> Why do we make kids learn how to do math if they can pull out their phone and open the calculator app? Because learning how to learn is important and there is value in understanding how the answer is produced, even if you have a machine that can produce it for you.

I actually appreciate this question very much because this question is extremely pertinent to our discussion. Before I continue my response, I want to turn around and ask you:

1. What's your definition of "learn how to do math"?

i. Would it be sufficient if they proved they understood what addition, subtraction, multiplication and division was? Or do they need to be able to correctly calculate what 4592 * 314 is? What if they could show you using diagrams of squares and rectangles *why* (a + b)** 2 expands to the equation it does but refused to chart out results for various values of a and b?

ii. Would you fail a student who could reliably chart out results for (a + b)** 2 given various values of a and b, but failed to explain that using diagrams of squares and rectangles?

iii. Would you fail a student who could reliably add 1 + 3 or 7 - 5 or 7 * 5 but fail to compute 4592 * 314?

iv. Is a student who could reliably add 1 + 3 or 7 - 5 or 7 * 5 but fail to compute 4592 * 314 at the age of 5 superior or inferior to a student who is capable of doing the same at age 7?

2. If an exam is composed of tables of long division and your score on the test boils down to your ability to how many of those long divisions you can complete in 45 minutes, does the person who scores the highest have a superior understanding of division than the slowest student who suffers from mental fatigue due to an underlying, undiagnoised health condition?

3. When you say "understand how the answer is produced", what level of abstraction is acceptable to be not considered as cheating? Do they need to understand how the calculator physically computes the floating-point math, or is pushing the button enough? If pushing the button is cheating, why isn't using a base-10 shortcut algorithm also cheating? What if the button pusher explained to you precisely how IEEE 754 worked, how a digital calculator works and then refused to do long division citing it was a complete waste of their time and yours? Would you refuse to let them pass the class or fail them unless they yielded to your demands and complied with your specific definition of learning?

Is the math class also doubling as ability to pass compliance and behavioral standards or is it purely a test of mathematical ability?

4. If a student uses an LLM to generate the boilerplate code for a script, but can perfectly explain the architecture, debug the logic, and scale the deployment, have they failed to 'learn how to learn' just because they didn't manually type the syntax?

Educational resources and classroom time is a zero sum game. We cannot afford to educate everyone if they all require 1:1 coaching from a qualified human in a room that has limited space. Time in a day is zero sum as well. Every minute someone spends on doing the 135th long division is a minute they're not spending thinking if solving long division problems is a meaningful differentor in their long term success - whether it's the long division that will make them wealthy, happy and successful or something else entirely?