My Mathematical Past

Reflecting on my early experiences with math learning, nothing really stands out. I think this is because the thing I always liked about math was that I could figure things out for myself. In a way, in my earliest experiences I was largely self-taught. Thus, my early math teachers didn't have a huge effect on my learning. However, reflecting on my university experiences, I remember the differences between my various math professors as being more pronounced. I think this is because I needed more help when the math became more challenging. I think my best professors had a sort of intellectual empathy. They were able to see the problems at the same level as their students and could teach to that level. The professors that I struggled to learn from didn't possess this kind of empathy. They were  obviously very smart people with a very advanced understanding of the material but they were unable to step outside this understanding to explain things on the students' level. I think this is a pretty common complaint about math teachers. Most people with an advanced understanding of mathematics are pretty smart but they can't teach it because they can't explain it in an accessible way. I think being able to get into the minds of your students is difficult but it is also one of the markers of a great teacher.