Sal's methodology

Hi all,

I am, in relation to it's lifespan, a long time user of your site, having been with you all (at least under my current profile) since 2014 or so with a lost profile that dated back further although I do not recall exactly how far; if I had to guess I would say around 2010-2011. All I know for certain is that, regarding your platform, it feels as though you all have been a part of my life since childhood; a notable thing considering I am pushing toward my mid thirties.

One thing I have always appreciated and, truthfully, the main attraction that has kept me interested, if not engaged, is Sal's natural mathematical algorithm in relation to the basic operations; addition, subtraction, multiplication and division. What he does is, honestly, something I have always been inclined to do as, not only do I feel my brain is better purposed when not forcibly dedicating all of my cognition towards rote memory (instead allowing it to happen naturally over time), but also it just seems to be a more commonsensical approach in something I have previously referred to as segmenting.

What I mean by segmenting is that he seemingly has a natural inclination to break apart a problem into the sum of it's parts. As an example let's take a simple addition, 88+27:

80+20=100

8+7=15

TF: 88+27=115

Or, even, a slightly more complicated problem I ran into earlier while brushing up on my geometry in preparation for trig, 14x=252:

252-112=140

14*8=112 (which can also be broken down with the same method ((10*8)+(4*8)=80+32=112))

(140/14)+(112/14)=10+8=18

TF: 252/14=18=x

While it might initially seem a little clunky, once habituated it is actually quite efficient and, while it might not be able to beat a calculator once the equals button is pressed, it can potentially beat out the input of the equation in the first place. Again, I have always appreciated and respected Sal's willingness to use this methodology (albeit quietly to himself as he works through problems) as it is, at least in my experience, typically not taught in public schools as they instead default to the rote memorization of tables. This method is basically (as I learned much later than its implementation) a base form and reasonable introduction to factoring.

All this being said, what I would like to see is an elaboration on his base methodology in regards to his base problem solving techniques (his algorithm if you prefer the verbiage). I view these types of things as cognitive tools. I feel that, in order for progress to be realized, we must share these tools amongst ourselves and that doing so would be nothing but beneficial to the students served within this community.

Regardless, I've been with you guys since this site was hardly anything more than a basic HTML directory, whether I ever see this implemented or not, I am sure I will continue to enjoy the content as is and still have many subject to work though as it stands. Thank you all for all you do, I look forward to whatever you all decide to do in the future.