What is missing in between high school and college?

[0kelvin]

In my university there is an issue regarding the step from high school to college. There is an entrance/admission exam with high competition in between the two. Nevertherless, the fail on disciplines rate is quite high, sometimes incredibly high.

Calculus: calculus continues from where high school has ended. To learn limits, derivatives and integrals you must be very well versed in functions and real number operations. Even though there is an admission exam, sometimes 80% or more of a class fails. In my first semester there was a teacher (Calculus I) who teached like this: in every topic he would go straight into problem solving, without explaining theory behind all calculations being done. He would solve an example problem, then do another one, but this time stopping in the middle, facing the class and asking "what's the next step?", then some ppl would randomly guess "factor! expand! substitute x by a!". Now, in the second semester there is another teacher (Calculus II), but this one draws graphs and explains theory. He did a diagnose test to see how much ppl learned in the first semester. Surprisingly, the half of the class who didn't fail and did pass, were unable to properly answer questions such as "explain why the function is continuous" or calculate some exponential function limit.

In a 0 - 10 scale. =>5 means approved, <5 means fail. About 50% passed, 50% failed. But if you count ppl who left, quitted before the end of the semester, fail rate would be over 50%. Majority of the ppl who passed, were in between 5 and 6 grade score grade.

Tip: don't *kill* youserlf with abstract proofs from the start. It's better to first solve many exercises, then go back to that proof. Some of the proofs require knowledge about things that are seen at a much later stage, it's kinda impossible to understand the proof if you skip the easy/medium exercises.

[Banana]

Very interesting points you got there...thanks for sharing 

And yeah without understanding the real meaning, you'll soon forget the idea anyway 

[astarmathsandphysics]

This issues are the same between primary schoolm and secondary school as secondary school and college and college/university.
People decide against every stage of education in that a new way of doing things dioes not suit them. Some come back to it after a while.

[0kelvin]

One thing that I've found myself and seems to be happening with my collegues too. Sometimes, or most likely most of the time, one book is not enough by itself. One book might contain a lot of exercises, but might have words replaced by math proofs. The other book might have very few exercises, but informal language to make it more readable by the general reader. And this also seems to be the case with teachers, some attempt to make calculations express themselves without going in detailed explanation with words. Other are the opposite, they want to stress out the theorem, the proof, not do dozen of calculations one after the other. There are the extremes, teachers that really push students with extremely hard tests, other who simple don't care if you are doing good or bad (never meet these two).