[vladislavp]

a) Individualized teaching methodology. We come with different backgrounds, therefore different types of analogies/examples, different levels of background material, different (but systematized) levels of presentation should be used. The same ask should be applied to kids learning through starting at preschool.

b) Readable mathematics papers where the compact notations are abandoned, and narrative, visualizations are introduced, while preciseness is maintained. It is possible that the same paper (or chapter or topic) should be renderable in multiple ways (for professional mathematicians in the field, for a casual reader, for a student, for an individual reader (as for (a) )

c) Mathematical logic / tooling for differentiable data/event computing. Where there are mathematical tools as well as CS implementation of this tools that allow to act on a difference in state, data, actions.

Typical mathematics (with exception of may be time series), does not view time as 'first class citizen' so to speak, be it abstract algebra and category theory or something else. But, I think, when we go to the 'applied world' we must introduce 'time dimension' as first class citizen. So having the mathematical machinery dealing with this dimension in organic way across many of the areas of mathematics -- will be beneficial to the application of this one of the most valuable human tools.

[ivansavz]

I've been thinking a lot about your point b) over the years.

I'm conceptualizing a piece of knowledge as an interface that can be `implemented` but with different classes (explanations renderings for different audiences).

For example, the "derivative interface" represents knowledge of the concept of derivative operations and basic skills to compute derivatives of various functions. The interface doesn't specify HOW to teach this topic or HOW DEEP, so there are multiple implementations:

  - basic visual explanations (for kids)
  - basic algebra steps (for high school)
  - standard explanation (for undergraduate students)
  - compact explanation (a reviee for grad students)

The above implementation are polymorphism due to the "reader level of knowledge," but there could be other, e.g. derivatives explained using code like in Sec 4.1 in this calculus tutorial[1].

It would be A LOT of work to produce all these explanations but it would make for a kick ass math textbook that you can pick up and learn, no matter what your level is (instead of getting lost or bored and looking for another resource).

[1] https://minireference.com/static/tutorials/calculus_tutorial...

[vladislavp]

@ivansavz, thank you for the followup and sharing your thoughts on b).

Some time ago, when my Dad asked me to teach him a bit of programming, I made a huge mistake. I was arrogant, and thinking to teach him in a way I learned. And it was totally wrong, totally wrong on many levels on the approach, on the emotional aspect of it.. just totally wrong.

He is no longe with me, and I keep coming back to this, as I cannot fix it.

So from that time, gradually I started unpacking, if he were alive today -- how would I do that differently.

It is at that time (now 20+ years ago) that I started coming up with these

personalized learning, audience specific rendering of the material. And think these two need to be combined together.

My Dad had different analogies and reference points than me, and also he was brighter, faster in many ways, while I tend to be slower and less visual and I have easier time with hypotheticals/and abstractions.

So the personalized part has to reflect the differences. Another example, every time I open a book on statistics I see pocker, cards and various other things -- I have no idea about. These are not great analogies/examples for me as I struggle to grasp the context.

Yet, I also appreciate (now, when it is late) that others are different than me.

So my thought here in a way, similar to yours but merging together student's-level plus students personal experience/background.

So in that context I would say

1). Each student has to built out (may be even gradually) a profile of preferences (background, subject level, visualization proficiency, many other nuanced cognitive differences). May be bulding it answering some sort of logntitudional survey (over time) is a right approach here.

2) The presentation material would be separate into core , presentation, assessment

3) core stays the same and developed by the core instructor/teacher author

4) presentation is developed my multiple means and authors 4i) by the author(s) themselves adopting some 'default student profiles) 4ii) by author(s) authorised contributors that develop materias for other student profiles

5) assessments done in same way as (4).

Then when I as student order (buy) or download or subscribe to the given textbook or a class I specify my profile (that's built in (1)), may be some other learning preference, click 'generate' (or subscribe if that's an online class) and I get the 'rendered' material that I then use.

(of course if the whole system also has online presense, then there is a benefit of a 'forum-like' community around similary-rendered materials -- as it will have folks with, presumably, similar profiles, and the same about assessments).

--

I agree with you that the students agent may dictate the type of rendering so to speak for the materials. In way, i am thinking to capture that with the longtitudional survey updating student profile, through their lifelong learning journey.

WRT a lot of work, agreed I am hoping that 4ii) is an attempt to partially address it.