Maurice Chiodo and Dennis Müller bust the myths holding back ethics in mathematics pedagogy

Mathematics pedagogy has long acknowledged politics, extending the subject’s socio-cultural aspects into a socio-cultural-political axis that includes social justice, equity, power, and identity. But, more recently, these arguments have been widened to include ethics. Whether considering black-swan events such as how, and if, to publish a fast factorisation algorithm, rendering RSA-based cryptography insecure, or the more common “Who would you tell, and what would you tell them?” when identifying vulnerabilities in mathematical systems, ethics is now an integral part of mathematics. However, since Ethics in Mathematics (EiM) is still in its infancy, myths and misconceptions remain.

Here we explore three common myths about EiM, chosen because, in our experience, they have posed significant hurdles to introducing EiM in various educational settings. EiM is currently taught in very few places, especially at the undergraduate level, and such courses are almost always voluntary or extra-curricular or carry little credit. Until these myths are better understood and dispelled among mathematicians, they will continue to stand in the way of more formal, recognised, and valued courses.

Myth 1: Mathematics is neutral and so any study of EiM is unnecessary

 Since at least the 1960s, new questions have been posed about the way science progresses, including questioning its moral and political neutrality. Mathematics might be different from other sciences in its methods, but it’s less neutral than commonly believed.

It may seem that including non-technical considerations in mathematics EiM adds unnecessary subjectivity, but mathematical practice is already laden with subjective values. Preferences, and other subjective aspects, are deeply embedded in mathematics from its inception. It is, as Paul Ernest says, a human practice, “entangled with human interests, choices and values”. Mathematicians subjectively decide what is worth publishing, what problems are worth pursuing, and how to formalise them. They subjectively determine if arguments contain sufficient clarity for a given readership. And educators subjectively decide on course syllabuses and which students to admit, and on teaching methods, exercises, and assessments. Just because some parts of mathematics contain some objectivity, in the form of logical arguments and reasoning, does not mean all of mathematics is objective. And what it means to be an “objective teacher” who teaches “objective knowledge” can vary among different people, and depends on their philosophical assumptions.

In the scientific community, considering ethics is standard practice, not an exception

At some point, most scientists have had to take on board questioning and understanding the morality of their work, even when such discussions were originally instigated externally by sociologists, philosophers, or journalists. The Manhattan Project raised moral questions for physicists, chemists addressed issues from poison gas to climate engineering, and computer ethics has been around for centuries. In the scientific community, considering ethics is standard practice, not an exception. The rise of moral questioning in mathematics is just part of this larger trend to reflect on the meaning of being a scientist in a world so heavily dependent and influenced by science and technology.

In teaching and research, existing laws, codes of conduct and teaching standards (for example, the Beutelsbach Consensus) only tell us the boundaries for good practice, but not precisely what is right and wrong when it comes to doing and teaching mathematics. To stay within these boundaries, be moral mathematicians, and provide students with the best education available, it is necessary to learn, understand, and do EiM. For many reasons, the rules one wishes to follow are rarely prescriptive enough to be properly translated into action without a deeper understanding.

Myth 2: EiM restricts academic freedom

At its core, academic freedom incorporates the right of academics to research or teach, and the right of students to learn, without outside interference. But just as philosophical ethics doesn’t dictate how people should act, EiM doesn’t enforce particular values on mathematicians either. By studying the different meanings of being a moral mathematician and doing good mathematics, EiM provides mathematicians with tools, insights, and understanding for their work, research, and education. Seen in this light, a diligent person understands that EiM adds to academic freedom by enhancing the knowledge and intellectual freedom a mathematician possesses. A more knowledgeable person – educated in mathematical techniques and the impact of mathematics on society – has a deeper appreciation of the complexity of problems, and thus can solve better problems in a better way.

This is the most important course I’ll ever take in my mathematical career

We can even invert this myth: does confining EiM to extra-curricular settings restrict academic freedom? This may well be true, as academic freedom includes the right of students to learn. Ethics and social justice are part of QAA Subject Benchmark Statements for mathematics, precisely because they’re relevant to the discipline and students’ future work. While the QAA doesn’t legislate, this suggests to us that it’s completely within a student’s right to study, and the lecturer’s duty to teach, these. That is, not teaching or acknowledging EiM can restrict academic freedom. So to avoid impinging on academic freedom, it should be factored into mathematical work, and taught. And this isn’t a hypothetical scenario: during the 2018 Cambridge EiM lectures, a student said, “This is the most important course I’ll ever take in my mathematical career” because “thinking over these ethical dilemmas actually made [students] love math more because [they] feel that [they] now have the ability to be intentional with how [they] use it”.

Myth 3: EiM is only for philosophers, not mathematicians or teachers

 Mathematics and its education is full of ethical questions that should concern and be of interest to everyone, including mathematicians. EiM is neither boring nor irrelevant. Rather, we say that such work is “interesting, tractable, nontrivial, well-defined, and (morally) good” for all mathematicians, students and teachers.

The three main areas of EiM focus on mathematics’ human aspects, including those pertaining to developing and maintaining mathematical knowledge, different mathematical communities, and the impact of mathematics on the world. Addressing these is not something that others (for example, philosophers) can accomplish on their own. Many problems require a deep understanding of mathematics, its teaching, and communities, and thus have a natural place for mathematicians, and teachers in particular.

In short, understanding EiM can make students better mathematicians

Mathematicians not only can, but must, participate if they want to fulfil their professional duties. Regarding teachers, we see that issues surrounding the socio-cultural-political axis, such as equitable learning and identity, inclusion and power are just some ways in which these areas manifest in the classroom. And regarding the student’s experience, we see that mathematical actions, including  analysing, arguing, critiquing, and model building, are part of any good mathematics education. Students engaged in such complex tasks can particularly benefit from teachers who are well versed in the subject’s ethical and social questions, including the ability to reflect on their own moral standpoints. In short, understanding EiM can make students better mathematicians. Better at identifying problems, better at formulating relevant mathematics, and better at interpreting the mathematical results. After all, what is the point of solving an equation if it’s not relevant to the original problem? If they want to do a good job, EiM is necessary for mathematicians, teachers, and students alike.

A collective effort

What constitutes ethical mathematical practice is being explored on many levels, but there remains much to do. The ethical bar provided by other mathematical disciplines, such as data science or statistics, indicates what might be possible, and indeed necessary, for EiM. However, to reach it, it’s critical that mathematicians do not fall into a chicken and egg trap of not researching or teaching EiM because they falsely believe it to be unacademic, and it appearing to be unacademic because there is insufficient research or teaching of it. Today, we’re a far cry from having to request information about EiM, as many resources are now freely available, but it still needs a collective effort to overcome the myths and misconceptions currently holding the subject back.

_____________________________________________________________________________________________ This post is opinion-based and does not reflect the views of the London School of Economics and Political Science or any of its constituent departments and divisions.    _____________________________________________________________________________________________ 

Main image: Bernard Spragg on Flickr