A better education system

I have read a lot of posts about how our education system has failed and it is ruining the lives of students but the element most of them lack is an example of what could be a better system to replace the existing one. So today I am gonna talk about what an education system should do.
First of all, teachers should grade the paper based on the approach used rather than whether the final answer is correct or not. I have a lot of students asking for final answer in maths exam because they know they just have to fill the sheet and put correct answer at the end. On the other hand, the student who actually knows the solution gets zero marks because he/she made a silly mistake somewhere and his/her answer varied from the actual answer.
The second step is more important one and it can only be implemented after the first step.This step is explained by Salman Khan(founder of Khan Academy) in one of his TED talks. In the video he talks about how we should teach for excellence not for grades. We should keep teaching a topic to a particular student until he/she gets full marks in it i.e. even if a Student gets 95 in a subject we should find out which topic cost the student 5 marks and reteach it so that the topic does not create a problem in next standard when it has another topic built on top of previous one.
I think these 2 steps will go a long way in terms of creating a better education system for next generation.