Richard Skemp

    The first point that made me stop was when I read about the difference between relational understanding and instrumental understanding. I had many experiences when I wanted to understand relationally but my teacher taught instrumental mathematics. This allowed me to memorize the formulas and forget everything when I was done with the content. The different advantages of instrumental mathematics have allowed me to realize one other benefit. When I was taught by a teacher who implemented instrumental mathematics, I was able to answer the questions quickly and efficiently which ultimately allowed me to understand relationally as I solved more questions. The last point that stood out to me was the potential reasons why a teacher might choose to teach instrumentally. Some units that are taught in high school may be too challenging to learn relationally. Hence, given the time limit, teachers may want to make sure they finish teaching their lesson plans. This allowed me to think about what I would do if I were a teacher who had to choose between allowing students to understand relationally or moving on to the next lesson. It was interesting to reflect on this from the perspective of a teacher.
    I believe that every student learns differently. I was mostly taught by teachers who implemented instrumental mathematics in their teaching. The benefits listed in the article were genuine; hence, I was able to teach myself to understand relationally as I solved a variety of problems. Thus, I believe that the ultimate goal for students should be to understand relationally, but they can start learning instrumentally if needed.