I have been teaching a data science class for high school students in the summers since 2016, and have wanted to catalog some of the work I have been doing with them for a while, so here is a post in that vein. For context, the class is an enrichment class for talented rising seniors in the New Hampshire public schools. It is a fun, gradeless, intensive experience where they basically take only this one class for 5 weeks, and is super focused on data analysis for performance as opposed to for theory. We use R and Tableau, though really any platform would work! Here are some things about dataviz that I have used:

The Power of Dataviz: W.E.B. Dubois, Visualizing Black America

First, what’s the point of Data Visualization? Well, it is to tell the story of some data, probably without people having to read all that much. For inspiration, we look to W.E.B. Dubois and the 1900 Paris Exhibition, where he presented a series of graphs in “The Exhibit of American Negros” that challenged narratives of the conditions of Black America at the time (h/t to my colleague Blake for suggesting it). But unlike in his essays, W.E.B. Dubois had to express these ideas in a form where people visiting an exhibition could understand important and nuanced ideas without reading a full essay! Enter… data visualization. Here is an article series about the exhibition and here is a video that gives some good context for the exhibition (from about 4:50-9:00).

But the main work we did with this came just from marveling at his graphs, which are both powerful and beautiful, as presented in this book below (you should be able to get a bunch online too):

With this book we looked at a bunch of graphs and used them to think about the following questions?

1. What message was Dubois trying to express with his graphs? How does each fit in with the wider context and purpose of his exhibition?
2. Some of these graphs are creatively presented – what messages are strengthened by the surprising visual choices?
3. Which are your favorites? Which do you find the most powerful? Which are the most effective?

Data Visualization as Storytelling: The 7 Types of Data Stories

With some motivation for the power of data storytelling, we then moved on to thinking about the types of data stories. With this as our grounding, I next help students understand the different types of stories they could tell using visualization. I use a framework from Tableau catalogued here. I find these helpful because sometimes students don’t know where to go with a dataset, but if we focus their eye on storytelling and give them some concrete frameworks to work in, they can find direction with a dataset more often rather than just making sick looking graphs.

With these, then we ask… which types of stories was W.E.B. Dubois telling? Can we find an example of each? Then we look at some other examples… here was a short homework assignment.

• Pick one of the data visualizations below and explore it. They are beautiful data visualizations. Which types of the 7 different Data Stories do you see in here (could be multiple)?
  • US Land Use [Bloomberg]
  • Gender Pay Gap [The Guardian]
  • Colorism in Vogue [Pudding]
  • Office Dialogue in Five Charts [Pudding]

Recreating Graphs: Running Data

Next, it’s time to learn the actual tools needed to create graphs. My class uses Tableau, which I would highly recommend if dataviz is something you will do all year long. I have my running data from the past couple years (I log every run!) and give them a bunch of graphs to recreate. You could do this with any dataset and any platform, but it’s a good way to get them going with the technical skills.

As they are creating the graphs, I have them write down one piece of insight they gained from each graph as a way to keep focusing their eye on a graph only being useful if it says something interesting.

Telling a Simple Story: Which was the Greatest NBA Team?

To then get them arguing with each other using graphs as evidence, we do a quick exercise with the stats of the 1996 Bulls and 2017 Warriors. Which was the best team? Which had the best typical player? What graphs (and descriptive statistics at this point too) can you use to argue your case?

A Performance Assessment: Exploratory Data Analysis

Next, it’s time to release them to work on their own. I have them do an exploratory data analysis on a data set. With raw data, how can you use the storytelling framework to tell the story of the dataset? Put together a series of graphs and measurements that give insight about the data. Here is a rubric for a similar assignment that I did during the year in a graded class.

I have used a million different data sets for this (I like to choose one that I get a lot of datasets from a newsletter called Data Is Plural. Some that I have liked in the past have been (these are all links to .csv files, sorry I don’t have them well documented with their sources!)

1. Movie gross vs. rating, length etc
2. School shootings since Columbine
3. Gun laws across the states
4. Driving deaths across the states vs. various laws

Wall-Sized Dataviz

And lastly, I wanted to outline two creative projects that my classes have done in the past to really explore dataviz in depth. The first, each year, my class has created a wall-sized Data Visualization based on a dataset. We used a mobile projector to project the graphs/titles on the wall and then covered them in painters tape. These were much easier to do in the summer than during the year, but we still did a cool one during the year too! Here are two examples, one about school shootings, and one about Wordle.

