Teaching a service course in statistics

Most students who enrol in an initial course in statistics at university level do so because they have to. I did some research on attitudes to statistics in my entry level quantitative methods course, and fewer than 1% of the students had chosen to be in that course. This is a little demoralising, if you happen to think that statistics is worthwhile and interesting.

Teaching a service course in statistics is one of the great challenges of teaching. A “Service Course” is a course in statistics for students who are majoring in some other subject, such as Marketing or Medicine or Education. For some students it is a terminating course – they will never have to look at a p-value again (they hope). For some students it is the precursor to further applied statistics such as marketing research or biological research. Having said that, statistics for citizens is important and interesting and engaging if taught that way. And we might encourage some students to carry on.

Yet the teachers and textbook writers seem to do their best to remove the joy. Statistics is a difficult subject to understand. Often the way the instructor thinks is at odds with the way the students think and learn. The mathematical nature of the subject is invested with all sorts of emotional baggage.

Here are some of the challenges of teaching a statistics service course.

Limited mathematical ability

It is important to appreciate how limited the mathematical understanding is of some of the students in service courses. In my first year quantitative methods course, I made sure my students knew basic algebra, including rearranging and solving equations. This was all done within a business context. Even elementary algebra  was quite a stumbling block to some students, for whom algebra had been a bridge too far at school. There were students in a postgrad course I taught who were not sure which was larger, out of 0.05 and 0.1, and talked about crocodiles with regard to greater than and less than signs. And these were schoolteachers! Another senior maths teacher in that group had been teaching the calculation of confidence intervals, without actually understanding what they were.

The students are not like statisticians. Methods that worked to teach statisticians and mathematicians are unlikely to work for them. I wrote about this in my post about the Golden Rule, and how it applies at a higher level for teaching.

I realised a few years ago that I am not a mathematician. I do not have the ability to think in the abstract that is part of a true mathematician. Operations Research was my thing, because I was good at mathematics, but my understanding was concrete. This has been a surprising gift for me as a teacher, as it has meant that I can understand better what the students find difficult. Formulas do not tell them anything. Calculating by hand does not lead to understanding. It is from this philosophy that I approach the production of my videos. I am particularly pleased with my recent video about confidence intervals, which explains the ideas, with nary a formula in sight, but plenty of memorable images.

Software

One of my more constantly accessed posts is  Excel, SPSS, Minitab or R?. This consistent interest indicates that the course of software is a universal problem.  People are very quick to say how evil Excel is, and I am under no illusions as to many of the shortcomings. The main point of my post was, however, that it depends on the class you are teaching.

As I have taught mainly business students, I still hold that for them, Excel is ideal. Not so much for the statistical aspects, but because they learn to use Excel. Last Saturday the ideas for today’s posts were just forming in my mind when the phone rang, and despite my realising it was probably a telemarketer (we have caller ID on our phone) I answered it. It was a nice young woman asking me to take part in a short survey about employment opportunities for women in the Christchurch Rebuild. After I’d answered the questions, explaining that I was redundant from the university because of the earthquakes and that I had taught statistics, she realised that I had taught her. (This is a pretty common occurrence for me in our small town-city – even when I buy sushi I am served by ex-students). So I asked her about her experience in my course, and she related how she would never have taken the course, but enjoyed it and passed. I asked about Excel, and she told me that she had never realised what you could do with Excel before, and now still used it. This is not an isolated incident. When students are taught Excel as a tool, they use it as a tool, and continue to do so after the course has ended.

When business students learn using Excel, it has the appearance of relevance. They are aware that spreadsheets are used in business. It doesn’t seem like time wasted. So I stand by my choice to use Excel. However if I were still teaching at University, I would also be using iNZight. And if I taught higher levels I would continue to use SPSS, and learn more about R.

Textbooks

As I said in a previous post Statistics Textbooks suck out all the fun. Very few textbooks do no harm. I wonder if this site could provide a database of statistics texts and reviews. I would be happy to review textbooks and include them here. My favourite elementary textbook is, sadly, out of print. It is called “Taking the Fear out of Data Analysis”, by the fabulously named Adamantis Diamantopoulos and Bodo Schlegelmilch. It takes a practical approach, and has a warm, nurturing style. It lacks exercises. I have used extracts from it over the years. The choice of textbook, like the choice of software, is “horses for courses”, but I think there are some horses that should not be put anywhere near a course. I do wonder how many students use textbooks as anything other than a combination lucky charm and paper weight.

In comparison with the plethora of college texts of varying value, at high-school level the pickings for textbooks are thin. This probably reflects the newness of the teaching of statistics at high-school level.  A major problem with textbooks is that they are so quickly out of date, and at school level it is not practical to replace class sets too often.

Perhaps the answer is online resources, which can be updated as needed, and are flexible and give immediate feedback. 

Emotional baggage

I was less than gentle with a new acquaintance in the weekend. When asked about my business, I told him that I make on-line materials to help people teach and learn statistics. He proceeded to relate a story of a misplaced use of a percentage as a reason why he never takes any notice of statistics. I have tired of the “Lies, damned lies, and statistics” jibe and decided not to take it lying down. I explained that the world is a better place because of statistical analysis. Much research, including medical would not be possible in the absence of methods for statistical analysis. An understanding of the concepts of statistics is a vital part of intelligent citizenship, especially in these days of big and ubiquitous data.

I stopped at that point, but have pondered since. What is it that makes people so quick to denigrate the worth of statistics? I suspect it is ignorance and fear. They make themselves feel better about their inadequacies by devaluing the things they lack. Just a thought.

This is not an isolated instance. In fact I was so surprised when a lighthouse keeper said that statistics sounded interesting and wanted to know more, that I didn’t really know what to say next! You can read about that in a previous post. Statistics is an interesting subject – really!

But the students in a service course in statistics may well be in the rather large subset of humanity who have yet to appreciate the worth of the subject. They may even have fear and antipathy towards the subject, as I wrote about previously. Anxiety, fear and antipathy for maths, stats and OR.

