In that vein of hope, Sage (a publishing company that specialise in research methods) asked me to share my experiences of online teaching our large intro statistics course, for an online event they were planning, for tertiary academics from the UK and USA. Here’s a link to the event: https://conferences.sagepub.com/supercharging-your-quantitative-online-teaching

Since the academic year tends to follow the seasons across the planet, the northern hemisphere have had a long break in the middle, whereas places like NZ have been teaching right through (with the end in sight!). Speaking to academics in the UK and USA, it was clear that many of them were nervous and unsure as to how they would deliver their courses, but more importantly, keep students’ engagement in an online environment.

My talk was aimed to provide advice on exactly this topic, and is at the core of several other blogs I have made:

Here’s a short video about my talk:

The main message I tried to convey was for academics to think about the student experience of being in an online environment. Talking from slides and uploading them to a virtual learning environment would leave their students feeling isolated and deflated. I wanted them to take a risk with their teaching and encouraged them to share a little something of themselves with their students, to include activities and learning opportunities that weren’t necessarily content linked. These approaches can then help to remind everyone (students and each other) that we’re human.

The talk was well received and formed a key theme at the event. By focusing on the well-being of students and each other, we can create an engaging and motivating learning experience. There was also a unanimous agreement that we form an online collective, mediated by Sage, to help support and encourage each other, and to share experiences of online learning. We also agreed that we needed a forum to tell others what went well, but also what hasn’t worked well.

Watch this space for more developments! And also, if you would like to be part of this collective, get in touch and I’ll make sure your name is added to the list.

So . . .. you may be wondering well why is part of the title catnaps? That’s mainly to remind me (and potentially those of you reading!) to take a catnap and try to take some sort of break this year. We’ve all worked so hard and I know many are feeling depleted. So, don’t feel guilty about giving yourself a well-earned break and recharge!

Take care and farewell for now!

]]>In summary, I feel like nothing says it better than the words of Jerry Springer: Take care of yourselves and each other Oh and take a catnap if you need it!

This what the question that I posed to my ArtsGen students (see this post for more about these students) at the start of this lesson. But I think we need some back story first.

Why witches? Usually I’m all about using real data when teaching statistics, however, in this case I made an exception. Firstly, I was trying to engage non-statistics students and the more intrigue I could bring into the lesson the better I thought my chances were. Secondly, these students had completed a history topic earlier in the semester on the Salem witch trials and I wanted to capitalise off this to draw them in. So I made up a data set of 120 women (60 witches and 60 non-witches) and compiled these into data cards.

Before this lecture I gave the students this article to read. The article describes how Target knew that a teenage customer was pregnant based on data about her shopping habits that had been collected and analysed. I showed the students how a basic classification model could be used to identify a possibly pregnant customer.

The aim of the following in-class activity was to use a similar technique to try and identify witches.

So, what do we know about witches? Or, more specifically, how are witches different from non-witches? We brainstormed and the students came up with some ideas, and I included some of my own (such as, based on the sketch from Monty Python and the Holy Grail, that a witch weighs the same as a duck).

Then we explored the data in iNZight Lite to see if any of the traits we expected showed up in the data.

Students (working in pairs) were then given a set of 20 data cards (10 witches and 10 non-witches) and instructed to develop a classification tree to separate the witches from the non-witches. They started with one rule and then moved on to using two rules. At the end they wrote down the successful classification rates.

Once the students had their rules I asked the pairs to swap data cards and to run the new cards through the classification tree. They re-calculated the success rates and almost all pairs noticed that their model was less successful with the new data cards. This gave me a chance to discuss training and testing data with the students and to share this YouTube clip:

My final message to students was that with great power comes great responsibility and that these models, and ones like them, are used by data scientists all the time with real world implications.

]]>For our model we needed to be careful, what if we misclassified someone as a witch? What if we correctly classified someone as a witch, but they’re a good witch? Thinking back to the example from Target, what are the real world implications with using data from shoppers to target advertising? The students were left with lots to think about!

… but I’m going to focus on the “answer” that gets highlighted and shown at the top of the results when you search for a specific question (the Featured Snippet). I taught a series of lectures during summer school where we used Google question/answer scenarios as inspirations for in-lecture investigation and in this post I’ll talk about one of these investigations.

