It Takes a Team

When I think of computer science educators, computer science education, and computer science curricula, I think about all the people needed to make it a successful endeavor in a school district and in a larger community as well.  Who are the they? How do you leverage their roles to help further computer science education? Three years ago, my district, Valhalla UFSD, embarked on a journey to bring computer science to ALL of our students, K-12.

Valhalla is a small middle to upper-middle class suburban district outside of New York City.  We have approximately 1600 students districtwide. Valhalla High School has always offered AP Computer Science A, but we needed more.  Once I began teaching the class, I petitioned for an Intro to CS course and was granted the class.  This was the beginning of the expansion, but I still had no one particularly interested in helping me promote these courses. It was up to me to make it happen.

The courses went well, but then in my very small school, AP numbers dropped and the trend in the district went away from AP courses and moved to dual enrollment courses with the local community college.  I taught C++ and numbers slowly increased over a few years. Students were getting hungry for more.

Here is where people matter.  I was approached by my principal, Mr. Jonathon Thomas, who told me that our superintendent at the time, Dr. Brenda Myers (winner of the 2017 CSTA Administrators Award), was interested in offering a game design course and wondered if I would be interested in teaching it.  Bingo! Here were my advocates for computer science education in Valhalla. A little petrified, but eager, I had a year to prepare. The course, as expected, was a big hit. As time went on, I suggested adding to our offerings a Mobile App Development course, which was also very well received.  

So now, juggling all of these courses, I realized I needed some help, in and out of school.  Outside of school, I turned to CSTA to find a local chapter to network with other teachers. To my dismay, there was no local chapter, so I chartered one.  

Inside school, I turned to Dr. Myers.  She was all for expanding CS education to the four buildings in the district, which include a K-2 primary school, 3-5 elementary school, 6-8 middle school, and the 9-12 high school.  In 2015, she called a meeting for a newly formed “Special Projects Team” of 4 computer teachers, one from each building. I looked around the room at my three colleagues, whose CS backgrounds were non-existent (they taught computer applications).  We were told we are all going to teach CS, we are all going to learn together, and yes this is going to be bumpy. I have amazing colleagues. No one blinked – we just did it.

Fast forward to today – I am back to teaching AP-CS A, and we have a comprehensive K-12 computer science, engineering, and robotics curricula, which we are currently aligning to the new CSTA Standards. Our kids are programming, thinking computationally, and problem solving in all grades.  We have the full support of our district Board of Education as well as our building and district administrators, and guidance teams. We have a community willing to approve budgets and offer grants to increase our offerings and expand our programs and invest in the technology. We owe our progress to the amazing people in Valhalla to believe in the future of computer science education.  Our children are the recipients of rich and diverse CS curricula from Kindergarten on.

So find your advocate, find your support, and find your team of players.  Reach out to your administrators, communities, and students to find out what you can do together to move computer science education forward in your district.  It’s made all the difference in ours.


Amy Fox, 9–12 Representative

Increasing equity and inclusion in computer science education

Last month I attended my first CSTA conference. I LOVED the positive energy. From the keynote speakers to the exhibition space to the breakout sessions, everyone at CSTA2018 seemed genuinely happy to be together and they were clearly excited to share, learn, and ultimately do more for students.

My favorite part of CSTA2018 was the session with Andy (Andrea) Gonzales. In short, while in high school, she and a friend created a viral video game, won a Webby Award, wrote a book, were covered by multiple media outlets and now she is on a full ride scholarship to both UNC Chapel Hill and Duke. Impressively, she’s determined to leverage her space in the spotlight to do more for other young women like herself.

Andy talked about the exclusion she felt as a young woman learning computer science. She shared that the early support of an adult (her male summer camp counselor) was key to her success today. She described the misconceptions she had about computer science and the stereotypes that so many other young women and women of color struggle with. She emerged from her experiences more empowered and now wants to empower others.

Andy and her story are impressive. And yet, the thing that struck me the most about Andy was the response she garnered from the adults in the room.

Nearly all the questions Andy fielded from the audience of 700+ computer science education teachers and advocates were about they could do more to support girls and students of color in their computer science classes. How can I get more girls to join? What do you think I can do differently? Of the few girls I have in my computer science classes, how can I get them to engage more? How do I best support my students of color?