People are less likely to learn if they have negative attitudes towards the subject. And when they do learn it may well be “learning to pass” rather than actual learning which is internalised.

So what?

Keep the faith! Statistics is an important subject. Keep trying new things. If you never have a bad moment in your teaching, you are not trying enough new things. And when you hear from someone whose life was changed because of your teaching, there is nothing like it!

Good, Bad and Wrong: Videos about Confidence Intervals

Videos are useful teaching and learning resources

There is much talk about “flipped classrooms” and the wonders of Khan Academy, YouTube abounds with videos about everything…really! Even television news reports show YouTube clips. Teachers and instructors use videos in their teaching, and get their students to watch them at home, ready to build on in class time. A well put-together video can provide a different way of looking at a problem that helps a student to learn. Videos are endlessly patient and can be paused and watched at the students’ pace. (See my earlier post on multimedia for a fuller discourse on good multimedia.) The problem is: How is a teacher to know what is good and what is not? This seems to be especially difficult in an area like statistics.

I decided this week to see what was on offer and summarise for you all. To narrow it down I chose the topic of Confidence intervals. This topic is pretty universal to statistics courses, and is conceptually tricky. I wanted to see if there was a quick way of working out if a video is any good or not, without having to watch them. I was prepared to suffer so that my readers would not have to.

Videos about confidence intervals are mostly awful

And suffer I did. Not to beat around the bush – many of the videos I watched were awful. There is no other word for it. Not only were they slow, boring, mathematically based, unscripted and unedited, but many of them were just plain wrong. Back in 2008 I went looking for a video about confidence intervals for my students, and realised I had to make my own. It is still true. I do not doubt that the videos are well intentioned. Many of them may have been made (as mine were originally) for a specific class (or family member), and thus were not intended for a larger audience. Maybe those ones should come with disclaimers. “I’m not sure I really know what I am talking about – view at your own risk.”

I put “Confidence Intervals” into the YouTube search engine and examined nine of the top offerings. Mostly I went for the videos with the most views, as this would appear to be a way of filtering out poor material. (wrong again, as you will see) I also included two of my own videos.

Most these videos should not be seen by a wider audience. No – that’s not right – most of them should not be seen – by anyone. The impression they give of statistics is of a bumbling professor talking about formulas and looking up tables. Nothing in them gives a single hint about how interesting, applied and relevant the subject of statistics is. Maybe there needs to be a wikipedia approach to supposedly educational videos to provide quality control.There is just one video other than my own two that I approve of – by Keith Bower. (Biased, I know – feel free to respond.)

A possible way if you wish to find useful videos, might be to get the students to find a video they think is good, then you check that it is correct. Trying to find a good video about statistics is not a good use of your time – unless of course, you just go straight to the Statistics Learning Centre channel or Keith Bower. 

If any of you gentle readers have a video you think is worth a second look, please put the link in the comments.

Brief reviews of ten videos on Confidence Intervals in no especial order except that I left the three good ones until last

I started with the videos that appeared at the top. They have paid to be first in the list, so I thought they might be good. As it turns out they are very similar to each other and from the same stable, it seems. I found them lacklustre, though not totally harmful.

1. Statistics – Confidence Intervals
Channel: EducatorVids2                Videos on the channel: 1192
17268 views  Loaded 24 Oct 2011 (32 views per day)    Duration 3:25

This video and the next one are part of some sort of course. This video seemed to start in the middle of a lecture “Now let’s go on to some examples”. The layout was utilitarian, with a talking head, and a screen showing the  working. The video, like most of them, was not scripted. The content was based on a Mathematical example with no context. I don’t really know what she was talking about. But at least it was short.

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2. Statistics: Confidence Intervals (Difference in Means)
Channel Educator.com                    Videos on the channel: 1914
7381 views, loaded 5 Nov 2009  (6 views per day) Duration 3:46

Very similar format to EducatorVids2. The bulk of the content was around a medical example with  7 subjects. Again it was not scripted. The  computation was tedious so that I had to fast forward.

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And here is the one you have all been waiting for: Khan Academy. I should know better than to suggest that the mighty Khan is less than perfect (my previous post about KA  continues to provoke defensive vitriol.) But here goes:

3. Confidence Interval 1
Khan Academy                                  Videos on the channel: 3492
167, 213 views, loaded 28 Oct 2010 (186 views per day) Duration 14:03
246 likes 20 dislikes.

Like all Khan Academy videos (as far as I know) the format is very simple with a black screen with printed example. Again the video is not scripted, and consists of a lot of repetition as Khan doesn’t like empty air while he is writing.It is actually a lead into confidence intervals, doing a theoretical exercise involving the sampling distribution. Thus it talks about probabilities.  It would have been better to entitle it, preparation for confidence intervals, as it doesn’t actually teach about confidence intervals, and includes probability. Khan included steps to using tables to find a t value. This video was really not nice.  And it took 14 minutes! That is 14 minutes I will never have again. It is also a long time to find out that it doesn’t actually teach about confidence intervals. This video is one of the worst of the ten I viewed, and has far more views than it ought.

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4. Statistics is easy: Confidence Interval
aghasemi4u                           Videos on the channel: 4 about statistics
a remarkable 296,456 views, loaded 23 March 2007, (136 per day)  Duration 5:00
186 likes and 83 dislikes

This video was simple and reasonably well put together, with nice diagrams, but only three slides in its five minutes.  The narration is unscripted and uses probability to describe the confidence interval (wrong!). There was a focus on the mathematical formula.

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5. . Confidence Intervals
Madonna USI                          Videos on the channel: 22
18,403 views        Uploaded 9 Nov 2009 (15 per day) Duration 9:42
102 likes, 2 dislikes

A brief description of what confidence intervals are as well as a couple examples.Live person working on a whiteboard. Refers to a textbook. Very slow. Definition wrong – Says that we are 95% confident that the value that we found is within the range. I’m hoping this is just a slip of the tongue, but it should have been editted out.

