I find the term “faux
amis” very interesting, because this is the word I have never seen it before (1). Along
with its definition, he mentions that it is seen in mathematics as well. This
makes me relate the idea of “faux amis” to problem solving situations. Just because
students have the same problem to solve, it does not mean that they all interpret
it in the same way. Students find their own way to solve math problems
regardless of what they have been taught. In addition to the meaning of “faux
amis” in math context, multiplication of fractions appeal to me as well (3). It is
easier for me to see patterns in numbers how or why they work the way they do. The
example of multiplication of fractions makes me understand the author’s purpose.
Moreover, the “mis-match” between the teacher and student in understanding
makes me think for a moment. I am surprised to realize that the way teacher
wants students to understand concepts does not always work the way they want.
Based on my
personal experience, I understand relationally and instrumentally. However, if
I have to choose between these two learning methods, I should say I learn
relationally. When I first see formulas, I try to see how the formulas work the
way they do and find the relations between variables rather than simply memorizing
the formulas. Such a habit of mine makes me remember the formulas for a long
time. However, I teach instrumentally most times when I try to explain math
problems to students. This is because I am concerned about them getting answers
wrong that affect their grades. Indeed, instrumental teaching method is easier
to use when helping students understand better; on the other hand, it often
causes problems when students can not solve other similar questions since they do
not have wide application. Over all, I should take advantages of both
relational and instrumental teaching methods to enhance students' understanding.
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