High-School Summer Camp: A Two-Week Path to Computational Thinking

The Summer Camp Was a Success!

How far can one get in teaching computational thinking to high-school students in two weeks? Judging by the results of this year’s Wolfram High-School Summer Camp the answer is: remarkably far.

I’ve been increasingly realizing what an immense and unique opportunity there now is to teach computational thinking with the whole stack of technology we’ve built up around the Wolfram Language. But it was a thrill to see just how well this seems to actually work with real high-school students—and to see the kinds of projects they managed to complete in only two weeks.

Projects from the 2017 Wolfram Summer Camp

We’ve been doing our high-school summer camp for 5 years now (as well as our 3-week Summer School for more experienced students for 15 years). And every time we do the camp, we figure out a little more. And I think that by now we really have it down—and we’re able to take even students who’ve never really been exposed to computation before, and by the end of the camp have them doing serious computational thinking—and fluently implementing their ideas by writing sometimes surprisingly sophisticated Wolfram Language code (as well as creating well-written notebooks and “computational essays” that communicate about what they’ve done).

Over the coming year, we’re going to be dramatically expanding our Computational Thinking Initiative, and working to bring analogs of the Summer Camp experience to as many students as possible. But the Summer Camp provides fascinating and important data about what’s possible.

The Setup for the Camp

So how did the Summer Camp actually work? We had a lot of applicants for the 40 slots we had available this year. Some had been pointed to the camp by parents, teachers, or previous attendees. But a large fraction had just seen mention of it in the Wolfram|Alpha sidebar. There were students from a range of kinds of schools around the US, and overseas (though we still have to figure out how to get more applicants from underserved populations). Our team had done interviews to pick the final students—and I thought the ones they’d selected were terrific.

Students at the Wolfram Summer Camp

The students’ past experience was quite diverse. Some were already accomplished programmers (almost always self-taught). Others had done a CS class or two. But quite a few had never really done anything computational before—even though they were often quite advanced in various STEM areas such as math. But almost regardless of background, it was striking to me how new the core concepts of computational thinking seemed to be to so many of the students.

How does one take an idea or a question about almost anything, and find a way to formulate it for a computer? To be fair, it’s only quite recently, with all the knowledge and automation that we’ve been able to build into the Wolfram Language, that it’s become realistic for kids to do these kinds of things for real. So it’s not terribly surprising that in their schools or elsewhere our students hadn’t really been exposed to such things before. But it’s now possible—and that means there’s a great new opportunity to seriously teach computational thinking to kids, and to position them to pursue the amazing range of directions that computational thinking is opening up.

It’s important, by the way, to distinguish between “computational thinking” and straight “coding”. Computational thinking is about formulating things in computational terms. Coding is about the actual mechanics of telling a computer what to do. One of our great goals with the Wolfram Language is to automate the process of coding as much as possible so people can concentrate on pure computational thinking. When one’s using lower-level languages, like C++ and Java, there’s no choice but to be involved with the detailed mechanics of coding. But with the Wolfram Language the exciting thing is that it’s possible to teach pure high-level computational thinking, without being forced to deal with the low-level mechanics of coding.

What does this mean in practice? I think it’s very empowering for students: as soon as they “get” a concept, they can immediately apply it, and do real things with it. And it was pretty neat at the Summer Camp to see how easily even students who’d never written programs before were able to express surprisingly sophisticated computational ideas in the Wolfram Language. Sometimes it seemed like students who’d learned a low-level language before were actually at a disadvantage. Though for me it was interesting a few times to witness the “aha” moment when a student realized that they didn’t have to break down their computations into tiny steps the way they’d been taught—and that they could turn some big blob of code they’d written into one simple line that they could immediately understand and extend.

Suggesting Projects

The Summer Camp program involves several hours each day of lectures and workshops aimed at bringing students up to speed with computational thinking and how to express it in the Wolfram Language. But the real core of the program is every student doing an individual, original, computational thinking project.

And, yes, this is a difficult thing to orchestrate. But over the years we’ve been doing our Summer School and Summer Camp we’ve developed a very successful way of setting this up. There are a bunch of pieces to it, and the details depend on the level of the students. But here let’s talk about high-school students, and this year’s Summer Camp.

