Homework Due 27^th.

In the article, the authors identify mathematical representations in two ways: internal representations which are “abstractions of mathematical ideas or cognitive schemata that are developed by a learner through experience; mathematical representations “such as numeral, algebraic equations, graphs, tables, diagrams, and charts” are referred as external representations.  However, I am quite confused about these definitions and it was clear to me until later when I read the Bruner’s learning model which explained representations in another way.  Bruner’s learning model classifies representations as enactive, iconic, and symbolic. But I like the way Miller & Hudson describe them: concrete, pictorial, and abstract. This definition is much clearer to me!  

I am convinced by the authors’ opinion on the importance of “students to practice the use of multiple representations”, which I believe is essential in developing critical thinking skills and constructing relational mathematical learning process, and solidifying abstract learning. 

I guess the kind of mathematical representation is missing in the article might be considered as environmental/real-world mathematical representation. For example, clocks and time, the shape of a sunflower, a snail, or nautilus etc. Connection can be made by showing students that mathematical concepts can be found in everyday life.  This representation could be particularly useful in incorporating aboriginal concepts. I would introduce the golden ratio and ask the students to find it in nature. I might demonstrate the first one using sunflower as an example, and ask the students to search the magic number in nature. Another way I would do this is to ask students to look for this ratio in man-made object (such as Mona Lisa). 

Reference

Pape, S., & Tchoshanov, M. (2001). The Role of Representation(s) in Developing Mathematical Understanding. Theory Into Practice, 40(2), 118-127. Retrieved September 27, 2020, from http://www.jstor.org/stable/1477273