While reading Skemp's article, there were several points that caught my attention and made me reread it. I would like to point out three of them:
First was when he talks about students who want instrumental learning and teachers who want to teach relationally. This situation is very familiar to me. During my years of teaching mathematics, I have tried as much as possible to convey the deep meaning and concept to the student, rather than just the blind use of formulas. Therefore, I understood with all my heart the teacher's frustration and despair described in this section, knowing that a student just wants to cling to a formula like a lifebuoy in the middle of the sea and cares about nothing else. Second, when modern mathematics was discussed, and the idea that if it is going to be taught instrumentally, the traditional syllabus is better taught instead. This part made me think; I had never looked at it from this perspective before. Although traditional syllabi, combined with instrumental understanding, might lead to an answer that is perhaps wrong, it still has some meaning. However, in modern mathematics, the lack of relational understanding can lead to completely absurd and meaningless results.
Third was the discussion about two different kinds of mathematics. Although I can guess the author's meaning, I believe this section needed more explanation given the importance of the topic. My position regarding the article is an emphasis on relational understanding, on the meaning and concept, and on showing the student a comprehensive perspective of the problem so they can see where we are initially, where we want to reach on this map, where the connecting routes are, and if they are not there, how they can be created. Of course, I also believe that in some places, the instrumental method might be more useful, similar to the examples given in the article.
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