September 9th Reading

While reading Kemp's article, I stopped to reflect when he discussed

1. Relational vs Instrumental Understanding,
2. The "math text" examples on pages 2 and 3, and
3. Relational vs Instrumental Math.

When he first explained the differences in (1), I paused to reflect on what the implications were to mathematics instruction. I was pleasantly surprised when I continued reading and he presented some brilliant examples of their differnces with the are of a rectangle, fraction multiplication, and circumference in (2). By presenting me with examples that didn't tell me which types of understanding he meant, I was able to learn for myself on how to distinguish between the two types. This allowed me to, coincidentally, demonstrate relational understanding to what is being presented in the examples.

Moreover, his discussions on (3) were a refinement to my belief that the math I learned in my education was separated by "Arithmetic" and "True Mathematics", each relating to Instrumental and Relational Mathematics respectively. Arithmetic allowed me to perform operations to obtain correct answers based on my subconscious routine action. Using this arithmetic as a tool, I was able to tackle harder more conceptional "relational mathematics" problems in what I believed to be "True Mathematics".

I believed that I finally caught wind of what the "True Math" was when I entered Grade 12 and had to rely on interpretive knowledge for functions and manipulating them as opposed to just performing algorithms to obtain the correct answer. By being aware of Kemp's distinct types of mathematics, which I agree to as a result of it aligning with my preconceived interpretations, I am mindful of broading my teaching in the subject of math.