It might sound silly, but I was so proud of myself. Being a past valedictorian, one wouldn't think a celebration would be in order for such a simple problem, but when it comes to math, it was my studious nature and study habits that led me to As, not my superior understanding. I was taught mathematical rules and procedures, and I obviously used them well enough that my grades made it look as though I knew what I was doing. For sure I would not have even considered solving 14 x 3 like I explained above. Now over twenty years later, I'm finally seeing math through the lens of number sense instead of a lens of rules and procedures.
If I could sit down with parents (and some teachers) who are distraught about the current state of math instruction, I'd want to share the above quote with them. Teaching algorithms straight up without the prerequisite understanding of number sense debilitates our mathematicians. Computation then equals the following of rules, rather than the understanding of numbers, and I can say this from personal experience. I am a product of that style of "learning" math.
The authors of Young Mathematicians at Work shared a problem similar to this one: 999 + 1341. If my younger self had seen this problem, I would have immediately stacked the numbers vertically and put an algorithm to work. Now when I look at this problem, I actually see the numbers and as a result, I also see the ridiculousness of trying to borrow and carry. Instead, it's empowering to transform those numbers into 1000 + 1340 and know the answer in an accurate, flexible, and fluent way. That is exactly how I want today's young mathematicians to feel.