Learning Through Games: Student Success Stories

The Inaugural Games for Change Australia/New Zealand Festival was recently held in Melbourne on November 15th & 16th. I was delighted to be one of the Curators for the conference together with having the opportunity to give a brief talk.

Find the recording & slides to Learning Through Games: Student Success Stories below.

Gaming Graph Theory

The Seven Bridges of Königsberg is an important historical problem in mathematics, explored by Leonhard Euler in 1735, that laid the foundations of graph theory and topology.

The city of Königsberg in Prussia (now Kaliningrad, Russia) was set on both sides of the Pregel River, and included two large islands which were connected to each other and the mainland by seven bridges.

 Mathematically the problem can be stated like this:

Given the graph above, is it possible to construct a path (or a cycle – a path starting and ending on the same vertex) which visits each edge exactly once?

Euler proved that it was not possible. He proved that for the existence of what he coined “Eulerian trails”, it is necessary that no more than two vertices have an odd degree; this means the Königsberg graph is not Eulerian. Mathematically, if there are no vertices of odd degree, all Eulerian trails are circuits. If there are exactly two vertices of odd degree, all Eulerian trails start at one of them and end at the other. A graph that has an Eulerian trail but not an Eulerian circuit is called semi-Eulerian.

This type of mathematics can be quite abstract for students (and teachers) and most find it quite difficult even when presented in context of network optimization, railway systems, traffic flow, shortest path problems etc. 

One Touch Drawing by Ecapyc Inc. is a nice puzzle game on iOS that deals exclusively with Graph Theory. It could be a nice way to get students thinking about Graph Theory before the topic is introduced and then used as a context for discussion and problem solving to give the topic more meaning to students. I have only played the first few levels, the the difficulty ramps quite quickly. Recommended.

Hive: A Game of Strategy

Hive is a 2 player strategy game of perfect information that shares elements of both tile-based games & board games – much like Chess but without the board.

The game uses hexagonal tiles to represent the various contents of the hive. There are 22 pieces in total making up a Hive set, with 11 pieces per player, each representing an insect and a different means of moving –

One Queen Bee that can move only one space around the edge of the hive at a time.

Two Spiders that can move three spaces around the edge of the hive.

Two Beetles that can move one space in any direction including on top of another peice which renders that piece unusable until the Beetle moves.

Three Grasshoppers that can jump over one or more pieces in a straight line.

Three Ants that can move anywhere around the hive.

Hive is a game that is getting a lot of play at Quantum Victoria at the moment as it contains many, varied strategies and games can be played in about 10 minutes. It only takes a game or two to discover that the key to winning is mobility—retaining yours while restricting your opponent’s. Immobilizing your opponents pieces is accomplished in two major, but sometimes subtle ways.

1) Placing your peices so that the opponents are unable to move due to the nature of the hive or

2) Placing your tiles so that your opponents tiles are required to keep the hive intact, rendering them immobile.

Some great discussion has taken place around effective strategies, counter strategies, optimal strategies based on your opponents style of play (agressive, defensive, offensive, defensive-aggressive etc.), advantages/disadvantages of going first/second, strong opening moves, end games, decision trees etc. 

(Hive is also available on iOS – the AI is sophisticated enough to keep you playing for a few hours.)

I have developed a strong opening sequence of moves that I consider a defensive-aggressive opening that allows for the transition to an offensive-aggressive strategy after only 4 moves – really putting the opposition on the back foot. This strategy only works if employed by Player 1. It involves placing a Beetle followed by a Spider, the Queen and then another Spider in the following configuration:


This opening configuration is essentially unbeatable at the moment given that I don’t make any mistakes. (I’m sure it is beatable, just haven’t been beaten yet!) This opening relies on utilizing the mobility of the ant and the grasshopper as the late arriving pieces used solely for attacking. The spiders and the beetle can be used to pin down your opponents peices but also form a defensive ring around your Queen giving you flexibility depending upon your opponents early moves. The Beetle in particular can be used to escape midgame ‘bunching’ to counter an opponents over agressive Beetle and can also be used as the basis of a midgame counterattack.

Highly Recommended & strangely addictive.

Play the online version here.

The Numbers Game: Putting Yourself In Other’s Shoes

Perspective is essential.

In life, in your work and in everything that you do. It’s also essential in game theory when attempting to reduce a game to it’s simplest form via a process known as iterative deletion of dominated strategies.

The lecture below gives a simple game that illustrates this idea:

During class you are given a sheet of paper on which you must write a number between 1 & 100. The average number of everyone in the class will be calculated. To ‘win’, the number you choose must be 2/3 of the class average.

This game forces you to consider other people’s perspective. In order to think logically you need to put yourself in other people’s shoes, imagining what they are likely to do, and then determining your own strategy in response to your assumptions about the other player(s). 

