Skemp reading short notes:

 The three interesting points that made me stop while reading are:

1. I appreciate how Skemp presents a vocabulary list that illustrates similar-looking words with different meanings in different languages. It reminds me of a previous experience when I watched a friend defend his PhD in mathematics. During the defense, an external professor asked about a notation in my friend's thesis and pointed out that the notation was not well-defined because it had a different meaning in statistics. This experience taught me the importance of ensuring that everyone is on the same page when discussing topics, or at the very least, that we approach them with a shared understanding during discussions; otherwise, miscommunication can easily occur.

2. An IQ 140 genius student struggled with math in his youth. I recall that during my high school years, my math grades were not impressive because I couldn't concentrate while sitting in a small classroom, just listening to the teacher. Additionally, my brain wasn't mature enough to grasp many abstract concepts until I entered my final year before starting university life.

3. The goal for students learning math may be merely instrumental, but teachers aim to help them understand math relationally. I often encounter questions like, 'Why am I sitting here and learning math? Will I ever use this stuff?' I always emphasize to my students that math is pervasive, happening everywhere, all the time. Math can take on various forms, and we unknowingly use it extensively in our daily lives.

Skemp also raised the question of whether understanding things relationally or instrumentally makes a difference and if one approach is truly superior to the other. I concur with Skemp's perspective that a relational understanding is superior and indeed crucial. I firmly believe that comprehending things relationally is essential for gaining insights into how our world operates. The instrumental approach to learning may lead to easier forgetfulness and challenges when confronted with changing circumstances, as it often lacks a deep understanding of the fundamental logic.