Using Game-Type Activities to Reinforce Mathematical Concepts (Darren Banfield)
Some of the concepts in the module I taught are easily understood abstractly by the students. But there is a difference between understanding the mathematical formalism and appreciating the practical implications. I believe that game-type activities could help with this.
Students can often become so involved with trying to understand the details that they fail to see the bigger picture. In terms of Kolb’s experiential learning cycle, the students are able to conceptualise, but don’t know how to experiment or experience the mathematics, which prevents the reflection which will reinforce this conceptualisation.
Gaining this insight should help cement the ideas in the students’ minds, and allow them more easily to draw analogies between different mathematical results they have studied (the use of analogies being an indication of depth of learning). Using some games could help to provide the link between the abstract concepts and the real-world application.
There has been research into the use of games in mathematical research although most of this has involved primary or secondary school children. For example both [1] and [2] state that games can help to motivate students and increase the time during which they are attentive to the mathematics. While [2] states that games can be used to introduce new concepts, the main focus for these age groups is to consolidate knowledge (such as multiplication tables). There has been relatively little research into the use of games at undergraduate level. One example is [3], although this also primarily deals with performance of tasks such as multiplication rather than the introduction or consolidation of concepts.
In the context of the error-correcting codes module one concept is how important it is to be able to correct errors in transmissions. The class could be split into groups acting as senders of messages, receivers of messages and “error generators”. The senders and receivers use a variety of coding methods, and the error generators are allowed to make a certain number of changes to the message before the receivers see the message. By varying the strengths of the codes and the number of errors which are allowed, the students can start to appreciate how the codes actually behave. I believe that this would assist them in understanding how the various factors in error correction interact with each other.
[1] Bragg, L. A. (2012) The effect of mathematical games on on-task behaviours in the primary classroom. Mathematics Education Research Journal 24(4) 385-401.
[2] Orim, R. & Ekwueme, C. (2011) The roles of games in teaching and learning of mathematics in junior secondary schools. Global Journal of Education Research.
[3] Muntean, C. et al. Investigating the Impact of an Immersive Computer-based Math Game on the Learning Process of Undergraduate Students. Paper delivered at the 48th Annual Frontiers in Education Conference, San Jose, USA 2018.
Response:
This sounds like a fun activity that would really help students consolidate theoretical knowledge! The classes I taught – statistical research methods – also have mathematical components that many students often find quite challenging, and we have used games (in the form of trivia questions) to help them learn these as well as gauge their skill level. I think it’s an excellent approach that ensures students find class content engaging whilst also helping you as teacher know what you are doing well and what needs to be worked on more.
(Laura Serra, Political Science)
Response:
In many more mathematical subjects areas, students often struggle to apply their knowledge. As you rightly point out , it is important for students to see the bigger picture of where this or that concept can be used. I suspect in most situations, one would try to give examples or applications, but, in a more abstract setting, these may not be so readily available. As a result, games or similar activities may help students consolidate what they have learned and start drawing ideas together. Overall, I think this is a great idea that I can perhaps also use in my own teaching especially when illustrating theoretical results from fields such as game theory.
(Grigory Aleksin, Economics)