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6. How to calculate Confidence Intervals and Margin of Error
Statistics is fun                  Videos on the channel: 80
25,750 views.   Uploaded 12 July 2011 (40 per day) Duration: 6:44
145 likes, 3 dislikes

Summarised before and after, which can be tedious. Mathematically based. Slick graphics, but glacially slow in parts. Gives an example with no context. This is not statistics! Tedious. To be fair, there are lots of positive comments, and as the title says “how to calculate confidence intervals” there is no requirement to explain what they are when you get them. The channel is all about “how to calculate” and nothing about context, so I think it is a bit of a misnomer to call it “Statistics is fun”.

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7. Confidence Intervals Part1 YouTube
Larry Shrewsbury Videos on the channel: 15
82,006 views. Uploaded on 12 Jul 2009 (128  per day) Duration 7:42
136 likes 53 dislikes

Part of an enterprise “Taking the Sadistics out of learning Statistics”
I found the voice irritating as it seems patronising. However some people find my accent distracting, (wot eksent?) so I can’t really be too hard on that. Very formula based, looking at the mathematics rather than the interpretation. The best part was an interesting animation – very nice way of looking at traditional confidence intervals that I hadn’t seen before.

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Here are the three good videos:

8. The history, use and certain limitations of confidence intervals in statistics.
Keith Bower   Videos on the channel: 49
32,883 views. Uploaded 5 Jan 2009 (21 views per day) Duration:3:25
66 likes, 5 dislikes

Keith’s presentation isn’t visually exciting, but he is correct and clear and that goes a long way. His is just a talking head – but he is an interesting presenter and very fluent. His video has branching, such that you can click to go to another video if needed. I’ve found all his videos sound and sensible. (I got “p is low, null must go” from one of his videos.)

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9. Confidence Intervals in Excel
UCMSCI              Videos on the channel
17797 views  Loaded 25 Dec 2008 (11 per day)
26 likes 0 dislikes

This was one of my earlier videos. It is scripted with visuals to help in comprehension. It takes the classical approach to confidence intervals and puts emphasis on the idea of level of confidence. Addresses the aspects that affect the width of confidence intervals. Discusses the formula for confidence intervals, and shows how to use Excel to calculate them. (I don’t think I really loaded it on Christmas day! Maybe some strange dateline thing)

10. Understanding Confidence Intervals: Statistics Help
Statistics Learning Centre   Videos on the channel: 19
550 views    Uploaded 26 March 2013  (31 per day)  6 likes 0 dislikes Duration: 4:02

This video will disappoint the mathematicians, as there are no formulas. But students love it. The point of the video is to explain what a confidence interval is, and what things affect the size of the interval. It makes use of diagrams and examples to help students understand the concepts. It is tightly scripted and edited with no wasted time. People can always pause if they need to, but it is difficult to speed up a slow presentation.

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Epilogue (Obituary?)

And there you have it, folks – there is no easy way to work out which videos are going to be useful for your students without watching them all. Sorry. And if you expect me to go through this again with another topic, you clearly didn’t get the subtext.

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.

Confidence Intervals: informal, traditional, bootstrap

Confidence Intervals

Confidence intervals are needed because there is variation in the world. Nearly all natural, human or technological processes result in outputs which vary to a greater or lesser extent. Examples of this are people’s heights, students’ scores in a well written test and weights of loaves of bread. Sometimes our inability or lack of desire to measure something down to the last microgram will leave us thinking that there is no variation, but it is there. For example we would check the weights of chocolate bars to the nearest gram, and may well find that there is no variation. However if we were to weigh them to the nearest milligram, there would be variation. Drug doses have a much smaller range of variation, but it is there all the same.

You can see a video about some of the main sources of variation – natural, explainable, sampling and due to bias.

When we wish to find out about a phenomenon, the ideal would be to measure all instances. For example we can find out the heights of all students in one class at a given time. However it is impossible to find out the heights of all people in the world at a given time. It is even impossible to know how many people there are in the world at a given time. Whenever it is impossible or too expensive or too destructive or dangerous to measure all instances in a population, we need to take a sample. Ideally we will take a sample that gives each object in the population an equal likelihood of being chosen.

You can see a video here about ways of taking a sample.

When we take a sample there will always be error. It is called sampling error. We may, by chance, get exactly the same value for our sample statistic as the “true” value that exists in the population. However, even if we do, we won’t know that we have.

The sample mean is the best estimate for the population mean, but we need to say how well it is estimating the population mean. For example, say we wish to know the mean (or average) weight of apples in an orchard. We take a sample and find that the mean weight of the apples in the sample  is 153g. If we only took a few apples, it is only a rough idea and we might say we are pretty sure the mean weight of the apples in the orchard is between 143g and 163g. If someone else took a bigger sample, they might be able to say that they are pretty sure that the mean weight of apples in the orchard is between 158g and 166g. You can tell that the second confidence interval is giving us better information as the range of the confidence interval is smaller.

There are two things that affect the width of a confidence interval. The first is the sample size. If we take a really large sample we are getting a lot more information about the population, so our confidence interval will be more exact, or smaller. It is not a one-to-one relationship, but a square-root relationship.  If we wish to reduce the confidence interval by a factor of two, we will need to increase our sample size by a factor of 4.

The second thing to affect the width of a confidence interval is the amount of variation in the population. If all the apples in the orchard are about the same weight, then we will be able to estimate that weight quite accurately. However, if the apples are all different sizes, then it will be harder to be sure that the sample represents the population, and we will have a larger confidence interval as a result.

Three ways to find confidence intervals

Traditional (old-fashioned?) Approach

The standard way of calculating confidence intervals is by using formulas developed on the assumptions of normality and the Central Limit Theorem. These formulas are used to calculate the confidence intervals of means, proportions and slopes, but not for medians or standard deviations. That is because there aren’t nice straight-forward formulas for these. The formulas were developed when there were no computers, and analytical methods were needed in the absence of computational power.

In terms of teaching, these formulas are straight-forward, and also include the concept of level of confidence, which is part of the paradigm. You can see a video teaching the traditional approach to confidence intervals, using Excel to calculate the confidence interval for a mean.

