Just a quick post to let you know that the mathstatic.co.nz site is hopefully only temporarily down, and I am working with my hosting company to get it back online ASAP. This affects the random redirect tool, the BYOP sampler tool and the experiment lab page, which will not be available until this gets sorted. I’ll update this post soon with a progress update!
It seems the issue is that some overseas dodgy folk have been using the random redirect tool for fraudalent things like phishing scams. So, I’m going to restrict the URLs that can be used – which means analysis time to identify which sites/URL patterns to accept e.g. Google forms, survey monkey etc. 🙂
mathstatic.co.nz is back up and running! It probably was a couple of hours ago, but I have been rewriting the code that processes the random redirect requests. Below are the main changes to the random redirect tool to better prevent issues in the future.
Due to abuse of this tool by dodgy folk, only links with domains on the approved list will now be accepted! Please complete this form to request a domain to be added to the approved list, but don’t expect any new additions to happen any time soon (this is a free tool remember and was created for simple classroom-based randomised experiments with Google forms).
Any random redirect URLs created using this tool can be disabled at any time. If this has happened to you and you are a legitimate teacher, educator or researcher, then send me an email and I might be able to help you.
After emailing me this morning to say everything was sorted with mathstatic.co.nz, my webhosting company then decided to set my site to “maintenance” mode this afternoon and remove some crucial code used to redirect the URLs to the right locations on my website 🙁 I’m trying to get things rest back to what they were now.
Today I demonstrated some in-class interactive activities that I had developed for my super large intro statistics lectures at a teaching and learning symposium. I’ve shared a summary of the activities and the data below.
Quick summary of the activity
1. Head to how-old.net upload or take a photo of yourself and record the age given by the #HowOldRobot
2. Complete a Google form (or similar) with your actual age and the age given by the #HowOldRobot
I also get students to draw things in class and use their drawings as data. Below are all the drawings of cats made from the demonstration today, and also from the awesome teachers who helped me out last night. If you click/touch and hold a drawing you will be able to drag it around. How many different ways can you sort the drawings into groups?
Last week I was down in Wellington for the VUW NZCER NZAMT16 Mathematics & Statistics Education Research Symposium, as well as for the NZAMT16 teacher conference. It was a huge privilege to be one of the keynote speakers and my keynote focused on teaching data science at the school level. I used the example of following music data from the New Zealand Top 40 charts to explore what new ways of thinking about data our students would need to learn (I use “new” here to mean “not currently taught/emphasised”).
It was awesome to be back in Wellington, as not only did I complete a BMus/BSc double degree at Victoria University, I actually taught music at Hutt Valley High School (the venue for the conference) while I was training to become a high school teacher (in maths/stats and music). I didn’t talk much in my keynote about the relationship between music and data analysis, but I did describe my thoughts a few years ago (see below):
All music has some sort of structure sitting behind it, but the beauty of music is in the variation. When you learn music, you learn about key ideas and structures, but then you get to hear how these same key ideas and structures can be used to produce so many different-sounding works of art. This is how I think we need to help students learn statistics – minimal structure, optimal transfer, maximal experience. Imagine how boring it would be if students learning music only ever listened to Bach.
Due to some unforeseen factors, I ended up ZOOMing my slides from one laptop at the front of the hall to another laptop in the back room which was connected to the data projector. Since I was using ZOOM, I decided to record my talk. However, the recording is not super awesome due to not really thinking about the audio side of things (ironically). If you want to try watching the video, I’ve embedded it below:
You can also view the slides here: bit.ly/followthedataNZAMT. I’m not sure they make a whole lot of sense by themselves, so here’s a quick summary of some of what I talked about:
Currently, we pretty much choose data to match the type of analysis we want to teach, and then “back fit” the investigative problem to this analysis. This is not totally a bad thing, we do it in the hope that when students are out there in the real world, they think about all the analytical methods they’ve learned and choose the one that makes sense for the thing they don’t know and the data they have to learn from. But, there’s a whole lot of data out there that we don’t currently teach students about how to learn from, which comes from the computational world our students live in. If we “follow the data” that students are interacting with, what “new” ways of thinking will our students need to make sense of this data?
Album covers are a form of data, but how do we take something we can see visually and turn this into “data”. For the album covers I used from one week of 1975 and one week of 2019, we can see that the album covers from 1975 are not as bright and vibrant as those from 2019, similarly we can see that people’s faces feature more in the 1975 album covers. We could use the image data for each album cover, extract some overall measure of colour and use this to compare 1975 and 2019. But what measure should we use? What is luminosity, saturation, hue, etc.? How could we overfit a model to predict the year of an album cover by creating lots of super specific rules? What pre-trained models can we use for detecting faces? How are they developed? How well do they work? What’s this thing called a “confusion matrix”?