**What’s in a name?**

The question/answer scenario used for this investigation is shown below:

After showing this Google result with students, we discussed investigating the “answer” provided by Google using students in the lecture. At this point in the course, we had not carried out a one sample* *t-test on a mean, so this activity also served as an introduction to this method.

After discussing the parameter (the mean length of first names for students in the lecture), the null hypothesis (µ = 6) and the alternative hypothesis (µ ≠ 6), I then asked students to discuss with each other how we were actually going to take a random sample of students from those sitting in the lecture theatre. One suggestion was that I could number everyone in the room (around 120 students) and then generate random numbers to select the sample.

Another suggestion was to use the ID number that each student is assigned when they login into Qwizdom QVR (an audience response system). We talked about an issue with using this approach – that only 56 students were logged in at this point in the lecture. Using this approach, the sampling frame would not match the population and we would have selection bias.

So we went with a sampling approach based on what day of the month a student was born. I explained I would generate a random number between 1 and 31 and then whoever was born on this day would be part of the sample. I asked students what I was assuming by using this method of taking a “random” sample and what the limitations were. I then showed my students data from Stats NZ based on births in NZ during 1980 to 2017 and we discussed the fact that not all the months have 31 days!

I then opened up a new Google sheet to record the sample data and demonstrated the use of the *randbetween()* function to generate random numbers between 1 and 31.

This was supposed to be a quick activity but it ended up taking ages to get a sample of nine students! There were around 120 students in the room, so I was expecting around four students per birthday randomly generated. But I found that as I generated random numbers and asked how many students were born on this day, students were reluctant to volunteer! While this part took longer than expected, it did provide a great opportunity to talk about other sources of bias in the sampling process.

I then imported the data into iNZight Lite and compared the sample mean to the hypothesised value by annotating this value (μ = 6) using the Web Paint chrome extension.

After visually assessing how different the sample mean was from the hypothesis mean (pretty close), I demonstrated using iNZight Lite to carry out a one sample t-test. Last summer when I used the same activity, I made the mistake shown below – can you spot it?

I realised I had not changed the null value for the test from 0 to 6 when I looked at the test results (recreated below using this summer’s results).

Again, this was a good opportunity to turn a mistake into a worthwhile discussion about how we need to “sense check” output. The t-test statistic has the wrong sign (it should be negative), the p-value is way too small based on our visual comparison and the sample size (not much difference and a sample size of 9) and of course the output shows hypotheses that do not match what was discussed at the start of the activity.

This time around, I didn’t make this mistake but maybe I should have intentionally! The correct t-test output is shown below:

This gives us no evidence against the null hypothesis that the mean length of first names for students in the lecture is equal to 6. We also interpreted the confidence interval to reinforce the important idea that our conclusion from this investigation was **NOT** that the mean length of first names for students in the lecture is equal to 6. We still don’t know what the value of the true mean is – that’s why the 95% confidence interval provides *a range *of plausible values for the mean length of first names for students in the lecture (in this case, 4.3 – 7.0).

We finished this activity by discussing the difference between our population (students in the lecture) versus the implied population for the Google “answer” (everyone in the world?). Next time I use this activity, I want to extend it to explore what data the average name length claim* is based on* (I’m thinking it’s the US) and whether first name length varies by country.

]]>Carrying out statistics investigations live in lectures means being prepared for things not to go exactly to plan. There’s also the potential for anyone – including the teacher – to make mistakes along the way. To me, this is worth the risk and helps to create an open and inclusive learning environment.

When I taught these two lectures in 2019 I was able to do so in person, this year I taught online via Zoom and so I had to make some changes.

I found myself wondering, *What the heck do Arts students want to know about Statistics?* But then I realised that I was thinking about Arts too narrowly and these students might be interested in a pathway in history, English, environment and society etc. These were all areas where some basic understanding of Statistics would be useful. I also remembered that statistical literacy is a fundamental skill for anyone, no matter their field. I wanted to keep the content interesting and engaging without getting technical, and I only had two lectures in which to cover everything I wanted to.