These questions clearly articulated the teachers’ desire to do more to help ALL their current or potential CS students succeed. They also illustrated the gaps that exist for teachers to find – and then implement – the resources that would help them reach this goal.

To be clear, I am not an expert on this topic. And in full transparency, I work for a tech company that is actively working on how it makes progress on diversity, equity and inclusion internally and how it can play a role in increasing equitable access to computer science education around the world.

I do know that there is a lot of good and important work that has been done on equity and inclusion in education broadly, and specifically in math and science. And while we are making progress, and there is a lot of great research on what the issues and challenges are in diversity, equity and inclusion in computer science, what I hear from teachers and others in CS education is that we still have work to do to make practical solutions easy for teachers to bring to life, specifically for computer science.

I know that by sharing a short list of resources, I am bound to leave things out. But with the goal to start somewhere, as I’ve been on my learning journey, others have told me that the following resources and information have been helpful in their work to support success for all students in their computer science classes and programs.

I’m sure you have some you want to share – please do! Post them on Twitter, tagging @csteachersorg with the hashtag #CSforAll so others can see them too. You can view all posts that use these two tags here.

Defining the issues:

Practical tools and resources for teachers and schools:

Recent blog posts by fellow CSTA board members:

Yvonne Thomas
Partner Representative CSTA Board

Shout out to chapter leaders!

If you’re reading this blog you probably know that the CSTA annual conference happened last month in Omaha. It was my first conference as Executive Director and I had a blast! If you weren’t able to make it I hope you could engage in some of the community and conversations via #CSTA2018. What you may not know is that 70 chapter leaders from 30 states and Puerto Rico came together for a pre-conference leadership summit. The energy and excitement from this group of passionate leaders was infectious.

Amy Fox, Fran Trees, Ramsey Young, and Chinma Uche made up the amazing team of volunteer chapter leaders led the full workshop and they all deserve a huge thank you for their hard work (and willingness to put up with long video calls). At the end of the workshop we had a survey for feedback, and there was one key comment that stood out to me:

Meeting everyone and hearing that we are making progress in my state in comparison to other states. It made me feel good about what we have accomplished but also give me direction as to what still needs to be completed.

During my first six months at CSTA I’ve had the opportunity to connect with most of our chapter leaders, and over and over I’d hear about innovative programs, strong communities and passionate teachers. I’d also always hear some form of “I just don’t know if this is enough, what else should we be doing.” It’s an important reminder that just like teaching CS, volunteering to lead a chapter or pushing for policy change in your local context is often lonely work.

It’s so easy these days to turn every minute of a workshop, conference or chapter meeting into targeted programming with a specific outcome, yet whenever we look at feedback it’s clear that the most important learning happens when dedicated volunteers are given the opportunity to interact with each other. None of us live in a vacuum, and without constant opportunities to connect and hear about what’s happening across town or around the globe, we’ll never be able to level set. As an outcome of this summit we’ll be launching regular video calls for chapter leaders to connect and learn from each other throughout the year.

Remember, you’re not measuring yourself or your chapter against perfection (it’s an impossible bar to set) and as we dive into the next school year I hope you use your CSTA community as a way to level set and celebrate the little wins. Oh, and let your chapter leader know when they’re doing something great — they all made big plans and deserve much love for the work they do!

Jake Baskin, Executive Director

Contexts and Roles in CS Education

To make the case for computer science and to develop an effective program, educators must understand the context and the roles people play.

First, a few clarifications:

  • Computer science (CS) here refers to educational experiences where the primary objective is to develop computing skills and knowledge.
  • Computational thinking (CT) refers to using computational practices in CS and in other disciplines.  For example, using computer modeling and simulation in science and engineering courses.

In this post I’ll focus on the subjects and teachers with an especially strong affinity with CS / CT.  These are people that might be already teaching CS, and most definitely should be incorporating CT. They include:

  • Digital Literacy / technology integration
  • STEM  (math, science, engineering, and computer science).
  • Career & technical education (e.g. IT, engineering, business)

Other teachers, for example social studies and humanities teachers, are less likely to teach CS – it’s certainly possible, but would be a more significant departure from their regular teaching duties than the above.  However, there are ample opportunities to incorporate CT practices.

