10 hints to make the most of teaching and academic conferences

Hints for conference benefit maximisation

I am writing this post in a spartan bedroom in Glenn Hall at La Trobe University in Bundoora (Melbourne, Australia.) Some outrageously loud crows are doing what crows do best outside my window, and I am pondering on how to get the most out of conferences. In my previous life as a University academic, I attended a variety of conferences, and discovered some basic hints for enjoying them and feeling that my time was productively used. In the interests of helping conference newcomers I share them here. They are in no particular order.

1. Lower your expectations

Sad, but true, many conference presentations are obvious, obscure or dull. And some are annoying. If you happen to hit an interesting and entertaining presentation – make the most of it. I have talked to several newbies this afternoon whose experience of the MAV conference could be described as underwhelming. This is not the fault of the conference, but rather a characteristic of conferences as a whole. My rule of thumb is that if you get one inspiring or useful presentation per day you are winning. (Added later) You can generally find something positive in any presentation, and it is good to tweet that. (Thanks David Butler for reminding me!)

2. Pace yourself

When I first went to conferences I would make sure that I attended every session, feeling I needed to fulfil my obligations to the University that was kindly funding (or in those days, part-funding) my trip and attendance. Fortunately I was saved from exhaustion by my mentor, who pointed out that you had diminishing returns, if not negative returns on continued attendance beyond a certain point. Consequently I have learned to take a break and not attend every single presentation I can. Some down-time is also good for contemplating what you have heard. Conferences are also a chance to step back from the daily grind, and think about your own teaching practice or research.

3. Go to something out of your usual area of interest.

When I used to teach operations research, many of the research talks went whizzing over my head. But every now and then I would find a gem, which for me would be a wonderful story I could tell in lectures of how operations research had saved money, lives or the world from annihilation. You never know what you might find.

4. Remember “Names” are just people too.

It may be my colonial cringe, but I tend to be a little in awe of the “big names” in any field. These are the people who have been paid to attend the conference, who give keynote addresses, and you have actually heard of before. Next year at the NZAMT conference in October, Dan Meyer is going to be a keynote speaker. I have to say I am a little in awe of him, but at the same time know that that is silly. Dick de Veaux is one of my favourite keynote speakers and you could not ask for a nicer or more generous person. The point is that speakers are people too, and are playing a certain role at a conference, which means that they should give the punters some of their time. – So this is my advice to paid keynote speakers – be nice to people. It can’t hurt, and it can make a real difference in their lives. Because of my YouTube videos I have a small level of celebrity among some teachers and learners of statistics in New Zealand. (I said it was small) I LOVE it when people talk to me, and hope no one would feel reluctant. If it is in your power to do good, do it

5.Talk to people.

This can be daunting and tiring, but is essential to make the most of a conference opportunity. The point of conferences is to bring people together, so if you do not talk to anyone other than the people you came with, you could have stayed home and watched presentations on YouTube. I am learning that some conversation topics are easy starters : “Where are you from?”, “What do you teach/research?”, “Have you been to any good sessions?” “What did you think of the Keynote?” are all reasonably safe. To my surprise, criticising the US President elect was not universally well received, so I have learned to avoid that one. Being positive is a good idea, and one I need to remember at all times. When I do not agree with what a speaker is saying I have a tendency to growl in a Marge Simpsonesque way. This can be disturbing to the people around me and I am attempting to stop it.

At the 2016 MAV conference I had yellow hair, and immediately found kinship with a delightful and insightful young teacher with magenta hair. Now if we could just have found an attendee with cyan hair we could have impersonated a printer cartridge! I went to Sharon’s presentation and she to mine, and I believe we were both the better for it.

We have Yellow and Magenta - but where is Cyan?

We have Yellow and Magenta – but where is Cyan?

6. Be brave and give a presentation

The biennial NZ Association of Maths teachers conference is being held in Christchurch on 3rd to 6th October 2017. I strongly believe we need more input from primary teachers, and more collaboration across primary, secondary and tertiary. It would be SOO wonderful to have many primary teachers giving workshops or presentations of work they are doing in their maths classrooms.

The abstracts are due by the end of May and if any primary teachers would like some help putting one together, I would be really happy to help.

7. Visit the trade displays

The companies that have trade displays pay a considerable amount for the right to do so. I believe that teachers need producers of educational resources, and when you visit producers and give them the opportunity to talk about their product, it makes it worthwhile for them to sponsor, thus keeping the price down. And you never know – you might find something really useful!

8. Split up to maximise benefit.

If two or more of you come from the same school or organisation, it is a good idea to plan your programme together. When there are 40 – or even 10 presentations to choose from in any one slot, it is more sensible to attend different ones.

