This is the first blog from the Mathematics Without Tears and Fears Project supported by the Education Incubator. It introduces the project and describes the Mathematical games that the students on the project have worked to develop in the first half of the project.
The Project Leads are: Dr Layal Hakim, Dr Weihan Ding, and Dr Pascal Steifenhofer, who have recruited the follow student researchers to work on the project: Tom Lewis (Engineering), Zsuzsanna Riedel (Economics), Elie Feinsilber (Mathematics), Ben Fuller (Physics), Eloise Williams (Mathematics), and Elliot Jones (Mathematics). The project has also recruited the following Digital Game Developers to assist in developing the Mathematical games: Ricky Bassom (Computer Science) and Matthew Yates (Mathematics).
Maths is hard. To most people, being presented with a new mathematical concept is an intimidating and challenging experience. Our project aims to change that by developing and testing a set of pedagogical games that address the concept of proof systematically. Pedagogical games are designed to promote learning by giving the player a sense of agency and control over their education. The games should introduce difficult concepts in a way that is playful, unintimidating, and enjoyable. The hope is that our games will be as – if not more – effective, than traditional teaching methods, while providing a fun environment in which to learn.
The group in charge of creating the games was composed of Eloise, Elliot, and Elie. It had to develop three different games: a single-player game, a small group game (2-3 players), and a large group game. Initially, all games hope to address the concept of proof by contradiction.
- Eloise was in charge of the single-player game. The game she created consists of linking three cities placed in a triangle with the fewest possible number of rails –knowing that there are two types of rails: 1 input 1 output rails, and 1 input 2 output rails (which are essentially 2 single rails connected with a 40° angle). Further levels of this game could easily be made more complex by changing the numbers of cities and types of rails available.
- Eliott’s game consists of going from A to B as fast as possible. A and B are separated by various natural barriers (water, mountains, etc.). Hence, given that some material might be faster to cross than the other, the player has to find the quickest path. Changing the layout of the terrain means that the challenge of the game can be easily adjusted as the player grows more skilled.
- Elie was in charge of the large group game. After discussion, the group came to the conclusion that the best/most fun way to do a large group game was to set up some knock-out stages. Tournament setups and competition have been shown to increase learning and engagement, and this format hoped to take advantage of that.
These games all have a similar structure that makes them pedagogical. In each, the player is given a statement, then told to assume its opposite. For example, the statement given in Eloise’s could be that you must use at least one will rail with 1 input and 2 outputs. They would then be told to assume that only 1 input 1 output rails are necessary. By playing the game, the player would find that their assumption is false, and therefore the initial statement must be true. This is the fundamental concept of proof by contradiction that our games aim to teach.
The games are designed following existing teaching styles and theories. For example, Elliot’s game only allows the player a certain amount of time to find the path. This element of time pressure has been shown to increase engagement and learning. Similarly, the players of all games will be able to access short hints if they get stuck, preventing them from getting stuck and losing interest.
Tom, Zsuzsanna, and Ben were working in the ‘statistics group,’ where our main task was to gather information on working on existing literature on different pedagogies and on both pedagogical and mathematical games. The main questions we wanted to answer are: how these pedagogical experiments are conducted; what are their main goals; who are the target audience; and how could we improve the process in our project?
We had two workshops focused on how to formulate our research into a cohesive text, from which we wrote literature reviews on our findings and how they can be used in our project. These literature reviews were used to inform the design of studies based around three games developed by the other group, each with their own method of measuring pedagogy and engagement with the game.
The games are currently being digitalised by our digital games developers, who are aiming to be complete their work by the end of January. Tom, Zsuzsanna, and Ben are currently working on merging our literature reviews into one. This will form part of the introduction of the paper we hope to write. We are currently searching for conferences on mathematics and education to attend so we can showcase our work so far and are working with the Education Incubator to plan this for later in term two. Keep an eye out!
The University of Exeter’s Education Incubator scheme. Promoting pedagogic innovation and collaboration with an aim to enhance learning across the University and beyond.