DD Day 11: odds and ends, family day! We gave them a tour of our finished school shooting data viz showing when and where school shootings happen, & the ages/ weapon sources of the shooters. The kids are (rightly) proud of this creation, lord stop in hall to ponder #datadriven22 pic.twitter.com/4KMuKtuL4V

— Bowman Dickson 🏳️‍🌈 (@bowmanimal) July 8, 2022

A brief tour of my stats class’s final project – a wall sized data visualization of some stuff about Wordle to help you play better!! #dataviz pic.twitter.com/sFrDr8OyQx

— Bowman Dickson 🏳️‍🌈 (@bowmanimal) May 31, 2022

Dear Data

And last, this is something I’ve used in the past and have loved – there are two data scientists who spent a year sending each other postcards of data visualizations based on a topic that they collected data on throughout the course of the week. They are beautiful!! I have students pick a topic, collect data on it about themselves for a few days, then creatively visualize it. Fun little exercise.

I wrote about that (and a fun data speed dating exercise) here, but check out their website for some amazing creative dataviz.

Phew!!! There are a million other things that pop up along the way, like chart junk and annotating a graph, and how pie charts suck, but these are the main pillars of my dataviz instruction.

Yesterday in Geo, I took some advice from Dan Meyer “You Don’t Have To Be The Answer Key” and set up a fun self-checking activity based on this blog post, Eye to Eye. The premise: place a sticky note on the wall, and then place a tiny mirror on the floor between you and the wall so that you can glance into the mirror and see the sticky note. The catch is that you can’t just stand and move around until you can see it, you need to place yourself, open your eyes and look, and see if you see it! The mirrors I found in the physics department were probably 3 inches in diameter, which was perfect for a little bit of precision, but enough wiggle room that this worked. It was fun because students would be really excited that it worked! And if it didn’t, they would just go back and check their calculations without needing direction from me.

Here were the three situations (I gave them the text and then they needed to show me their diagram kind of like the ones I drew below, and calculations before they were allowed to try it physically):

1. The sticky note is 7 feet up on the wall, and the mirror is 3 feet from the wall. Where should you place yourself so you can see the sticky note in mirror?

2. Now place yourself 5 feet from the wall, and place the mirror 4 feet from you. Where should you place the sticky note so that you can see it in the mirror?

3. Now place yourself 5 feet from the wall, and place the sticky note 3 feet up. Where should you place the mirror so you can see the sticky note in the mirror?

These got more difficult as they went a long, and kids did a great job with the last one solving it in a ton of different ways (most using some sort of x and 60-x on the bottom). My favorite was a boy who measured his eyes to be 63 inches off the ground.

“Well, I’m 63 inches tall, so the ratio of my height to the sticky note is 63:36, which simplifies to 21:12, but 21+12 = 33, so if I break the 60 inches on the floor into 33 pieces and then multiply that by 12, that’s how far I should place the mirror from the wall.”

Cool!

One of the things that I changed most about my teaching approach at my previous school (I’m joining a new one this fall) is an expansion of my approach to summative assessment. Our curriculum there was a collaborative problem solving curriculum based on the Exeter materials. Students would work together in class discussing and debating about ideas, and exploring the problems presented to them, so by giving traditional, sit-down, silent, period-long individual tests, we found that we weren’t really assessing them in the way we were teaching. Due to a scheduling snafu one winter, we were left without a midterm during our exam period (lollll), but we were all like… oh well, who cares? Let’s do creative things! We all tried oral exams that winter in class, and then our minds were open from there…

Here are some of the different things that I have in my toolbox now:

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The Oral Assessment

Good for: Areas of math with layered conceptual ideas underpinning them

How it could work: This was a staple for our math department. We would assign a set of problems (maybe 6-8 meaty problems) and students would have the couple of days beforehand to complete them (either with or without each other, I preferred with!). They could use whatever materials they wanted, but knew that they not only needed to solve a problem, but needed to understand it deeply, so there in essence was no way to cheat (just having the correct work on the paper didn’t really help!). Then students would come in one at at time for a 5-10 minute oral where we would roll a dice and randomly pick a couple of the problems to talk through. I preferred students just to show me work they had already completed to save time, but some colleagues had students re-do the problems for them on the board. Then I would ask questions like, “Hmm, how do you know that?” and “Does that work all the time?” or “Was that the only way to do that?” For each problem we discussed, I would give them a grade on the accuracy of their work, their mathematical discourse with me, and then a completion/accuracy grade for the rest of the assessment we didn’t get to talk about it.