This is a great game to introduce to a class of any age, regardless of experience in game theory, game thinking or mathematics. It’s simple enough that everyone can play, develop their idea of a winning strategy and engage in discussion around ‘why’ and ‘what if.’ Game Theory requires students to put themselves in other’s shoes – a valuable skill in life.

The solution to this particular game can be found by an iterative process whereby you systematically delete dominated strategies by considering other player’s actions. However the solution is not as obvious as you may first think.

Watch the video for a detailed analysis of a ‘solution.’

For a detailed description of some ideas on Game Theory check out Brian Weatherson’s notes.

STEM: F1 in Schools

Quantum Victoria will be hosting the Victorian State Finals of the F1 in Schools Competition on the 8th & 9th of November 2012.

Having written about how I think this is an amazing STEM project before, this is the task that student teams embrace:

  • Design and manufacture a miniature F1 Car to travel down a 20m track in the shortest possible time using a specified amount of energy.
  • Utilise Computational Fluid Dynamics (CFD) software and wind tunnels to help perfect the aerodynamics of the design.
  • Utilise Finite Element Analysis (FEA) software to increase sustainability and reliability of the design.
  • Utilise Rapid Prototyping strategies to help construct components of their car.
  • Develop a 20 page portfolio which highlights the design iterations undertaken, the innovation included in the design and the interaction they had with industry through the design process.
  • Develop a marketing and promotions plan to sell their team’s capabilities and end product to industry. This includes the development of a 3m x 1m display booth.
  • Generate sponsorship by promoting their capabilities to industry and then manage all budget items associated with their team
  • Implement a communications strategy to ensure that sponsors are kept informed of progress
  • Make a 10-minute formal presentation to a panel of judges on their project highlighting the work they have undertaken, their innovation and what they have learnt by participating in the project.
  • Present to a panel of Engineers their design, the manufacturing strategies they have adopted and the unique engineering technologies they have applied to the development of their car.

After all this their end goal is to:

  • Attempt to break the 1-second barrier over the 20-metre track.
  • Win the best Engineered Car award.

Good luck to Victorian schools Kyabram P-12 CollegeTrinity Grammar as they head to Abu Dhabi for the World Finals.

The Learning (2.012) Continues

How cool is this?

After attending my Game-Based Learning extended session on Day 1 of Learning 2.012 and skyping her class during the session, Naynay Montilla has taken the concept of game modding and put it straight to use in the classroom.

During the session we talked about trajectories of student participation when ‘gaming’:

  • All students start as a newb
  • Students start gaining a certain level of mastery
  • Students start investigating winning strategies, optimal strategies, counter strategies etc.
  • Students start asking ‘What if…”

What happens if we change the rules? What variations can we introduce and how does this affect game play? Can we add bias to the game?

The original game in this instance was called the Game of 31. It is a two player game that is played with a standard deck of playing cards. The students from the International School of Manilla have got to work, added a variation and re-named it “Beachball: First to 21.”

Have a listen to one of their Grade 1 “Explanation Experts” explain their game 🙂

Student Game Art #2

(Original post – Student Game Art)

‘Jeremy’ continues his concept art for a graphic adventure game…


Games? In Learning? I’m Confused…

Confused Sonic by ~EdoBean

It’s evident from recent weeks that many are confused when talking about games in the same breath as education. This is understandable. The question, “What is a game?” still elicits varied responses depending on who you talk to.

Most fields of study have been around for thousands of years, have fairly clear definitions and boundaries and have a vast body of knowledge to draw from. Whilst games in various forms have been around as early as 2600BC (see Exploring Games Through Culture) and are a universal part of human experience, definitions from Callios, Huizinga, Salen, Zimmerman, Pearce, Wittgenstein etc. have no real agreed definition of what a ‘game’ actually is.

Whilst there is no concise definition that is universally agreed upon, we can draw from the literature and by examining many of these definitions and synthesising this work into something that is coherent, we can establish a baseline for our discussion around games. Briefly, the common elements are:

  • Games are an activity that generally have an uncertain outcome.
  • Games have rules and to a degree, conflict.
  • Games have a clearly defined set of goals.
  • Games are artificial, safe, make believe, and they are outside ordinary life. This is sometimes referred to as the players stepping into the “Magic Circle” (see Games, Play & Porous Membranes)
  • Games are voluntary
  • Games are systems
  • Games are a medium unto themselves and a form of art

If we now add relatively new fields like game design and gamification into the mix, you can start to understand where the confusion comes from.

Meeting with Donald Brinkman from Microsoft Research in Melbourne recently and having several meetings the DEECD folk (who have not long completed their serious games and virtual worlds trial), it is important that there is a shared understanding of not only the literature, but also of a critical vocabulary – a set of words or common language that enable us to have meaningful discussions around the use of games, and at the higher level, allow DEECD folk to make informed choices and decisions in regard to policy development.