This year I titled my lectures* 7 handy tips that will change how you consume media forever – What you learn in this lecture might surprise you!* I went with a purposefully click-bait title as this led to some great discussion around how consumers are encouraged to read articles. I’ll summarise my seven handy tips and how I taught about them below:

I discussed with students how two things could be related without one necessarily causing the other one and often this meant that there was a third (lurking) variable that was doing the causing. In the case of the ice cream this was the weather. I put students into breakout rooms again to discuss what they think might be going on with the claim made in this article ( https://www.nbcnews.com/health/womens-health/sleeping-tv-may-lead-weight-gain-study-suggests-n1015816) that sleeping with the TV on leads to weight gain. Students then rejoined the main lecture to share their ideas. In spite of this being quite a difficult concept for students there were a lot of really good ideas presented and we talked about how each “lurking variable” might impact on both weight gain and on the likelihood of someone sleeping with the TV on.

After both of these lectures the students had an opportunity to ask questions. We stopped the recording and asked them to turn their cameras on. The quality of the student questions showed they had been really thinking about what we had discussed and I was quite pleased. While I definitely prefer teaching in person I think through making use of the chat box and the breakout rooms I managed to engage foundation Arts students in important statistical thinking, and for me that’s a win!

]]>Statistics courses, whether they’re introductory or more advanced, often have heavily weighted test and exam components that require students to attain a certain mark to pass the paper. Students are often told to look at past papers to see the style of questions that have been presented in previous years, to help give them an insight into what they can expect for their test/exam questions.

Introductory statistics courses tend to have multiple choice questions (MCQ) presented in tests and exams, with past papers presenting the students with solutions that often involve just the correct response. There also tends to be little or no explanation behind why the options presented in this form of assessment are incorrect. In addition, since there is the possibility of student’s randomly selecting an answer and getting it correct, they still might be unsure as to why the answer they selected is the right response to a particular question.

This can leave students very anxious, and present barriers to their ongoing learning, potentially leaving gaps in their mind.

With many of our educational institutes being closed during the pandemic, many of our controlled assessments that are usually administered on campus have had to be adapted. In our institute, we transferred many of our course’s tests and exams online, with extended assessment durations, as well as allowances being made for issues such as WI-FI connection issues and tech problems.

During semester one this year (March – June), I began to think a lot more about how students learn from certain assessments in the course that have a high contribution to the student’s overall mark, especially the test and exam assessments. So, I decided to create a series of videos going through past tests and exams, providing detailed explanations for each option in the MCQ questions. I also wanted to present them with feedback from my experiences of looking at previous student performance, sharing information about which concepts and areas of the course students find particularly challenging.

I also wanted to provide a feedback mechanism (using Google Sheets) for the students to tell me how they found the test, asking them to comment on areas related to the amount of time they had to complete it, and also whether they found it easy or challenging. I also provided them with another opportunity to tell me about parts of the course that they were finding difficult and then grouped their responses into common themes (for example, some students wanted help with understanding the difference between practical and statistical significance). Then I produced a video going over their responses, offering a series of explanations in greater detail, addressing the areas of the course they were finding difficult or were unsure if.

Students responded very well to these additions and sent me thank you emails for helping them to learn from the questions they had gotten wrong in the test, and helping them to understand some of the more difficult parts of the course they had asked for help with.

]]>Creating videos that explain past tests and exams in greater detail and developing short videos in response to student feedback can help to create a dialogue with your students, something that works on several levels. It shows that you care about their learning and want them to succeed. It also shows that you are listening to their questions and concerns, and that you can address them specifically. It also helps to form a mutual trust with your students, which can aid to build their confidence with getting to grips with the course content.

Most of us have been there, asking question after question to a room (or computer screen!) full of student’s, blank looks (or no responses online) as if you’re speaking a completely different language. The whole experience feels barren and desolate, like the surface of mars. Is it the case that no one knows the answer to your questions? Are they too difficult?. Are the students too afraid to answer because they think it’s going to be a right or wrong type situation, so they would rather keep quiet? How do I know what the problem is?