Right before the camp we (well, actually, I) came up with a list of about 70 potential projects. Some are quite specific, some are quite open-ended, and some are more like “metaprojects” (e.g. pick a dataset in the Wolfram Data Repository and analyze it). Some are projects that could at least in some form already have been done quite a few years ago. But many projects have only just become possible—this year particularly as a result of all our recent advances in machine learning.

Project suggestions from the 2017 Summer Camp


I tried to have a range of nominal difficulty levels for the projects. I say “nominal” because even a project that can in principle be done in an easy way can also always be done in a more elaborate and sophisticated way. I wanted to have projects that ranged from the extremely well defined and precise (implement a precise algorithm of this particular type), to ones that involved wrangling data or machine learning training, to ones that were basically free-form and where the student got to define the objective.

Many of the projects in this list might seem challenging for high-school students. But my calculation (which in fact worked out well) was that with the technology we now have, all of them are within range.

It’s perhaps interesting to compare the projects with what I suggested for this year’s Summer School. The Summer School caters to more experienced students—typically at the college, graduate school or postdoc level. And so I was able to suggest projects that require deeper mathematical or software engineering knowledge—or are just bigger, with a higher threshold to achieve a reasonable level of success.

Project suggestions from the 2017 Summer School


Matching Projects to Students

Before students start picking projects, it’s important that they understand what a finished project should look like, and what’s involved in doing it. So at the very beginning of the camp, the instructors went through projects from previous camps, and discussed what the “output” of a project should be. Maybe it’ll be an active website; maybe an interactive Demonstration; maybe it’ll be a research paper. It’s got to be possible to make a notebook that describes the project and its results, and to make a post about it for Wolfram Community.

After talking about the general idea of projects, and giving examples of previous ones, the instructors did a quick survey of this year’s suggestions list, filling in a few details of what the imagined projects actually were. After this, the students were asked to pick their top three projects from our list, and then invent two more potential projects of their own.

It’s always an interesting challenge to find the right project for each student—and it’s something I’ve personally been involved in at our Summer Camp for the past several years. (And, yes, it helps that I have decades of experience in organizing professional and research projects and figuring out the best people to do them.)

It’s taken us a few iterations, but here’s the approach we’ve found works well. First, we randomly break the students up into groups of a dozen or so. Then we meet with each group, going around the room and asking each student a little about themselves, their interests and goals—and their list of projects.

After we’re finished with each group, we meet separately and try to come up with a project for each student. Sometimes it’ll be one of the projects straight from our list. Sometimes it’ll be a project that the student themself suggested. And sometimes it’ll be some creative combination of these, or even something completely different based on what they said they were interested in.

After we think we’ve come up with a good project, the next step is to meet individually with each student and actually suggest it to them. It’s very satisfying that a lot of the time the students seem really enthused about the projects we end up suggesting. But sometimes it becomes clear that a project just isn’t a good fit—and then sometimes we modify it in real time, but more often we circle back later with a different suggestion.

Once the projects are set, we assign an appropriate mentor to each student, taking into account both the student and the subject of the project. And then things are off and running. We have various checkpoints, like that students have to write up descriptions of their projects and post them on the internal Summer Camp site.

I personally wasn’t involved in the actual execution of the projects (though I did have a chance to check in on a few of them). So it was pretty interesting for me to see at the end of the camp what had actually happened. It’s worth mentioning that our scheme is that mentors can make suggestions about projects, but all the final code in a project should be created by the student. And if one version of the project ends up being too difficult, it’s up to the mentor to simplify it. So however the final project comes out, it really is the student’s work.

Much of the time, the Summer Camp will be the first time students have ever done an original project. It could potentially seem daunting. But I think the fact that we give so many examples of other projects, and that everyone else at the camp is also doing a project, really helps. And in the end experiencing the whole process of going from the idea for a project to a real, finished project is incredibly educational—and seems to have a big effect on many of our students.

A Few Case Studies

OK, so that’s the theory. So what actually happened at this year’s Summer Camp? Well, here are all the projects the students did, with the titles they gave them:

Final projects from the 2017 Summer Camp


It’s a very interesting, impressive, and diverse list. But let me pick out a few semi-randomly to discuss in a bit more detail. Consider these as “case studies” for what high-school students can accomplish with the Wolfram Language in a couple of weeks at a summer camp.

