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“Teachers do not provide experiences. Students create experiences.” – Ralph Mason
[...W]hat stands out for me [...] is the linguistic distinction in some languages1, 2 between the immediate experience of an event and what endures in memory from it, something for which the single English word experience does double duty. I believe that the ambiguity makes it easy to forget that a transformation must take place before one’s experience of an event becomes an internalized experience, one which has meaning.
This transformation is not automatic; it must be self-initiated. Giving students an activity to do does not by itself generate production of meaning that makes the experience foundational for something else in the future. Working backwards, we can see that educators seek to provide activities (i.e. kokemus-type experiences) which engage and build upon previous foundational (i.e. elämys-type) experiences of students. In mathematics, mathematical thinking is a catalyst for transforming an event into a meaningful experience, but the problem-solving skills involved in mathematical thinking do just as well when applied to other subject domains or ‘real life,’ because math or math-like problems show up everywhere.
I feel that my most significant experience in this course was the reawakening of a long-dormant curiosity for recreational math puzzles and the putting of a name and a “face” to a kind of thinking that I have taken for granted since childhood. For such things it is impossible to nurture it in others without first knowing what it is and recognizing how it works in oneself.
[...W]hat stands out for me [...] is the linguistic distinction in some languages1, 2 between the immediate experience of an event and what endures in memory from it, something for which the single English word experience does double duty. I believe that the ambiguity makes it easy to forget that a transformation must take place before one’s experience of an event becomes an internalized experience, one which has meaning.
This transformation is not automatic; it must be self-initiated. Giving students an activity to do does not by itself generate production of meaning that makes the experience foundational for something else in the future. Working backwards, we can see that educators seek to provide activities (i.e. kokemus-type experiences) which engage and build upon previous foundational (i.e. elämys-type) experiences of students. In mathematics, mathematical thinking is a catalyst for transforming an event into a meaningful experience, but the problem-solving skills involved in mathematical thinking do just as well when applied to other subject domains or ‘real life,’ because math or math-like problems show up everywhere.
I feel that my most significant experience in this course was the reawakening of a long-dormant curiosity for recreational math puzzles and the putting of a name and a “face” to a kind of thinking that I have taken for granted since childhood. For such things it is impossible to nurture it in others without first knowing what it is and recognizing how it works in oneself.
