Less is more

“Less is More” is a bit of a funny title for a mathematical blog!

Garlic bread and Ice Cream Sundaes

Back in the seventies, garlic bread became very popular in our household. I loved its buttery, salty, garlicky goodness, and made it quite often. One time I decided that if a little bit of garlic was yummy, then lots of garlic would be even more delicious. I was wrong! The garlic bread was barely edible, and the house and its occupants gave off a distinctive aroma for several days. More garlic did not mean “better”. From then on whenever I used garlic, I would recite in my head “More is not always better.”

Similarly it is fun to see children given a whole range of ice cream flavours, sauces and toppings and watch them create a dessert with EVERYTHING. From experience we know that there are only so many different forms of sugar and fat that should be added to ice cream at one time. If we are smart, we have several bowls, one with chocolate and nuts, one with caramel and crunchy toffee, one with raspberry and biscuit crumbs. That way we can appreciate the different flavours, without having them overridden. Having said that, we then discover that there comes a point of diminishing or even negative returns on investment. The final bowl of ice cream is often regretted.

Enough of food!

“Less is more” applies to teaching

The statement “Less is more” applies to teaching, and particularly subjects like Statistics and Operations Research.

As I learned with the garlic bread, we need to be careful not to give students too much. It is tempting, when developing on-line resources to keep including every possible activity, video and link that is relevant. However we have found that too many activities become overwhelming. It is tempting, as instructors to want to give plenty of practice and every possible resource. We assume that students can pick which items are useful for them. Instead we found that conscientious students want to complete EVERYTHING, and get discouraged when there is so much to do. They possibly don’t need to do all the activities, and waste their time on the easy ones.

We need to be selective about how we use our students’ time. Unless the homework or activity is going to help them learn and accomplish the goals of the course, it should not be there. I am reminded of the hell that was homework for my older son and me when he was going through middle-school. The teacher believed that more homework was better, and the result was misery in our family. Eventually I cried, “Enough!” and arranged an interview with her. I asked her for the specific learning objectives of the “worksheet”, which I know was an unfair question. Clearly the objective of worksheets is to keep the parents of conscientious girls (and the very uncommon conscientious boys) happy because their children were getting homework to do. She never did come up with learning objectives that satisfied me, so William (or rather, I) ceased to do her homework sheets, concentrating instead on times-tables, reading and handwriting. (Or generally nothing at all!)

But I digress. The point is – don’t waste student time on “busy” work. If students understand the process and internalise a skill after ten examples, then they do not need another ten. I DO believe in drill or practice, but it needs to be well developed and practising the skills we wish students to develop. For example there is no need for students to calculate by hand the standard deviation of ten sets of numbers devoid of context. However there is great value in large numbers of questions getting students to determine which test is appropriate in a given scenario.

If you really want to make more resources, rather than making more tests, provide a larger question bank for the current quizzes. That way students can do the quiz multiple times to achieve mastery, but those who have mastered the material immediately can move on.

We should not teach all we know

And as with the ice cream sundaes, when choosing content, what we leave out is as important than what we put in. We should not attempt to teach all we know. When writing the scripts for my videos I find it is important to stick to the main ideas and get them well explained. Sometimes total accuracy is sacrificed in the interests of comprehensibility. I come back to the dreaded question, “Where do babies come from?”, the answer to which depends enormously on the source of the question and context. Seldom is a full biological explanation required or even desirable.

Leonardo Da Vinci is purported to have said, “Simplicity is the ultimate sophistication.” It is the art of the true teacher to be able to reduce complex ideas into a simple form. Bill Bryson is the master of this. In his book, “A Short History of Nearly Everything”, Bryson puts forth complex ideas in ways that a layperson can understand. This is a skill I seek after as a teacher, and try to use in my videos and resources.

Choosing the statistical test – in simple terms

I was unhappy with the branching diagrams commonly used to teach how to choose a statistical test. I felt that there was a more integrative way to express this that would also help peoples understanding. I came up with quite a different diagram that is featured in our most popular video to date.

The students love it. But there are aspects about the diagram which could be looked at a different way. For example I ask “How many samples?”, and say that an independent samples t-test is used on two separate samples. Really it could also be defined as one sample with two variables – the measurement variable and another variable for group membership. When people are just coming to grips with new ideas, they don’t need to see multiple ways of doing things. If they are at the stage to see the other way of looking at it, they aren’t going to need the diagram.

Another very cool thing Da Vinci said was “Art is never finished, only abandoned.” On that note, I will stop now.

4 thoughts on “Less is more

  1. I wonder whether by putting “Purpose” third in your list you aren’t in danger of reinforcing the idea that Statistics is all about choosing between a bunch of tests rather than trying to provide information with a definite purpose in mind?

      • Myself I would put purpose first.🙂 The purpose of the analysis determines what data should be collected – and more data is not necessarily more informative. In my view it is more useful to think ‘what am I trying to achieve’ with this analysis before collecting the data (so the right data have a chance to be collected). This in contrast to: collecting the data and then going ‘now what can I get from this data?’ (although this is sometimes an appropriate research technique). I think because we’ve already collected the data any time we’re illustrating particular modelling tools or statistical tests, we reinforce the ‘collect the data first then worry about analysis’ approach – at least subconsciously.

        On a related topic:

        Less is definitely more especially when it comes to relating mathematical concepts to people who don’t have a background in mathematics (and are not interested in the mechanics or multiple methods of obtaining results – sadly it seems this encompasses the vast majority of the population). However, the same argument applies to presentation of results. There is no need to present absolutely everything the statistical analysis uncovered – only the pertinent results need to be reported on (with supporting evidence or lack thereof).

      • So true about the results! I wish I’d thought of that. Nothing worse than page on page of printout with little synthesis.

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