Making Your Own Sense

Reflections on maths, learning and maths learning support, by David K Butler

Tag: statistics

  • Roosters don’t lay p-values

    I’ve just started teaching an online course, and one module is a very very introductory statistics module. There are a couple of moments when we ask the students to describe how they interpret some hypothesis tests and p-values, and a couple of the students have written very lengthy responses describing all the factors that weren’t controlled in the experiments outlined in the problem, and why that means that the confidence intervals/p-values are meaningless. When all we wanted was “we are 95% confident that the mean outcome in this situation is between here and here”.

    It’s happened to me a lot before. Many students in various disciplines are extremely good at coming up with worries about experimental design or validity of measurement processes, and so they never get to the part where they deal with the statistics itself. They seem to treat every problem like the classic “rooster on the barn roof” problem,  essentially declaring that “roosters don’t lay p-values” and choosing not to answer the question at all.

    Don’t get me wrong, I really do want the students to be good worriers: they should be able to think about experimental design and validity and bias and all those things that impact on whether the statistics answers the question you think it does. But what they can’t do is use it to avoid talking about statistics at all! There are quite a few students who seem to be using those worries to discount all statistical calculations, and to sidestep the need to understand the calculation processes involved. “Your question is stupid, and I refuse to learn until it’s less stupid,” they implicitly say.

    The weirdest part is that the assignment or discussion questions don’t usually discuss enough details for the students to actually conclude there is a problem. They say “the groupss were not kept in identical conditions”, but nowhere does it say they weren’t. I realise that in a published article if it doesn’t say they were then you might worry, but this is just an assignment question whose goal is to try to make sense of what a p-value means! Why not give the fictitious researchers the benefit of the doubt? And also, take some time to learn what a p-value means!

    I do realise it’s a bit of a paradox. In one part of the intro stats course, we spend time getting them to think about bias and representativeness and control, and in another part, we get grumpy when they think about that at the expense of the detail we want them to focus on today. It must be a confusing message for quite a few students. But on the other hand, even when reading a real paper, you still do need to suspend all of that stuff temporarily to assess what claim the writer is at least trying to make. It’s a good skill to be able to do this, even if you plan to tear down that claim afterwards!

    I am thinking one way to deal with this is to start asking questions the other way around. Instead of asking only for “what ways could this be wrong?”, ask “how would you set this up to be right?” And when I ask about interpreting a p-value, maybe I need to say “What things should the researcher have considered when they collected this data? Good. Now, suppose they did consider all those things, how would you interpret this p-value?” Then maybe I could honour their worries, but also get them to consider the things I need them to learn.

  • Context fatigue

    Context fatigue is a particular kind of mental exhaustion that happens after having to make sense of multiple different contexts that maths/statistics is embedded in. I feel it regularly, but I feel it most strongly when I have spent a day helping medical students critically analyse the statistics presented in published journal articles.

    The problem with maths in context is that the contexts themselves require understanding of their own in order for the maths to make sense. This is nowhere more true than in statistics, where you have to use your understanding of whether you expect the relationship to exist, what direction you expect it to be, and whether you think this is a good or bad thing. The classic one in my head is an old first year statistics assignment where they used linear regression to investigate the relationship between manatee deaths and powerboat registrations in each month in some southern coastal American city. You have to know what a manatee is, what it means to register a powerboat, and why those things might possibly be connected in order for the statistical analysis you’re asked to do to make sense, not least because at least one part of the question will ask you to interpret what it means. When helping students read published articles recently, I’ve had to find out what’s been done to the participants in the study, how things have been measures, what kind of measurements those are, why they’ve been measured that way, and all sorts of little details to decide how to interpret the numbers and graphs that are presented.

    Even ordinary everyday word problems are a minefield. Across two recent assignments, some financial maths students had to cope with album sales for AC/DC, flooding of the land a factory is built on including insurance, bull and bear markets, machines in a mining operation, committees with various named positions, road testing electric cars, contraband being smuggled in shipping containers. This is a lot of context that has to be made sense of before you can get a handle on the maths, and there is nothing in the question itself to tell you what any of this context means if you don’t already know. Even if you are already familiar with the context, you actually have to suspend some of your understanding in order to do the maths problem, because it’s much simpler than the actual situation any of the questions are talking about.

