…for a ninth-grade student who said “Students in my class don’t know how to reason.” It is good that he grasps such a thing, and is learning from my work with him what reasoning is.
…for a fifth-grade student who, under my guidance, is learning how to think and use reason. She is being trained in methods deeper than and beyond math — of which latter she is getting a solid, objective grasp.
…for a high school senior who, under my tutelage, increased her SAT score from a 1630 (before I worked with her; this was a real SAT, not one administered for record purposes) to a 1970. That’s 340 points. And we did not even cover all the material I wanted, in the number of sessions I thought appropriate — i.e., she could have done better.