Rule of Thumb

In the New Zealand curriculum at year 12, students are introduced to the concept of inference using an informal method for calculating a confidence interval. The formula is median +/-  1.5 times the interquartile range divided by the square-root of the sample size. There is a similar formula for proportions.

Bootstrapping

Bootstrapping is a very versatile way to find a confidence interval. It has three strengths:

1. It can be used to calculate the confidence interval for a large range of different parameters.
2. It uses ALL the information the sample gives us, rather than the summary values
3. It has been found to aid in understanding the concepts of inference better than the traditional methods.

There are also some disadvantages

1. Old fogeys don’t like it. (Just kidding) What I mean is that teachers who have always taught using the traditional approach find it difficult to trust what seems like a hit-and-miss method without the familiar theoretical underpinning.
2. Universities don’t teach bootstrapping as much as the traditional methods.
3. The common software packages do not include bootstrap confidence intervals.

The idea behind a bootstrap confidence interval is that we make use of the whole sample to represent the population. We take lots and lots of samples of the same size from the original sample. Obviously we need to sample with replacement, or the samples would all be identical. Then we use these repeated samples to get an idea of the distribution of the estimates of the population parameter. We chop the tails off at a given point, and we give the confidence interval.  Voila!

Answers to the disadvantages (burn the straw man?)

1. There is a sound theoretical underpinning for bootstrap confidence intervals. A good place to start is a previous blog about George Cobb’s work. Either that or – “Trust me, I’m a Doctor!” (This would also include trusting far more knowledgeable people such as Chris Wild and Maxine Pfannkuch, and the team of statistical educators led by Joan Garfield.
2. We have to start somewhere. Bootstrap methods aren’t used at universities because of inertia. As an academic of twenty years I can say that there is NO PAY OFF for teaching new stuff. It takes up valuable research time and you don’t get promoted, and sometimes you even get made redundant. If students understand what confidence intervals are, and the concept of inference, then learning to use the traditional formulas is trivial. Eventually the universities will shift. I am aware that the University of Auckland now teaches the bootstrap approach.
3. There are ways to deal with the software package problem. There is a free software interface called “iNZight” that you can download. I believe Fathom also uses bootstrapping. There may be other software. Please let me know of any and I will add them to this post.

In Summary

Confidence intervals involve the concepts of variation, sampling and inference. They are a great way to teach these really important concepts, and to help students be critical of single value estimates. They can be taught informally, traditionally or using bootstrapping methods. Any of the approaches can lead to rote use of formula or algorithm and it is up to teachers to aim for understanding. I’m working on a set of videos around this topic. Watch this space.

Twitter for educators

Why I love Twitter

This post is about the What and Why of Twitter. I’ll leave more about the “How” for another day. Thanks to Priscilla Allan (whom I met on Facebook) for asking!

Twitter

I love Twitter. Given the choice between Facebook and Twitter, there is no competition. I once read a really good summary (in 140 characters) of the difference, but can’t find it. The essence is that on Facebook we lose friends we’ve had for years, whereas on Twitter we make friends with people we have never met. Twitter was there for me in the year of earthquake aftershock hell that we in Christchurch lived through, and hope is over.  When I was woken in the night with my pulse racing by the bed and room rocking, preceded by the sound of a large truck or train barrelling towards me, Twitter, and all my #eqnz friends were there. When I have something to say, I have an audience. No one may be listening – but sometimes they are. I have become a better and more connected educator as a result of Twitter. And often I just lol at the funny things people tweet.

I can imagine much what I just wrote made little sense to the uninitiated, so let me back up a little.

The fundamentals of Twitter explained 

For the technical stuff and how Twitter came about, just Google it. Or look at the official Twitter site. To me Twitter is like a river of communication from myriad sources. Anyone can read what anyone writes, in 140 characters or fewer, which is called a Tweet. The river of tweets flows continually, and you use a web application or a phone application to gain access to it. You can use search terms like a fishing net to find any recent tweets about any subject of interest. When you find a person you think is interesting, you click on “Follow”, and from now on anything they tweet will be channelled off automatically to your Home tab. They will also be able to send you a direct message privately. I currently follow 830 people, which gives me a fairly large amount to read. I skim a lot, or just don’t care if I miss something. Often tweets include links, which fortunately are shortened automatically by Twitter so you don’t use up your 140 characters on a really long url. I always tweet when I upload a blogpost.

I started out following app developers, as we had just brought out our game app, Rogo, and had met several developers at an iOS barcamp. I also tried to build a customer base for Rogo using Twitter, but it wasn’t successful. I follow some celebrities until they annoy or bore me and then I stop following them. I like to follow QI because it is funny and informative. I follow Jon Winokur ‏ @AdviceToWriters because one day I would like to write something longer and more gripping than a statistics teaching blog. I follow several other bloggers, because what they say interests and inspires me. I follow several news sources because you get the news through Twitter faster than any other way. Sometimes I follow people because I want them to follow me – it often works. I follow some inspirational sites, but generally only for a short time, and then I get bored and unfollow them.

I’ve ended up with a rather eclectic mixture, though generally it has left-leaning tendencies as I unfollow people whom I vehemently disagree with.

Twitter is delightfully democratic. When I bought a Pilates DVD, I tweeted to @suzannecbowen to say how much I liked the stretching part. And she tweeted back. I love it when people tweet to me, particularly in praise of my blog, videos, app or website.

When I post my blog each week, I love seeing that people “Favorite” or “Retweet” my tweet. When they do this it gets the blog out for more people to see.

Twitter for educators

It is good to hear what other people are up to and connect and share ideas. Sometimes a certain time is set aside for a discussion, such as #mathchat.  Someone posts a discussion question, and people respond. It can be a bit confusing as the comments pass each other, but also invigorating. Having to concentrate your thoughts into 140 characters is an interesting discipline.

Through #mathchat I found some teacher blogs, which are so inspiring. I’ve also had almost heated exchanges with maths teachers about the nature of statistics in relation to mathematics.  Sometimes you can attend a conference vicariously through your twitter friends. I’m looking forward to hearing about the NCTM meeting in April, via the twitter stream.

