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).

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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.

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.

hp EliteBook 2560p. 12gb ram, 120 gb ssd.

Bob Ross -- the painter analogy comes to mind.

When Bob was drawing, it looked amazingly simple. That simplicity invited people into trying painting.

Probably very few could ever draw anything remotely similar in quality to him, though.

Interesting study hint by the author (Robert Plantz) . I have never thought of it this way , but it probably makes sense:

> " Do not copy and paste code. We all copy code, and we all like to see our programs work. Copy and paste is the fastest way to do that. But if you type in the program, even if you are copying it, you are forced to read every single character. This is the fastest way to learn the programming language. As you know, getting a single character wrong can mean the difference between a working and non-working program. "

While I agree with some observations: a) most only use basic maths at their daily jobs)

b) math and computer science degrees are used as a filtering criteria, by recruiters hiring for actuary/stats/finance and programming jobs

I disagree with what appear to be a conjecture, and the subsequent conclusion:

  > Acceptance of the conjecture should have revolutionary 
  > educational implications . 
  > In particular, it undermines the legitimacy of requiring higher mathematics of all students. 
  > Such mathematics is actually needed by only a 
  > minute fraction of the workforce

Being able to abstract business-specific/domain specific problems into something that already has well-researched, validated and implement solution -- is critical, and gives a business an edge.

This is the type of capability (together with knowing a broad universe of solved topics), that the graduates with CS and Math degrees should bring in into the workforce.

I do agree with the author's implication, that there is a 'placebo-style' filtering that's going on by most of the recruiter.

And it is unfortunate, because it brings into Computer Science, especially, a huge number of people who have neither the passion, no life-long perseverance to be current in the subject.