Response to the Skemp article

    I find it that much of my pedagogy education so far consists of rigorously re-visiting, and sometimes challenging what can be thought of as "common" sense. Two of my personal three standouts relate to this theme:

• Instrumental instruction prevails in part due to the teachers themselves not having learned mathematics on a relational level themselves; indeed, it seems that engineering majors and mathematics minors are more common, and I know that in both of those programmes, you can mostly get by with an instrumental approach. To make matters worse, I have known many arrogant and cliquey mathematics majors who think they are bound to become the next Terry Tao.
• Perhaps it does take a special kind of pupil to actually appreciate the relational approach, which is not to say that you can help pupils acquire the marvelous taste of relational instruction. Considering how much emphasis is placed on the teacher being able to transform the pupil, and just how much onus and pressure can be placed on the teacher, it was validating to see Skemp emphasize the mindset of the pupil. 

Separate from this, I truly look forward to what is being researched in terms of this novel qualitative model for assessing mathematical thinking  mentioned towards the end of the article. There has got to be something beyond the traditional end-product-based evaluation; this is education, where  we are supposed to be thinking about how to make teaching better.

    As for where I stand with regards to this article, it takes so many words right out of my mouth that I cannot muster anything; indeed, anything I may write are merely interesting case studies in support of Skemp's points. For instance, in EDST 401, a curious case study from Newfoundland was presented in which a professor criticized the undergraduate students for not being able to do logarithms. 

    Still, I think Skemp does neglect something, which is addressing the parents. Speaking of pupils only being interested in the mechanics of mathematics so that they can crunch some numbers and get a job, there really are parents who encourage their children to treat just like mathematics like that; they just want their children to get out of their hair as soon as possible, and count every year of parenthood like a prison sentence. They are actually hampering their children's professional and academic potential by instilling such a lazy attitude because if you merely aim for "good enough" in adulthood, you will never actually be "good enough" in adulthood. At the professional level, somebody always finds something in your work to bring it down a few pegs even if you bring your absolute best; by setting your starting point as "good enough", you are almost guaranteeing your own failure.