2 letters from former students 10 years from now

Short note from a student who thought you were the greatest, and a student who struggled in your class. And a summary afterwards of hopes and worries

Ms Ludeman,
I just wanted to let you know how much you impacted my life. Your enthusiasm when teaching math really helped me get engaged. Because I was engaged and wanted to understand, you helped me see that I am good at math! I went on to University in (a math-related field), something I wasn’t sure I would be able to do even though it is something I was always interested in.
Thank you so much for your help!
Future student 1

Ms Ludeman,
Looking back on high school, I realize now where my aversion to math came from. I didn’t understand why you always insisted on going into such detail when I only wanted to learn the formulas, I never cared about the why! I thought you made class much more difficult than it needed to be. I’m good at memorizing formulas and knowing how to apply them. All this other work you had us do was so unnecessary and made me confused. I wanted to let you know, because I think you should simplify your lessons and go back to the proper way of teaching math.
Sincerely,
Future Student 2

Writing these 2 letters, I noticed it was a lot easier for me to write the second one, which leads me to think I have more worries than hopes at this moment. I’m worried that trying to introduce students to logical thinking and getting away from memorizing formulas where possible will be detrimental instead of helpful. What I am most hopeful of is that I can learn from my mistakes and that if I try something and it doesn’t work, I don’t keep trying it. I’m hopeful that introducing students to logical thinking will engage them and get them excited to learn.