Let's teach for mastery -- not test scores | Sal Khan

I think a lot of people need to start from the basics because they don't have a good foundation in math. The core problem is schools will push you along if you can somehow produce the correct answer for 70% of the problems on a test. Combine this with intense pressure not to fail and you will very likely end up in higher level math courses with many gaping holes in your foundational knowledge. You thus end up relying on tricks and memorization rather than useful understanding. Here is a TED talk where Sal Khan of Khan Academy talks about this: ▶ this video After struggling to understand advanced math in a lot different contexts I decided to go through the entire K-12 set of exercises on Khan Academy. I blazed through the truly elementary stuff like counting and addition in a few hours, but I was suprised at how quickly my progress started slowing down. I found I could not solve problems involving negative numbers with 100% accuracy. Like (5 + (-6) - 4). I would get them right probably 90% of the time but the thing is Khan Academy doesn't grant you the mastery tag unless you get them right 100% of the time. I found most of my problems were due to sloppy mental models. Like, I didn't understand how division works -- if someone were to ask me what (3/4) / (5/6) even means conceptually I would not have been able to provide a coherent, accurate explanation. "Uh... it's like taking 5/6 of 3/4... wait no that's multiplication... you need to flip the second fraction over... for some reaso

I've run across this quote a few times recently and like it a lot. But there's always the nagging doubt / imposter syndrome telling that you don't really have taste either. Like the people who can taste good food, can't necessarily cook good food. Perhaps it's just enough that you care about something and want to get good at it. I liked Sal Khan's TED lecture [0] about the possibility of us all having the capacity to be cancer researchers in the same vein that people 200 years ago assumed that only the best would be able to read. [0]: ▶ this video

In many cases what differentiates a programmer who is better at dealing with inherent complexity than another has a lot to do with the ability to apply the right patterns, tools, or strategies under the right circumstances. This ability is largely influenced by having been exposed to similar problems in the past and having applied various strategies to solve those problems. One reason why a lot of programmers struggle is because our current educational systems do not expose students to computational thinking at an early age. They've simply not have had enough exposure to that kind of thinking. Even though computational thinking draws on computer science as a formal discipline the insights are applicable to various other domains and virtually everyone will benefit if they're able to apply the same kind of thinking to other problems in their personal and professional lives. Without having to solve any problems specific to computer science people can still acquire the ability to effectively apply computational thinking by solving other problems in their lives because the inherent complexities of those other problems are going to have some similarities to the inherent complexities in designing software systems. Now some people may already have highly developed computational thinking abilities without ever having touched a computer because intuitively they've understood how to solve analogous problems in a different domain. Such people may be far better at dealing with inherent co