    All of this interpreting is exhausting stuff! It just tires you out if you have to even a moderate amount all at once. You just feel like you don’t have any more energy to deal with any more today. That feeling there is context fatigue. Yesterday the first year maths students were doing related rates and every question was a new context with little nuances created by the context that had to be dealt with. Those poor students were exhausted after just one problem, letalone three or four.

    As teachers, we need to realise that as the people writing the assignment questions, or at least people who have dealt with them before, we are much more aware of the details and nuances of the context than the students are, so we don’t have to work so hard to make sense of them. Not only that but we’re usually simply more experienced in both life and language than most of our students so it’s easier for us. Imagine the context fatigue you would get reading ten research papers in an unfamiliar area in one day (I feel this in real life regularly). That’s the sort of context fatigue your students have just from your assignment questions. Cut them a little slack, and make sure there is adequate time to process the context with appropriate rest time between context-interpretation. Also it wouldn’t be the worst thing to explicitly teach them strategies for making sense of context, such as ignoring the goal, and finding out about what some of the words mean. Strategies can make the work less intimidating, especially in the face of knowing how tiring it is already!

    PS: If you’re in charge of tutors in a drop-in support centre, especially one that deals with statistics, please be kind. Context fatigue is real and tends to wear us down some days!

  • When the data doesn’t work

    This week I’ve been running the tutorials for the core first year Health Sciences course. The tutorial is a very light intro into how data is part of communication of health science research, and one of the activities involves the students arranging a set of data cards to investigate relationships between variables. Something happened today that I hadn’t observed before and I need to talk about it.

    The students had been going for a little while on the activity, and I walked over to one group just as they were pulling apart some groupings of cards. I asked them what they were doing and they said “We’re starting again because the one we did didn’t work.”

    “What do you mean it didn’t work?” I asked.

    “We we’re looking at hat wearing and happiness and we didn’t see anything,” they replied.

    I was momentarily shocked as the implication on this began to dawn. These students had made a picture that showed there was no relationship, and decided to take it apart because it didn’t work. That is, in their minds, it only works if there is a relationship!

    I said to them I’d love to have them put their picture back, because it’s still good to show there isn’t a relationship. (They didn’t, which made me sad.)

    I wonder if they had come to this conclusion just because of their natural thinking, or because their past experience was that if a teacher asks them to look at data then there is always a relationship. Either way it’s a bit of a dangerous thing to set up because we are in a bit of a crisis in medical publishing where only positive results get published.

    Perhaps we need to give students more examples of data working effectively to argue a lack of relationship.

  • The unexpected fear of statistics

    Statistics is the cause of a lot of fear. There are thousands of students studying psychology, sociology, economics, biology, medicine, animal science and education who thought they would be free of mathematics and suddenly discover they have to deal with statistics. In the case of psychology it is absolutely everywhere: both in whole courses about statistics, but also embedded in almost every other course they do. For most of these students, their fear of statistics carries over from their existing fear of mathematics, and so as sad as it is that they are afraid, it’s not wholly unexpected.

    What is unexpected is the the thousands of students who have done the highest levels of mathematics at school, and are doing the most mathematical disciplines like physics, engineering and mathematics itself, and yet somehow have a deep aversion to statistics when it appears in their degree. Indeed, my own staff at the Maths Learning Centre often express a fear at having to help people with statistics. As I often say “Mathematicians are afraid of statistics in a similar way to how other people are afraid of mathematics.”