One blogger describes Twitter as like being at a party with some of the great minds of education, and just listening in.

Here is a link to a handbook on Twitter for teachers:

http://plpnetwork.com/wp-content/uploads/2012/06/twitter-handbook-for-teachers.pdf

This morning I asked the following into the ether:

Writing a blogpost about Twitter today. How do you feel about Twitter, as an educator? As a human being? #mathchat #edchat #orms #stem

I got the following responses:
Gregory Taylor ‏@mathtans
As educator, get to see new perspectives along with some echos of my own struggles. Also see there is life outside teaching.

Also, for both, get to share my interests (and sense of humour) in hope that others find it useful. Teaches being concise too!

protëa ‏@isomorphisms
twitter is a great place to discuss what one is reading.

Luis A. Apiolaza ‏@zentree
Great way to communicate with people that share my oddities; I have met a few of them in person. Learned lots. Taught some.

Reduced sense of isolation. Got tips and copies of PDF. Ignored idiots. Fascinated by breadth of interests;

What I Tweet about

And to give you an idea of what I tweet about as @Rogonic

• Mar 8 We submitted our next app for review. AtMyPace: Timeseries. It’s always exciting waiting. We hope people like it. And buy it.
• Mar 7 Not even the incentive of a Lego minifigure is enough to stop me procrastinating about writing some more questions on graph interpretation.
• Mar 7 An 8-foot-tall woman is destroying the entire music industry @amandapalmer (via @Upworthy) http://www.upworthy.com/an-8-foot-tall-woman-is-destroying-the-entire-music-industry?g=3&c=upw1 …  (This one was a Retweet)
• Mar 6  My iPhone was puppy love and my iPad was a fling. But my iPad mini is my soulmate.
• Mar 4 Shibboleth, Myxolydian, Heteroscedasticity – and Kipling http://wp.me/p24HeL-g4  Statistics #stem #orms
• Mar 2 Billy Connelly on Route 66. Magic! Maybe one day M, J and I will travel Route 66 and I’ll blog, Mark take photos, Jonathan perform.

I will leave you with some of my favourite tweets from others:

Dan Rockwell ‏@Leadershipfreak
All meetings should move from complexity and confusion to simplicity and action. Leading meetings means finding simplicity.

Patrick Honner ‏@MrHonner
@RogoNic My question is: how can someone really understand statistics without understanding probability and set theory? I don’t see how.

Renee ‏@approx_normal
@RogoNic I love your blogs and videos. I show them in my stats classes all the time. And you have great things to retweet!

Stat Fact ‏@StatFact
‘To understand God’s thoughts we must study statistics, for these are the measure of His purpose.’ — Florence Nightingale

Shaun Dakin ‏@IsCool
In one year, GUNS murdered 35 in Australia, 39 in England and Wales, 194 in Germany, 200 in Canada, and 9,484 in the United States.

Quaker Quotes ‏@QuakerQuotes
Success is the ability to go from one failure to another with no loss of enthusiasm – Churchill

Sesame Street ‏@sesamestreet
Oscar: First day of summer. For most that means it’s time to dust off the ol’ grill. Me? I prefer to leave the dust on!

Statistical Story-telling with time series data

Statistics is about story-telling.

For people who understand them, graphs tell a story. To the initiated, even a p-value, and some summary statistics can help to tell a story. Part of the role of a statistician is to extract the story from the data. The role of a statistics teacher is to enable students first to recognise that there is a story, then to enable them to tell the story through the tools of analysis and communication.

This idea of statistics as story-telling is explained in an award-winning paper byPfannkuch, Regan, Wild and Horton,Telling Data Stories: Essential Dialogues for Comparative Reasoning, which won  the inaugural Journal of Statistics Education Best Paper Award.

Time series data, especially seasonal time series data, yields its story abundantly. For this reason I changed my mind about the teaching of time series analysis at high school. I used to think that it was far too complex for high school students and should be left to higher education. In a way that is true, but if you stick to the basic concepts, it is a contextually rich area of study.

Time series data is full of little hazards, not the least being auto-correlation. We can use moving averages to take out the bumps and exponential smoothing to be more responsive to more recent data. We can deseasonalise and fit a trend line, predict and then put the seasonality back in. There are weighty (in more ways than one) volumes dedicated to time series analysis and the various discoveries and inventions that have helped us draw meaning from the past and forecast the future.

Because of the inherent complexity of time series analysis, I used to think that time series was not an appropriate part of the high school curriculum.

However, if a storytelling approach is used, backed up by appropriate software, then time series is a wonderful introduction to statistics. It is a good example of modelling, it has clear purpose, and the contexts can be fascinating.

Time series analysis is a clear example of the concept of a model, as there are so many different ways that it is possible to model a set of time series data. In contrast, when you teach linear regression with only one possible predictor variable, on data that is nicely behaved, there is generally one sensible model to use. This gives students the idea that you are trying to find “the right model”. This is not the case with time series, as models change, depending on how we choose to define the model.

Another selling-point for time series analysis is that its main function is forecasting. We all want to have crystal balls that can predict the future. The main reason we study a time series is to understand the patterns of data so that we can project into the future, usually for economic reasons. There is no question of “Why are we doing this, Miss?”, as the purpose of the analysis is self-evident.

There are numerous economic time series available from official statistics sites. In New Zealand I went to Infoshare and in the US there is Economagic.  Some of the series are fascinating. (I like the three peaks per year in jewellery sales in the US – December, February and May.)

Analysis can be difficult, and Excel is hideous for time series graphing and deseasonalising. There has been a free front end for R set up, called iNZight, which enables straight-forward time series analysis. One drawback is that it only allows for one model, which I fear perpetuates the “there is one model” mindset.

But the opportunities for storytelling are there. You can talk about trend, seasonality, variation, the relative contribution of each. As teachers and students are exposed to more and more time series graphs, they are better able to tell stories. The graphs of the seasonal shape are rich with story-telling potential.