Routing Airplanes around Mountains

One young man at our camp had quite a lot of math background, and told me he was interested in airplanes and flying, and had designed his own remote-control plane. I started thinking about all sorts of drone survey projects. But he didn’t have a drone with him—and we had to come up with a project that could actually be done in a couple of weeks. So I ended up suggesting the following: given two points on Earth, find how an airplane can get from one to the other by the shortest path that never needs to go above a certain altitude. (And, yes, a small-scale version of this would be relevant to things like drone surveying too.)

Here’s how the student did this project. First, he realized that one could think of possible flight paths as edges on a graph whose nodes are laid out on a grid on the Earth. Then he used the built-in GeoElevationData to delete nodes that couldn’t be visited because the elevation at that point was above the cutoff. Then he just used FindShortestPath to find the shortest path in the graph from the start to the end.

I thought this was a pretty clever solution. It was a nice piece of computational thinking to realize that the elements of paths could be thought of as edges on a graph with nodes removed. Needless to say, there were some additional details to get a really good result. First, the student added in diagonal connections on the grid, with appropriate weightings to still get the correct shortest path computation. And then he refined the path by successively merging line segments to better approximate a great-circle path, at each step using computational geometry to check that the path wouldn’t go through a “too-high” region.

Finding the shortest flight path, here from Los Angeles to New York City with an elevation ceiling of 7000 feet

Finding Kiwi Calls

You never know what people are going to come to Summer Camp with. A young man from New Zealand came to our camp with some overnight audio recordings from outside his house featuring occasional periods of (quite strange-sounding) squawking that were apparently the calls of one or more kiwi birds. What the young man wanted to do was automatic “kiwi voice recognition”, finding the calls, and perhaps distinguishing different birds.

I said I thought this wouldn’t be a particularly easy project, but he should try it anyway. Looking at what happened, it’s clear the project started out well. It was easy to pull out all intervals in his audio that weren’t just silence. But that broke up everything, including kiwi calls, into very small blocks. He solved that by the following interesting piece of code, that uses pattern matching to combine symbolic audio objects:

Wolfram Language code for kiwi-call identification project

At this point it might just have worked to use unsupervised machine learning and FeatureSpacePlot to distinguish kiwi from non-kiwi sound clips. But machine learning is still quite a hit-or-miss business—and in this case it wasn’t a hit. So what did the student do? Well, he built himself a tiny lightweight user interface in a notebook, then started manually classifying sound clips. (Various instructors commented that it was fortunate he brought headphones…)

After classifying 200 clips, he used Classify to automatically classify all the other clips. He did a variety of transformations to the data—applying signal processing, generating a spectrogram, etc. And in the end he got his kiwi classifier to 82% accuracy: enough to make a reasonable first pass on finding kiwi calls—and going down a path to computational ornithology.

Biomechanics of Walking and Running

One young woman said she’d recently gotten a stress fracture in her foot that she was told was related to the force she was putting on it while running. She asked if she could make a computational model of what was going on. I have to say I was pessimistic about being able to do that in two weeks—and I suggested instead a project that I thought would be more manageable, involving studying possible gaits (walk, trot, etc.) for creatures with different numbers of legs. But I encouraged her to spend a little time seeing if she could do her original project—and I suggested that if she got to the stage of actually modeling bones, she could use our built-in anatomical data.

The next I knew it was a day before the end of the Summer Camp, and I was looking at what had happened with the projects… and I was really impressed! She’d found a paper with an appropriate model, understood it, and implemented it, and now she had an interactive demonstration of the force on a foot during walking or running. She’d even used the anatomical data to show a 3D image of what was happening.

She explained that when one walks there are two peaks in the force, but when one runs, there’s only one. And when I set her interactive demonstration for my own daily walking regimen I found out that (as she said was typical) I put a maximum force of about twice my weight on my foot when I walk.

Biomechanics of walking and running

Banana Ripeness Classifier

At first I couldn’t tell if he was really serious… but one young man insisted he wanted to use machine learning to tell when a piece of fruit is ripe. As it happens, I had used pretty much this exact example in a blog post some time ago discussing the use of machine learning in smart contracts. So I said, “sure, why don’t you try it”. I saw the student a few times during the Summer Camp, curiously always carrying a banana. And what I discovered at the end of the camp was that that very banana was a key element of his project.