    But why? What is it that causes this fear of statistics in those with lots of mathematical experience? I have some ideas…

    One of the biggest reasons is that statistics isn’t 100% maths. A large part of statistics is whatever discipline the statistics is being used for today. That discipline dictates the kinds of data that can be collected, how it is recorded, and most importantly how it is interpreted after the statistics is done. In a generalist statistics course this will change moment-to-moment as each new assignment question brings up a new context. In Question 1 it’s ecology, in Question 2 it’s quality control in food production, and in Question 3 it’s engineering. Each new question requires you to think about a new context and understand various subtleties about what the context means. For a professional statistician, this is often what they say is the most exciting thing about their job. They absolutely love that they get to “play in everyone else’s backyard”. They love that the same tools can be used for a large variety of different problems. However, for many a maths student, this annoys them at best and terrifies them at worst. They didn’t sign up to learn ecology/food science/engineering; they signed up for maths. They prefer to work with the numbers and word problems have made them worried from a young age. Think of how terrifying it would be to suddenly be forced to do a course where every single problem is a word problem! And spare a thought for how hard it is to do the statistics when you don’t have a clue what the context means. As I said, each new context has subtleties that impact a lot on how the statistics is applied and interpreted, and not everyone will have the general knowledge (or indeed language skills) to understand those subtleties without considerable effort. And now imagine having to go through that effort for every single assignment question. It’s exhausting!

    I’m not really sure what to do about this particular problem, other than making sure you give students space and time to talk about the contexts. Don’t treat them like idiots for not understanding contexts they have never experienced before, and definitely don’t think they don’t understand the statistics just because they don’t understand the context. Allow them the grace to have to ask what a manatee is and to ask why manatee deaths would be expected to have anything to do with powerboat registrations. I can imagine assignment questions having links to further information so they can find out more, or a quick whole-class discussion about contexts when you hand out assignments – possibly something like a numberless word problem. They might go a long way to alleviate context fatigue.

    The second reason is that statistics involves making decisions, the biggest of which is deciding what statistical procedure to do and which bits of your situation go with which parts of the procedure. With so many to choose from, and no consistent naming system for the various procedures even inside the one discipline, this is a hugely daunting task for the beginner. It all just seems like a big cloud of random stuff and the students often can’t see what it is that distinguishes between the procedures and what information is being used to decide one over the other. This is only compounded by the fact that part of the decision is made based on information that comes from the context the statistics is being used for today, which was already a problem. It’s further compounded by the fact that many who succeed in mathematics at school have done so by having a list of problem types and how to solve each one, and are not actually used to making decisions at all.

    I think a good dose of actually analysing that decision process and comparing situations that produced different decisions would go a long way to helping this, rather than leaving the decision to chance. Indeed, I’ve written before about how important it is to give students practice at the act of making the decision.

    The final reason I can think of right now is that doing statistics requires making a computer do what you want. This is a completely separate skill from understanding the context, understanding the maths and deciding what stats to do, and has a whole host of its own frustrations, not least of which is just getting access to the computer program itself or figuring out how to install it! And yet it is the gatekeeper of producing actual statistical results. Learning how to communicate with the statistics program is just one more language process that has to happen to succeed in statistics, on top of the decision-making and context-interpreting language processes I already mentioned! Added to this, for the mathematically experienced, they have spent a lot of time learning how to assert their independence from technology and rely on their own reasoning. To not be able to do something themselves and be forced to get a machine to do it for them leaves a bad taste in their mouth.

    Again I’m not too sure how to do something about this problem. Certainly you can make sure there is a lot of support available for getting the program to work, and for asking help specifically with the program. At university you could elevate it to the regular lecture time rather than leave it to practical classes that students may avoid. (Yes I know if they struggle with computer stuff they should go to computer classes, but humans are nothing if not illogical when emotions like guilt and fear are involved.)

    Now that I have written this all down, it occurs to me that these problems are a lot about language, and so this issue may be related to your high-maths-experience students avoiding language in much the same way that other students avoid maths. Perhaps the main thing we can do for them is help them process the fact that it will be about language and support them in their language, and perhaps help them realise that they have a lot more language skills than they thought they had. (Those of us who teach students at earlier stages in their lives might do well to help them realise that maths is all about language anyway!) On top of that, we can have some compassion on them because learning statistics actually is hard work.

