I started to tutor some highschooler, and in the first lesson I saw that he is unsure about almost every step, makes arithmetical errors etc. There's some literature etc. already about what I'm trying to formulate, I'm sure, so I will drop it here and go back to googling afterwards.
What I'm thinking about, is some kind of CAS, adapted for pedagogy, that allows you to make steps (transformations of given problem) until you reach the necessary end state and problem is solved. For example: solving linear equation by choosing in each step allowed transformations... in easy mode, computer does them authomatically and one just chooses, in medium mode, one chooses transformation and writes result of given step and computer checks it immediately, in hard mode one goes until the end (successful or not) and then computer evaluates correctness of each step and announces mistakes if found.
Coq is something like this for proofs because one can choose tactics and computer "just does them". Until one reaches succesful end (proof accepted) or not. An "easy mode" of proving stuff, if one can call it like this.
Another idea is that each step can be (optionally) zoomed in (or out) if necessary. For example, if quadratic equation is solved in one step but student want's to see all the substeps of this, he can zoom in and either try his hand at doing it, or either see how computer does that.
Okay, step away from posting and back to sleepy googling.
"If you had a touch/pen-focused tablet UI that made algebraic manipulations very easy and fluid by dragging and writing (instead of a mouse-driven mess full of menus and buttons) it might make it easier for students to experiment with various algebraic manipulations, rather than harder." - comment from Math subreddit, where I posted practically the same thing as here.
After some searching I found about
1) Maphi - The Math App (app for phones, afaict)
which seems to realize the idea/suggestion from the comment. Will check them out soon.
Last updated: Dec 07 2023 at 17:01 UTC