[NamTaf]

Teach and test for understanding why and how the answer comes to be, not what the answer is. Maths education, in my experience, relies too much on testing of the arithmetic rather than the logic. This just results in plug and chug because it's lazy testing and students apply lazy solutions.

Good examiners will ask students questions that make them think about why and how, not what the answer is. These often don't even need algebra or arithmetic because it assumes students know the equations and instead goes a level deeper to test understanding of why those equations are the way they are.

I had the gamut in uni. I found that engineering more often successfully tested understanding as I describe above. Some didn't; my thermo was a case of 'learn how the equations work, then read the right graphs and go' but particularly some of my fluid and aerospace courses were great at asking questions that really tested deep understanding of the theories.

One good example of this that I came across more recently is some of the edX courses that used to exist featuring Walter Lewin (before his sexual harassment came to light). He was very successfully able to question his students on the why and how, not just the what. This actually proved even more important in the MOOC environment, where you can't as tightly control the environment in which students undertake examination.

It's hard, it requires good lecturers really spending a bit of time devising questions as well as supporting their tutors as they teach the students, but it's possible.