    Megan 15 May 2018:

    I personally love statistics but I certainly know plenty of maths learners and educators who don’t. I think statistics is often mathematically simple (mostly plug and chug often with technology) but conceptually challenging. For example, even a simple p-test (covered in Year 12) is not entirely intuitive (Wouldn’t we want a large probability to reject H_0?…We reject for a large test statistic…). As a result, students who usually do well in maths are suddenly struggling not because they can’t do the maths but because they need more time to understand the context and interpret what the numbers actually mean as you say. Maybe more discussion of what is actually happening when we perform different tests could help.

    David Butler 25 May 2018:

    Thanks for the comment Megan. Yes I agree that people might struggle because it’s not the maths that’s the problem! I reckon more discussion of how the context relates to the maths might help them make the connection.

  • Likeable primes

    There is a Twitter account that tweets the prime numbers once an hour in sequence. (The handle is @_primes_ .) Since before I joined Twitter, it’s been working its way through the six-digit primes and some of them are very nice. A lot of other people think they’re nice too, based on the fact that they are given likes and retweets. But what is it that motivates people to do this? What is it that makes a prime likeable? Well, that’s what this post is about.

    You can read the rest of this blog post in PDF form here. 

  • Book Reading: Which One Doesn’t Belong – Teacher Guide

    This is another post about a teaching book I’ve read recently. This one is about the Which One Doesn’t Belong Teacher Guide by Christopher Danielson.

    (You can read this blog post and all other Book Reading posts in PDF form here. )

    It goes with a beautiful little picture book called “Which One Doesn’t Belong?”, which is a shapes book different from any you’ve ever seen before. In this book, each page has four pictures, and asks the readers to say which one doesn’t belong, and why. The fabulous thing about the book is that there is at least one reason why each of the four pictures doesn’t belong, and talking through these with children (or indeed anyone) is a rich conversation about the properties that shapes have and don’t have.

    The Teacher Guide is all about these rich conversations: why it’s important to have them, what you and your students/children can learn through them, and how to facilitate them. Chris has a friendly and welcoming style which draws you easily into a new appreciation of the sophisticated thoughts of children as they make sense of geometry and the world.

    There are a few key things Chris talks about that really impacted my thoughts about teaching and learning maths. I’ve organised them by quotes from the book:

    Commonly in maths class, student responses are compared to a standard answer key – the measure of what’s right is what’s in the back of the book, or what the teacher has in mind. In a conversation about a well-designed Which one doesn’t belong? task, the measure of what’s right is what’s true. – page 3

    I read this quote first when someone else tweeted it out of the book and it struck me as awesome then. In my job at the Maths Learning Centre, students are always asking me if things are right, as if the measure of rightness is if I say it is. But in most places in maths, correctness is measured by truth. Your vectors will either be an orthonormal basis for the subspace or not. A number is either prime or it’s not. You can tell if you’re right by thinking about whether it’s true. I very much want to see opportunities to talk about the truth of things with students, to put the measure of rightness outside an authority figure.

    The van Heiles haven’t argued that it is difficult to go from level 1 thinking directly to secondary school geometry; they have argued that it is impossible. If students don’t have experience and instruction building informal geometry arguments, they will not learn to write proofs. – page 8.

    Chris is referring to the van Hiele model of “how childrens’ geometric thinking develops over time”. In this model, there is a build-up from noticing that shapes look like things they’ve seen (level 0), to noticing properties that shapes have and don’t have (level 1), to relating properties between properties of shapes (level 2), to logically supporting claims about these relationships (level 3).

    The thing in the above quote that really struck me is the idea that it’s impossible to learn to write proofs without experiencing informal arguments first. I see so many students at university every day who struggle with proofs, and it makes me wonder that they maybe need more experience with informal arguments. Indeed, it makes me wonder if they need more experience simply noticing properties, since that’s an even earlier level. This is essentially applying the van Hiele models to other types of maths, but certain aspects of the progression still feel right to me, especially for things vaguely geometrical like vectors or matrices or graphs of functions.

