Many subjects are cumulative. Mathematics by nature is; many sciences end up being practically cumulative, since even if a theory is proven wrong at some extreme limit and replaced by another theory there, typically the old theory is still applicable enough to the phenomena it adequately addresses that it is still useful. A typical example in physics is the continued importance of classical mechanics, despite the fact that it has shown limitations and has had to be replaced by theories such as relativity and quantum mechanics. History and analysis of literature by nature are cumulative, and even subjects that deal “mostly” with analysis of current snapshots can still benefit from learning from the past in order to make better judgments and decisions for the future, making them somewhat cumulative as well.
This may beg a question in relation to education in these subjects. If subject matter will always be cumulative, with different topics building upon each other, then there will just be more and more material to teach, and more and more background material required to get up to speed with the current state of things. This may be especially true when the current state involves the intersection and combination of multiple branches of knowledge. How do we deal with this?
Scaling Against Coverage Time
If the amount of material increases cumulatively, then degree programs may become longer and take up more years. If human lifespans increase at least as quickly, then it is plausible that people can still spend the same proportion of their lives full-time in education. Maintaining this would require sufficient ongoing advancements in biology, medicine, nutrition, and so on. In terms of number of years (not proportion), in the beginning people would still spend less time on activities that could earn them money, raising the question of how we can structure things so that people can support a similar standard of living as time progresses.
The Role of Automation and Disruption
Many people make arguments today that “low-education” or “manual” tasks can become automated by better artificial intelligence, or otherwise disrupted in some way. If that is the case, then the kind of work that will earn people money will require increasing levels of education, which can contribute further to this problem. What economic, social, societal, and pedagogical strategies and frameworks can we come up with to address this and prepare people better, so that their educational trajectories are better aligned with their eventual career and standard of living goals?
Better and More Efficient Instruction
As students learn material from different instructors and absorb different ideas and perspectives about how to approach and teach the subject matter, education can improve over time, in analogy with “standing on the shoulders of giants.” This can lead to ways to more efficiently teach larger amounts of material while hopefully not increasing confusion or not decreasing understanding. For example, I would argue that a program like Art of Problem Solving (an extracurricular educational platform for math) would provide some of the best instruction in math today, and it would only have been possible through the instructors’ individual experiences with math education in their generations, which in turn would have been similarly based on the education given to previous generations, and so on.
Integration of Applications and Related Topics
There can be other trends as well that can contribute towards more efficient instruction over time of larger amounts of material. For instance, as time progresses, it is often the case that new applications of existing material are found; this is par for the course in math, physics, computer science, and related subjects. As a specific example, some of the early (pre-1980s) practitioners of a math subject called number theory may not have seen the breadth of applications of the research they were conducting, yet today this subject is fundamental to the algorithms that underlie much of modern computer security. Thus, later education can integrate material for both the “theoretical” side and the “applied” side better, allowing more efficient combined instruction of both. And in general, as more insights are derived over time and more connections are found between topics and subjects, this can open up newer and more creative ways of integrating material and teaching more of it more effectively.
Online Education
The highly connected global nature of the Internet, along with the massively wide availability of information on it, could lead to greater efficiency in education that could allow for teaching more material more effectively. For example, I discussed one aspect of education that can be improved in the online setting in my post on interactivity in online courses. In the past couple of years, COVID has brought online education to the forefront by making it an essential requirement during lockdown, but with it our society was exposed to some of the challenges that might be present as well in an online approach to education. While I still believe in the ultimate potential of online education to democratize learning at a level that hasn’t been seen before, it is interesting and pertinent to discuss how this can be done effectively while also addressing some of the issues that can arise.
General Approaches
Closer and more detailed analysis of the ideas above would be required to determine whether they can scale adequately against the growth of material. If those ideas aren’t always enough, then it is also worth thinking about how we can develop more general methods and frameworks to ensure that people receive the educations they need to maintain similar standards of living over time. It would be useful to have a larger societal discussion around this, involving administrators of schools and degree programs too, so that if it is determined that degree program lengths should increase, then more appropriate expectations can be communicated to incoming students. What general strategies can we come up with to deal with this problem of curriculum growth?
