This article speaks to me as a teacher candidate. I fully believe in being vigilant about one's actions such as reviewing and making adjustments all the time, whether it's teaching, how we present ourselves, the words we use, or how we treat others. The authors mention that "to reflect is to look back on what has been done to extract the meanings which are the capital stock for dealing with further experience" (p.6). I wholeheartedly agree with this, because how else would we improve if we don't look back at what we did and learn from our mistakes. If we neglect looking at ourselves, we lose track of how others perceive us. In doing so, we will lose the ability to influence them, since we no longer have a baseline for how we are viewed by them, i.e. "do they like us?", "are they more or less likely to follow through with the homework?".
A quote that struck me was: "However, the question of what to teach, and to whom, precedes the question of how
to teach" (p.2). While this may be true, logically, since first we need to
know what to say, before how we say it, I believe that the how is more important than the what. Inspiring students, and perhaps people in general, involves having a good rhetoric. Using language to relay our passions towards mathematics is, in general, the main vehicle for delivering enthusiasm. Tone of voice, emotional delivery, from my experience, seem to have more weight in terms of influencing a person, rather than the actual content.
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