    I wonder if a student struggling with proofs might benefit from talking through a progression like this, and then helping them have experiences at the earlier levels before helping them with proofs.

    Of course being able to state new facts is an aspect of learning, but much more important to me is being able to ask new questions. – page 21

    I had never thought of this idea explicitly before, but immediately I saw that new questions were important to me as well. I was reminded of the time someone asked me if my students were understanding my statstics lectures. I said that I wasn’t completely sure, but certainly the students were asking very deep and complex questions. Instinctively I knew that a new type of question indicated learning.

    Also, in the Drop-In Centre, there’s a certain joy when a student asks new questions you’ve never thought of before. They are wondering about the connections between things, which means they are learning, because learning is all about connections.

    I am excited to listen out for new questions as a sign of learning, and to tell the students that it’s a sign of learning to have new questons!

    … I hope you will begin to see geometry through children’s eyes as well as through the eyes of a mathematician. Mostly, I hope you will come to understand that these two views of geometry are not nearly so distant as the school curriculum might lead us to believe. – page 37

    Now, I already believe that children’s investigations and ideas are actually very close to the way mathematicians work. You can’t be married to a very excellent early childhood educator without coming to some appreciation of this! It’s so nice to have someone publish a book telling teachers and parents the same.

    Even more, this whole section is all about noticing and naming things and their properties. It’s about whether properties need names at all, or whether the objects that share those properties need names. It’s about what properties are important to make a thing a special thing and what aren’t, and in what context. It’s about the relationships between things. All of these are the work of professional mathematicians both pure and applied. And they are the work of children sorting out how the world works.

    The geometry of children and the geometry of mathematicians are definitely not so far removed.

    I have come to understand that talking about this difference is more important than defining it away. – page 54

    Along with the rest of this chapter, this quote got me thinking about a whole new way to approach definitions in mathematics. As a pure mathematician, definitions are very important to me, and I always used to start with the definition. But I know those very definitions took years and even centuries to come to their current forms, and I also know that humans don’t learn through definition but through comparison of things that do and do not fit an idea. I think this is precisely what Chris is getting at here.

    By skipping straight to the definition, we’re robbing people of a key part of mathematical thought, and we’re skipping them through the van Hiele levels before they’re ready. You don’t need a definition until you have a need to distinguish a thing from the other things around it. You don’t need a definition until you’ve noticed the properties you can use to define something.

    The classic example in my own teaching is subspaces in linear algebra. The properties used to define a subspace aren’t even discussed until the definition is given. Little wonder, then, that the definition is meaningless to students!

    It’s not just definitions either. I help a lot of students learn statistics, and one of the things that is never explicitly taught in your traditional statistics course is how to choose what is the most appropriate statistical procedure for the situation. I have been teaching this by focussing on some specific aspects of these procedures that statisticians use to distinguish things. Reading this chapter and this quote in particular helped me realise what I was doing was exactly “talking about this difference”. To distinguish between things you need to notice the properties that make them different, and to notice them, you need to compare things. I now have a much clearer idea of what I’m doing when teaching in the way I do.

    I want to spend more time putting students in situations where they notice the differences between things and have to talk about them, so that they can distinguish between things they need to, and so that the properties I use to define things make more sense.

    Thanks Chris for a most thought-provoking book.

  • The Zumbo (hypothesis) Test

    Here in Australia, we are at the tail end of a reality cooking competition called “Zumbo’s Just Desserts “. In the show, a group of hopefuls compete in challenges where they produce desserts, hosted by patissier Adriano Zumbo. There are two types of challenges. In the “Sweet Sensations” challenge, they have to create a dessert from scratch that matches a criterion such as “gravity-defying”, “showcasing one colour” or “based on an Arnott’s biscuit”. The two lowest-scoring desserts from the Sweet Sensations challenge have to complete the second challenge, called the “Zumbo Test”. In this test, Zumbo reveals a dessert he has designed and the two contestants try to recreate it. Whoever does the worst job is eliminated.