The truth is, it could be all or none of these reasons. So how can I encourage my students to participate more, you might ask? The main approach I take is to try and create a learning environment that is friendly and safe, where participation is rewarded, and students can see the value of actively engaging with the content you create. Easier said than done right?!

Since many of us are now delivering our classes online or in a remote learning mode, my tips will focus on this. Some of them can be adapted for in person teaching, however I will save this for a future post, being optimistic that one day we will get back to in person teaching! Here’s some approaches I take.

**Student choice:** Giving students low risk opportunities to have some say in what happens in the learning environment gives them some of the power. It also shows them that you value their input and are listening to them. This helps to develop trust, which is ESSENTIAL if you want them to engage, communicate and participate. One strategy I picked up was to ask students to send me a song request (a youtube link for example) which I play at the beginning of the session (mine are recorded but this can also be done in a synchronous/live online session). I ask them to make sure the song request is clean (i.e. no swear words so that it’s not offensive).

**Get to know your students and let them know something about you:** Asking students to contribute to a Google Doc you’ve set up is a great way to find out stuff about them. This could be as simple as asking where they are from, do they have pets (ask them to include pics), what’s their favourite food etc. Then you can build this into the next session, and talk about the data, perhaps explain how it could be organised or how to visualise it. This is something I talked about in more detail in another post, which I found went down really well and had a high level of participation. You can also put stuff up about you, so the questions you ask your students, get them going by putting a picture up of your pet, or tell them what your favourite food is. It makes you come across as being more human (unless you’re an alien! :))

**Gentle nudges:** Often getting your students to engage with activities, especially like the ones in this post and others I have made, might be hard to get off the ground. I’ve found that giving your students gentle nudges helps to remind them that you’re interested in what they write (on a Google Doc or Google sheet for example, or in a group blog, or online class discussion) and you actually want to listen to them. This helps to build a mutual trust, which makes it much more likely for them to communicate with you and others in the class.

Some of you may be asking, well what has all this got to do with learning about statistics? My students just want to be passive learners and sit there listening to me talk (whether this be on their laptops or in person lectures). The truth is, we live in a world where information is ubiquitous, students can find out information for themselves, they don’t need to sit there and listen for hours on end about stuff they can find out for free on the internet. Getting your students to engage with you and others in your classes is a really important first in creating a safe learning space, where they are encouraged to volunteer answers and not worry as much about getting things wrong. This will make them much more likely to engage with the actual course content you are delivering.

]]>This post has outlined several tips to get your students to participate and engage with you, whether this be online or in person. By creating a safe learning space that encourages participation and engagement, this will help your students engage with the actual content in your courses and hopefully improve their (and your!) enjoyment as well!

The activity starts by asking everyone to stand up. I show the spinner on the projector in the lecture theatre and ask students to pick a colour.

The colours – blue and silver – are based on the two colours of the chocolates that I bring to the lecture.

The game then plays out as follows:

- Pick a colour (blue or silver)
- If the spinner lands on this colour, stay standing, otherwise sit down
- Repeat!

I keep going until the number of students still standing is no more than how many chocolates I brought to the lecture AND I’ve done at least eight spins. The students still standing at the end win the chocolate that matches the colour they’ve chosen on that last spin.

I’ve seen this game used at teacher professional development sessions many times, usually with a coin rather than a spinner. My “spin” is to add chocolate that matches the two colours of the spinner and also to use this special spinner!

Give it a spin a few times, what do you notice?

I’ve found that students start to get skeptical about the spinner after about four or five spins, but the random angle/position of the spinner after each spin helps keep the “trick” going for longer than when I’ve used something more static (for example, a pack of cards where all the cards are red).

By the time we’ve got down to the “lucky” few who do end up with chocolate, the students sitting down are justifiably upset about the game and their lack of chocolate. So, I ask them to write me an argument convincing me why they deserve the chocolate!

Part of the fun with rejecting their arguments is reminding them that I never stated at any point that the spinner was fair i.e. the probability of a blue spin being 50% was something they assumed.

Sure, the probability of getting 7 or more blue spins out of 8 is pretty low **if** the probability of a blue spin is 50%, but it’s pretty high** if** the probability of a blue spin is 85%.