This common understanding is important otherwise we risk propagating misconceptions and misunderstanding which has implications for a learning method that is just starting to gain real traction in education circles. Understanding the differences between Game Theory, Game-Based Learning, Game Development & Gamification is paramount to elevating the dialogue.

Misconceptions that I have come across recently include:

  • Game Theory is the theory of using games in learning.
  • Gamification is the use of games in learning. 
  • Gamification could be seen as dumbing down the curriculum. 
  • Game Design & Development is digital only. 
  • That the study of games needs to be integrated into a subject.

This is part 1 of a series of posts that will look into the differences and similarities between Game Theory, Gamification, Game-Based Learning and Game Development.

Testing F1 Vehicles

Our first run of testing F1 racing cars that were designed and manufactured at Quantum Victoria using CAD/CAM processes, on a 25m elevated track with timing gates. (Best run was 25m in 1.6sec – we need to be shaving at least 0.6 second – kudos to Joel Willis for beating me thoroughly by 0.2 seconds, even though I had the best reaction time – makes my design even worse!)

The actual design, once machined looks like this.

F1 Car

Mindsets of Nostalgia

Extroverted or successful people in social situations tend to be sensitive and appropriately responsive to verbal and nonverbal cues. 

On the nonverbal level, much information is communicated telepathically without our conscious awareness. Humans have evolved to notice body language and subtle clues during social interactions that allow us to adhere to societies norms. Maintaining eye contact with someone portrays confidence, but staring at the eyes of another person for too long won’t win you any friends. Mimicking another’s body language can lead to positive social outcomes such as an unspoken rapport or a sense of unconscious trust, and yet mimicking another’s dialect or accent is a bit weird (and yet I am guilty of this). Yawning can perhaps signal boredom and disinterest, and yet research suggests that yawning serves an important neurological function in improving alertness and concentration, lowering stress and regulating brain temperature. Verbal conversation functions simarlily; people who talk too much are annoying, but so are people that hardly talk at all. Over a lifetime people develop and learn the implicit social rules of responsiveness to a greater or lesser degree.

When engaging students in immersive gaming environments, people new to the medium talk about the difficulty they have relaying information due to a lack of visual body language clues, the lack of ‘control’ or the ‘impersonal’ feel of the space. Granted, it’s a little different at first but this is due to the medium’s affordances differing to traditional settings in both style and space – it’s not really the space itself though, but that the space demands a shift in control, and as a consequence people feel uncomfortable. Giving up this power/control struggle is seen as relinquishing one’s duty as a teacher – but this mindset is one that is steeped in tradition and nostalgia.

The Greek word for “return” is nostos. Algos means “suffering.” So nostalgia is the suffering caused by an unappeased yearning to return. ― M. Kundera

The story of Odysseus is a good illustration of nostalgia as it was originally conceived. Odysseus’s epic 10 year journey can be seen as a hero experiencing nostalgia as he struggles to return to the way things were and get back to his home and ultimately his wife in Ithaca.

Current definitions of nostalgia generally follow a sentimental longing for the past, especially in reference to how things used to be better (whether they were or not). Games have now been around for long enough that it’s not uncommon to encounter people thinking romantically about the good old days of gaming, when 20 cents got you three lives and there were no such things as health packs. (Personally, the other week, I found myself wanting to play the classic old arcade game Pengu…)

Nostalgia creeps into our everyday lives without people giving it any thought – the floppy disk icon for the save function in Microsoft Word or the most recent example of nostalgic nonsense of cc’ing someone on twitter when including them in a tweet.

Carbon copying was the technique of using carbon paper to produce one or more copies simultaneously during the creation of paper documents. With the advent of email, the legacy of ‘cc’ was kept and referred to sending someone who was a secondary recipient of an email a copy of the original. With Twitter this isn’t necessary, and yet people insist on ‘cc’ing…

Nostalgia causes ignorance. When you long and constantly think about the past you do not pay attention to what goes on in front of you and you apply old ways of thinking to new questions. You do old things in new circumstances. This isn’t to say we should ignore the past. We learn from others and become well-versed in the literature, but we see further than others because we stand on the shoulders of those who have come before us.

Will we ever overcome the nostalgic yearning for the good old days of education? Maybe. What we can do now though is have an open mind and come to the realisation that everything changes. Celebrate the power of being in the now and have a rational perspective on things. We cannot be dismissive of new ways of learning and new environments. An incredible amount of hubris and arrogance is involved when spending 5 minutes with something and then being dismissive of it. Playing a game for only 5 minutes is like listening to classical music for 5 minutes and then making a judgement – you are not going to be able to understand the nuances or the complexities in that short time frame.

Gaming environments are empowering for the introverts among us. They give introverts a sense of freedom, social agency and confidence that they would not have otherwise. The doubters need to throw away their nostalgic yearnings because many are using this as a way of avoiding the present – and by not thinking about the present, you risk your students’ future.