    I find it very interesting that the Zumbo test is the harder of the two tests. In the Sweet Sensations challenge, the contestants can choose to use whatever skills they are already good at, and design their dessert in a way that they can personally achieve. In the Zumbo Test, the contestants have no control over the techniques that are required, and must try to do things they are not familiar with in ways they may not have seen before.

    And why am I talking about this? Because my medical students find themselves in similar situations. Our medical students have two projects to do as part of their research curriculum during their third year. One project is a research proposal: they work in a group with a supervisor to plan a hypothetical research project, including ethics, literature review and (this is where I come in) statistics. The other project is a critical appraisal: they work in pairs to analyse a published article, including where it fits in the research, the writing, the importance and (again where I come in) whether the statistics is appropriate.

    I have noticed over the years that in terms of statistics, the critical appraisal is harder than the research proposal. A meeting with students about the critical appraisal usually takes twice as long as one for the research proposal, and twice as much preparation for me. Many more students come to me to talk about the critical appraisal, and the ones who do come are more worried about the statistics they find in the critical appraisal than the statistics they need in the research proposal. Why is this?

    When watching Zumbo’s Just Desserts, it occurred to me that the reason why is the same as the reason the Zumbo Test is harder than the Sweet Sensations challenge.

    When doing your own research you can choose to only investigate questions in such a way to use the statistical methods that you understand. Even if you need a new statistical method, you just need to learn that one. Either way, you have complete control over your own decisions and know the things you are measuring and what they mean. It’s just like in the Sweet Sensations challenge the contestants get to make all the choices and use methods they are familiar with.

    On the other hand, when reading someone else’s research, you have no control over the wacky statistical methods they choose to use. Even if they are the appropriate ones (they often are in medicine, actually), the paper almost never describes how the researchers decided to use them – it just says what they used. And they often measure new things in new ways that you don’t deeply understand. It’s just like in the Zumbo Test the contestants have to do things that are new to them in ways that are new to them.

    It’s much much harder to understand the statistics in someone else’s research than it is to make your own.

    Let’s just hope we don’t eliminate all the students by asking them to do it with less support.

  • Why don’t people bring me raw data?

    We often get research students visiting us to get help with analysing their data, even though it is not actually our job to help them and we are not formally qualified to help either. But I still sit with them and listen to their woes and give what advice I can, because I know how little support for statistics there is at this university.

    Anyway, a lot of them come with their data all neatly organised into summary statistics: they have gone to quite some effort to calculate the mean or percentage in each group and present it in a lovely little table. They then ask how they can get their statistical analysis program to compare the means or percentages. Unfortunately, it’s at this stage I need to tell them that those summary statistics are of little use and what their stats program needs is the original big list of data. Indeed, their stats program could have quite simply calculated those summary statistics for them from the raw data.

    The poor students are usually quite crestfallen at this point because they really believed they were being helpful, and because they feel that all their hard work has been in vain. After the sting has worn off they are actually very surprised to learn that it’s the original data that the statistician and stats program needs. I long ago ceased to be surprised by their surprise, but still I wondered why they were surprised.

    I think I’ve come up with two plausible explanations.

    One of the explanations might be the way that results are presented in published research. If you pick up a research article in almost any discipline and flick to the results section, what you will see is a table listing the means or percentages in each group, with a p-value attached to tell you how different they are. If you look at the analysis section, they will say that they used this or that procedure to compare the means or compare the percentages. It’s not that surprising then that they think that it is the means themselves or the percentages themselves that are being directly compared in the statistical procedure, and that these values are the inputs the stats program needs.

    Another reason might be that we are inadvertantly sending this message in our own traditional introductory statistics courses. Usually, when we teach hypothesis testing, we focus very strongly on the null hypothesis, making sure the students carefully define the parameters of interest. And many of us teach them that the best way to choose which statistical procedure to do is to look at the null hypothesis they have made.