9. Plan ahead

It is really helpful to know when conferences are approaching, so I have added links below to the maths teaching conferences I know about, in the hope that many of you may think about attending. Do let me know any you know about that I haven’t listed.

10. Wear sensible shoes

This particularly applies to the MAV conference at La Trobe University. It is held on a massive campus, which is particularly confusing to get around, so one tends to cover far more ground than intended. I was pleased I sacrificed style for comfort in this particular instance, after a bad attack of blisters last year.

11.Add your own hints

Any other conference attenders here – what other suggestions could you make?

Mathematics and statistics teaching conferences in New Zealand and Australia

Primary Mathematics Association 25 March 2017, Auckland

AAMT 11 – 13 July 2017, Canberra, Australia

2017 MANSW Annual Conference 15-17 September 2017.

NZAMT 3 – 7 October 2017 Christchurch New Zealand

MAV Early Dec 2017 Melbourne, Australia

 

 

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The normal distribution – three tricky bits

There are several tricky things about teaching and understanding the normal distribution, and in this post I’m going to talk about three of them. They are the idea of a model, the limitations of the normal distribution, and the idea of the probability being the area under the graph.

It’s a model!

When people hear the term distribution, they tend to think of the normal distribution. It is an appealing idea, and remarkably versatile. The normal distribution is an appropriate model for the outcome of many natural, manufacturing and human endeavours. However, it is only a model, not a rule. But sometimes the way we talk about things as “being normally distributed” can encourage incorrect thinking.

This problem can be seen in exam questions about the application of the normal distribution. They imply that the normal distribution controls the universe.

Here is are examples of question starters taken from a textbook:

  1. “The time it takes Steve to walk to school follows a normal distribution with mean 30 minutes…”.
  2. Or “The time to failure for a new component is normally distributed with a mean of…”

This terminology is too prescriptive. There is no rule that says that Steve has to time his walks to school to fit a certain distribution. Nor does a machine create components that purposefully follow a normal distribution with regard to failure time. I remember, as a student being intrigued by this idea, not really understanding the concept of a model.

When we are teaching, and at other times, it is preferable to say that things are appropriately modelled by a normal distribution. This reminds students that the normal distribution is a model. The above examples could be rewritten as

  1. “The time it takes Steve to walk to school is appropriately modelled using a normal distribution with mean 30 minutes…”.
  2. And  “The time to failure for a new component is found to have a distribution well modelled by the normal, with a mean of…”

They may seem a little clumsy, but send the important message that the normal distribution is the approximation of a random process, not the other way around.

Not everything is normal

It is also important that students do not get the idea that all distributions, or even all continuous distributions are normal. The uniform distribution and negative exponential distributions are both useful in different circumstances, and look nothing like the normal distribution. And distributions of real entities can often have many zero values, that make a distribution far from normal-looking.

The normal distribution is great for things that measure mostly around a central value, and there are increasingly fewer things as you get further from the mean in both directions. I suspect most people can understand that in many areas of life you get lots of “average” people or things, and some really good and some really bad. (Except at Lake Wobegon “where all the women are strong, all the men are good looking, and all the children are above average.”)

However the normal distribution is not useful for modelling distributions that are heavily skewed. For instance, house prices tend to have a very long tail to the right, as there are some outrageously expensive houses, even several times the value of the median. At the same time there is a clear lower bound at zero, or somewhere above it.

Inter-arrival times are not well modelled by the normal distribution, but are well modelled by a negative exponential distribution. If we want to model how long it is likely to be before the next customer arrives, we would not expect there to be as many long times as there are short times, but fewer and fewer arrivals will occur with longer gaps.

Daily rainfall is not well modelled by the normal distribution as there will be many days of zero rainfall. Amount claimed in medical insurance or any kind of insurance are not going to be well modelled by the normal distribution as there are zero claims, and also the effect of excesses. Guest stay lengths at a hotel would not be well modelled by the normal distribution. Most guests will stay one or two days, and the longer the time, the fewer people would stay that long.

Area under the graph – idea of sand

The idea of the area under the graph being the probability of an outcome’s happening in that range is conceptually challenging. I was recently introduced to the sand metaphor by Holly-Lynne  and Todd Lee. If you think about each outcome as being a grain of sand (or a pixel in a picture) then you think about how likely it is to occur, by the size of the area that encloses it. I found the metaphor very appealing, and you can read the whole paper here:

Visual representations of empirical probability distributions when using the granular density metaphor

There are other aspects of the normal distribution that can be challenging. Here is our latest video to help you to teach and learn and understand the normal distribution.