An intended theme across my talk was to compare what humans can do (and to start with this), with what we could try to get computers to do, and also to emphasise how important human thinking is. I showed a video of Joy Buolamwini talking about her Gender Shades project and algorithmic bias: https://www.youtube.com/watch?v=TWWsW1w-BVo and tried to emphasise that we can’t teach about fun things we can do with machine learning etc. without talking about bias, data ethics, data ownership, data privacy and data responsibility. In her video, Joy uses faces of members of parliament – did she need permission to use these people’s faces for her research project since they were already public on websites? What if our students start using photos of our faces for their data projects?
I played the song that was number one the week I was born (tragedy!) as a way to highlight the calendar feature of the nztop40 website – as long as you were born after 1975, you can look up your song too. Getting students to notice the URL and how it changes as you navigate a web page is a useful skill – in this case, if you navigate to different chart weeks, you can notice that the “chart id” number changes. We could “hack” the URL to get the chart data for different weeks of the years available. If the website terms and conditions allow us, we could also use “web scraping” to automate the collection of chart data from across a number of weeks. We could also set up a “scheduler” to copy the chart data as it appears each week. But then we need to think about what each row in our super data set represents and what visualisations might make sense to communicate trends, features, patterns etc. I gave an example of a visualisation of all the singles that reached number one during 2018, and we discussed things I had decided to do (e.g. reversing the y axis scale) and how the visualisation could be improved [data visualisation could be a whole talk in itself!!!]
There are common ways we analyse music – things like key signature, time signature, tempo (speed), genre/style, instrumentation etc. – but I used one that I thought would not be too hard to teach during the talk: whether a song is in the major or minor key. However, listening to music first was really just a fun “gateway” to learn more about how the Spotify API provides “audio features” about songs in its database, in particular supervised machine learning. According to Spotify, the Ed Sheeran song Beautiful people is in the minor key, but me and guitar chords published online think that it’s in the major key. What’s the lesson here? We can’t just take data that comes from a model as being the truth.
I also wanted to talk more about how songs make us feel, to extend thinking about the modality of the song (major = happy, minor = sad), to the lyrics used in the song as well. How can we take a set of lyrics for a song and analyse these in terms of overall sentiment – positive or negative? There’s lots of approaches, but a common one is to treat each word independently (“bag of words”) and to use a pre-existing lexicon. The slides show the different ways I introduce this type of analysis, but the important point is how common it is to transfer a model trained within one data context (for the bing lexicon, customer reviews online) and use it for a different data context (in this case, music lyrics). There might just be some issues with doing this though!
Overall, what I tried to do in this talk was not to showcase computer programming (coding) and mathematics, since often we make these things the “star attraction” in talks about data science education. The talk I gave was totally “powered by code” but do we need to start with code in our teaching? When I teach statistics, I don’t start with pulling out my calculator! We start with the data context. I wanted to give real examples of ways that I have engaged and supported all students to participate in learning data science: by focusing on what humans think, feel and see in the modern world first, then bringing in (new) ways of thinking statistically and computationally, and then teaching the new skills/knowledge needed to support this thinking.
We have an opportunity to introduce data science in a real and meaningful way at the school level, and we HAVE to do this in a way that allows ALL students to participate – not just those in enrichment/extension classes, coding clubs, and schools with access to flash technology and gadgets. While my focus is the senior levels (Years 11 to 13), the modern world of data gives so many opportunities for integrating statistical and computational thinking to learn from data across all levels. We need teachers who are confident with exploring and learning from modern data, and we need new pedagogical approaches that build on the effective ones crafted for statistics education. We need to introduce computational thinking and computer programming/coding (which are not the same things!) in ways that support and enrich statistical thinking.
I’m pretty excited about the talks and workshops I’m doing over the next month or so! Below are the summaries or abstracts for each talk/workshop and when I get a chance I’ll write up some of the ideas presented in separate posts.
Keynote: Searching for meaningful sampling in apple orchards, YouTube videos, and many other places! (AMA, Auckland, September 14, 2019)
In this talk, I shared some of my ideas and adventures with developing more meaningful learning tasks for sampling. Using the “Apple orchard” exemplar task, I presented some ideas for “renovating” existing tasks and then introduced some new opportunities for teaching sample-to-population inference in the context of modern data and associated technologies. I shared a simple online version of the apple orchard and also talked about how my binge watching of DIY YouTube videos led to my personal (and meaningful) reason to sample and compare YouTube videos.
