Why it is Good to Talk Mathematics
"The success of any STEM project depends not only on technical expertise but also on the ability of employees to engage and communicate effectively with expert and non-expert stakeholders alike."
Mathematics is rarely just about solving a problem and obtaining the right answer. More often than not it is the journey, or method as mathematicians call it that is more valuable than the final result.
The practices of describing, discussing and justifying the method and, therefore, the result, all form part of the processes of mathematical communication.
Communication skills are highly sought after in the workplace. Top of a list of 10 employability skills compiled by a range of UK based Science Technology Engineering and Mathematics (STEM) companies is “Communication and Interpersonal Skills: the ability to explain what you mean in a clear and concise way.” Demonstrating that a proposed method is appropriate, and an identified result is correct, is essential for any technical analysis to be of value. Real world examples include making a calculation of the strength of a bridge, the value of an investment, or the efficacy of a medical treatment. The success of any STEM project depends not only on technical expertise but also on the ability of employees to engage and communicate effectively with expert and non-expert stakeholders alike.
The Mathematical Association of America and MIT both place considerable importance on the communication of Mathematics with courses and websites devoted to it (see mathcomm.org). They identify two aspects of mathematical communication from a learner’s perspective. Firstly, “learning to communicate” which equips students with the skills to explain their solutions. Secondly, “communicating to learn” which deepens students understanding of Mathematics through the processes of describing and discussing the subject matter.
One of the opportunities the new Mathematics Honours Program at St Catherine’s provides is for students to practice and strengthen their mathematical communication skills. The small group environment creates opportunities for verbal communication and collaboration between students. Students are regularly challenged to explain their ideas and solutions to their peers – a task that demands a deeper conceptual understanding than just arriving at the answer for themselves. This is “communicating to learn.”
The Mathematics Honours Program also aims to strengthen student’s written mathematical communication skills with increasingly high expectations placed on rigor and precision in written solutions through years 7 to 9. Students are “learning to communicate” and are encouraged to write up solutions to complex multi-step problems such that they can be read and understood by a peer. At the Year 9 level, the Program provides opportunities to explore more formal notation and structures of proofs. An example of a problem solved by the Year 9 students is: “The medians of ΔABC intersect at the point G. Prove that the area of ABG = area of BCG = area of CAG.” At this level the challenge for students is not to just successfully work out how to solve the problem but also to optimise the written solution such that it is as concise and elegant as possible. Algebra plays an increasingly important role in written communication as the concepts become more abstract.
In the Junior School Problem Solving classes, a variety of structured approaches to presenting written solutions are explored. These include logic charts, systematic tables and diagrams. This year the Year 6s have enjoyed creating their own logic problem clues and then swapping them with each other to solve.
The benefits of practicing and perfecting mathematical communication skills are many. They can increase understanding of the subject material, improve performance in examinations, develop valuable workplace skills and foster enthusiasm for the subject through discussion and sharing of ideas.
Enthusiasm is infectious which is why it is good to talk about Mathematics.