To support this we have made four videos about time series analysis, and an app, which is still in the pipeline. We hope that these will help develop the confidence of teachers and students to tell stories about time series data. We also have further quizzes and step-by-step guide to writing up a time series analysis. You can get much of this for free from our Free Resources page on StatsLC.com.

For teachers where there is limited access to computer resources, I have an earlier post with some ideas of how to overcome this problem and emphasise the story in time series data: Teaching Time Series with Limited Computer access.

Understanding Time series analysis

Time Series analysis using iNZight:

How to write up a time series report:

and an example of a time series report (aimed at Year 13 students in New Zealand, but a good general framework for report writing.)

Excel, SPSS, Minitab or R?

I often hear this question: Should I use Excel to teach my class? Or should I use R? Which package is the best?

It depends on the class

The short answer is: It depends on your class. You have to ask yourself, what are the attitudes, skills and knowledge that you wish the students to gain in the course. What is it that you want them to feel and do and understand?

If the students are never likely to do any more statistics, what matters most is that they understand the elementary ideas, feel happy about what they have done, and recognise the power of statistical analysis, so they can later employ a statistician.

If the students are strong in programming, such as engineering or computer science students, then they are less likely to find the programming a barrier, and will want to explore the versatility of the package.

If they are research students and need to take the course as part of a research methods paper, then they should be taught on the package they are most likely to use in their research.

Over the years I have taught statistics using Excel, Minitab and SPSS. These days I am preparing materials for courses using iNZight, which is a specifically designed user interface with an R engine. I have dabbled in R, but never had students who are suitable to be taught using R.

Here are my pros and cons for each of these, and when are they most suitable.

Excel

I have already written somewhat about the good and bad aspects of Excel, and the evils of Excel histograms. There are many problems with statistical analysis with Excel. I am told there are parts of the analysis toolpak which are wrong, though I’ve never found them myself. There is no straight-forward way to do a hypothesis test for a mean. The data-handling capabilities of the spreadsheet are fantastic, but the toolpak cannot even deal well with missing values. The output is idiosyncratic, and not at all intuitive. There are programming quirks which should have been eliminated many years ago. For example when you click on a radio button to say where you wish the output to go, the entry box for the data is activated, rather than the one for the output. It requires elementary Visual Basic to correct this, but has never happened. Each time Excel upgrades I look for this small fix, and have repeatedly been disappointed.

So, given these shortcomings, why would you use Excel? Because it is there, because you are helping students gain other skills in spreadsheeting at the same time, because it is less daunting to use a familiar interface. These reasons may not apply to all students. Excel is the best package for first year business students for so many reasons.

PivotTables in Excel are nasty to get your head around, but once you do, they are fantastic. I resisted teaching PivotTables for some years, but I was wrong. They may well be one of the most useful things I have ever taught at university. I made my students create comparative bar charts on Excel, using Pivot-Tables. One day Helen and I will make a video about PivotTables.

Minitab

Minitab is a lovely little package, and has very nice output. Its roots as a teaching package are obvious from the user-friendly presentation of results. It has been some years since I taught with Minitab. The main reason for this is that the students are unlikely ever to have access to Minitab again, and there is a lot of extra learning required in order to make it run.

SPSS

Most of my teaching at second year undergraduate and MBA and Masters of Education level has been with SPSS. Much of the analysis for my PhD research was done on SPSS. It’s a useful package, with its own peculiarities. I really like the data-handling in terms of excluding data, transforming variables and dealing with missing values. It has a much larger suite of analysis tools, including factor analysis, discriminant analysis, clustering and multi-dimensional scaling, which I taught to second year business students and research students.  SPSS shows its origins as a suite of barely related packages, in the way it does things differently between different areas. But it’s pretty good really.

R

R is what you expect from a command-line open-source program. It is extremely versatile, and pretty daunting for an arts or business major. I can see that R is brilliant for second-level and up in statistics, preferably for students who have already mastered similar packages/languages like MatLab or Maple. It is probably also a good introduction to high-level programming for Operations Research students.

iNZight

This brings us to iNZight, which is a suite of routines using R, set in a semi-friendly user interface. It was specifically written to support the innovative New Zealand school curriculum in statistics, and has a strong emphasis on visual representation of data and results. It includes alternatives that use bootstrapping as well as traditional hypothesis testing. The time series package allows only one kind of seasonal model. I like iNZight. If I were teaching at university still, I would think very hard about using it. I certainly would use it for Time Series analysis at first year level. For high school teachers in New Zealand, there is nothing to beat it.

It has some issues. The interface is clunky and takes a long time to unzip if you have a dodgy computer (as I do). The graphics are unattractive. Sorry guys, I HATE the eyeball, and the colours don’t do it for me either. I think they need to employ a professional designer. SOON! The data has to be just right before the interface will accept it. It is a little bit buggy in a non-disastrous sort of way. It can have dimensionality/rounding issues. (I got a zero slope coefficient for a linear regression with an r of 0.07 the other day.)

But – iNZight does exactly what you want it to do, with lots of great graphics and routines to help with understanding. It is FREE. It isn’t crowded with all the extras that you don’t really need. It covers all of the New Zealand statistics curriculum, so the students need only to learn one interface.

There are other packages such as Genstat, Fathom and TinkerPlots, aimed at different purposes. My university did not have any of these, so I didn’t learn them. They may well be fantastic, but I haven’t the time to do a critique just now. Feel free to add one as a comment below!

Assessment – a necessary evil

My northern hemisphere twitter buddies are well into the academic year, and facing the demands of grading, while here in New Zealand we are enjoying the sunshine and trying hard not to think about going back to work. However the teachers of High School statistics in New Zealand are facing (or trying not to) an interesting challenge in the coming year. They are going to have to mark (our word for grade) essays. Eek.