Workshop: Expanding your toolkit for teaching statistics (AMA, September 14, Auckland, 2019)
In this workshop, we explored some tools and apps that I’ve developed to support student’s statistical understanding. Examples were: an interactive dot plot for building understanding of mean and standard deviation, a modelling tool for building understanding of distributional variation, tools for carrying out experiments online and some new tools for collecting data through sampling.
The slides for both the keynote and workshop are embedded below:
Talk: Introducing high school statistics teachers to code-driven tools for statistical modelling (VUW/NZCER, Wellington, September 30, Auckland, 2019)
Abstract: The advent of data science has led to statistics education researchers re-thinking and expanding their ideas about tools for teaching and learning statistical modelling. Algorithmic methods for statistical inference, such as the randomisation test, are typically taught within NZ high school classrooms using GUI-driven tools such as VIT. A teaching experiment was conducted over three five-hour workshops with six high school statistics teachers, using new tasks designed to blend the use of both GUI-driven and code-driven tools for learning statistical modelling. Our findings from this exploratory study indicate that teachers began to enrich and expand their ideas about statistical modelling through the complementary experiences of using both GUI-driven and code-driven tools.
Keynote: Follow the data (NZAMT, Wellington, October 3, 2019)
Abstract: Data science is transforming the statistics curriculum. The amount, availability, diversity and complexity of data that are now available in our modern world requires us to broaden our definitions and understandings of what data is, how we can get data, how data can be structured and what it means to teach students how to learn from data. In particular, students will need to integrate statistical and computational thinking and to develop a broader awareness of, and practical skills with, digital technologies. In this talk I will demonstrate how we can follow the data to develop new learning tasks for data science that are inclusive, engaging, effective, and build on existing statistics pedagogy.
Workshop: Just hit like! Data science for everyone, including cats (and maybe dogs) (NZAMT, Wellington, October 2, 2019)
Abstract: Data science is all about integrating statistical and computational thinking with data. In this hands-on workshop we will explore a collection of learning tasks I have designed to introduce students to the exciting world of image data, measures of popularity on the web, machine learning, algorithms, and APIs. We’ll explore questions such as “Are photos of cats or dogs more popular on the web?”, “What makes a good black and white photo?”, “How can we sort photos into a particular order?”, “How can I make a cat selfie?” and many more. We’ll use familiar statistics tools and approaches, such as data cards, collaborative group tasks and sampling activities, and also try out some new computational tools for learning from data. Statistical concepts covered include features of data distributions, informal inference, exploratory data analysis and predictive modelling. We’ll also discuss how each task can also be extended or adapted to focus on specific aspects and levels of the statistics curriculum. Please bring along a laptop to the workshop.
Recently I’ve been developing and trialling learning tasks where the learner is working with a provided data set but has to do something “human” that motivates using a random sample as part of the strategy to learn something from the data.
Since I already had a tool that creates data cards from the Quick, Draw! data set, I’ve created a prototype for the kind of tool that would support this approach using the same data set.
I’ve written about the Quick, Draw! data set already:
For this new tool, called different strokes, users sort drawings into two or more groups based on something visible in the drawing itself. Since you have the drag the drawings around to manually “classify” them, the larger the sample you take, the longer it will take you.
There’s also the novelty and creativity of being able to create your own rules for classifying drawings. I’ll use cats for the example below, but from a teaching and assessment perspective there are SO many drawings of so many things and so many variables with so many opportunities to compare and contrast what can be learned about how people draw in the Quick, Draw!
Here’s a precis of the kinds of questions I might ask myself to explore the general question What can we learn from the data about how people draw cats in the Quick, Draw! game?
Are drawings of cats more likely to be heads only or the whole body? [I can take a sample of cat drawings, and then sort the drawings into heads vs bodies. From here, I could bootstrap a confidence interval for the population proportion].
Is how someone draws a cat linked to the game time? [I can use the same data as above, but compare game times by the two groups I’ve created – head vs bodies. I could bootstrap a confidence interval for the difference of two population means/medians]
Is there a relationship between the number of strokes and the pause time for cat drawings? [And what do these two variables actually measure – I’ll need some contextual knowledge!]
Do people draw dogs similarly to cats in the Quick, Draw! game? [I could grab new samples of cat and dog drawings, sort all drawings into “heads” or “bodies”, and then bootstrap a confidence interval for the difference of two population proportions]
Here’s a scenario. You buy a jumbo bag of marshmallows that contains a mix of pink and white colours. Of the 120 in the bag, 51 are pink, which makes you unhappy because you prefer the taste of pink marshmallows.