I loved this because it’s pretty immediately clear who knows what they’re talking about and who doesn’t. How often do we try to assess this on written tests and get stuff like this that seem to go viral all the time (usually attacking Common Core, which is not why I’m sharing this):

Instead, you can ask specific questions, and just rephrase a bit until students understand what you are asking. I also loved when a student would have incorrect work, and I would ask a question, and they would figure out a mistake and correct their work – learning happens DURING the assessment!

If you’re wondering, “when do you have time to do something like this?” I would often do it DURING a normal written test, or give them problems to work on and try to power through my whole class in one period. I trust my students, and I know that is a luxury, but that works for me.

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The Group Assessment

Good for: When you want to assess something that takes slow thinking, or is too complicated for a written test, or when you just want to get your students sharing knowledge and ideas with each other

How it could work: There are some things that students just need to know how to do individually (how to factor, how to take a derivative etc), but problem solving skills are amplified by others, and *real* mathematicians work together.  I would have the students work on a problem together on a big whiteboard and then whenever they felt ready, they would erase their work, and then silently and individually solve the problem on their own, and this is what their grade would be based on. Some colleagues just had them do the problem together and grade that product, and my way takes longer, but I preferred not having students’ work determine each other’s grades. This was often great evidence to help people see that their way of learning and collaborating wasn’t working (if their group mates got a problem that they totally didn’t).

A fun modification is to give them the problem with the values blacked out, like this example:

They can then discuss HOW they would go about the problem, focusing on ideas, instead of specific numbers. And then, when they felt like they were done with the group, I would give them the problem with the numbers included to complete individually.

I usually would combine this with a standard test (maybe the first question) and found that it really cut the tension in the room around an assessment (it was exciting!).

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The Screencast

Good for: Presenting challenge problems, assessing understanding with homework, doing oral tests without taking up class-time, assessing understanding with coding

How it could work: This is an idea taken from Andy Rundquist (@arundquist) and many other science teachers that do this – students would take a picture of their work, upload it and record a brief 2-3 minute explanation of their work. They talked through the WHAT of their work, but also the WHY. Similar to the oral assessment, it was always super easy to tell who really understood what was going on and who was faking it. I would watch the videos and give them feedback, sometimes even requesting another video or a written response to my feedback. I especially loved this as a way to change up homework, and as a way to assess students’ understanding of the really tricky problems that we went over in class, or solved collaboratively. It was also great for assessing code because, again, it didn’t matter if everyone had the same code, I was assessing their understanding of it.

You really need an LMS, and to insist students do it the way that makes it easy for you to grade them in order for this to work, because otherwise it’s a technological hassle. I found students figured out the easiest way to do this, but would suggest Screencast-O-Matic if they needed a suggestion for an easy way to do this.

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The Toolbox Assessment

Good for: Reviewing many learning objectives, forcing students to find their own examples of things and do the art of “problem-finding”

How it could work: When I have taught Statistics, I have used coding, which makes a lot of things quicker, and generally “get through” most of the material with 3-4 weeks to go at the end of the year. I found that students struggled with APPLYING the ideas though, so came up with the toolbox assessment. I had a list of standards and skills that covered the whole year (“Running a t-Test”, “Using a Boxplot” etc.), and they needed to design small, quick statistical studies that showed proficiency on these ideas. I had 13 of them, but they could check off multiple with a single study. They would complete a study and then “present” to me and have a conversation to show me their work and understanding. I told them not to worry too much about what their product looked like (i.e. no need for tri-fold poster presentations) and would sometimes send them back to fix or re-do something. Their grade at the end was about how many of the objectives they checked out. I loved this because it put the onus on them to really figure out where something applied, instead of just regurgitating problems I made up. Though it’s not as applicable to other math classes, I could totally see this working as a review activity before a final exam.

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Twas the week before Christmas Break, when all through the school, students were complaining, and trying to do new content would make me a fool… so we did something kind of interesting in my statistics class that was a cool application and reviews a lot of great stuff with inference testing. Inspired by this book called Nabakhov’s Favorite Word is Mauve by Ben Blatt, a super cool statistics-based analysis of literature, and this post on the Stats Medic, “Does Beyonce Write Her Own Lyrics?”. The basic questions are “How can we use basic statistics to examine and tell apart writing styles? What do statistics about your own writing say about your style?”

STEP 1: WHICH OF THESE AUTHORS ARE THE SAME?

To start, I gave them a page (available here, spoilers down below) from three different books (page 154 from each book, thanks Siri for the random number!). I told them two of these were written by the same author and one was written by a different author. How could we tell who wrote what? I told them the story of Hamilton, Madison and the disputed Federalist Papers to whet their appetite as a “real-world” example of this, but to be honest, they didn’t care about this, but were VERY intrigued just by the puzzle of figuring out which authors were the same.

