I wonder if it is a question of dimensionality somehow. When a person is immersed in a language, they are being bombarded with all of the language’s features repeatedly and more or less constantly. This means any language task they can succeed at, they will; then they can expand from these islands of competence outward.
Math class is a strictly sequential and linear endeavor. Normally we get exactly one sequence of problems, which has exactly one ordering, and once a type of problem is past it will never appear again. There is no flexibility at all in how to approach learning math in a class, unless initiative is undertaken by the student completely independent of the instruction.
I learned much more about math once I abandoned the math class approach; I did more immersive things like reading history about math concepts, and different applications, and explanations for why things are wrong.
Semi-separately, I also consider the issue of feedback loops. During talking and wrangling my kid, feedback is mostly instantaneous. Feedback in math class is usually delayed by at least a day, and usually only sparse feedback to boot, in the form of a binary correct-or-incorrect result. Reflecting on it, the sparse complaint is also an issue of dimensionality of a sort.
I wonder if it is a question of dimensionality somehow. When a person is immersed in a language, they are being bombarded with all of the language’s features repeatedly and more or less constantly. This means any language task they can succeed at, they will; then they can expand from these islands of competence outward.
Math class is a strictly sequential and linear endeavor. Normally we get exactly one sequence of problems, which has exactly one ordering, and once a type of problem is past it will never appear again. There is no flexibility at all in how to approach learning math in a class, unless initiative is undertaken by the student completely independent of the instruction.
I learned much more about math once I abandoned the math class approach; I did more immersive things like reading history about math concepts, and different applications, and explanations for why things are wrong.
Semi-separately, I also consider the issue of feedback loops. During talking and wrangling my kid, feedback is mostly instantaneous. Feedback in math class is usually delayed by at least a day, and usually only sparse feedback to boot, in the form of a binary correct-or-incorrect result. Reflecting on it, the sparse complaint is also an issue of dimensionality of a sort.