Digital literacy, educational technology, digital citizenship.

These areas, in general, are about the safe and effective use of technology for a variety of uses.  Business teachers will focus on using technology for business purposes. Technology integration specialists or library / media specialists tend to support the integration of technology across the curriculum.  While these areas are not strictly CS, these educators are excellent candidates to become CS teachers. They are also great candidates to support the integration of CT.

Note:  A comparison between these areas and computer science is available at the K12 CS Framework.  (K12CS, Defining Computer Science.)

STEM education.

In a nutshell: science is about systematically exploring phenomena; engineering is about designing and developing technologies.  Mathematics and computing are tools that are used to do science and engineering.

Computer science is fundamentally mathematical, rooted in formal logic.  Math educators are great candidates to teach CS, but it’s important to consider the primary objective.  CS can have a strong mathematical focus, for example, when you are working with data and analysis.

Computer science is a science – it is the study of the principles and use of computers.  CS is also an engineering discipline – it includes the design and development of computer hardware and software.  It’s important to remember that using computing tools to advance other science and engineering disciplines is not exactly CS – this is computational science and engineering, which is very much in the realm of CT.

I think it’s important to remember that teaching CS and incorporating CT into other subjects are different things, albeit both very important.

Note: The K12 CS Framework also includes great information on computational thinking, including a venn diagram that connects CS / CT practices with math, science, and engineering practices.  (K12 CS, Computational Thinking).

Career & Technical Education

Career & Technical Education (CTE) is an umbrella term that includes a number of career clusters (occupation groups) and pathways (leading to specific occupations).  CTE programs are generally two-year programs that students may take towards the end of K-12.

The Information Technology (IT) cluster in CTE​ includes the following pathways:

  • Network Systems Pathway
  • Information Support & Services Pathway
  • Web & Digital Communications Pathway
  • Programming & Software Development Pathway

While the IT pathways are clearly closely related to CS, there are a few important points worth making.  CTE programs are upper-HS level, and focus on specific skills for a certain career pathway. This is different from a K-12 CS program, which focuses on core CS skills and knowledge that are applicable in many careers not only in IT, but also in other clusters such as engineering, business, etc.

The bottom line is that students should learn fundamental CS skills and knowledge earlier in K-12 so that they can apply them to whatever pathway they pursue, whether or not they participate in a CTE program.

For more information about career clusters, please visit: Advance CTE, Career Clusters.

The social sciences and humanities

While I focused on strong affinity groups here, I don’t want to entirely leave out other groups.  Like other sciences, the social sciences are increasingly data-driven and rely on computational methods.  The humanities are a great place to explore the impacts of technology on society. Arts educators employ practices that are related to engineering design and development processes.  The discussion could go on into other disciplines.

Aside from systemic constraints, the degree of CT incorporation into these areas is limited only by the knowledge and imagination of the educators, and can be strongly aided by effective collaboration.  

So… where does CS / CT go?!?

Educators need to determine how to build a CS program that fits their need.  Schools need a strong CS program, and they also need to incorporate CT across the curriculum.  There is no magic bullet, but any solution starts with a solid understanding of the context and possibilities, and a concrete plan to move forward.

David Benedetto

David Benedetto, At-Large Representative

Tips for CS PD Facilitators

As we gear up for the new school year, many of us are entering into professional development (PD) soon. I am lucky enough to have the opportunity to plan and facilitate PD for teachers in San Francisco, and based on this experience, I’d like to offer some tips that I believe contribute to successful learning experiences for teachers.

