Does knowledge = understanding? This simple equation suggests that the extent of a person's understanding is purely equal to the extent of their knowledge. Proponents of this claim suggest that it grounds understanding in something real and, therefore, avoids some mystical quality separate from knowledge itself.
This idea has an interesting parallel in biology, which I don't think is a coincidence. Here the question was about life. The mechanists and reductionists would claim that life is just mechanical, like mindless machines. Others, however, felt something was missing from this conception, which didn't capture what it means to be a living organism. The idea of a "vital spirit" took hold to fill the explanatory gap. The vitalists were condemned for inventing a mystical (non-scientific) quality.
The vitalists didn't reject the physical and mechanistic nature of life, they just didn't accept that all life should be reduced to mechanical parts. In the same way, understanding must be based on knowledge itself but doesn't necessarily have to be reduced to it alone.
While vitalism per se doesn't exist in science anymore, the endeavour to understand life as something more than just mechanical parts has accelerated (see, for example, Ball 2023) and scientific answers have been given along the way (e.g. autopoiesis, see Weber & Varela 2002).
Let's return to the equation of knowledge = understanding. It's easy to think of how this could be derived via induction. Let's say we ask a group of students to write an open question about things they have studied. Let's also say the question would encompass many topics covered in a school year. Then, we organise the answers from best to worst and deliberate the difference that makes the difference.
We observe in the best answers more technical or precise vocabulary, which is employed correctly. The best answers also contain more concepts from the school year organised into a coherent claim. Through induction, we conclude that the best answers were produced by students who knew more.
This, then, is a claim made a posteriori, via induction. It is also a quantitative explanation of understanding, it sets our sights on "how much knowledge".
What happens when we turn it around to attempt inferences about future performance? The equation suggests that to increase one's understanding, one must simply learn more knowledge. Suddenly, it fails to give us any insight into what to do about our learning because it says nothing about what we should learn or how.
The equation suggests that rote learning (knowledge that is meaningless to a student) somehow increases understanding. I'm sure every teacher has experience of students who have rote learnt in a way that allows them to answer narrow questions but appears to have no understanding of what they are doing. For example, I kept data on my students' ability to memorise facts and compared it with their official IB exam performance. Knowledge of the answers alone could not account for the differences in student performance.
What the knowledge = understanding equation misses is the qualitative side of understanding. In other words, understanding isn't something that can simply be quantified; there is also the aspect of the way of seeing and using that knowledge. Students must gain a feel for when to employ their knowledge such that their actions are adequate for a situation.
This brings us back to the parallel between biological and non-biological views, this time in the field of cognitive science. Classical cognitivism sees the brain as analogous to a computer; a storage device for a database of knowledge items with which the person could problem solve (Engel et al. 2013). If we take this view literally, then knowledge = understanding begins to make sense. A computer, for example, can only carry out tasks encoded in its memory. There is no "feel" for how and when it should be put into action.
A biological view of cognition differs. Unlike computers and machines, organisms evolved normativity, which began with their drive to survive. With this drive came a distinction between good and bad, qualitative value was given to perceptions and actions, and meaning emerged (Thompson 2010).
In fact, "cognitive processes are so closely intertwined with action that cognition would best be understood as ‘enactive’, as the exercise of skilful know-how in situated and embodied action" (Engel et al. 2013, 202).
Action is not synonymous with movement: "Actions are driven by goals; often involve volitional control; planning and decisions among alternatives; prediction or anticipation; often associated with a sense of agency." (203).
Nevertheless, when I've written about these ideas the critique has often been "they just have more knowledge" in a way that reduces knowing and being to items of knowledge of equal value. That feel for how and when to use knowledge is "just more knowledge". This is the claim that "everything is knowledge", a claim that removes distinctions to create only one possible entity. Complexity, however, comes from drawing viable distinctions, not removing them entirely such that there is nothing to think about.
Research on sudden insights also presents a particular challenge to the claim that "everything is knowledge". This is when the knowledge learnt appears unchanging but somehow someone suddenly, in a flash of inspiration, sees something in a new light. Their perception of the knowledge changes, while the underlying facts remain the same.
Ference Marton et al. (1994) analysed transcripts of discussions with Nobel laureates spanning 1970 to 1986. They found something key to their experiences: "the sudden insight that occurs without any obvious reasons at all, the pieces of the jigsaw puzzle falling into place, the sudden revelation of the solution." (Marton and Booth 1997). Knowledge in this sense isn't the acquisition of another knowledge token, but a new way of seeing.
This brings me to a trend in (UK secondary school) educational discourse: the prerequisite knowledge check. The idea is that before a lesson can begin a student must have certain knowledge tokens stored in their memory to access that lesson. The term prerequisite suggests that these knowledge items are absolutely necessary and that they can be neatly separated from the concept to be learnt (and previous concepts).
I've read about teachers asking closed-answer questions to students at the beginning of a lesson to check their readiness. Then, when the students don't get them right, they reteach as a necessity.
Sometimes, I've seen that the number of questions asked exceeds ten. What are the chances that every student can recall the answers to all those questions? We all know that people forget. And, what are the chances that each student forgets the same thing? It's more likely that, across the whole class, every question is unknown by at least one student. The reteaching could then take half a lesson and the process must be repeated for the next.
There is something not quite right about this view. Not only does it seem impractical but the focus seems to be off. Before this relatively new trend came about, students appeared to manage regardless. In fact, I don't carry out any prerequisite knowledge checks at all and my students learn. Students do, of course, need knowledge to access new ideas. I can't get my 11 year-old biology students and place them in a lesson on the immune system with my 16-year-old students. The question is what this knowledge is.
