We do need to think about learning trajectories, but we also need to think about search costs to find the info that populates that trajectory (search time/search costs).
When you said āsearch costsā, my first thought was āsearch for knowledgeā as in āwhich book to chooseā. The big difference between 1990 and 2020 as I experienced in my own learning is that I used to spend a lot of time searching for gold knowledge. Today gold is everywhere and the search cost is minimal. My search method is a lot of reading and sifting. In tons of books and articles there is always that breakthrough nugget. Sifting is costly too, but each sentence processed provides some value.
After reading your message further, I realize you speak of the search of the next knowledge node to which another piece of knowledge can be attached. This process is also relatively cheap in learning (as opposed to problem solving). the brain just activates a set of concept maps when confronted with new information. When a matching piece of jigsaw is found, the happy lightbulb turns on and we are ready to attach.
When I go deeper into your text, I realize that you rather speak of long shortcuts in the net of knowledge. From point A to point B. I would not label that āsearchā because the shortcuts you have in mind are rather not findable. The distance is too long. This is where you see the role of the teacher. the problem with this approach is that for the shortcut to work as a viable memory, the goal B must be of high valuation, e.g. as you say āknowing Quantum Mechanicsā. However, how can be build valuations without explorations. Your scenario sounds like āMy dad told me that QM will give me a good job in engineering. QM is the future. I want QMā. This is unhealthy from the very start. Dadās word can be used as guidance to make small steps in the direction of QM, and each step will affect further trajectory. perhaps competing pathways of exploration will tell the kid: I like Geometry better than QM.
If I dig into my own brain and wonder when I would personally ask for a teacher, I see only one major area: shopping advice. When I want to buy a device for recording video casts, I may decide that I do not plan to learn details of the technology that might die in 2-3 years. I would rather ask an expert: which device is best for me. In a few iterative interactive steps we can narrow my interests, and 5 minutes later I might have the device. I lose knowledge, I gain time. I accept that form of teaching.
There is also interaction with Ollie. You are teaching me your point of view. However, I would rather call it communication because it is a two-way system. We reconcile differences. My learn drive detects high value in your words. I go for a hunt for more.
I might be at a point in life where there are no major blocks of learning (like QM) that are well-defined to be ready to buy a book and study. I explore the edges of what is known and what is to be found about the brain. An 18-year-old might buy some Brain Bible and study page by page. Conversations with some great scientist in the field would be helpful too. However, I doubt an uninjured 18-year-old would enjoy being taught, unless on a partnership basis one-on-one with a great tutor.
For example: if itās my goal to learn about quantum mechanics, perhaps a discovery approach will mean that the trajectory is optimised. That is, at each stage in the journey I learn some knowledge item that has a short semantic distance from something I already know. Challenge is, if Iām self-directing that learning, it may take me a significant amount of time to identify what it is thatās likely to be right on the edge of my current knowledge network
QM is vast and requires a great deal of support knowledge. Oneās own explorations would be dramatically more valuable that interactions with a teacher. Shortcuts are great for speed, but a great deal of supplementary knowledge may be overlooked, customization will be absent, original thinking will be limited, creative exploration will be limited, and we may end up with a student fluent in QM. Instead, we want an open-minded experts that will uncover shortcomings in theories he read about in books. Thatās the first step to progress.
if Iām working with a teacher (or other relevant domain expert), that teacher is likely to have pretty reasonable idea of the kind of learning progression thatās likely to help a student to traverse short semantic distances in order to build a coherent understanding and (if they teach responsively), they can iteratively adjust their explanation/the learning trajectory in response to feedback from me (overt feedback āI donāt knowā or more covert āconfused facial expressionā)
- if the choice of the teacher and the subject is voluntary, if the student sits in the driver seat, the above concept stands in compliance with the optimality of the learn drive
- I like to use the mountain climb metaphor to show how hard it is for an expert/teacher to see into the mind of the student. The greater the knowledge gap, the greater the illusion of superior guidance, and the greater the risk of harm.
theyāre likely to know which ānodesā in a network are most relevant to building expertise
If you say ābuilding a picture of QMā, I would find it more acceptable. āExpertiseā will always be highly customized. Experts are valued for they are hard to replace due to their uniqueness. A teacher can provide foundations of a block that helps understand other areas of knowledge, however, a teacher will not produce an expert. For that own explorations are indispensable.
Granted, this approach wonāt establish as diverse a knowledge network as a discovery approach will, but itāll likely help to build some of the major highways first between the most salient nodes first (time efficiency), from which further exploration can take place
You are right, but why the hurry? Why not build best quality knowledge in a systematic manner? Why take shortcuts that may undermine coherence, stability, resistance to interference, applicability, creative substance, and the optimality of structure? I accept the reasoning for cases where knowledge is secondary (e.g. shopping assistance). QM sounds like a good material for deep exploration with a great deal of fruit to discover. Doing this in a hurry feels like an opportunity missed.
To extend the metaphor which this post has seems to be heading towards, a āteacher as tour guideā can help point out the most important sites within a knowledge domain, and support the student to work out how to get between those key sites, as a basis for further exploration
If I was to study QM tomorrow, I would pick some great book, and chat interactively and occasionally with my best friends with solid QM background (oceans away). I somehow cannot imagine sitting down with some local QM expert and sense it was a good use of time (unless we could combine it with a dozen other interests and socializing
It seems unlikely to me that the benefits of a (potentially?) optimised learning trajectory through discovery would wholly and reliably counteract the increased search costs associated with a discovery approach (that is, I can see how this could happen in some scenarios, but feel itās an overclaim if we suggest it happens in all cases)
I claim that the learn drive is the best optimization device in the process. It may pick a teacher on the way to the goals. However, a child who never experienced schooling is far less likely to ever ask for āteaching-likeā assistance. Humans have advantages over Google, but the way the brain likes to interact with āeasily accessibleā knowledge has very little in common with what we see at school.
Perhaps try to make this judgement for me using your own brain: How would it feel to set a 45 min. time limit on your explorations with Google in where you can only choose a limited set of keywords (corresponding with the area of interest of an expert). To me that mental experiment approximates the interaction one-on-one with a single tutor. High quality teachers are still unbeatable. But the reality of schooling is left behind by Google far and fast. One-on-one is rare, quality feedback is rare, expertise is not as high as in your idealized case, pedagogy is lacking, freedoms are limited (e.g. bathroom visits), creativity is suppressed, explorations are suppressed, etc. I see the best teachers driven by the idealistic image that you present. However, after centuries of trying, we seem to be making things worse for kids who are better sensors of the future.
What evidence is there that a discovery approach leads to optimised learning trajectories over that which is designed by a domain expert
To optimize the trajectory, you need two pieces of information A and B, and an assessor of the value of the connection (which can only be done in the context of an individual brain). We have that assessor in the brain. On a high level, we need a similar comparator for streams of information X and Z. We have such a comparator in the brain. The devices are not optimum in their ability to pick the best pieces to learn from the universe of knowledge. However, they are best for evaluating knowledge at hand. There is no alternative (beyond erroneous extrinsic evaluators). This implies optimality. I wrote a few more words here
I think explicit instruction is extremely efficient when preparing students under limited time conditions for performance on exams with finite boundaries of required knowledge and performance
I agree. However, ālimited timeā and āperformance on examsā entails the whole spectrum of harms, and should never be a yardstick in learning. For me the only true yardstick is human opus vitae, and the optimality of the learn drive is easiest to appreciate from the lifetime perspective! I simplify to the pleasure of learning. As long as learning is fun, the future is secure