I wanted to come up with a name for a certain type of rhetorical fallacy or subtle error in reasoning that I’d often hear or read about in regards to learning theory, but for which I’d previously had no label for. The fallacy is to do with learning theory – more specifically it’s a fallacy of false assumptions regarding simplicity versus complexity in study and craftsmanship, and how skill-cap relates to learning curves. OK in that respect, I suppose it’s a two-part issue tangent…
First, a learning curve just means loosely how easy/difficult an object (physical thing) or concept (idea or abstraction) is to comprehend, use, get into, master, etc. In fact, Wikipedia defines it more objectively:
“A learning curve is a graphical representation of the changing rate of learning (in the average person) for a given activity or tool.”
For example, a musical triangle might be said to have a “gentle” or “gradual” learning curve (or not!), meaning there’s a faster rate in meeting your learning goals; whereas a harp might be said to have a “steep” or “difficult” learning curve (in comparison), i.e. a slow rate of learning. This may be to do, depending on one’s theory or goals, with the ease or difficulty with which a learner grasps the basic operation of the instrument in question. E.g. how hard it is to strike a piano key vs. harp string vs. triangle frame accurately to produce a resonant note; or how painful this is on the fingers and how this affects learning time compared to another instrument.
But how could we possibly know how capable we may potentially become at a given art or craft, in order to know how to set the learning curve?! This is what masters seem to do; push our expectations of what can be achieved with a certain craft or skill-set. I mean, if something begins easily, then all that’s happening in terms of your learning is that you’re then mastering more of it, and faster, and so pushing the boundaries (going “up” the learning curve faster), and thus bumping into more difficult concepts or techniques again! So we’ve gone full circle and you’ve hit you’re skill cap.
Do we somehow statistically “average out” a given population’s skill cap to measure skill and success?
When I see or hear about learning theory fallacies, it’s usually because someone’s wildly presumed something about a given discipline, such as:
“It’s so much easier to learn to build a simple sand castle than to sculpt a complex ice figurine. Sand castles are for amateurs, whereas sculpting ice is for true artists and masters!”
Or perhaps it takes the form:
“There’s only so much you can do with a sand castle; you’re limited in scope and building materials and can build far from the sea initially, with predictable timings for water coming in. With ice sculpting, you have to consider so many variables: light & transparency, temperature/melting, complex tools, surface details, and so on.”
(OK, I randomly picked sand and ice for some reason out of my head and know virtually nothing about these two arts, just for the record! Just stay with me here…)
In sole terms of quantity of strings, the fiddle is “superior”. That is simply to say, if and only if I assume “more strings is better” – only then would I conclude the fiddle is superior; by definition/context only and not of intrinsic fact. This is because “better” or “superior” is otherwise utterly subjective, i.e. SUBJECT to we the observer defining (as part of our gedanken) our specific goals and criteria for success. And by “success” we only mean to select over other choices according to an item’s accuracy in meeting given criteria; or that which we suggest/recommend as the preferable option based upon those criteria. It is precisely because learning is a dynamic relationship between the object of learning (a math puzzle, an instrument, a sand castle) and the subject i.e. the learner that its measurement and definition always invokes a high degree of subjectivity.
We may use ‘quantity of strings’ as one criterion for judging a potential learning curve, perhaps because: (1) it seems intuitively obvious to us that more strings loosely equals greater learning complexity (i.e. possible variations for expression/output) – and is thus a harder instrument to master/develop (more variables, factors); or (2) a one-stringed instrument seems psychologically easier (as sort of inverse placebo) to our learner – and thus might be picked up quicker by them e.g. reduced learning stress.
You see, these are just a couple amidst countless factors in analyzing learning complexity and we’ve already had to make assumptions and speculations. For measuring outcomes we’d probably have to start using a good-old SMART system to be as objective as possible! At least by pre-agreeing a logic structure or SMART criteria in our learning system we can avoid key terms or goals being muddled or causing confusion and disagreement (subjective interpretation).
How do we approach learning objectively? Well, it’s not a riddle. I think it just requires some empathy towards the sensitive and subjective experiences of learners, a check on our own assumptions, the context and setting, unambiguous definitions and the use of those key terms. There is and never will be any “objectively better” learning methods, principles or environment. Not only because “objectively better” is an oxymoron by casual definition to begin with, but “better” alone depends upon criteria of measurement or on our individual learners’ preferences. What we can do is perhaps decide empirically, e.g. by using statistical analyses or learner feedback, as to what might generally be the case for most or many learners, given certain assumptions and/or scenarios. We might conduct research that informs us (via some already tentative interpretation of data!) that many learners tend to dislike learning piano over the violin, say, or find e-learning more off-putting than one-to-one tuition.
So what have we learned so far? That there are trends, similarities and themes in learning styles and approaches, but no absolutes or perfect methods to aid us. People even change their own minds about or are alarmingly unsure of their own learning experiences! (Note, a related topic: Happiness economics).