Model best practices

  • Facilitate learning. Teachers should experience sessions in a format similar to their students. Be the guide on side, not sage on the stage. And, please, please, please don’t lecture about active engagement.
  • Be explicit about strategies used. Then, allow teachers to reflect on whether and when the same strategies could be useful in their own classrooms.
  • Set explicit learning goals and measure progress towards those goals. If you want to develop a strong community of practice, state this explicitly as a goal, actively work towards this goal through collaboration and team building, and measure progress through surveys and observations. Do the same with content and pedagogy-oriented goals.
  • Differentiate. Groupings or breakouts based on grade level, content area, or other contextual factors can be useful, but this in itself is not differentiation. Consider multiple means of representation, action/expression, and engagement. Set consistent baseline objectives for everyone, and create different levels of scaffolding and extensions to challenge teachers at the appropriate level.
  • Allow choice. Let teachers decide what is important and relevant to them. They cannot choose everything, but make sure have some agency.

Record, reflect, assess

  • Compile all resources and make it easy to access them. Consider a simple website or hyper doc (e.g, SFUSD’s PLC site).
  • Create shared notes documents so everyone can benefit. This allows a good record for teachers to remind themselves during the school year and allows those who missed out to reap some of the benefits. Ask for volunteers to contribute to the notes documents at different times.
  • Prioritize time for reflection. It’s important for teachers to process their learning and consider how they will apply new ideas and strategies. Thoughtful reflection improves transfer to classrooms.
  • Ask for feedback. This can help you evaluate, plan for future sessions, and improve facilitation. Don’t wait until the end to ask for feedback. Create formative measures.
  • More importantly, use the feedback to change plans and improve. And, show a summary of participant feedback each day, and explicitly note the things you’re changing to respond to feedback.
  • Assess learning. Don’t rely solely on feedback. Use similar assessment measures to those used in the classroom. Collect teachers’ projects to examine more closely.

Attend to the environment

  • Create a welcoming and inclusive space. Try to choose a room that is colorful and filled with natural light. Take down any Star Trek posters and replace with something that appeals to everyone. Create table groupings to make it easier to collaborate.
  • Set and reinforce norms. As teachers come from different communities and cultures, it can be helpful to adopt a set of common norms. Reinforcement can come through reflection, a norms tracker, and celebration of colleagues.
  • Make it fun! Throw in some corny jokes and spontaneous dance parties. Play music during breaks. Put candy and LEGOs on the tables.
  • Include breaks. Breaks allow teachers to take care of personal needs, engage in informal collaboration, and maintain better focus during sessions.
  • Get teachers up and moving. No one likes sitting all day. Movement is especially important after lunch because this is when most people’s attention starts to fade (the “trough”).
  • Mix up groupings. Many teachers default to choosing teammates whom they already know, but they also prefer to get to know new people. Facilitate this by thoughtfully designating grouping strategies and consider when teachers should collaborate with teachers from different and similar contexts.
  • Switch up the facilitation. Just like students get tired of hearing the same teacher all day, teachers feel the same way. Work to mix up both the facilitator and methods of facilitation as much as possible.
  • Empower teachers to lead and share their best practices. One way to do this is an unconference in which teachers select and run sessions based on their interests.

Show teachers you value them

  • Pay teachers. Teachers already work hard enough. If the PD doesn’t happen during the contract time, it’s important to compensate teachers for their commitment.
  • Provide good food. It doesn’t have to cost a lot to be thoughtful. Make sure to include some healthy options and attend to dietary restrictions. Unlimited snacks go a long way.
  • Provide the materials needed to implement lessons/curriculum. It is a huge lift off of teachers to give them ready-to-go materials. They’ll be very appreciative of the time (and money) you saved them.
  • Celebrate success. A fun and easy way to close the week is for teachers to create their own superlative awards to celebrate something they are proud of and share with the community (e.g., best debugger, craziest sock wearer, biggest risk taker).
  • Don’t treat adults like they’re children. Let teachers decide what’s best for them. Structure can enable productivity, but too much structure or accountability can foster resentment.

Other pro tips

  • Sprinkle in tips and tricks, and allow teachers to share these. Examples are new tech tools (e.g., yellkey.com), brain breaks (e.g., GoNoodle.com), team builders (e.g., Zip Zap Zop!), and showcasing strategies (e.g., Michelle Lee’s tips for amplify student voice).
  • Go beyond the (one) curriculum.Teachers new(er) to CS need to develop a decontextualized knowledge of CS and be empowered to determine the best ways to teach concepts to their students. Try to not just use one lesson or curriculum but offer several options on a related topic and ask teachers to contribute others and reflect on the usefulness in their own contexts.
  • Don’t try to do too much. You cannot do everything in one hour, one day, or one week. Decide what’s most important based on the teachers who will be attending and set measurable and achievable learning outcomes for the time you have. Expect things to take ~50% longer than you think they will.
  • Don’t let it be a one and done. Ensure there are follow-up mechanisms throughout the year. An effective way to do this is to create a community of practice, with both an online presence and regular, in-person convening.