In biology there are almost countless facts, some nice to know, some they should know to progress through a curriculum. But "need to know" shouldn't be perceived as a stored fact in the brain that can be decontextualised. Rather, that knowledge is situated and emerges through conversing in the context of the concept.
I often have students who diligently learn the facts in a surface approach to learning and who adequately complete standardised exam questions. I also have students who are more attentive to ideas as wholes and what they mean, who can't reproduce the details so well. Of the two, the latter type, devoted to a deep approach to learning, has, in my experience, been the type of student most ready to access new material.
How can this be if knowledge = understanding? The lack of distinction between knowers and what they can perceive and do with knowledge can't adequately explain my experience. Somehow we must distinguish between students like these.
The Cognitive Revolution began as a movement to consider the workings of the mind, something behaviourism hadn't done. Jerome Bruner and David Ausubel both produced seminal work on the idea of meaning construction and meaningful learning as distinct from mere rote learning. Then, cognitivism quickly moved into the information processing paradigm based on the computer metaphor. Computers, as nonliving entities, don't have a sense of meaning, therefore the drive to explain meaning making was lost.
"This turn, according to Bruner, was a loss of the original target, since meaning in its nuances, vagueness, polysemy, and connotations could not be reduced to bits of information." (Di Paolo et al. 2019). Ausubel also begins his book by stating that information processing and computer models were opposing movements to his work (2000): These "theoretical trends also dealt more in practice with rote rather than with the meaningful aspects of learning and retention." (xv).
Rather than "prerequisite knowledge" which presents itself as a list of facts, maybe what students need is a prerequisite meaning, a general perception of a concept. Sometimes students do need to know facts but our perception of what it means to know facts is what is in question.
The recent EduCogSci movement (that has dominated discourse in the last ten years) has focused (among other things) on memory storage and forgetting. Forgetting played a key role in its development and referred often to the work of Ebbinghaus and his so-called forgetting curve.
If we accept that people forget naturally then we must also acknowledge that our students will forget most of the details we teach them once they leave our schools and move on. What persists? Does understanding simply decrease, or is it more complicated? Is there something else to understanding?
How many adults, for example, can explain why diffusion occurs, why energy dissipates, the second law of thermodynamics, or whatever else we define in our teaching? But can understand how perfumes spread through a room, how radiators heat a home, and how their clothes will deteriorate with time.
Somehow we are confident that what we do matters beyond exams. Somehow, our students gain something despite all the forgetting. In other words, knowledge of facts is definitely necessary but not sufficient alone. Meaning is crucial and this emerges from understanding how we can be and act in the world.
"The virtue of knowledge lies not in its transcendental truth but in its usefulness in our performative engagements with the world." (Pickering 2010, 150).
I'd like to end with a different definition:
Knowledge is adequate action (distinctions, inferences, reflections, behaviours, etc) in a domain specified by an observer (Maturana 1987).
The idea here is that knowledge is accepted or not by someone. Understanding is not an absolute quantity but a relationship between an actor and an observer.
Therefore, in the classroom, the teachers, as experts, embody what knowledge looks like. We determine what knowledge is and students adapt to our actions.
If we take knowledge = understanding too seriously, if we ignore the idea of meaning, and if we consider knowledge only in a quantitative sense, then this becomes understanding in our classrooms. Students will adapt accordingly by seeing our subjects as endeavours to quantitatively accrue knowledge, rather than find meaning in their embodied experience of the world, which allows them to act adequately in ever more situations. Ultimately, how we define, or conceive, understanding, is how understanding will become when we teach and our students learn as perception guides action.
If you want to see how I co-construct meaning with my students, without lecturing, slide decks, or leaving students to discover for themselves? Learn how and why in my books. Download the first chapters of each book here.
References
Ausubel, D. P. 2000. The Acquisition and Retention of Knowledge: A Cognitive View. Dordrecht: Kluwer Academic Publishers.
Ball, P. 2023. How Life Works: A User’s Guide to the New Biology. Pan Macmillan.
Di Paolo, E., Buhrmann, T., Barandiaran, X. 2017. Sensorimotor Life: An Enactive Proposal. Oxford University Press
Engel, A. et al. 2013 Where’s the action? The pragmatic turn in cognitive science. Trends in Cognitive Sciences 17: 5, 202-209.
Marton, F., & Booth, S. 1997. Learning and Awareness. New York: Routledge.
Marton, F., Fensham, P., & Chaiklin, S. (1994). A Nobel’s eye view of scientific intution: Discussions with the Nobel prize-winners in Physics, Chemistry, and Medicine (1970–1986). International Journal of Science Education, 16, 457–473.
Maturana, H. 1987. “Everything Is Said By An Observer.” In Gaia, A Way of Knowing: Political Implications of the New Biology, edited by William I. Thompson, 67–84. USA: Lindisfarne Press.
Pickering, A. 2010. The Cybernetic Brain: Sketches of Another Future. London: University of Chicago Press.
Thompson, E. 2010. Mind in Life: Biology, Phenomenology, and the Sciences of Mind. Ebook Edition: Harvard University Press.
Weber, A, and Varela, F. 2002. "Life after Kant: Natural purposes and the autopoietic foundations of biological individuality." Phenomenology and the Cognitive Sciences, 1(2), 97–125.