Very well. One of the things that needs to be explained, or the information made available is why rote computation and timed tests are important. Both of those are weaknesses of mine and it did not help my motivation not understanding why it was needed. I came to the answer on a post of yours somewhere in Reddit and now I actually want to get better at it. The idea I got from you and my experience is:
Timed tests make sure I know and use the optimal approach to solve the exercise. I found this while solving systems of equations, where naively I could carry fractions around making calculation cumbersome and error prone, while an initial analysis trying to find a multiplier that does away with fractions is the right approach. I kept failing until in the review lessons I paid proper attention. Analysis and optimisation is being taught. I had a similar experience about choosing a generic ln or an appropriate base logarithm.
Rote calculation was a tough one to swallow until you said that only through much computation one starts seeing patterns that will be useful later in more abstract manipulation. I agree with it but doing the first chapter of spivak’s calculus that focuses on proving very basic entities with math’s arithmetic axioms helped a lot. It is incredibly simple maths but hammers down the axioms that are then the basis of all manipulations.
Also I like the lack of human interaction upon failure. A machine does not get disappointed when I fail, nor annoyed that today I am having a bad day intellectually. It just fails me and gives me the opportunity to do something else and do repeats until it is successful. It also does not let me continue with faulty understanding because the program needs to be on schedule. It gives me an expectation of completion based on current progress history. If am not happy I can just apply myself better. The price being steep also makes it painful when I see no experience gained in the whole calendar week, further adding a motivation.
On a more personal experience I dread tests and especially timed tests. I am kind of “fortunate” that my nightmares often are about failing exams or not having time to finish them. When doing math academy I always was afraid of the “quiz” tab coming up, especially because I have kids and house chores that sometimes need to attend. Anyway in mathacademy quizzes are so frequent they normalize the act of test taking and I feel more like they are a challenge for me to “show off” then something to dread. This is in contrast to my experience in college where there was one make or break exam for the whole semester: fail and you will need to repeat the whole semester.
To finish I so much wish my kids will be able to benefit from this approach. I have been trying to convince others of the worth of relearning maths as an adult. It gives an analytical mind and teaches intelectual humility. I find myself successful in life yet I still struggle in some tests and tasks.
I normally say if you are in need of some reality checks regarding your intellectual ability just do maths. There is always a problem of extreme simplicity that one cannot solve, and makes you feel dumb.