One of the main reasons I majored in operations research, and became a mathematics teacher was that I was required neither to write nor grade essays. This must sound funny coming from someone who can’t stop blogging! I remember exam time as a new high school teacher, happily putting little red ticks against numerically correct answers, and occasionally pausing to decide if the working were adequate. Next to me was the also new English teacher having to give grades for essays, agonising over what the work was telling her and what grade to assign. It was hard not to feel smug.  In the end I felt sorry for her and helped with some of her marking.

Then at university I taught operations research and statistics, both of which I thought could be reasonably assessed with mainly numeric questions. But as time went on and I gained a greater understanding of my discipline and of teaching and learning I realised there was no escape. I dabbled with orals, essays, assignments and on-line assessment. I put on a brave face, and tried to focus on what I was learning from the mistakes they were making. To be sure you do learn a lot from marking student work, but the effect wears off on the 50^th script. Or sooner.

There is no escaping it…

Marking/Grading is difficult, often unpleasant and extremely important.

Feedback is a vital part of learning. Research into education and learning has shown that specific, timely feedback is possibly THE most useful thing to help people to learn. Well duh!  As an aside, this is one of the reasons I have reservations about giving too much homework in mathematics. If the students don’t check their work as they go, in the absence of correct feedback they can often entrench wrong procedures and thinking.

As we learn we need to make sure that we are learning correctly, in a physically and emotionally safe environment. This is why flight simulators were invented, so pilots could practice crashing – or rather not crashing, while remaining alive.

This is one of the reasons I fell in love with my Learning Management System. Originally it was hosted by WebCT, then Blackboard and (I hope finally) Moodle. (Clearly a non-specific love-affair!) A good LMS can give non-judgmental, correct, timely, specific feedback FOREVER! It never gets tired. We had a student who struggled with English, who sat one of our on-line tests over 70 times. He got there in the end, with the help of several of my more patient tutors. But there is no way we could have given him the time he needed, in the way the LMS did.

Of course there is only a certain range of assessment possible for automatic grading, but I have been experimenting with different ideas, and have managed to come up with ways to provide worthwhile automated feedback to students in most circumstances. Another great thing about the LMS is that you can collect the results and quickly see what the students are getting wrong, and which distractors are most distracting!

The first reason we need to grade is to give feedback, to help students learn. This is known as formative assessment. In a school setting we can usually make this low stakes, and the students will still participate, but at university level, time pressure means that unless the assessment is “worth something”, the students who need it most are least likely to do it. We found a sizable correlation between participation in the small tests and grades in the course as a whole. We don’t claim causation, but that doesn’t mean it isn’t there!

The other main reason for assessment is to evaluate the learning at the end of the course. The formal term for this is summative assessment. This is what tells the student and future employer how well they did in the student did in the assessment at the time. It may or may not tell anyone how much the student knows, especially some time later.

Miscellaneous thoughts on assessment and grading:

• Align assessment with learning objectives. Don’t ask what you haven’t specified and taught. (Except for scholarship exams when you can do what you like!)
• Students will only learn what is assessed – if you want them to learn something, put it in the objectives, tell the students and then assess it.
• Be clear in your mind what the assessment is for. Normative or summative? Mastery or brilliance? Encouragement through success or scaring them to do some work? Signalling important points to students in later years? Propaganda?
• Spend the time devising a good test, and you will save time and pain in the marking.  Write-on answer booklets save time.  On-line saves even more!
• Don’t ask more questions of the same type than you need to. You aren’t getting more information.
• Be careful with the word “how”. It is almost always ambiguous.
• Make sure that ignorance of the non-subject-specific context of the question will not affect the ability to answer. An example – There can be questions involving reading tables that assume that the person knows that Shirley is a girl and will therefore use the female sizing chart. For non-native speakers (and even people from other English-speaking countries) this is not a reasonable expectation.
• Don’t agonise – if a student is borderline you are probably being too generous. It isn’t personal.
• Do not assign half marks.
• Be creative. Try orals.

This is not the last you will hear about assessment. I am currently developing a suite of videos, quizzes, writing guides and an app for teaching and learning basic time-series analysis. Assessing learning for this topic is an interesting problem. Watch this space.

Mathematical recreation

Here in New Zealand it is still the summer holidays, and it is difficult to feel too excited about topics of great moment, even if it is the International Year of Statistics and the start of Mathematics of Planet Earth 2013!

While the sun shines in a clear blue Christchurch sky, in the interests of mathematical recreation I will tell you about Rogo, a new number puzzle that we hope will soon become as popular as Sudoku.

A  simple Rogo puzzle

We came up with the idea for Rogo a few years ago. I have always loved board games, and was trying to invent one based around the sport of Rogaining. (I still have hopes to bring that one to fruition one day.) Instead we came up with a puzzle that can be done with pen and paper, or on an iPhone/iPad/iPod touch. It is based on the traveling salesperson problem, with prize collection and subset selection, all on a rectilinear grid.

It’s surprisingly fun and engrossing (and to use a somewhat overused term, addictive!).

Children as young as six or seven like to play on the Rogo app, as do adults all over the world. Our greatest fan is Martin, in Austria, and having solved the 384 puzzles on the iPad, he is keen for us to make another set. I think we need to sell some more of our current version first!

You can see a YouTube video on how to play on the iPhone here:

Or an early Youtube video on how to solve Rogo on paper here:

You can buy the app here (sorry only iOS at present): Link to the AppStore. (Please do!)

You can get daily paper puzzles here: Daily puzzles

We have a website dedicated to Rogo, where there is a useful page about how Rogo can be used in teaching. This is aimed at school level problem-solving, science fair, extension and numeracy development. For a University course involving heuristics, Rogo is a great medium through which to illustrate and teach different search algorithms.

We have done some research into what makes a Rogo difficult. We came up with twelve potential  factors in the determination of difficulty.  You can read about that in our paper:Determining Degree Of Difficulty In Rogo, A TSP-based Paper Puzzle

Solving Rogo

The computational solution of Rogo is mathematically challenging. In the early days of developing our algorithm my laptop would overheat and shut down if I tried to solve too many bigger Rogos.

Hakan Kjellerstrand wrote about solving Rogo in a blog about constraint programming.