What tips did I miss? Tweet @btwarek and @csteachersorg.

Bryan Twarek School District Representative

Jennifer Rosato elected as incoming chair of CSTA’s Board of Directors

Dear CSTA community,

I am delighted to inform you that at the CSTA summer board meeting on July 11, 2018, Jennifer Rosato was elected as incoming chair of the board.

photo of Jennifer Rosato, CSTA chair-elect

Jennifer Rosato, CSTA chair-elect

Jennifer (“Jen”) Rosato is Director of the Center for Computer Science Education at the College of St. Scholastica and an Assistant Professor in Computer Information Systems. She leads the Mobile CSP project, including curriculum and professional development for the AP CS Principles course. Rosato also works on teacher education initiatives, including integrating computer science and computational thinking in pre-service programs as well as a graduate certificate program for current teachers.

Jen began her term as incoming chair immediately upon the election results being announced; at next year’s summer board meeting, she will become chair and I (Fred Martin) will become past-chair!

Also at the board meeting:

  • Newly elected board members Kristeen Shabram (K–8 Representative) and Amy Fox (9–12 Representative) began their 2-year terms.
  • Elections were held for 1-year terms on the Executive Committee. Serving for 2018–19 will be Anthony Owen, Bryan (“BT”) Twarek, and Jane Prey.

Our organization is fortunate to have such accomplished, dedicated, and generous volunteers to help make CSTA great.

Thank you to all CSTA board members, and a special congratulations and thank-you to Jen Rosato.

Yours,
Fred Martin, Board Chair

Microsoft Philanthropies has announced a $2 million commitment with CSTA

Today Microsoft Philanthropies announced a $2 million commitment, over three years, to CSTA. Support from Microsoft will help us launch new chapters and strengthen existing ones, expand professional development opportunities across the network, and attract new members and partners in order to build the foundation and community that every computer science teacher needs. With computer science skills more important for students than ever before, we are thrilled to join forces with Microsoft on this effort to broaden access for all students. Learn more about the commitment from Mary Snapp, Senior Vice President and Lead of Microsoft Philanthropies: Read the Announcement!

Welcome to the Silicon Prairie!

The 2018 CSTA Annual Conference is only days away, and I am looking forward to welcoming everyone to Omaha. We have an exciting conference planned, with workshops on Saturday and Sunday (along with a Chapter Leader Summit), birds-of-a-feather session on Sunday afternoon, and keynotes and sessions on Monday and Tuesday. There are numerous social and networking events, including a big reception on Sunday evening and a tour/reception at the University of Nebraska Omaha on Monday. This looks to be a record-breaking conference in a number of ways (no spoilers) and we locals are working to make it the friendliest as well.

Some last-minute pieces of advice as you prepare to come to Omaha:

  1. The convention center and conference hotels are only 3 miles from the Eppley International Airfield, and both the Hilton and Marriott have free shuttles. If you choose a cab or ride-share, we are still talking 5-10 minutes to get from one to the other. Pay attention on you ride from the airport and you will notice that you briefly pass from Nebraska into Iowa and then back to Nebraska. It’s an interesting historical fact that the Missouri River, which forms the boundary between the two states, changed its course in 1877, leaving a small piece of Iowa stranded on the Nebraska side.
  2. There is a lot to see and do around the convention center and hotels. If you are a baseball fan, TD Ameritrade Park, where the College World Series is held every year, is just next door. There are restaurants, bars and a movie theater adjacent to the park. The Marriott is connected to the new Capitol District, which also has restaurants, bars and shops and an outdoor social space. Within easy walking distance is the Old Market district, which has all kinds of dining, shopping and social establishments. If you are considering dinner some evening, I would recommend getting reservations ahead of time, as it is a busy place.
  3. If you have time to explore Omaha, I would recommend downloading the Omaha Savings app from the Omaha Visitors Center (https://www.visitomaha.com/savingsapp/). It has discounts on museums, restaurants, and the Henry Doorly Zoo & Aquarium. The Doorly Zoo has been named the #1 zoo in the world by TripAdvisor, and is well worth the trip (it is 6 miles from downtown, and can be reached using the hotel shuttle). My institution, Creighton University, is less than a mile to the west of the conference hotels. It is a beautiful urban campus, so if you are looking to stretch your legs, I would recommend checking it out. We will have maps of the downtown area available at registration.
  4. This has been a hot summer across the country, and Omaha has been no exception. The weather forecast calls for highs in the upper 80’s and lower 90’s. Currently, there is no rain in the long-term forecast, but that can certainly change. If you are staying in the Hilton, there is an enclosed walkway that goes directly to the convention center, so you won’t have to go outside if you don’t want to. The Marriott is on the adjacent block, and many other hotels are close by as well. Plan to bring some warm-weather clothes and get out. In addition to the Old Market, you’ll want to walk across the award-winning pedestrian bridge that crosses the Missouri River to Iowa. There are many walking and bike paths along the river and over on the Iowa side. There are several bike rental stations in the downtown area, including one right by the pedestrian bridge.
  5. Omaha is a clean, vibrant, and friendly Midwestern city. The population in the metropolitan area is around 930K, but it still has the feel of a small-town. The area also has a rapidly growing tech-sector, earning it the title Silicon Prairie. If you have never visited here before, I know you will find Omaha welcoming and engaging. Enjoy your time here!

On a personal note, this meeting marks the end of my term on the CSTA Board of Directors. I have made so many great friends and colleagues over the past nine years, and want to thank you all for the hard work and passion you bring to CS education. I look forward to continuing to work with you all, and I know that CSTA’s future is bright with Jake and Fred at the helm.

JRN, Journalism, Media, Computing faculty members


Dave Reed
CSTA Board Member, Past-Chair

It’s Conference Season!

Ah, summertime – a time for rest and relaxation. For educators, summer is also often a time for professional development. A highlight of my summer PD each year is the annual CSTA Conference. I love a conference where I don’t have to search the program trying to find computer science sessions. With the start of the conference only a little over a week a way, my conference planning has begun!

Do you make a plan for a conference before you attend? I’m not talking about planning a session or workshop, if you are a presenter. I am talking about planning your experience as an attendee. I do.

Before going to a conference, I read the conference program and create a document of the sessions that I think I would like to attend. I include information from the conference program along with any resources that have been shared for the session. I also try to find links to the presenters which might include their Twitter handles, LinkedIn profile, website, etc. This helps me to follow up after the conference if I didn’t get information from a session during the conference. My list of sessions always includes more than I could possibly physically attend so I rely on crowd-sourcing to get information on sessions I can’t actually attend.

During the conference:

  • If I am attending with colleagues, we get together to make sure to attend different sessions. Then, we all add information to a collaborative document for those sessions. I can then use that to update my document.
  • I share my document on Twitter using the conference hashtag and ask for collaborators. This lets people who are in the room contribute pictures, notes, and other resources from the sessions that I can’t physically attend.
  • I use the document to watch for tweets from those sessions I’m not in and add the information to my document as the conference progresses. If I see people tweet about a session without much information, I will reply to their tweet asking for links to resources so I can add them to the document.
  • I also use the document to see where I want or need to be. I don’t know about you but often sessions at conferences can spark a curiosity that I didn’t have before. This means I might want to change my mind on which sessions I attend as the conference progresses. It’s nice to have all the sessions I might be interested in on one document rather than having to click multiple times to see descriptions of sessions on the actual program.

For this year’s CSTA conference, I have included the sessions from the program that are applicable to K-8 CS on my document. I always try to check my document against the conference program just before the conference starts because there are sometimes room changes or cancellations.

