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I'm a LaTeX user, but I'll stake out a devil's advocate position against this proposal. Reasons: Quality of mathematical thinking neither causes nor results from using a certain piece of software. Tech ed belongs in tech ed. K-12 education should mainly be about enriching people's intellectual lives and creating the level of education that makes it possible ...

This is not an answer to the posed question, but only an anecdote. This semester, teaching US college students (Discrete & Computational Geometry), I prepared all my assignments in LaTeX, and made available a .zip file of the .tex, .bbl, .bib, Figure/ directory constituting the assignment. Students could submit assignment answers in any form—from ...

I don't think it should be a base skill for students in general. Have held jobs in engineering, chemistry, military, and finance and never needed it. Nor did my colleagues. Didn't need it for a thesis or science papers either. Just MS Word was fine. (I think I did enable the MSFT equation editor since it helps with typesetting sub and super scripts on ...

I suggest Geogebra. There are some great conceptual activities there that will help you with volume. My favorite creator is Tim Brezezinski. The following link will take you to an activity that does what you want: https://www.geogebra.org/m/YpqytNph#material/BZWTCPfd For a wider range of activities that look at volume of many kinds in depth you can go ...

This is clearly an opinion based question. I will answer based on my experience and opinion. No, LaTeX should not be taught at high school. It is a skill that is costly to learn with essentially no benefit at high school level. Even at college level, it is not particularly useful. Homeworks are typically submitted handwritten which works perfectly fine. And ...

I only want to give anecdotical advice since I happened to have been taught LaTeX in regular school (10th grade in the German system, iirc). However, I attended a school with a MINT focus and especially maths, also this was not part of the actual curriculum but the teacher "showed" us LaTeX and the interested students that we were promptly picked it up. And ...

There's Abstract Algebra: Theory and Applications by Judson and Beezer. It doesn't get to Grobner bases but does cover the standard material (and some non-standard stuff, too). It has Sage code and exercises throughout. I will also add that it includes chapters on coding theory, cryptography and lattices and boolean algebras, all of interest to people in ...

No, teach Markdown Separation of content This and future generations of students should learn to separate content from formatting. IT professionals have been very successful in applying this concept for over a decade. However, absent marketing and strong commercial interests have kept wider audiences from applying this very useful principle. Focusing on ...

I'd suggest exposing students to LaTeX, perhaps by having them doing a assignment/project with it, perhaps in a group, but not requiring them to learn much about it. This would seem to have several advantages: It gives students an idea of a tool that they might later use. It increases their understanding of what's out there, broadening their general ...

Dave from Boyinaband had a song about all the stuff he found useless in school. While I disagree with some particular things, his opinion in general is right. There are too many things taught that aren't needed by most students. Latex might be good for maths professors. How many people go to that field? Not a lot. Those who go there can learn Latex easily (...

First, LaTeX is a markup language and should be taught as such; trying to use it as a programming language would be an exercise in frustration. Second, I believe that all HS students should learn a markup language as an alternative to WYSIAYG. Third, while I routinely use LaTeX both for papers and for short documents, I am not convinced that it is suitable ...

Wanted to make this a comment but don't have enough reputation. There's Scratchwork and WorldWideWhiteboard that do what you want. They allow you to write in latex and it appears automatically on the board.

Your profile suggests that you are still a teen ager. Therefore my advice is, for now, to explore a lot of things and don't try to specialize too much in any one thing. It is a big world with a lot of possibilities. I'm not suggesting that you give up your study of Category Theory, but there is a lot of other mathematics that is interesting and which ...

It sounds like iMovie or a similar software would be plenty for your needs. If you want to get into other production, there is a bit of a learning curve and many resources online that can get you started. Most of the high end video production software is expensive and does more than you could possibly need, but once you've picked a program, just jump onto ...

I hope I'm not too late to offer some resources. I wrote a book, Hacking Math Class with Python, to promote the use of programming in math education in high school and beyond, and I'm also a big fan of Processing and p5.js for learning math using art, games and interactive, dynamic graphics. I've posted a bunch of sketches on openprocessing.org which I did ...

At an advanced undergrad level, I have had an encounter with "programming-versus-math" in the crypto course and equally-"applied"-but-different error-correcting codes course that I developed in the late 1990s. First, let me say that I myself find contemporary computers substantially helpful "even" for purposes that existed prior to them. Communication! ...

You have perhaps heard of code.org. They have developed a curriculum which teaches algebraic and geometric concepts through computer programming. It is described here: Computer Science in Algebra. Here is a bit more detail: Algebra goes beyond just solving for x, and Code.org CS in Algebra goes beyond this writing code. Through learning to program, ...

Here is one idea for a project. Have them implement Descartes' Theorem on four tangent circles: Given three tangent circles, the theorem can be used to construct a fourth:           (Image from Wikipedia.) You could start with the special case when one of the first three circles has an infinite radius and so is a straight line. ...

I misread the question, and this doesn't answer it (because Dopapp specificially wants to use the Processing language). But I will leave it here for the links. (1) The Khan Academy has 10 drawing and animation projects based on JavaScript. See their curriculum at this link. (2) Scratch is even easier to learn than JavaScript. Some intro projects can be ...

The most well-known organization that teaches algebra (along with physics and data science) using programming is Bootstrap. Its team even involves the university professors that have a number of publications about the Bootstrap teaching approach. It's not implemented in the curriculum at the official level but they organize a lot of professional development ...

I used Mathematica in my High School Mathematics classroom, but not primarily as a computer algebra system, more as a programming language that happens to have excellent support for mathematical functions. What I mean by this is that my primary goal was to introduce my students to the logic of algorithms and give them a tool to use in and out of the ...

My feeling is LaTeX could be part of a very gentle introduction to computer programming. Maybe. Or it could be taught by a math instructor if the students have already seen HTML. Otherwise there are plenty of other things that could be taught in its place. Suppose you want to very slowly work up to coding -- like "AP Programming Principles" does. Learning ...

You seem like a real go getter, so I would suggest learning a real language that will generate some nice graphs and is going to come in handy down the line. Maybe try Python? I made you a little starter notebook for solids of revolution here: https://colab.research.google.com/drive/19hdZziUxA3RoXg0OEG2ktX1elQWQrfZW You should get an idea of how to ...

Learning how to code and code well is an incredibly useful skill in math research in all fields. (I can code, but not code well, but I've been very lucky to have collaborators who are much better than I am. Around half of my papers involve serious computer calculations) But perhaps more importantly, category theory is one of the closest fields in math ...

My advice would be to be open to areas of math that allow for programming skill. You can still take some theoretical classes and such. But there is a lot of good stuff in optimization theory, data processing, cryptography, etc. that uses both math and programming (and even sometimes other fields like OR, business, mechE for finite element analysis, etc.) ...

Here's a Processing sketch that allows users to draw circles and line segments for geometric constructions. boolean lineMode; boolean circleMode; boolean dragMode; boolean last_shape_line; boolean last_shape_circle; boolean mouse_Is_Pressed; int xSize = 1200; int ySize = 640; int clicknumber; int numberoflines=0; int numberofcircles =0; Circle[]...