Operations Research and Statistics: BFF

As they say on Twitter: That silence after you tell someone you teach Operations Research (or Statistics).

Those in the OR and Statistics communities know what conversation stoppers our disciplines are. When asked what subject I teach I take a punt and respond with “Operations Research”, “Management Science” or “Statistics”. “Operations Research” is met with incomprehension, “Management Science” with miscomprehension, and “Statistics” with thinly disguised antipathy. Apart from being undervalued, what the disciplines have in common is that we do practical stuff with numbers. The pedagogies of these disciplines have much in common.
Operations Research and Management Science (which for many people are synonymous) use statistics and other mathematical analysis techniques to solve real world problems.
Operations Research/Management Science is a discipline which seeks to improve a problem situation by supplying decision makers with information and insights gained through problem analysis, often involving mathematical modelling. (Nicola Ward Petty)
A knowledge of probability and statistics forms part of the OR/MS toolkit, along with linear and non-linear programming, decision analysis, queueing, simulation, heuristics, multicriteria decision-making and operations management tools such as Critical path and inventory control. OR/MS is more than just a set of tools, however, and includes a philosophy of improvement through modelling (as stated in the definition).
Statistics focusses on extracting information from data, and provides the backbone to research in just about all human endeavours, including physics, astronomy, medicine, business, education, psychology, sport and agriculture. Statistical analysis is an essential part of the scientific method. It is often used to inform decision-making, as is OR/MS
I think it is fair to categorise both Statistics and OR/MS as decision sciences, and mathematical sciences. It is also fair to say that the average person in the street has little comprehension of either of them.
So how does this affect teachers of these disciplines? There has been considerable research into the teaching of statistics, and much less into the teaching of operations research (probably because of the number of students taking each of the subjects.) Volumes such as “The challenge of developing statistical literacy, reasoning and thinking”(2004), and “Developing students’ statistical reasoning: connecting research and teaching practice”, (2008) edited by Dani Ben-Zvi and Joan Garfield provide inspiration and guidance to statistics teachers and educational researchers.
The statistics education research literature accepts as given that there are challenges in teaching quantitative courses. Ben-Zvi & Garfield (2004) state four main challenges to success in teaching and learning statistics, which must resonate with many OR instructors. These can be paraphrased as: It can be hard to motivate students to do hard work. Many students have difficulty with the underlying mathematics, and that interferes with learning the related content. The context can mislead students who rely on experience and intuition, and students expect the focus to be on numbers, computations, formulas and one right answer. This can be summarised as
• motivation to work
• mathematical
• contexts
• inexact

Motivation to work

We accept that Statistics and OR/MS are not as inherently motivating to the majority of our students as we would like. Part of our brief is to help them understand how important the subject can be, which can be done through the use of real world examples, and preferably real-world data. What is also motivating to most humans is learning for its own sake. If students feel the joy of passing from incomprehension to comprehension to mastery, this is deeply motivating. Experiences which lead to successful learning aid student motivation.

Mathematical

It’s true. We use mathematics. But we are not mathematics. And when we can get the same result by avoiding the mathematics, all power to us! No one should calculate standard deviations or solve linear programs by hand any more. The ubiquitous spreadsheet has removed that necessity in all but trivial and explanatory examples. It is increasingly possible to do plausible analysis relying totally on computer packages. This way we can give students non-trivial exercises using real data. A little aside here – I personally found mathematics unappealing when there ceased to be numbers in it other than as subscripts, and promptly switched majors to Operations Research, where I my love of numbers and practical problem-solving was indulged.

Contexts

One of my heroes, George Cobb, points out that statistics does not exist without the context. I would suggest the same is true of OR/MS. Remove the application area and we are back in mathematics or math programming. Context can be given in a mathematical example as an unnecessary little story to give pseudo-reality to problems that are inherently abstract. Now there is nothing wrong with abstract – it’s just that statistics and OR/MS aren’t abstract. All problems in statistics and OR/MS should have a context which is relevant and forms part of the answer to the question. Questions like “Find the expected value for the following (context-free) discrete distribution” are to be avoided. Why would we want to know the expected value? What do we do with it when we have got it? Statistics and OR need to answer questions. However, the context can also become a stumbling block when students construct incorrect knowledge based on generalisations of contexts, or allow their own intuition to over-ride what the analysis is telling them.

Inexact

What I used to love about mathematics as a child was getting lots of red ticks (checkmarks not irritating insects) down beside my work. My son once gave me a handmade birthday card covered in red ticks as he knew how much I liked them. In mathematics there was one correct answer. (See my post on Re:Solutions). You had to find x, and when you found it you knew you had the right one. This is SO not true in statistics and Operations Research. Everything “depends”. I now embrace the ambiguity, whereas it felt distinctly uncomfortable at first.
By articulating these four challenges we are better equipped to face them. Let’s try to make our subjects motivating and doable, mathematically appropriate to the audience and with interesting contexts that embrace ambiguity. In this way we can better teach the Science of Better and the Science of Data.