During my engagement with the discovering mathematics module, and my research for my essay, I came across an enlightening post from Linda M. Gojak, the president of the National Council of Teachers of Mathematics (NCTM). Within the post she states the importance of making connections within mathematics, and how one experience of connections being made within topics gave her one of her most memorable experiences whilst teaching.
“One day, a student commented that this was just like what they had studied at the beginning of the year. When I gave a puzzled look, the class pointed to the posters still on the wall from our first unit of study and said, “You know, that factor and multiple stuff.” I had a new appreciation for the power of providing experiences that enable students to make connections among mathematical ideas.” http://www.nctm.org/News-and-Calendar/Messages-from-the-President/Archive/Linda-M_-Gojak/Making-Mathematical-Connections/
Linda’s experience of a class recognising connections between two otherwise unrelated topics shows how learning topics in isolation within mathematics is far less efficient than taking a mathematical concept and considering how it originates, extends, and connects with other concepts. Teaching maths as a unified body will inevitably help teachers develop a profound understanding of mathematics (Ma, 2010) and in turn will give students the tools and instruction that students need to make their own connections and create their own perception of the mathematical topics and processes.