And the statistics began, but not from a canned dataset that they ran pre-prescribed tests on – in fact, I was scrambling that week and hadn’t tried anything myself. I had no idea this was going to work! What things could we measure about the text to tell the difference between them? Some suggestions were too difficult to measure (i.e. tone), some had nothing to do with the writer (i.e. how many lines there were on the page), but others seemed easy to measure and perhaps distinctive of a writer (frequency of commas, length of words etc.). The students were skeptical that those things could distinguish authors, but we went after it anyway! We spent about a half-hour counting various things about the text, collected them on a document and then highlighted which two of the three were roughly more alike on each measure:

Of the 16 things we measured, 8 were the same between writers G and U (and 2 others were pretty much the same between all 3). Here come some interesting statistical questions… Why might one random page be off (one sample could be skewed for no reason other than randomness)? What’s the advantage and disadvantage of measuring a bunch of things (more things = more opportunity for random associations, but more opportunity to see a pattern). Which of these differences are “significant”?

We then spent about a class on that last question. Given that we know a chi-squared test and a t-test, how could you use those on these things we measured? We did this in R, and I can give some details about that for anyone interested, but the interesting part here is getting kids to imagine how you format data so that you could use a statistical test. What do you stick in about the sentence length in a t-test? How could -ly adverbs be a chi-squared test? Are either even appropriate here? (Meh, mostly… )

THE REVEAL:
Page G is from The Causal Vacancy by J.K. Rowling.

Page U is from The Cuckoo’s Calling by Robert Galbraith.

Page S is from Big Little Lies by Liane Moriarty.

Wait… what? Those are three different authors. NOT SO FAST! Robert Galbraith is actually a pseudonym for… J.K. Rowling! (I wish I had played that up a bit more) So our statistics worked in a way – there were more similarities between G and U than the other combinations. So even when J.K. Rowling was writing under a pseudonym, her writing style was similar Cool!!!!!!

STEP 2: WHAT DOES YOUR WRITING STYLE LOOK LIKE?

Now, I wanted them to do something similar with their own writing. They had just written a joint paper with a partner, and I wanted them to see if their joint paper more closely resembled their own writing or their partners HAHAHAHAHAHA. They were hilariously sheepish about this idea, which told me immediately who had done what 🙂 (but it was all in good fun).

Enter a new tool, Count Wordsworth, an online tool that automatically measures a WHOLE BUNCH of statistics about any text that you paste in there (at which point they got mad at me because they had done so much by hand for the pages of the books, but they’re always mad at me for stuff like that). For example, here is just part of the output when I put in my teaching philosophy from my teaching portfolio:

I had them all put in a recent English paper and then find the THREE biggest differences between their paper and their partners. Again, a bunch of fun data questions – do the quotes in the paper mess things up? How about the number of words? What about the topic (English vs. a lab report)?

Then, once they had discovered the three biggest differences, I had them put in their joint paper and try to figure out whose writing style is more closely resembled. This class was a blast, and once they finished this, they were so curious so just kept exploring… Some kids put in their freshman year papers, some put in the headmaster’s emails etc. Lots of fun curiosity!

STEP 3: HOW DOES A PROFESSIONAL STATISTICIAN DO THE SAME SORT OF ANALYSIS?

Lastly, we read a short 10-page segment of the book I mentioned in the beginning,Ben Blatt’s Nabokhov’s Favorite Word is Mauve, specifically a chapter called   “Searching for Fingerprints.” It was fun to see what a professional statistician does and we talked about how he could possibly measure some of the things that he did with the computing power we have nowadays.

 

Good stuff! Happy Holidays everyone!

I played a quick, but fun and mathematically rich game in precalculus the other day that I thought I’d share. Let’s call it Rock, Paper, Triggers for now, (it’s kinda like Rock, Paper, Scissors but with Trig functions) but if you have a better name, let me know.

Each person secretly picks a trig function (SINE, COSINE or TANGENT) for themselves, and an angle to send to the other person. Then, once ready, both reveal and each person thinks about…
TheirFunctionOf(theAngleSentToThem)

Whoever’s value is higher wins.  No need for exact values, just figure out which one is bigger (and DNE automatically loses). So for example:

PERSON 1:
sin()
269°

PERSON 2:
cos()
190°

Person 1 has sin(190°) and person 2 has cos(269°). Well, both are negative, but 269° is so close to 270° that cos(269°) is a little less negative. So person 2 wins!

This was really good for number sense (no calculators), for thinking about what values of the different functions are possible, and where those values are on the unit circle.