Examining my L & T diagram

I was discussing yesterday’s blog post and a couple of questions came up, which prompted me to re-evaluate the simple diagram and look for a cleaner form. Among those questions:

  1. Are learning and teaching such distinctly separate activities? What about what we learn while we’re teaching?
  2. Is it just very good students who rise to the teaching level amongst their peers?

The sketchy model in the previous post is based on the flow of knowledge. (I note that I’ve been relaxed in my use of the terms information and knowledge semi-interchangably. That’s something for another post but, very briefly, I support the data/information/knowledge model where knowledge is the contextualised and useful form of what entered our sphere as raw data.) The notion of the necessity of an external supply of knowledge, produced by teachers and consumed by learners, is obviously generally false, as the formation of complex knowledge occurs somewhere in our species, in reaction to the data we are exposed to, but that is far more suited to a discussion of research. Our research locates, classifies and develops new knowledge into a form where this can then be used, or passed onto learners to provide a basis for their development in a discipline area. So, specifically for learning and teaching purposes, our system is effectively built on the idea that the teachers have identified areas of knowledge that are to be passed on, in some form, and they provide the mechanisms and structures required for learners to gain this knowledge. Some of this knowledge may be in the area of knowledge location and development, our research training is, of course, an area of concern for both learners and teachers.

So, to answer question 1, why have I separated learning and teaching? When thinking about flows, flows start somewhere and finish elsewhere. Hence, any model of knowledge flow has to show it starting from somewhere and going somewhere else. Much like working out in a gym, standing there with static muscles doesn’t do very much – static and stagnant knowledge flows do even less because you’re not even sweating. I have implicitly accepted that there is some sort of knowledge repository, somewhere, that has transferred a quantity of knowledge to the teachers, somehow, and that these teachers will send the knowledge out again into a communication medium that the learners can then draw knowledge from. But what about the things we learn when we are teaching? Where does that fit in this model? Have I chosen a model that presumes too much?

Thinking about it, what is it that we learn while teaching? If it’s that something has changed in the material, where did we find it? If it’s from the literature, or colleagues, or any other external source, then we switched into learning mode outside of teaching. If it was during a class, where we hit upon a student question that changes the way we think about something, I would argue (and hopefully not as an empty argument of pure semantics) that while we are absorbing this, we are really not capable of teaching this new ‘discovery’ until we have finished the learning phase and then can project it back out to our learners. Even so, our own thoughts on the matter (and my earlier digression on research) indicate that there is some sort of internal learning/teaching mode that does not require external knowledge, per se, but is an internal transformation of data in the context of our existing knowledge. The arrows of knowledge that traverse the boundaries of student and teacher do form a proscriptive barrier to the teacher who learns from themselves and, of course, the learner who teaches themself.

Thus, the sketch is incomplete. I still believe that learning and teaching are separate activities for a given body of knowledge in a single individual, much as an internal combustion engine has different activities at different times, but I need to show the possibility of learning and teaching working together inside an individual.

But how do we fix the sketch? Here are some attempts that I came up with.

The first shows learners learning from themselves, and teachers teaching themselves, but the arrows, for clarity, leave the individual and loopback. I’ve also tried to show that the learner and teacher can be the same person by linking together both bubbles with a link. I don’t like this as it makes it look as if you have to stand in a room and yell the knowledge, then listen to it. This led to the second diagram, where the arrows are now inside the bubbles, and learners can teach teachers, and teachers can learn from learners. The third diagram is a similar concept but with the introduction of the ‘disconnecting medium’ that means that all teaching is viewed through a veil, of sorts, no doubt darkly on occasion. What we teach may not be interpreted in the way that we meant it to be.

I thought about this some more and came up with the final diagram, which unifies the two activities, but without the confusion of the arrows. Learning is still mostly an in-flow activity from multiple sources, teaching is still an out-flow activity to multiple recipients, but the intersection reflects the ‘&’ state: this is the point where people can teach themselves, without recourse to any additional knowledge sources. Latent knowledge, experience, raw data, thinking time, all live in the space called ‘&’ and complete the sketch.

I produced two versions of this in a neater form (I generally use OmniGraffle Pro and Adobe Illustrator for my diagrams, on OS X, if you’re curious. These are both Illustrator). I’m unsure which most embodies the idea the best, although I lean towards the horizontal version as it does not provide a visual hint that one is subordinate to the other. Reading left to right, as we do in English, it also implies that learners can become teachers.

I’m also happy because I was able to use the Caslon italic ampersand, which is a fundamentally beautiful character. Apart from the slightly dynamic air to the diagram lent by the use of italics, the italicised L and T are now of the same type family and style as the ampersand. They will almost always be more visually pleasing to most viewers and, for those who know their typefaces, the diagram will look more consistent.

To, finally, address question 2, I realise that I was too vague in meaning in my last post. While I believe that a student has to be a good student to move to the teaching phase, that is a point at which many students may find themselves at a certain time or in a certain area. A student needs to be confident, accurate and capable of communication in order to share their knowledge but, with careful maintenance of the environment, provision of opportunity and encouragement, on their day, any learner can be a teacher. The new diagram reinforces that: add knowledge, add the correct medium, stir, a teacher may emerge.

This new diagram also provides a basis for measurement that can also be handy. MIKE: Measurement Is Key to Everything. But that’s another blog post…

4 Comments on “Examining my L & T diagram”

  1. […] ← SWEDE: Scale Will Eventually Demolish Everyone Examining my L & T diagram […]


  2. Alex H says:

    Hello Nick,

    I’ve only just found this blog, so I decided to start at the beginning. Chances are I’ll be perpetually behind the times (since the present day won’t stand still), but I’m used to that…

    So far it’s all about knowledge. Have you thought about whether skills are the same sort of stuff as knowledge, or whether teaching skills requires a different attitude? Probably I’ll find out in a future post that you have.


    • nickfalkner says:

      Hi Alex,

      Welcome! (Warning note: there are about 280,000 words between where you are and the current end of the blog.)

      As to knowledge and skills, it’s a very interesting question and it’s not one that I cover here that extensively or with a core regard for their separation. In CS we have a very clear separation between anything that requires muscle memory (typing, for example) while strongly emphasising programming itself as a skill that requires dedicated practice to develop both the programming skill and a set of associated skills, all of which depend upon various levels of knowledge. You can (potentially) be an excellent designer while being a lousy programmer, a fantastic programmer while typing with a stick.

      We, as a discipline, don’t really seem to have a handle on where our pure mathematical origins (knowledge focus) actually make the transition to turn-the-handle code template assembly (much more of a skill application).

      We should discuss this over coffee!



      • Alex H says:

        Actually, I think mathematics education tends to badly overlook the skills component. There is a whole bunch of skills in areas such as problem-solving, constructing an argument, style and aesthetics (more important than we care to admit!) where some students pick up what’s needed by osmosis and some “just don’t get it” (because they’re never explicitly told that there’s an “it” that needs getting).

        Will email you re coffee.


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