At an NCTM conference session on teaching statistics I suggested that there was no point in teaching how to calculate a standard deviation. It caused a somewhat heated response, mostly in opposition, but it did get us thinking.
Similarly I have suggested that using the graphical method of Linear Programming is not helpful for most students, with similarly mixed response. The paper was rejected by reviewers.
Each of those issues can have a post all of their own. What I want to discuss here is when calculation is useful, and when it isn’t.
Type of student and purpose of the class
Students are different. Think about who your students are and the purpose for the calculation, before deciding if it is necessary or helpful to their learning.
If you are a mathematics teacher, and the aim is for students to engage in purposeful use of mathematics, then calculate away. Statistics and operations research are disciplines that use mathematics in an applied setting. It can be easy to see the purpose of mathematics to find out the optimal product mix, or the number of servers needed at a supermarket, or to decide whether a marketing approach has improved sales. Deriving the EOQ formula is a wonderfully simple application of calculus. Two variable linear programming on a cartesian plane is a great way to practice graphing skills. These are really good for teachers of mathematics who are teaching students of mathematics.
This is being enabled in several US states by the MINDSET project, which, in its own definition, “uses decision making tools from Industrial and Systems Engineering and Operations Research in a fourth-year high school mathematics curriculum. Principal performance related goals of the project are to improve upon the math students’ ability to formulate and solve multi-step problems and interpret results, and to improve students’ attitude toward mathematics.”
When statistics is taught as part of a mathematics curriculum, then there may be some point in the use of calculations and table-reading when the aim is to develop skills that transfer to other areas.
However, apart from that, for most beginning level students of statistics and operations research it is counter-productive to calculate by hand.
Type of student: Business statistics
In a business statistics course, there are often students who dislike mathematics, and calculation is something they reluctantly learn to do by rote. But a key to understanding and enjoying statistics is being immersed in the context. Get a data set, and let them use the package to find out what they can from it. Decide what test is needed, interpret the output and apply it to the context. This is exciting and involving. They don’t need to calculate by hand anymore. Researchers don’t – that is what packages were invented for. I’m aware that Excel statistics add-in has some flaws, but it is there and mostly harmless. Let students have the fun of spending the time on the exciting part of statistics, not the hand calculations.
What about an MBA Management Science course? Linear programming is a versatile and powerful tool, and by limiting problems to two decision variables to make plotting possible, we trivialise it. The answer is often self-evident, and there are artefacts of two-variable models that can be generalised erroneously. Let students have something approaching real-life size models and cases and they will enjoy the power of the technique.
Applying a formula repeatedly does not lead to comprehension. If you are a mathematician, you can read the formula and understand what is happening without applying it. If you are not so inclined, repeated application of an algorithm is done automatically and disconnected from understanding. Let the students have real data, and use real methods.
In our video on Confidence intervals, you can see how the formula is used to show what is happening, but then Excel is used for the calculation. What do you think?