Difficult concepts in statistics

Recently someone asked: “I don’t suppose you’d like to blog a little on the pedagogical knowledge relevant to statistics teaching, would you? A ‘top five statistics student misconceptions (and what to do about them)’ would be kind of a nice thing to see …”

I wish it were that easy. Here goes:

Things that I have found students find difficult to understand and what I have done about them.

Observations

When I taught second year regression we would get students to collect data and fit their own multiple regressions. The interesting thing was that quite often students would collect unrelated data. The columns of the data would not be of the same observations. These students had made it all the way through first year statistics without really understanding about multivariate data.

So from them on when I taught about regression I would specifically begin by talking about observations (or data points) and explain how they were connected. It doesn’t hurt to be explicit. In the NZ curriculum materials for high school students are exercises using data cards which correspond to individuals from a database. This helps students to see that each card, which corresponds to a line of data, is one person or thing. In my video about Levels of measurement, I take the time to show this.

First suggestion is “Don’t assume”.  This applies to so much!

And this is also why it is vital that instructors do at least some of their own marking (grading). High school teachers are going, “Of course”. College professors – you know you ought to! The only way you find out what the students don’t understand, or misunderstand, or replicate by rote from your own notes, is by reading what they write. This is tedious, painful and sometimes funny in a head-banging sort of way, but necessary. I also check the prevalence of answers to multiple choice questions in my on-line materials. If there is a distracter scoring highly it is worthwhile thinking about either the question or the teaching that is leading to incorrect responses.

Inference

Well duh! Inference is a really, really difficult concept and is the key to inferential statistics. The basic idea, that we use information from a sample to draw conclusions about the population seems straight-forward. But it isn’t. Students need lots and lots of practice at identifying what is the population and what is the sample in any given situation. This needs to be done with different types of observations, such as people, commercial entities, plants or animals, geographical areas, manufactured products, instances of a physical experiment (Barbie bungee jumping), and times.

Second suggestion is “Practice”. And given the choice between one big practical project and a whole lot of small applied exercises, I would go with the exercises. A big real-life project is great for getting an idea of the big picture, and helping students to learn about the process of statistical analysis. But the problem with one big project is that it is difficult to separate the specific from the general. Context is at the core of any analysis in statistics, and makes every analysis different. Learning occurs through experiencing many different contexts and from them extracting what is general to all analysis, what is common to many analyses and what is specific to that example. The more different examples a student is exposed to, the better opportunity they have for constructing that learning. An earlier post extols the virtues of practice, even drill!

Connections

One of the most difficult things is for students to make connections between parts of the curriculum. A traditional statistics course can seem like a toolbox of unrelated but confusingly different techniques. It takes a high level of understanding to link the probability, data and evidence aspects together in a meaningful way. It is good to have exercises that hep students to make these connections. I wrote about this with regard to Operations Research and Statistics. But students need also to be making connections before they get to the end of the course.

The third suggestion is “get students to write”

Get students to write down what is the same and what is different between chi-sq analysis and correlation. Get them to write down how a poisson distribution is similar to and different from a binomial distribution. Get them to write down how bar charts and histograms are similar and different. The reason students must write is that it is in the writing that they become aware of what they know or don’t know. We even teach ourselves things as we write.

Graphs and data

Another type of connection that students have trouble with is that between the data and the graph, and in particular identifying variation and distribution in a histogram or similar. There are many different graphs, that can look quite similar, and students have problems identifying what is going on. The “value graph” which is produced so easily in Excel does nothing to help with these problems. I wrote a full post on the problems of interpreting graphs.

The fourth suggestion is “think hard”. (or borrow)

Teaching statistics is not for wusses. We need to think really hard about what students are finding difficult, and come up with solutions. We need to experiment with different ways of explaining and teaching. One thing that has helped my teaching is the production of my videos. I wish to use both visual and text (verbal) inputs as best as possible to make use of the medium. I have to think of ways of representing concepts visually, that will help both understanding and memory. This is NOT easy, but is extremely rewarding. And if you are not good at thinking up new ideas, borrow other people’s ideas. A good idea collector can be as good as or better than a good creator of ideas.

To think of a fifth suggestion I turned to my favourite book , “The Challenge of Developing Statistical Literacy, Reasoning and Thinking”, edited by Dani Ben-Zvi and Joan Garfield. I feel somewhat inadequate in the suggestions given above. The book abounds with studies that have shown areas of challenge or students and teachers. It is exciting that so many people are taking seriously the development of pedagogical content knowledge regarding the discipline of statistics. Some statisticians would prefer that the general population leave statistics to the experts, but they seem to be in the minority. And of course it depends on what you define “doing statistics” to mean.

But the ship of statistical protectionism has sailed, and it is up to statisticians and statistical educators to do our best to teach statistics in such a way that each student can understand and apply their knowledge confidently, correctly and appropriately.