[carabiner]

Not all students are like you. I went to a low-ranked university my first year before transferring out. I met freshmen who really struggled with basic concepts, like what a vector is. I'm not sure they would ever get it even with all the tutoring in the world.

[ironman1478]

They would in my opinion. I was a tutor in high school and college for algebra. I worked with people some people who struggled. They all eventually got it if they wanted to get it, which they generally did to not get held back :p. You just have to work with them and truly understand what they are not understanding. The big issue is concepts are not learnable in isolation. You said vectors are basic, but are they? They were initially just abstractions to model sets of physics problems. Without the context, its pretty difficult to understand them IMO, especially things like dot products. "oh, i multiply two vectors and I get a number? what? Oh and that number can be described as the multiplication of magnitudes of the vectors multiplied by the cosine of their angle? Oh how do I get the magnitude? What's cosine again? etc." It goes forever and generally you'll find that people will struggle with basic things because they never had an opportunity to sit down and genuinely internalize those ideas.

Everything builds on other concepts and people's misunderstandings generally came from not truly understanding the basics. Its hard to personalize education at scale though.

[oceanghost]

I tutored a 20 year old CS major who could not understand the equation to convert from Fahrenheit to Celsius. Nice guy, talented guitar player. Was not meant to be a programmer.