I like to use the following story of a parent interacting with their 3-year-old to make a point.
Parent: “OK Everybody get your shoes on.”
3-year-old: “Why?”
Parent: “Because we need to get in the van.”
3-year-old: “Why?”
Parent: “Because we need to go to WalMart.”
3-year-old: “Why?”
Parent: “Because we need to get some groceries.”
3-year-old: “Why?”
Parent: “Because we don’t have any food and if we don’t buy some groceries, we will not eat lunch.”
3-year-old: “Oh, OK, I’ll get my shoes on.”
The principle I’m illustrating is the technique the 3-year-old is already using. He wants to know how the world works. As humans, we an an innate desire for things to make sense. We an an innate desire to know why. 3-year-olds do this instinctively. Unfortunately, sometimes people loose this desire to ask why.
Notice how the technique is used. The child did not just ask why once. As the parent and child play this game, the parent knows that this will only end when the answer is something that is inherently true, foundational (so the parent is trying to work to an answer that is so obviously true that the why-asking can end).
In mathematics (and school in general) we should always ask Why — and we should ask, in response to each answer, why again. In this way we often work our way to foundational truths – which are very important truths. Furthermore, connecting foundational truths to today’s problem adds powerful connections in the brain.
This technique of asking why repeatedly until a foundational truth, or underlying cause or principle is found has been studied and advocated by Sakichi Toyoda and was used within the Toyota Motor Corporation during the evolution of its manufacturing methodologies. See https://en.m.wikipedia.org/wiki/5_Whys
After you solve a math problem, in the Look Back and Extend phase (among other things) ask WHY.