THE USE OF MAGIC IN MATHEMATICS : FROM PRIMARY SCHOOL TO HIGHER EDUCATION
LA MAGIE A LA CARTE (FRANCE)
About this paper:
Appears in: ICERI2009 Proceedings
Publication year: 2009
Conference name: 2nd International Conference of Education, Research and Innovation
Dates: 16-18 November, 2009
Location: Madrid, Spain
Abstract:The aim of the magician is to hide the principles he uses (using maths, physics, psychology, slight of hand, etc...) by disguising the trick so that the audience has no way of discovering how it is done thus allowing the Magic to remain.............
The teacher can do exactly the opposite : unraveling a Magic trick to high-light the principles used!
Why use Magic for teaching Mathematics?
Magicians know that once the surprise has worn off the audience will seek to understand how the trick works. This is particularly true in France. Is it our “esprit cartésien”?
The aim of every teacher is to interest their students, to provoke their curiosity and a magic trick will bring them to ask how? and Why? and the lesson can begin:
• Surprise the class and provoke the curiosity of the students
• Trying to understand a trick by yourself requires concentration and attentiveness
• The lesson begins quicker than usual : “today we are going to do a little magic”
• Learning a trick isn't always easy : you have to work at it.
• The fun aspect of the presentation means it will be memorized more easily and for longer.
• A spectacular example will interest even the student who shows the most aversion to calculus or mathematics, and the ensuing lessons will benefit from this.
• The student who is convinced that (s)he doesn't understand anything to do with Maths and therefore makes no effort, will be shown that (s)he is wrong and that (s)he can improve (for secondary schooling).
• It shows the students that one can teach one subject and yet have other interests, even an art form.
• Whatever the student's professional ambitions, (s)he will be able to see the impact that originality and creativity have when combined with an interest in one's work.
• The pupils or students will go home knowing how to “perform” a magic trick for their family and friends, a trick that they will be able to explain and so enjoy a certain amount of success. Sharing a mathematical demonstration is not easy and that they do so means that they will have worked on, understood and are capable of explaining this knowledge. Isn't this the aim of all teaching?
What happens in a lesson?
• So, at any level, the teacher begins the lesson with a magic trick rousing interest of the students, then help them to discover how the trick works before the theory behind the trick is finally high-lighted with/by the students themselves.
In this article we will consider only card tricks underpinned by mathematical principles. Martin Gardner, a university lecturer, has written several books and articles on these well-known tricks in the magazine Science.56
We will begin with a trick for the Primary school classroom, showing how to use memory techniques to learn the nine times table and explaining why this property can be used to check when we “carry” and work out multiplication using several numbers/digits. We will use this same trick to explain equations to middle school pupils.
We will then continue with a trick for the High School classroom, used to explain first order differential equations and also the modulo operation.
This trick can also be used at university level to explain injection, surjection and bijection as well as palindromic properties, alternative colors, etc....
But let's not reveal all the secrets just yet!
Keywords: math, magic, teaching, bijection, gilbreath, nine proof, line equation, modulo.