Want to give this activity a go? You can access the dodgy spinner here or improve the janky JavaScript code here.

]]>I haven’t tried this activity online so I’d be interested to know whether it’s as effective in this context, particularly without the lure of chocolate and the atmosphere that builds in a room each time the spinner comes up blue! Used within a large lecture environment, it’s fun way to challenge (and teach) about assumptions, which is pretty important for hypothesis testing.

So how do we choose a context that’s meaningful, and how can we learn from our experiences in knowing what types of contexts work well with our students, in terms of engaging and motivating them well? Both new and more experienced educators can find this a difficult task.

Here are several points to get you to think through, when selecting a context to explore statistical ideas and concepts:

- Which contexts do you choose? Discipline specific or interdisciplinary contexts?
- Are the contexts you have chosen interesting to your students or to you?
- Are you confident in using the context correctly, as well as the statistical terms being used?
- Can students make the conceptual leaps/relational understanding between the contextual information, and the statistical thinking skills you want them to develop?
- If you do choose an interdisciplinary context, how easily will the students be able to weave information from different disciplines together?
- Be mindful that choosing certain topics could touch a nerve with students in your class, choosing topics based on cancer for example, where someone in their family might be suffering from the disease. However, we should also endeavour not to shield our students from reality and the world that exists around us, showing them the many forms of data that exist, applicable to lots of exciting and interesting contexts.

We are currently living through a pandemic that is producing a lot of data, being an interesting and timely context. Should we use it? I think we should, although we should be mindful of the points above (being sensitive to students who may have been affected by this).

There are several other things to think about when choosing a context to teach statistical ideas, and a lot will depend on what you are actually teaching! However, I hope the points above will help you to think about the topics you choose to share with your students.

If you are thinking of doing an experiment with your students, I have written a paper that explores ways to get students to measure creativity and intelligence that you might find useful: onlinelibrary.wiley.com/doi/10.1111/test.12169

Several of the ideas shared in this post also link to a paper I wrote based on using video clips to kick-start statistical thinking: sdse.online/posts/SDSE20-002/

]]>This post outlines key points that I use to think about, when choosing engaging and motivating contexts to teach statistical ideas and concepts to several of the statistics classes I teach at university. These prompts can also be used for students in secondary schools. Please please please PLEASE! Get in touch if you’d like to bounce around ideas in relation to this post. Always happy to offer advice and love learning from others Diolch!

I scraped data from LEGO.com to get a rectangular data set containing all the LEGO sets currently for sale on the website. I introduced this to a brand new class of students in their first lecture with me and I asked them first to go on to the website and think about the following things:

- What information could be collected?
- What variables (factors) might we be able to get data on?
- How might the data be organised?
- What do you want to find out?
- What questions do you have?

I didn’t realise it at the time, but this initial exploration of the website paid off in a big way throughout the next few lectures. Students had a chance to really see where the data came from and what it was about, they could connect the variables to something they could see on the website, they got to think about what they might want to investigate and by flicking through several of the sets they built up an intuition (which may turn out to be wrong) about what they might find. On top of that LEGO was a great leveller – every student in my class had played with LEGO!

I got the students to feed back to me what variables they thought might appear in the dataset. I got some of the more obvious things like *price* and *number of pieces* but they also suggested some things that were more novel. We discussed why some of those factors could or couldn’t be measured (e.g. awesomeness) or how some of them we would have to code ourselves after scraping the data from the website (e.g. *based on Film/TV*). We discussed some issues with the data, such as how some sets didn’t have any ratings but others did. The students had some fantastic ideas.

Then we launched into exploring the data. We began with *price* and first I had the students look through LEGO.com and make an estimate of what they thought the average price was for a LEGO set. This was really interesting as some students got quite close but others had estimates that were too high because the sets they chose to look at were more high end. We then opened up the data in iNZight and created a dotplot of *price* and continued to explore from there. Over the next few lectures we created all kinds of plots and explored all kinds of variables.

I really enjoyed using a data context that was easy for every student to relate to and that got so many of them interested and excited. It created a low floor entry point as every student could look at the website and explore, plus there was a high ceiling as some students got creative with what they wanted to investigate.

