There are many
curious ideas I have noticed after reading this article. First and foremost, I
liked Skemp’s explanation for the wrong use of word ‘understanding’ in
instrumental understanding. Like Skemp says, I also do not see any kind of
intellectual learning in the instrumental understanding. Instrumental learning
does not only include a list of unreasonable rules that pupils just apply to
get an answer for any mathematical problem, but also keeps students away from
actual content. Another important point Skemp mentioned is the possibility of
happening of different mathematical mismatches in any particular math learning
class. In my teaching experience, I sometime face a mismatch between myself and
my students. I usually prefer to teach relationally whereas my students appear
to be interested only in learning by instrumentally. Apparently, I end up using
the mix of both approaches. Furthermore, another mismatch that says pupils are
willing to learn relationally but, teacher’s approach is instrumental. Personally,
I seldom see myself in this situation during my teaching, but I do notice this
mismatch more frequently with my kids. This point makes me to think even more
carefully about how important is that for a teacher to recognize the way a
student wants to learn. Undoubtedly, teacher’s ignorance toward student’s
relational learning may lead to significant damage on student’s overall
learning.
Although there are good arguments on the both side of issues Skemp
raises about instrumental and relational understanding, I strongly believe that
the relational understanding leads to have more positive impacts on the
students. Even though an instrumental learning for students sometimes can be
very handy, quick and rewarded, it certainly not applicable for the situations
where students need to build, connect and explore their learning. As an
example, I learned most of the mathematics formulas with relational
understanding. As I noticed so for, unlike in the most of North American
educational institutions, students in India do not get any cheat sheet of
formulas in the exam centre. Consequently, I had to learn these mathematical
formulas relationally so that I could build them whenever I needed them in the
exams. Also, the formulas that I learned without any logical connection did not
remain in my mind after a few years of their learnings.
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