At first he searched the web for images of bananas described as “underripe”, “overripe”, etc., then arranged them using FeatureSpacePlot:

Banana Classifier: Is it a banana? If so, is it ripe?

Then he realized that he could get more quantitative by first looking at where in color space the pixels of the banana image lay. The result was that he was actually able to define a “banana ripeness scale”, where, as he described it: “A value of one was assigned to bananas that were on the brink of spoilage. A value of zero was assigned to a green banana fresh off a tree. A value of 0.5 was assigned to the ‘perfect’ banana.” It’s a nice example of how something everyday and qualitative can be made computational.

For his project, the student made a “Banana Classifier” app that he deployed through the Wolfram Cloud. And he even had an actual banana to test it on!

Banana classifier: A FeatureSpacePlot network of ripeness in images of bananas

Number Internationalization

One of my suggested projects was to implement “international or historical numeral systems”—the analogs of things like Roman numerals but for different cultures and times. One young woman fluent in Korean said she’d like to do this project, starting with Korean.

As it happens, our built-in IntegerName function converts to traditional Korean numerals. So she set herself the task of converting from Korean numerals. It’s an interesting algorithmic exercise, and she solved it with some nice, elegant code.

Wolfram Language code to translate Korean numerals to Hindu-Arabic ones

By that point, she was on a roll… so she decided to go on to Burmese, and Thai. She tried to figure out Burmese from web sources… only to discover they were inconsistent… with the result that she ended up contacting a person who had an educational video about Burmese numerals, and eventually unscrambled the issue, wrote code to represent it, and then corrected the Wikipedia page about Burmese numerals. All in all, a great example of real-world algorithm curation. Oh, and she set up the conversions as a Wolfram Language microsite on the web.

Is That a Joke?

Can machine learning tell if something is funny? One young man at the Summer Camp wanted to find out. So for his project he used our Reddit API connection to pull jokes from the Jokes subreddit, and (presumably) non-jokes from the AskReddit subreddit. It took a bit of cleanup and data wrangling… but then he was able to feed his training data straight into the Classify function, and generated a classifier from which he then built a website.

It’s a little hard to know how well it works outside of “Reddit-style humor”—but his anecdotal study at the Summer Camp suggested about a 90% success rate.

"Is this a joke?" classifier assesses how funny a question and answer are

Making and Checking Checksums

Different projects involve different kinds of challenges. Sometimes the biggest challenge is just to define the project precisely enough. Other times it’s to get—or clean—the data that’s needed. Still other times, it’s to find a way to interpret voluminous output. And yet other times, it’s to see just how elegantly some particular idea can be implemented.

One math-oriented young woman at the camp picked “implementing checksum algorithms” from my list. Such algorithms (used for social security numbers, credit card numbers, etc.) are very nicely and precisely defined. But how simply and elegantly can they be implemented in the Wolfram Language? It’s a good computational thinking exercise—that requires really understanding both the algorithms and the language. And for me it’s nice to be able to immediately read off from the young woman’s code just how these checksum algorithms work…

A checksum algorithm in the Wolfram Language

4D Plotting on a Tesseract

How should one plot a function in 4D? I had a project in my list about this, though I have to admit I hadn’t really figured out how it should be done. But, fortunately, a young man at the Summer Camp was keen to try to work on it. And with an interesting mixture of computational and mathematical thinking, he created ParametricPlot4D—then did a bunch of math to figure out how to render the results in what seemed like two useful ways: as an orthogonal projection, and as a stereographic projection. A Manipulate makes the results interactive—and they look pretty neat…

Plotting a tesseract

State-Level Mortality

In addition to my explicit list of project suggestions, I had a “meta suggestion”: take any dataset, for example from the new Wolfram Data Repository, and try to analyze and understand it. One student took a dataset about meteorite impacts; another about the recent Ebola outbreak in Africa. One young woman said she was interested in actuarial science—so I suggested that she look at something quintessentially actuarial: mortality data.