There is ambiguity in notions of learning/experience curves, i.e. those defined outside the context of an objective ‘graphical representation’ of data, which leads to confusion. LCs as discussed particularly in pedagogic circles are often thought of as very general learning principles to guide tuition, but the sheer importance to most learners about their own preferred methods, anxieties, biases, and decisions when learning seemingly wields little influence over the world of academia. This of course has a lot to do with natural bias by employment. Working in academia means you’re likely wedded to certain preconceptions, traditions, or even dogmas about teaching and learning (e.g. the notion of education as a whole can and has been critically scrutinized). In private business one criterion for success must be profit, i.e. financial sustainability, which may also be mixed with top-level client satisfaction, which in turn may be already somewhat abstracted from the needs of the actual learners ‘in the trenches’. Yet it can also be a very useful method of measuring true learning success (that is, how content the learners themselves are in the product or service, e.g. e-learning software for their iPad). Else why would they voluntarily continue to pay for something they dislike or find inferior? And so on.
The second aspect however, is mainly to do with the outputs required by a system of learning, and how that affects its spectrum of expression or expected results in a given analysis. Exams are designed as very closed systems as a measurement for knowledge. Portfolios and marked projects are coming from an opposing (but often complementary) angle. It’s like having an MCQ (multiple-choice question) format in your e-learning where you restrict scope (e.g. closed-answer MCQ) intentionally, versus leaving answer fields more open (e.g. text input field of 140-chars). This is because at some point you’re to work within some pre-agreed system of logic and rules, like a curriculum, or assessment methodology, or business goal.
But there may be unexplored ways to learn that truly help the student progress, ways that become obscured by assumptions and imposed general systems. Two learning heroes of mine are Michel Thomas (polyglot linguist, language teacher, and decorated war veteran), and Cesar Millan (self-taught expert in dog handling and dog training for people). They both developed their own styles and approaches through a lifetime of study and dedication to their art, and both shook up the preconceptions we previously held about their relevant disciplines. Both have taught individuals as well as groups (and in Cesar Millan’s case, canines too!) and developed learning methodologies (repeatable processes) to pass on to others.
I speculate that they are successful because they (1) became skilled at their craft through trial and error; (2) taught themselves how to learn (in other words, worked out what works for their unique brain/body and why); (3) extrapolated a general principle from this, which was not “my method works universally” but rather, “a unique method worked for me, which implies that unique methods generally work for others similarly”; which then (4) lead to a new understanding of a successful “meta-methodology” that takes into account any sub-methodologies proven useful for a unique learner and/or scenario.
They learned how to help others learn, essentially. This is true teaching, or mastering the art of learning itself. (Notably, Josh Waitzkin was fiercely self-taught as well, following his own path freely and spontaneously, developing complex learning techniques along the way by absorbing and merging principles from multiple unrelated disciplines, from chess to tai chi.)
OK, tangent over! Let’s go back to my musical instrument analogy for a moment. Just because our ektara has one string, that does not necessarily mean it’s simpler in musical scope or expression than a four-stringed fiddle. Nor does it necessarily mean there’s less avenue of exploration, although there might be. Therefore, we must conclude that the learning curve here can feel gradual to many, steep to others, and contain a more or less equal spectrum of musical possibility depending on how far the artist (learner) wants to take the learning. The physical instruments are not equal (identical in form or usage), but the opportunity for mastery is; adding components only shifts the focus of learning. One may specialize in a specific focus area, whereas another might generalize into many areas of study.
In other words, we know (i.e. can confidently predict with testable accuracy) that eating arsenic will poison and slowly kill us, but we cannot know with anywhere near as much confidence whether peanuts won’t. Most likely, we’ll be fine, but peanuts are lethal to some. There are only degrees of universality. Does focusing in on one string rather than four require as much initial skill or creativity? How about a 23-stringed sitar? Maybe the fiddle allows you to play chords (harmonic sets of two or more notes); but does that allow for artistic greater expression/output? How will you measure that? How does this affect the learning curve? What are the criteria you’re using?
You might have an ektara master, or a sitar master, or a cello master, or a master of sand castles or ice sculpting who have all spent decades honing their art and excel at what they do. It could be said that having some physical boundaries (e.g. a piano with fewer keys) inspires skill and innovation because it shifts focus to exploring within those limitations, and inspires greatness equally as it would with fewer physical boundaries, all else being equal.
A lesson here I’m trying to impart is that the way we use language is crucial, and in pedagogy what’s important to one learner’s development is likely not to be the same to another learner’s. Learning curves are affected by as much by one’s personal motivation as with psychological and historical associations with learning, mental or physical makeup, situation and environment, the techniques employed, as well as just entirely chance factors. Also, it’s the way we fell about and relate to what we do, not the object or system itself. We can be creative with both less and more, and learning curves in every discipline depend on how far we are willing to push our own boundaries and creativity.
Remember, there are virtuosi considered masters of the triangle, as well as virtuosi masters of sitar. Learning philosophy is not nearly a science, but rather a fine and subtle art. We need to do more with less, not less with more, but that requires fresh thinking. So we shouldn’t only think outside the box, but play around inside it too!