]]>My student evaluations at the end of the semester were peppered with comments about how great it was having LEGO as a theme but even without those, they had fun and I had fun and that’s what learning is supposed to be.

The activity I’ll focus on in this post is somewhat of a “classic” lesson: you know the one where you compare non-random sampling vs random sampling to demonstrate bias. Existing activities include the “Eighty circles” activity in the GAISE report PRE-K-12 (Figure 22, p. 53) and the “Gettysburg Address” activity from Beth Chance and Allan Rossman’s textbook *Investigating Statistical Concepts, Applications, and Methods* (pp. 172-189). STATS MEDIC (Luke Wilcox and Lindsey Gallas) have developed a very cool version of this activity which involves sampling words from song lyrics to explore the question *Does Beyoncé Write Her Own Lyrics?*

My “online” version also uses song lyrics/word length as the context for sampling, using whatever song I like from the Top 40 charts the week I teach this activity! After telling students they need to select five words from the lyrics, I share the link to the app with them during the “live lecture”. Give the app a go below – take a “carefully selected” sample of five words (pretend like you don’t know how this activity goes!)

Because the app is linked to a Google sheet, as soon as my students complete the task, I have access to their sample means and can show them how well they did.

I do this by pre-publishing the Google sheet as a CSV, and creating a “data link” to iNZight Lite (see this video I made for the Auckland Maths Association about this process). Because I’m doing this live, after making a dot plot/box plot of the sample means, I use a Chrome extension called *Web Paint* to annotate the plot with the mean length of ** all** the words in the lyrics (3.8 characters).

Round two is repeating the lyric sampling task, but using a random sampling method instead. To facilitate the process, I share a link with students to a very similar looking app, except this one does not allow you to choose your own words. Try it out below to select five words:

This new data (the sample means) gets added to the same Google sheet, and now we can compare the two methods.

I then ask students to write a short comment about what they have learned from the activity. Depending on the class/vibe, this can be done in the chat box (which will show their names if they participate), through another app which supports anonymous comments, or in breakout rooms for group-based discussion. After reviewing some of the comments to check what I intended to be the learning outcome *actually happened*, I have a couple of slides ready to summarise the key ideas (which pretty much just reference the course notes).

This “ZOOMifyed” example follows the same approach I would use in large face-to-face lectures:

- Students interact with an app that collects data in a Google sheet.
- The data is used straight away in the lecture, typically visualised using a web-based app (iNZight Lite a Shiny app).
- Students have to discuss and write something about what we’ve learned from the activity.
- I do some sort of “wrap up” of the key ideas, including filling in any gaps or clarifying any points that didn’t quite get covered in the comments/discussion.

If you want to do something similar, but don’t know how to create a Google sheet-based app (yet – check back here in a couple of weeks!), then you could try these alternative approaches:

- Show the lyrics on your slides, ask students to pick five words, count the letters, calculate the mean, and submit their sample mean through a Google form. Make sure to add a question asking for the sample mean (use validation to ensure it’s a number) and another question asking for the sampling method (e.g. careful selection vs random selection).
- You can then use the Google sheet attached to the Google form to visualise their sample means using the software tool of your choice. If you don’t want to publish the Google sheet as a CSV, you can download the sheet as a file type of your choice (e.g. CSV, XLSX etc.)
- For the random selection of five words, you could create and share a Google sheet for students to make their own copy of, that has each word on its own row in the sheet. Students can then highlight the words and use the
*Randomise range*function from the*Data*menu to shuffle up the words, and use the first five in the shuffled list as their random sample.

]]>Before “lockdown”, a question I was often asked by colleagues concerned about the amount of “on the fly” activities in my lectures was

What about students watching the recorded lecture?I get the same question now, re-worded asWhat about students who can’t attend the “live lecture”?For both learning situations (face-to-face vs online), my students have told me that they enjoy the fact the lectures are so interactive, even when they watching a recording of the lecture. I think a key part to this is that as much as possible, all of the interactivity is captured on the recording and often there are live “whoopsies” or interesting discoveries/surprises. Even though a student who misses the lecture can’t take part in the “live” data collection activity, they seem to still appreciate the teaching approach oflearning through doing.