Month: December 2016

To some the thought of mathematics can be tedious, so to imagine maths as play seems quite unusual.

However this is not the case as all games contain an element of mathematics.

In the input on play we were able to explore some of these areas:

Yahtzee: A game of chance and probability, made up of 5 regular dice and a score card the aim of the game is to fill the card with as many high scoring options as possible with the the total added up score of the highest number being the winner. Mathematical elements within this game are: addition, problem solving, probability/chance and number recognition.

Monopoly: Work around the board purchasing properties and avoiding paying competitors for landing on their purchase date squares while picking up chances and avoiding jail. The aim of the game is to bankrupt every other player or finish with the highest amount of money or property value. Mathematical elements within this game are: Money, addition, problem solving, subtraction, chance and negotiation.

Guess who: Using yes/no questions eliminate every character on your oppositions board apart from the one they have hidden on their chosen card, first person to guess the opponents character wins. This game is not evidently associated with mathematics however realising the number of characters with iconic similar features allows you to clear the board quicker also recognising patterns this way.

Scrabble: Each competitor gets 7 letters chosen at random each turn and can use as many of these to create words on the board, after the first word is palced the rest must always connect to another word already played. Letters are worth points with those that are more uncommon scoring higher, positions on the board also are worth more points than others. Mathematics is present in the addition of scores and multiplication when on appropriate board spaces.

Having thought initially that this mathematics module would open my eyes to how to teach mathematics I would never have suspected how this would come about.

When asked what my thoughts on the fundamentals of mathematics are at the start of the semester I may have stared you blankly in the face or uttered the basics which I believed to be addition and subtraction.

However I now realize this is certainly not the case and there is far more to mathematics than + or -.

Mathematics is everywhere, from my previous blogs you may have realized that it is in fact all around us. All it takes is an understanding of connectedness, the ability to approach a problem from every angle, an understanding of the basic ideas, and to realize where problems are relevant and how to pass on tis information to others. Liping Ma defines these things the key elements. With an understanding of these 4 universal principles we can solve any math’s problem anywhere (Ma, 2010). How Exciting!

 

References

Ma, L. (2010) Knowing and Teaching Elementary Mathematics. New York: Routledge

It might seem ridiculous already, maths in Art? Nature? and now Music! Alas it truly is all around us, put in your headphones and count out the beats to your favourite songs, recognise patterns and repetition in the rhythm, get louder and quieter throughout the tune. It is all mathematics.

Symmetry in music is a very regular occurrence, skip to 3.41 in the video below for an example of a very impressive yet simple example of not just symmetry, but repetition and pattern as well.

The tune in the video is made up of the same combination of notes just at varying speeds, or flipped by symmetry using several instruments. This piece was created by J.S.Bach and this style of composing was frequently adopted by him.

Another element of mathematics in music is pitch, pitch is measured in Hertz (Hz) and is the rate at which vibrations are produced. The mathematics in pitch is that it can be  measured as a frequency (Wiggins, 2012).

The tones in music are all worth numerical values, it is these numbers that determine the sound of the tone. These are related to pitch also.

Musical Intervals correspond to precise and simple ratios, The harmonic series intervals with the simplest ratios are named “perfect” in music theory. Medieval composers favoured the P8, P5 and P4 as the most consonant intervals, partly because of their mathematical simplicity and elegance. (Rogers, 2004)

 

References

Rogers, G.L. (2004). Interdisciplinary Lessons in Musical Acoustics: The Science-Math-Music Connection Music Educators Journal . Available at: http://mej.sagepub.com/content/91/1/25.citation (Accessed: 01 December 2016)

Wiggins, G.A. (2012): Music, mind and mathematics: theory, reality and formality. Journal of Mathematics and Music: Mathematical and Computational Approaches to Music Theory, Analysis, Composition and Performance. Available at: http://dx.doi.org/10.1080/17459737.2012.694710 (Accessed: 01 December 2016)