Time to write a letter of complaint to the company manufacturing the marshmallows?
The thing we work so hard to get our statistics students to believe is that there’s this crazy little thing called chance, and it’s something we’d like them to consider for situations where random sampling (or something like that) is involved.
For example, let’s assume the manufacturing process overall puts equal proportions of pink and white marshmallows in each jumbo bag. This is not a perfect process, there will be variation, so we wouldn’t expect exactly half pink and half white for any one jumbo bag. But how much variation could we expect? We could get students to flip coins, with each flip representing a marshmallow, and heads representing white and tails representing pink. We then can collate the results for 120 marshmallows/flips – maybe the first time we get 55 pink – and discuss the need to do this process again to build up a collection of results. Often we move to a computer-based tool to get more results, faster. Then we compare what we observed – 51 pink – to what we have simulated.
In particular, you can show that models other than 50% (for the proportion of pink marshmallows) can also generate data (simulated proportions) consistent with the observed proportion. So, not being able to reject the model used for the test (50% pink) doesn’t mean the 50% model is the one true thing. There are others. Like I told my class – just because my husband and I are compatible (and I didn’t reject him), doesn’t mean I couldn’t find another husband similarly compatible.
Note: The app is in terms of percentages, because that aligns to our approach with NZ high school students when using and interpreting survey/poll results. However, I first use counts for any introductory activities before moving to percentages, as demonstrated with this marshmallow example. The app rounds percentages to the closest 1% to keep the focus on key concepts rather than focusing on (misleading) notions of precision. I didn’t design it to be a tool for conducting formal tests or constructing confidence intervals, more to support the reasoning that goes with those approaches.
If you’ve been keeping track of my various talks & workshops over the last year or so, you will have noticed that I’ve become a little obsessed with analysing images (see power of pixels and/or read more here). As part of my PhD research, I’ve been using images to broaden students’ awareness of what is data, and data science, and it’s been so much fun!
The power of pixels: Using R to explore and exploit features of images
Thursday, Oct 18, 2018, 6:00 PM
G15, Science Building 303, University of Auckland 38 Princes Street Auckland, NZ
30 Members Attending
Kia ora koutou Anna Fergusson, one of our R-ladies Auckland co-organisers, will be the speaker at this meetup. We’ll explore a range of techniques and R packages for working with images, all at an introductory level. Time: 6:00 arrival for a 6:30pm start. What to bring: Laptops with R installed, arrive early if you are a beginner and would like hel…
This is not a teaching-focused workshop, it’s more about learning fun and cool things you can do with images, like making GIFs like the one below….
…. and other cool things, like classifying photos as cats or dogs, or finding the most similar drawing of a duck!
It will be at an introductory level, and you don’t need to be a “lady” to come along, just supportive of gender diversity in the R community (or more broadly, data science)! If you’ve never used R before, don’t worry – just bring yourself along with a laptop and we’ll look after you 🙂
But I haven’t seen dot-shaped ones yet, so this led me to re-develop the Quick! Draw! sampling tool to be able to create some 🙂
I was also motivated to work some more on the tool after the fantastic Wendy Gibbs asked me at the NZAMT (New Zealand Association of Mathematics Teachers) writing camp if I could include variables related to the times involved with each drawing. I suspect she has read this super cool post by Jim Vallandingham (while you’re at his site, check out some of his other cool posts and visualisations) which came out after I first released the sampling tool and compares strokes and drawing/pause times for different words/concepts – including cats and dogs!
The drawing and pause times are in seconds. The drawing time captures the time taken for each stroke from beginning to end and the pause time captures all the time between strokes. If you add these two times together, you will get the total time the person spent drawing the word/concept before either the 20 seconds was up, or Google tried to identify the word/concept. Below the word/concept drawn is whether the drawing was correctly recognised (true) or not (false).
I also added three ways to use the data cards once they have been generated using the sampling tool (scroll down to below the data cards). You can now:
download a PDF version of the data cards, with circles the same size as the circle punch shown above (2″/5cm)
download the CSV file for the sample data
show the sample data as a HTML table (which makes it easy to copy and paste into a Google sheet for example)
In terms of options (2) and (3) above, I had resisted making the data this accessible in the previous version of the sampling tool. One of the reasons for this is because I wanted the drawings themselves to be considered as data, and as human would be involved in developed this variable, there was a need to work with just a sample of all the millions of drawings. I still feel this way, so I encourage you to get students to develop at least one new variable for their sample data that is based on a feature of the drawing 🙂 For example, whether the drawing of a cat is the face only, or includes the body too.
