I just noticed your profile says you're a mathematician. Cooool. I fancy myself an amateur mather. What areas interest you most? Am curious!
Discussion
I am an applied mathematician by degree but most of my math work has been as a teacher at a supplemental learning center focused on math and critical thinking. Most math teachers have a limit to their scope of mathematical expertise as teachers, i.e. 3rd grade teachers really only need to be masters of 3rd grade level math while being cognizant of what to expect coming out of 2nd grade and what 4th grade teachers expect to come into 4th grade. I taught all ages so I had to master pretty much everything up through high school level stuff.
That said, most of my stuff applies to learning grade school and high school level math. If someone wanted their kid to be bad ass at math, they could do a LOT worse than having me shadow and teach the kid. The track record doesn't lie. My students won awards in increasing quantities each year they competed.
I have a lot of mental math tricks. I look at etymology and morphology and use that to help students understand. I work narratives into my teaching. I lean heavily upon the Socratic Method.
I haven't taught in a while though. I've been working as an engineer. I still don't use a ton of high level math for that though.
Oh cool. Thats a noble pursuit imo. Have to run, but maybe we can chew on some math topic someday
If you want, memorize the first 25 square numbers and I'll show you how that's useful for certain mental math calculations.
You probably already know 0 squared through 12 squared.
20 squared is a piece of cake.
You're over halfway done already lol.
🫡 🙏 🪶
Oh wait, you gonna teach me how to multiply large numbers? Friends dad used to be able to do that and told me to learn squares... I can do that easy enough, no doubt
Yes, but like every tool, it applies best to certain situations/problems.
If teamed up with other little algorithms and other concepts, the range of situations to which it applies can be extended.
Most math teachers don't take algebra and retroactively apply it to arithmetic for anything other than demonstration/proof purposes. They could dedicate some class time and homework to making the students practice arithmetic problems that, when leveraging certain algebraic concepts (like perfect square binomial/trinomial forms, like difference of squares, etc) are convenient to mentally calculate.