Skemp defines instrumental understanding as
knowing how and what to do, and relational understanding as knowing what to do
and why. This made me stop because it has happened to me when I was a student
and in my experiences working with students. Many students learn math by
remembering the rules without really thinking about the reasons. I think part
of the reason is that traditional math questions asks students to solve
equations and number, without giving students actual context to apply to. I
think as we move towards problem solving and apply realistic context for
students to relate to, it will encourage students to see math in a different
way and have a deeper understand.
I stopped when Skemp discusses
the analogy of two music classes. I think this can be related to any subject.
Students learn better when they are doing the exploration and doing activities
hands-on. I also stopped in the devil’s Advocate section. Instrumental
mathematics are prevalent in classes due to the limited amount of time, a great
amount of curriculum to cover, large classes and high stakes examinations. Instrumental
mathematics is sometimes much easier for the majority of students to succeed on
the exams, and hard for teachers to tell if the students actually understood
the contents. I think as we move away from examination, we will be able to move
towards a more student centered learning.
I agree with Skemp’s ideas
that we need help students develop relational understanding. I think it is more
important for students to practice critical thinking. The process of learning is
more important than the results.
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