Have you ever missed something at a conference that you meant to attend? To try to avoid this, I add any workshops, sessions, meet-ups, etc. that I am definitely attending, presenting, or proctoring to my Google Calendar. Then, I have reminders sent to me at whatever interval I like which is typically 15 minutes to 30 minutes before something is scheduled to start. This helps me to be where I am committed to be.

What are you waiting for? The 2018 CSTA Conference starts in just over a week. Create your own #CSTA2018 resources document for the conference and add your must attend events to your calendar.

What if you’re not attending the 2018 CSTA Conference? No problem, you can still create your own document of sessions that you would have liked to attend and follow along on Twitter using the #csta2018 hashtag to collect resources from the sessions. I have done this the last few years for the ISTE Conference, which I have not attended. It is amazing what you can learn from a conference even when you’re not physically there. Create your own #NOTATcsta2018 document and follow along virtually!

Vicky Sedgwick
K-8 Teacher Representative

Mathematics and Computer Science

As attention in England (and elsewhere) turns to the World Cup, I’ve been reading a couple of books about the mathematical modelling of football: Anderson and Sally’s The Numbers Game and Sumpter’s Soccermatics. I’d recommend them both if you’re interested in learning more about some of the patterns in the data that football (i.e. soccer) generates. I suspect young (and not so young) people are already quite familiar with the computational modelling of football, not through books such as these, but through computer games such as FIFA and Football Manager. These games make extensive use of real data, and are excellent examples of what the English computing standards describes as ‘computational abstractions that model the state and behaviour of real world problems’

The parallel between mathematical modelling and computer programming is no coincidence: there are deep historical connections between computer science and mathematics, and these remain strong to this day. Doing mathematics, at its heart, is a two-step process of thinking about a problem and then manipulating symbols according to rules: before Turing’s day the symbol manipulation (typically arithmetic) was done by people called computers, since his time (in the real world, if not always in school), this work is done by machines called computers. In either case, it’s the thinking about the problem and its solution where the real mathematics lies. Similarly, programming is a two-step process: thinking about the problem and how to solve it (the ‘computational thinking’), and then writing the instructions (the code) which mean the solution can be carried out by a dumb machine.

In his classic 1957 text, How to Solve It, Polya identifies four principles for problem solving in mathematics: understand the problem, plan a solution, carry the plan and review or extend the solution. I think all of these apply to problem solving in computing, with all but the third stage sitting comfortably within most approaches to computational thinking. There’s much common ground between computer science and mathematics: both domains demand logical thinking and a systematic approach, both result in computation, and both draw on the idea of abstraction. In her 2008 paper, Wing drew a distinction between abstraction in computer science and abstraction in mathematics, indicating that in CS, abstraction was both more general and more practical than it is in mathematics.

For those teaching in elementary school, there are so many opportunities to exploit the connections between mathematics and computer science, as they’re likely to find themselves teaching both to their class. Papert’s turtle graphics have long had their place in the mathematics curriculum as well as providing what remains a great way into coding. Scratch introduces pupils to four quadrant coordinates. Away from programming, dynamic geometry software such as Geogebra or graphics programs like Pixlr can introduce the ideas of transformations. Pupils can be introduced to probability through simulations in Scratch or Excel, and statistics through online surveys and data logging with the micro:bit.

Further up the education system, it becomes harder to bridge the artificial gap between CS and mathematics, but it’s well worth the attempt. Take any mathematics investigation or open-ended problem and, after trying a few ideas with pencil and paper, explore how you might program a computer to solve it: personal favourites are problems like ‘how many ways can you make 50 cents using coins?‘, or ‘how many perfect shuffles does it take to get a 52 card pack back in order?‘ Modelling works well here too, perhaps showing how a ball bounces, or estimating pi through the ratio of random points inside to those outside a unit circle, to creating a class (and overloaded operators) to perform fractions arithmetic. All of these are great coding activities, but they’d also develop pupils’ mathematical understanding of these ideas.

There are some great resources out there for folks interested in linking mathematics and computer science more closely. Top of my list would go the Scratch Maths project for 4th/5th grade math from University College London, and the Bootstrap World courses for algebra and data science. It’s notable that both of these have taken impact evaluation very seriously.

Miles Berry, International Representative