The advantages of instrumental understanding Skemp lists in
this article can be viewed as study strategies for students who want to have easier
grades and see apparent progress. This type of learning could help students who
have had serious problems with mathematics and just need the grades to pass a
course. Although my teaching experience is very limited, I have witnessed quite
a few students who say they hate mathematics, and some of those students even think
that they would not need mathematics in the real world. They might be right in
some way, but if they were taught to learn relationally rather than
instrumentally, their mathematical approaches towards the world might have been
very different. With instrumental mathematics taught, students might think they
understand, but they are not able to apply those concepts they learned to
different situations. Lack of this skill leads to memory work and eventually
boring classes. In boring classes students tend to strive for easy grades, and
the cycle goes on. A different approach to teaching math, such as relational
understanding, would not just enhance the depth of students’ understanding but
also increase their interest in the subject.
Our math art project was based on Margaret Kepner's A Magic Knight's Tour . A knight's tour is a path that visits each cell of the 8 by 8 chessboard once in knight's moves. All the moves are connected with black lines, and we can see that it is a closed magic path, where a starting point can also be an ending point. Observing Kepner's art, we realized that the inner squares change colour every move in a specific order. As there are 8 colours that were used, the colours keep changing, and the sequence repeats after the 8 colours. The background colour also changes. The first 8 outer squares - the first colour being red since the small black circle is the starting point of the path as described - are red, the second 8 are orange, the third 8 are yellow, etc. The colour black is used when the inner shape's colour matches the outer square's colour. In this way, there are a lot of interesting patterns that have been embodied in Kepner's art. It was at fir...
It's interesting that we say a student 'needs' grades to pass a course. Outside of bureaucratic regulations within schools, what kind of 'need' is that? What does it serve anyone to make a lot of kids bored, I wonder? I appreciate your call for more relational understanding!
ReplyDeleteI guess it's essential to teach students why we need to learn Math first rather than just teaching them the content that is in the curriculum. Students must realize why they learn what they learn. Until then, everything they do at school is just what they have to do because they were told to. Relational mathematics can be one of many approaches that teachers can take in order to guide their students in that way.
DeleteI like your comments!
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