    For example, in a situation where a numerical outcome might be different on average in two different situations, we make sure they always say “H0: μ1 = μ2” right at the beginning. Upon seeing this null hypothesis they are supposed to respond “Of course! The unpaired t-test.” And right there we have associated the statistical procedure to directly comparing means! And then the connection is strengthened because in this case the test statistic itself actually is calculated using summary statistics — the means and standard deviations of the two groups. So we teach them to think about means and proportions as the basis on which the statistical methods work.

    But the problem is that if you’re going to get a computer to do any part of the analysis then you might as well get it to do all of it. It’s much simpler to get the computer to calculate all of those summary statistics and the test statistics and p-values all in one go for you. In fact, most statistical programs do not even give you the option of starting with aggregate data. And worse than this, some of the most common procedures such as ANOVA most emphatically do not work on the aggregate data directly, but the calculation requires all the data. And let’s not even get into non-parametric procedures where the null hypothesis itself doesn’t even have parameters.

    It seems to me that by focussing so strongly on means and proportions in our research publications and statistics teaching, we are setting up a whole lot of people to waste their time finding aggregate statistics.

    Now we can’t control the way data is presented in published research – it really does make sense to report the means of each group! However, we can control where we put the emphasis when we teach. I think that perhaps we could teach them to decide what stats to do based on the raw data, how it is organised, and the variables it contains. It’s only a theory, but I think that then they might expect that it is the raw data they need to bring to their statistician, and not the aggregates.

    This comment was left on the original blog post:

    Paul Priz 19 November 2013:
    Thanks for thinking and posting about statistics. Having struggled through the first year statistics course (2011) I now find myself more confused not less. The biggest problem that I have is the lack of discussion around the limitations of statistics. There is also something fundamentally wrong with the way in which statistics is being taught. It almost feels like there needs to be an introduction to introductory statistics.

  • Ancient boxplots

    When we learn things, we tend to get the impression that the things we learn have been passed down to us from the ancients. We think that the ways of thinking and doing we are presented with are the only way to think and do, and they were decreed by some all-knowing prophet in prehistorical time.

    This can cause some problems if you happen to be one of the people who does not naturally think and do in the ways you are shown. You can feel a bit stupid because you can’t understand the only legitimate way of understanding, which people seem to have understood since time immemorial.

    But of course, it’s just not true that the things we learn have always been known.

    This was brought home to me very clearly the other day when I learned that the boxplot was only invented in 1977. 1977! That means that when I first learned about them, they had only been in existence for twenty years!

    In some disciplines, the students get the impression that boxplots are the most natural and best possible choice for displaying numerical data, as decreed by the ancients. (To be fair, they are not told this explicitly, it’s just the impression they get.) Yet boxplots are not actually all that easy to understand for a lot of people because there’s quite a bit of abstraction between the data itself and the boxplot. If you as a student can’t understand this “most natural” way to display data, you can feel a bit like you’re stupid and have no hope to ever learn statistics.

    But they were only invented in 1977! No-one before that time thought they were the most natural way to display data or they would have been invented earlier. Even Tukey himself only created them because he thought they could clearly show very particular aspects of the data. You can’t feel stupid for not understanding something that no-one thought of until quite recently!

  • Things I didn’t learn from OZCOTS 2012

    A couple of weeks ago I found out that OZCOTS (Australian Conference on Teaching Statistics) was being held here in Adelaide. I thought that I should go to it, since I seem to be spending rather a lot of time teaching statistics these days. And so I went.

    As it turned out, I didn’t learn all that much I didn’t already know. But this is a good thing: It’s always nice to have the things you knew instinctively confirmed by those with more experience than you. So, here is a list of things I didn’t learn from OZCOTS 2012:

    1. “Real life” examples are good for teaching stats, but much more important is to have MORE examples.
    2. Successful stats courses depend on all the staff who interact with the students having the same goals.
    3. Statistical software often distracts students from the real learning.
    4. The reason students find maths boring is because they don’t understand it – being useful is secondary.
    5. Students like to have the option of talking to someone about their learning, no matter how many other resources you give them.

    Of course, there were a few new things I DID learn (such as all about how to measure ESP, and the behaviour of badgers under pressure), but they can wait for some other time…