There are other cool things possible to expand the variables provided. Students could create a new variable by adding drawing_time and pause_time together. They could also create a variable which compares the number_strokes to the drawing_time e.g. average time per stroke. Students could also use the day_sketched variable to classify sketches as weekday or weekend drawings. Students should soon find the hemisphere is not that useful for comparisons, so could explore another country-related classification like continent. More advanced manipulations could involve working with the time stamps, which are given for all drawings using UTC time. This has consequences for the variable day_sketched as many countries (and places within countries) will be behind or ahead of the UTC time.
If you’ve made it this far in the post…. why not play with a little R 🙂
I wonder which common household pet Quick! drawers tend to use the most strokes to draw? Cats, dogs, or fish?
Have a go at modifying the R code below, using the iNZightPlots package by Tom Elliott and my [very-much-in-its-initial-stages-of-development] iNZightR package, to see what we can learn from the data 🙂 If you’re feeling extra adventurous, why not try modifying the code to explore the relationship between number of strokes and drawing time!
Simulation-based inference is taught as part of the New Zealand curriculum for Statistics at school level, specifically the randomisation test and bootstrap confidence intervals. Some of the reasons for promoting and using simulation-based inference for testing and for constructing confidence intervals are that:
students are working with data (rather than abstracting to theoretical sampling distributions)
students can see the re-randomisation/re-sampling process as it happens
the “numbers” that are used (e.g. tail proportion or limits for confidence interval) are linked to this process.
If we work with the output only, for example the final histogram/dot plot of re-sampled/bootstrap differences, in my opinion, we might as well just use a graphics calculator to get the values for the confidence interval 🙂
In our intro stats course, we use the suite of VIT (Visual Inference Tools) designed and developed by Chris Wild to construct bootstrap confidence intervals and perform randomisation tests. Below is an example of the randomisation test “in action” using VIT:
Last year, VIT was made available as a web-based app thanks to ongoing work by Ben Halsted! So, in this short post I’ll show how to use VIT Online with Google sheets – my two favourite tools for teaching simulation-based inference 🙂
2. Under File –> Publish to web, choose the following settings (this will temporarily make your Google sheet “public” – just “unpublish” once you have the data in VIT Online)
Be careful to select “Sheet1” or whatever the sheet you have your data in, not “Entire document”. Then, select “Comma-separated values (.csv)” for the type of file. Directly below is the link to your published data which you need to copy for step 3.
4. At this point, your data is in VIT online, so you can go back and unpublish your Google sheet by going back to File –> Publish to web, and pressing the button that says “Stop publishing”.
The same steps work to get data from a Google spreadsheet into VIT online for the other modules (bootstrapping etc.).
[Actually, the steps are pretty similar for getting data from a Google spreadsheet into iNZight lite. Copy the published sheet link from step 2 in the appropriately named “paste/enter URL” text box under the File –> Import dataset menu option.]
In terms of how to use VIT online to conduct the randomisation test, I’ll leave you with some videos by Chris Wild to take a look at (scroll down). Before I do, just a couple of differences between the VIT Chris uses and VIT Online and a couple of hints for using VIT Online with students.
You will need to hold down ctrl to select more than one variable before pressing the “Analyse” button e.g. to select both the “Prompt” and “Height estimate in metres” variables in the giraffe data set.
Also, to define the statistic to be tested, in VIT Online you need to press the button that says “Precalculate Display” rather than “Record my choices” as shown in the videos.
Note: VIT Online is not optimised to work on small screen devices, due to the nature of the visualisations. For example, it’s important that students can see all three panels at the same time during the process, and can see what is happening!
Want to make some awesome gift tags/labels for Christmas or holiday-related presents? Here’s a fun little statistical art project. Write whatever words you want in the app below, create some secret snowflakes (the secret part being no one else will know what words you used unless of course you choose to display them), play around with colours if you want (uncheck the option to use random colours), freeze the snowflakes when you get something you like, download your masterpiece and use in some way.
Oh yeah, the snowflakes are made by rotating each letter in the words in a magical statistical way (i.e. randomness).
To make our gift labels, I made the first colour white (the background #ffffff), made the other two colours black (#000000), and then printed on to adhesive sticker paper I had left over from our wedding.
Enjoy and have a great holiday break!
Secret snowflakes app should be shown below (otherwise here is the link) – works best using a Chrome browser 🙂