Simplifying the complex and getting to the hub: Communicating mathematics in writing

Abstract

The ability to communicate mathematical ideas simply and articulately in writing is an important skill in mathematics-heavy workplaces (Wood, 2012). Many curricula around the world address the importance of developing written mathematical communication skills (e.g. The New Zealand Curriculum, 2000). However, in practice, these learning objectives are not often met; in fact research has revealed a great difference between the intended and enacted curricula (Stein, Remillard & Smith, 2007). I believe that this lack of written mathematical communication implementation could be attributed to the lack of a framework with which to guide the analysis of students’ mathematical writing. I create a framework that can be used to analyse students’ written mathematical communication. The existence of such a framework may allow written mathematical communication to become a more prominent feature in education and effectively reduce this gap between education and the workplace. This framework was developed through mathematical modelling tasks in which students described their mathematical models in letters to a hypothetical client and also tasks that aimed to improve students’ skills in this area. I applied my framework to the students’ letters to analyse how students are currently performing and how to improve this and also how effective my framework is for analysis. I define two theoretical contributions to the field of written mathematical communication. First, client awareness refers to a student’s acknowledgement of a client’s existence and their appreciation that this client has certain mathematical and communicative needs that have to be met. Second, orienting with respect to client awareness refers to students directing the client’s attention to the value of different parts of their letters and explaining the uses of these parts. These two notions are necessary to consider when analysing students’ written mathematical communication as the higher a student’s client awareness, the more helpful an explanation that student will give because they are conscious of the fact that a client needs it. I also conduct a case study of two workers in mathematics-heavy occupations that illustrates the importance of written mathematical communication in the workplace, the various characteristics of effective written mathematical communication and the lack of tertiary education in this area. Because of its importance in many workplaces, written mathematical communication needs to be a more prominent in formal education. This implies the need for further research into ways to increase students’ client awareness and consequently, their written mathematical communication skills.