In this blog post I want share my thoughts on the differences between Maths taught in the classroom and that used in professional life.What often appeals about Maths is the routine of applying a clear set of instructions. Regardless of the context, this remains a large part of any mathematicians career. The big difference once you have left the classroom, is what comes before and after.
Generally in the classroom who are taught a particular statistical test: its assumptions, how to apply it and how to interpret the output. Then when it comes to the end of year exam, the question specifically asks you to perform said test, often on data generated (by a computer) to give a particular answer.
Now, once you are employed as a statistician (or any role where statistics forms part of the job description), the question no longer guides you in exactly what to do. More likely you will be given a data set, and some premise of what you required to extract out of the data. The level of detail of your task is highly variable and likely dependent on the statistical ability of the person asking. The less they know the more vague or far-fetched the question, whereas a fellow statistician is likely to set out a clear hypothesis having already worked through much of the thought process you would have gone through.
Before you can actually start any number crunching, you need to deduce what the hypothesis is. Then you need to decide whether it is actually testable in the data you have. If you think the data can’t answer the question in hand you may have to adjust the question, and present your superior with what you can establish sometimes leading to a protracted negotiation until you are both happy. Once you have finalised the hypothesis, you can then think about which statistical test to use and how.
What I think is missing in the classroom is this thought process of deciding what procedure to use and when. In my experience, I was always explicitly told what I was going to need to do. As a results of this I remember stressful interactions, when at university, friends on other courses would ask for advice on what statistics to use in their dissertations and I would grapple through what I knew to try to advise them. Since my degree, I have had to learn how to answer these questions for my own work, but also to help colleagues in their projects. It can be challenging to convert their biological question into the underlying hypothesis and the mathematical concept that may be represented by.
Experience is the key, but communication is what is going to get you through. Being able to decompose their question into the relevant parts (if they are asking you for help, they probably have overcomplicated it) allows you start thinking in terms more familiar to you. Keep asking them questions with the aim of getting them to refine their question into a testable hypothesis. While there may be moments of utter confusion or complete miscommunication, these interactions are good for both parties and can lead to some novel ideas neither party would have come to on their own.
The other main difference I want to discuss, is that the way Maths is taught can be quite limited. Not only what has been decided should be on the curriculum which is true of all subjects, but also in the structured style of exams. This means you can only do what you are directly asked to, and once you get to the require answer that’s the end. There is no opportunity to show off additional skills or explore further, the way you can with an English or History assignment. Within my role, I am given a lot of freedom to explore datasets beyond the primary purpose. I can generate and test additional hypotheses and try out more advanced or new routines. This creativity really helps improve my skill set and gives me confidence in adopting new areas of statistics I have not encountered before.
The reality is, I have probably learnt more about how Maths really works outside of my initial education and training. You can never discount the value of experience. I would advocate, therefore, that more Maths assignments or assessments take on a more flexible framework. We should give students a chance to follow a project through from design to completion, rewarding the thought process as much as the ability to compute the answer. The skill most employers value from Maths is problem solving, and how can we really teach that if when we set the question we tell them how we want it answered too?