I suggested that maybe she could look at the (somewhat macabrely named) Death Master File. I wasn’t sure how far she’d get with it. But at the end of the camp I found out that she’d processed 90 million records—and successfully reduced them to derive aggregate survival curves for 25 different states and make an interactive Demonstration of the results. (Letting me conclude, for example, that my current probability of living to age 100 is 28% higher in Massachusetts than in Indiana…)

Aggregate survival curves for Indiana vs. Massachusetts

“OCRing” Regular Tiling

Each year when I make up a list of projects for the Summer Camp I wonder if there’ll be particular favorites. My goal is actually to avoid this, and to have as uniform a distribution of interest in the projects as possible. But this year “Use Machine Learning to Identify Polyhedra” ended up being a minor favorite. And one consequence was that a student had already started working on the project even before we’d talked to him—even though by that time the project was already assigned to someone else.

But actually the “recovery” was better than the original. Because we figured out a really nice alternative project that was very well suited to the student. The project was to take images of regular tilings, say from a book, and to derive a computational representation of them, suitable, say, for LatticeData.

The student came up with a pretty sophisticated approach, largely based on image processing, but with a dash of computational geometry, combinatorics and even some cluster analysis thrown in. First, he used fairly elaborate image processing to identify the basic unit in the tiling. Then he figured out how this unit was arranged to form the final tiling. It ended up being about 102 lines of fairly dense algorithmic code—but the result was a quite robust “tiling OCR” system, that he also deployed on the web.

Analyzing regular tilings

Finding Buildings in Satellite Images

In my list I had a project “Identify buildings from satellite images”. A few students thought it sounded interesting, but as I thought about it some more, I got concerned that it might be really difficult. Still, one of our students was a capable young man who already seemed to know a certain amount about machine learning. So I encouraged him to give it a try. He ended up doing an impressive job.

He started by getting training data by comparing satellite images with street maps that marked buildings (and, conveniently, starting with the upcoming version of the Wolfram Language, not only streets maps but also satellite images are built in):

Comparisons of satellite images with street maps to identify buildings

Then he used NetChain to build a neural net (based on the classic LeNet network, but modified). And then he started trying to classify parts of images as “building” or “not building”.

Classifying whether image sections contain buildings

The results weren’t at all bad. But so far they were only answering the question “is there a building in that square?”, not “where is there a building?”. So then—in a nice piece of computational thinking—the student came up with a further idea: just have a window pan across the image, at each step estimating the probability of building vs. not-building. The result was a remarkably accurate heat map of where buildings might be.

Heat maps showing building locations in images

It’d be a nice machine learning result for anyone. But as something done by a high-school student in two weeks I think it’s really impressive. And another great example of what’s now possible at an educational level with our whole Wolfram Language technology stack.

Beyond the Summer Camp

OK, so our Summer Camp was a success, and, with luck, the students from it are now successfully “launched” as independent computational thinkers. (The test, as far as I’m concerned, is whether when confronted with something in their education or their lives, they routinely turn to computational thinking, and just “write a program to solve the problem”. I’m hopeful that many of them now will. And, by the way, they immediately have “marketable skills”—like being able to do all sorts of data-science-related things.)

But how can we scale up what we’ve achieved with the Summer Camp? Well, we have a whole Computational Thinking Initiative that we’ve been designing to do just that. We’ll be rolling out different parts over the next little while, but one aspect will be doing other camps, and enabling other people to also do camps.

We’ve now got what amounts to an operations manual for how to “do a camp”. But suffice it to say that the core of it is to have instructors with good knowledge of the Wolfram Language (e.g. to the level of our Certified Instructor program), access to a bunch of great students, and use of a suitable venue. Two weeks seems to be a good length, though longer would work too. (Shorter will probably not be sufficient for students without prior experience to get to the point of doing a real project.)

Our camp is for high-school students (mainly aged 15 through 17). I think it would also be possible to do a successful camp for advanced middle-school students (maybe aged 12 and 13). And, of course, our long-running Summer School provides a very successful model for older students.

Beyond camps, we’ve had for some time a mentorships program which we will be streamlining and scaling up—helping students to work on longer-term projects. We’re also planning a variety of events and venues in which students can showcase their computational thinking work.

But for now it’s just exciting to see what was achieved in two weeks at this year’s Summer Camp. Yes, with the tech stack we now have, high-school students really can do serious computational thinking—that will make them not only immediately employable, but also positioned for what I think will be some of the most interesting career directions of the next few decades.