Reading Susan's article "Ancestral genres of mathematical graphs," has not only made me eager to pursue further knowledge on the importance of incorporating historical and cultural relations to mathematical graphs but it has also raised interest for using "multisensory pedagogies" and "making cross disciplinary connections" to help students connect better with mathematics. I think this ties into the idea of relational and instrumental understanding. Prior to all these readings my views on mathematics education were narrow and one dimensional. Particularly skewed towards the instrumental side. However, it seems as if using multisensory pedagogy and making connections to other disciplines and history provides great benefits. The power of actually knowing and understanding the mathematics far outweighs linear memorization. Susan provides a great example of this in her graphs and gestures project. I wrote a reflection at the start of the program in another class and I was convinced that we should be isolating mathematics as it's own unique discipline and that the way we should teach it should be instrumentally(mainly because this is the way I was taught). Maybe I am just easily persuaded but after only 3 or so short weeks my original opinions are still remotely present but I am definitely swaying to the other side of the pendulum.
Susan focuses more specifically on the cultural, historical, and human equivalences with respect to mathematical graphs. Who knew the "up-right," "down-left," positive, and negative of graphs were so heavily influenced through our culture, history and so many other factors!! After years and years of working with mathematical graphs I still found this quite intriguing. Bringing this knowledge to a young student could provide the insight and motivation needed to enjoy mathematics. Even though the article more specifically focuses on mathematical graphs, I think this can be translated to other subjects within mathematics.
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