Hewitt refers to the ‘arbitrary’ if it is something that students need to be informed by someone else and is concerned with names and conventions that students have to memorize (1999). It is the role of the teacher to assist students with retrieving this information through memory. The ‘necessary’ is something students can become aware of without being informed by someone else (1999). The teacher should provide tasks to help students educate their awareness to the arbitrary.
Thinking about this
distinction between arbitrary and necessary will help me plan my lessons and
develop as a teacher with regards to how I teach. Hewitt refers to ‘received
wisdom’ as the fact given to students by the teacher and perceived by the
student to be true as a result (1999). For example, when learning about the
order of operations, students are told about BEDMAS OR PEDMAS by the teacher, which
is an acronym reminding students the order they should perform arithmetic
operations. If a student does not memorize this acronym, then they will
incorrectly solve order of operation algebra problems. Even myself, I do not
know why this order is the standard, but it is the agreed upon convention used
everywhere. One of the points Hewitt makes that stands out to me is to give
students time to use their own intelligence to become aware of why certain
procedures must give certain answers instead of constantly giving them teacher’s
wisdom. For example, when determining the area of a rectangle, students first
must be told the definition of the area, and then be given the opportunity to “discover”
how they can determine the area before being told the equation for finding the
area. This allows for self-discovery before immediately being told the equation
and eliminates the big question of “why is this the equation the area of a
rectangle?”
Reading:
Hewitt, D. (1999).
Arbitrary and Necessary Part 1: A way of viewing the mathematics curriculum. For
the Learning of Mathematics, 19:3, 2-9.
Good!
ReplyDelete