I saw a lot of this kind of thing when I was at university. If you aren't interested enough in the subject to do projects on your own time you just never connect classroom knowledge to the real world.
I can concurr - I did teach at a uni and the things we got to see from time time ... mind boggles.
Its more prevalent (but less obviously hilarious) in computer science. If you ask a graduating class to produce a simple application 80% of them will start by implementing a linked list from scratch in C.
Well, I had undergrads give me blank stares and then claim that my blackboard calculation is wrong, because "it is not what the calculator says!". Guess what - I have used fractions. Elementary school stuff. Total Chinese to them.
Or something like operator priorities - no idea. Many students I had kept punching numbers into calculators until one combination "worked" and gave the expected result. Thank God for the modern calculators that can handle such difficult problems like multiplying before adding for them.
Another such horror was a computer science master final year (!!!) student in a computer vision course who couldn't multiply two matrices. When confronted with it (it is freshman year stuff), he claimed he has never needed it - even though computer vision pretty much cannot be done without them and he has passed several other courses where they were needed.
So I can perfectly believe that the board posted by OP is real. Not everyone going to university and studying an engineering curriculum actually has the mental faculties for it. However, many are often very good at "winging it" just well enough to pass when there are too many students or the teacher/TA doesn't really care (exam resits mean extra work).
Teaching is not rewarded, at most unis you don't get any credit for it, so many profs will do only the bare minimum required. If you don't and try to care about what your students are doing you are actually shooting yourself in the foot, because then you don't have time for research and writing papers - which are directly tied to your lab's budget and the extension (or not) of your contract or chances at tenure.
Speaking from experience - spent 4 years as an assistant professor, had two semesters where I have been running 10 different courses with no TAs (insane!), the rest were 3-5 courses (normal load is 1-2 courses max). Then was told that "sorry, but your contract will not be renewed, we don't have an associate position for you". The guy who got it instead was a terrible teacher, but he was churning out papers like a printing press (and knew who to rub shoulders with). I had two papers published in that time - with 10 courses on my back I had barely time to prepare the classes and go to bed in time to get at least few hours sleep before another day of lecturing.
The result of this are university grads that are barely able to add two numbers together ...