradigm which is at odds with the way our brains work and the way we really learn.
If we graph learning over time, we really do know that it follows a rather erratic curve, but one which is most often much closer to one side of a parabola than a straight diagonal line. But how often is teacher training designed to encourage “learning parabolas”? This is true for schoolchildren, but also for workers in training and just everyday adults learning to do new things. It is also true both of learned competencies and deeper learning where perspectives and paradigms change.
Many of us adapt to this reality as we learn the ways we learn best. And then we are often frustrated by it when we find ourselves in a linearly ordered instructional situation like a training session or a formal course for credit. For the way you really learn, you start slowly and then pick up the pace rapidly as you get the hang of some of the basics and begin to accelerate your learning. Most curricula, much training, and almost all teacher preparation still fit the straight line better than the accelerating curve.
To be complete, it is also true that some learning looks most like one side of a hyperbola, gaining rapidly until it approaches a limit line and then growing only ever so slowly as you fine tune your learning in a particular area. Learning progress is still not a straight line sort of thing, though.
Consider a simple illustration. I assemble a new bike for my son to be waiting under the tree, Christmas morning. I follow the written and illustrated instructions. (I know. What a dweeb!) At the end, the bike is together (It did actually have all its required parts this time.) and I have followed a linear path of assembly which may be a path of learning, also. For me, who is neither very mechanically nor spatially minded, I’ve probably learned very little but I did get the bike together. Next time, I will still need the instructions.
Conversely, my son is learning to ride the bike. Maybe I use a linear component of learning with training wheels to get the hang of steering and braking, or maybe I don’t. Still, learning to ride a bike is that muscle and body sense of balance which comes with practice being pushed and balancing a little while and then falling down, only to get up and try it again. Once he ‘gets’ it, he rarely falls, and then only because the basic conditions of speed or terrain or obstacles changed. And he can ride other bikes and even motorcycles (if we would let him). That is a very non-linear process of learning where progress seems non-existent at first but then rises dramatically. It’s probably more of a ledge of learning than a parabola in this case, but you get the idea.
This is a huge area of learning theory and practice, but we can start to get a perspective on it through five key examples.
Curricular scope and sequence || Pacing and the division of content and skills into lesson units structured often around alignment to some set of standards and usually keyed to chapters and units in textbooks and other curricular materials.
Building learning culture || Where we prepare an environment and behaviors in a class setting and among students so that they can engage and invest in their own learning.
The Carnegie Unit vs. competency-based credit || Time served contrasted with abilities acquired.
Bite-sized pieces with action sized packaging || Shaping learning occasions to fit attention span while structuring a learning program where students gain real abilities in order to practice them.
Personalized learning || Trendy buzzword but also revolutionary potential for learning advances.
1. Curricular scope and sequence
We often divide curricular objectives into lessons of substantially equal length for which we create pacing charts based on the calendar and the length of the textbook, truncated perhaps and prioritized some, but still largely determinative of the shape of instructional time.
I won’t claim for a moment that it’s easier to work toward a non-linear alternative, just that it’s better. Our learning objectives, our lessons, our pacing, our textbooks, our class periods, our school day, and our school year should all look more like the way we learn, rather than the way we build spreadsheets with nice even grids. Ironically, with spreadsheets, we allow ourselves the choice to reformat and change the width and depth of cells, rows, and columns. With school, we more often get frustrated that we weren’t better planners or that the kids weren’t more attentive and engaged so we could have covered the material it made sense to cover if our pacing chart for scope and sequence was going to get done.
This is not a topic for flippancy. It is hard to put true flexibility and non-linear arrangements of instructional time into our plans and our days. But if that’s how learning happens or happens best, it can’t make much sense to continue ignoring it. The same could be said for corporate training. And certainly the whole subject should show up in teacher preparation if we expect it to show up in the classroom.
2. Building learning culture
The whole concept of building learning culture is recognition that conditions and preparations for learning are a non-linear, yet essential, component for encouraging learning to happen and even allowing it to ‘get prepared’ and then ‘get rolling’. Whether it’s Daily Five strategies for growing student independence, Workshop methods preparation for student engagement and interaction, or class environment preparation through Harry Wong on “classroom management” (though I continually struggle with even the terminology used in such an extrinsic, behaviorist endeavor), these and so many other approaches to learning culture in our classrooms acknowledge that we break the hold of friction first to then build momentum in our ‘learning car’ to then navigate the course of discovery at varying speeds as the hills, flats, twists and turns come along the way.
3. The Carnegie Unit vs. competency-based credit
We’ve “done our time” in course work with the Carnegie Unit since about 1910 but used competency placement in one-room schoolhouses before and are beginning to move back into knowledge and abilities acquired standards for credit. For a time, some objectives of American education probably benefited from standardization of seat time but it never was the way learning really happened.
4. Bite-sized pieces with action sized packaging
Attention span is a human fact and means that learning must occur in some bite-sized pieces, though the time variability of learning engagement at the video game and learning in the class lecture is astounding. But just as importantly, learning must be packaged in such a way that students learn how to do new things so that they can see they have learned and can practice what they’ve learned. There’s more recognition of this point in corporate or vocational training, though even there, schedule demands often take control away from learning progress.
A good example is the story of Singapore Math (here just highlighting one of several important characteristics), where it was recognized that the students regularly beating much of the world in math competence and understanding was covering fewer topics each year than those they were beating, especially the United States ranked somewhere around 17th. American curricula were covering perhaps 25 topics a year but through a pattern of introduction one year, mastery a few years later, and then practice in years to follow. Inoculation rather than learning started the process, little deep-running mastery was achieved in the middle, and forgetting was more the characteristic of later practice. A single geometric or algebraic concept appearing 12 times on the grade chart of scope and sequence for a math textbook series seemed to be such good planning, but the planning took little account of the shape of real learning.
Human beings learn when they learn they have learned something and can really do something with it. If they’ve been ‘curricularly covered,’ they tend to be aware of that as well, even if they are children who are too young to describe it as such. Further, if equal weight is given to most all learning objectives in single instructional engagements (though the concept, if important, may be salted in a number of times later), we have blatantly ignored the non-linearity of learning. If the point is foundational, it should look different in our instructional plan, should be attacked with intentions of mastery, and then certainly should come up many more times in applied work because it was foundational to the subject.
5. Personalized learning
The machines may well help us through this quandary. Though digital programming counts on linear algebra for foundational grounding, computer software may well be what it takes to help us shape our instruction in non-linear patterns. Personalized learning is certainly a preeminent buzzword today in educational circles, but it doesn’t have to be either meaningless or impotent just because it is popular. I’ll return to discussion on this, but the point here is that the whole area of personalized learning takes the old if/then path divergences of instructional programming and transforms by applying to real effect the lessons of artificial intelligence and context adaptive software. We may even see some fuzzy logic and q-bits enter the practical picture over the next decade.
Just as it’s a big deal that our instructional planning so often looks linear while our learning is not, it’s also a big, new, hopeful deal that our instructional programming may be blazing trail in a teaching world which can begin to fit our learning world.