Recently Chris Kuip blogged about Rogo in AIMMS Rogo Solver using constraint programming

You can read about our algorithm in the Journal of Information Processing.

Have fun!

Teaching time series with limited computer access

How do you teach statistics with limited access to computers?

Last century this wasn’t really an issue, at least not in high schools, as statistics has been a peripheral part of the mathematics curriculum and the mathematics of statistics has been taught as a subset of mathematics.

But this is changing, and it looks as if the change is starting in New Zealand. The NZ school curriculum has leapt ahead of the rest of the world. Statistics is taught at all levels and at the higher levels of high school, statistics is taught as it is actually done in practice – using computers. All analysis is done by a computer package, particularly using iNZight, a purpose-built, free package. The emphasis is on understanding, concepts and critical thinking, rather than the mechanical and slow application of formulas. The rigour has moved from the calculations to the meaning. It is SO exciting!

One big concern for many teachers is access to computers. In many schools there aren’t enough computer suites to schedule the students in for their statistics classes. So how do we deal with this?

It might seem that the computers are needed every day, but in fact they aren’t. And neither is it necessary to have one computer per student.

Make them share

I’ve never had a problem when students have had to share computers. I find the people who do share a computer, learn better than those who are trying to work it out on their own. I actively encourage sharing computers in a lab.

I recently had the opportunity to be on the learning end, with computer instruction. The teacher was showing what to do at the front, and we in the class were echoing her steps on our computers. This is not ideal, as it requires everyone to be at the same pace, but as we were adults it was fine. I hadn’t brought my laptop, so I was sharing with another student. I’m pretty sure I learned more, as I got to follow what was happening on both computers, rather than trying to work it out and keep up. I was also able to help my partner, as she would lose track of what was happening when her computer wasn’t doing what it was meant to.

I have found this to be true at all levels, especially when learning a new package. Having two heads at the computer encourages discussion, which is an important element in learning. Students are also more likely to ask questions when they have already discussed a problem with another student. Pairing is so useful that some software companies get programmers to work in pairs, sharing a computer and work desk, because they have discovered that this has benefits.

Think about what we are trying to teach

I am currently developing resources for a unit in time series analysis, based on the New Zealand curriculum, and using the free software, iNZight. At first glance, you might think that the entire unit would need to be taught in a computer lab. This is definitely not the case. And because of the layout of many computer labs, in fact you are better to stay out of them for most of the unit so that students can work in groups.

I find that it is worthwhile to think about the attitudes, skills and knowledge that we wish our pupils to develop in a unit – in that order of importance! These examples are illustrative rather than exhaustive.

Attitudes – By the end of the topic all students should feel that time series analysis is interesting and relevant (and maybe even fun!).

Time series analysis is pretty straightforward at the beginner level, but can be quite exciting. Once you know the basics, and with a convenient package to speed up the mechanics, you can do some interesting detective work. I would want the students to share some of this excitement, and start to explore on their own.

Skills

Students should be able to:

• identify elements of a time series, relating them to the real life context.
• write a report on a time series analysis using correct terminology, clear enough for a non-expert reader to understand.
• use iNZight to analyse different time series.

Knowledge

• Student should be able to explain and apply the following terms correctly: time series, trend, seasonality, stationary, noise, variation

And that is about it really!

So how do we do this, with or without full computer access.

Even with unlimited computer access I would get students to work in pairs for much of the time. I would start away from the computers. First display graphs of time series to the class and get them to write down sentences about them in their pairs. Then share with the class. We should get sentences like, “It mainly goes up, and then it goes down” and “there is a pattern that repeats”. From that the teacher can introduce the ideas of trend, seasonality and noise, modelling the correct use of specialist language.

Then I would talk about the context – or maybe the context should have come first… The time series chosen should be one with an easy to identify context, such as retail sales of recreational goods, or patterns of tourist arrivals. These series are available in New Zealand at Infoshare or in iNZight format via Statslc. Other countries will have similar series available. Again get the students to write down sentences, this time relating them to the context.

Homework could be to find a graph of a time series on-line or in a magazine. Or to make a list of things that might show seasonality.

Next I would get the students onto the computers in pairs. They should have a worksheet like the one here, so that they can work step-by-step through the package at their own pace in pairs. At some time during the class they could swap roles, if one has been instructing and the other operating.

The data set here RetailNZTS4 has four series in it, which show different behaviours. Students should see if they can get all the graphs they need for further analysis.

Four time series compared using iNZight software

The next class is away from the computers again. Here they are writing sentences about the graphs. They should do this alone, and in pairs, and compare in groups. It would be good to have a computer or two available for students to take turns to get any graphs they might find they need. When people are in front of a computer it tends to dominate their thinking and they can produce far too much output with very little thought. Moving away from the computer encourages a more reflective approach.

Then start on another data set. I would use the one about accommodation, AccRegNZTS13 comparing the seasonal patterns of occupancy in different regions of New Zealand. If there are enough computers, the students can spend one day creating the graphs and exploring, then the next day writing it up. Maybe different groups could take different regions, and find out why the pattern is the way it is for that region, then report back to the class.

Then the teacher may like to give some of the mathematical background to how a computer package would go about producing the output.RetailNZTS4

The learning is in the writing and the talking.

The point I’m trying to make is that you actually need to move away from the computers quite often. If you are REALLY stuck for computers you could even print off (and laminate?) the outputs from the different time series, so that the students can study and discuss them. Number or name them for easy reference, and have question sheets to go with them.The computer is only the tool, and with a bit of creativity, we can still teach the important attitudes, skills and knowledge with limited computer access.

I am aware as I am writing this that it is some time since I taught a class of high school students. I would be thrilled to hear comments from the “chalk-face” as to how realistic you think this is! And of course other suggestions will be welcome for teaching a computer-rich subject in a computer-poor environment.

Having said that, one of my experiences as a trainee teacher was having to teach my first lesson to a class at Rotorua Lakes High School during a powercut – which meant no computers and no OHP. We did desk-checking (how you can use pen and paper to look for bugs in code) and it went surprisingly well.