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The End of Discovering Maths

Before this module I saw maths as a boring subject which I wasn’t very good at and had no interest in. However now that the module has finished I see maths as a fascinating subject, which I use on a daily basis without even realising.

Three months ago I wrote my first blog post saying how I never had a good experience with maths over secondary school and how the thought of doing this module scared me. I can now happily sit here today, and say how I think this module has taken away my fears and anxieties I had relating to maths. Throughout my life I always heard people say ‘im bad at maths’ or ‘I’m not a maths person’, which I think made me believe I wasn’t either. Throughout this module I have learned that this isn’t the case as maths is involved in nearly all aspects of my life from baking, participating in sports and even planning what train I’m going to get, and considering I make my dinner and make uni on time (most times) I must not be too bad.

I have thoroughly enjoyed learning the four principles Liping Ma speaks of, ‘to fully promote mathematical learning’ (Ma, 2010, pp.210). Having a knowledge of the four principles connectedness, multiple perspective, basic ideas and longitudinal coherence will help me to ensure I teach my pupils about the links between mathematical topics and how each mathematical topic depends on one another. It will also remind me to promote the many different ways there are in order to reach an answer to a maths problem (Ma, 20100.

I am no longer scared at the thought of teaching my future class maths, as iv learned it doesn’t have to be all fractions and percentages from a textbook, instead I am exciting to make maths creative and show pupils the relevance of maths in their daily lives. One of my new aims I want to have as a teacher is to avoid maths anxiety in my classroom by incorporating the 6 ways I have learned maths anxiety can be avoided. These six things include: playing maths games, being aware of my own attitude towards maths, practising the subject with my class, getting rid of the idea that someone ‘cant be good at maths’, giving help from an early stage and getting children to shake off mistakes (Lee, 2016).

Lee, K. (2017) How You Can Help a Child Who Has Math Anxiety. Available at: https://www.verywell.com/how-you-can-help-a-child-who-has-math-anxiety-620833 (Accessed: December 2017)

Ma, L. (2010). Knowing and Teaching Elementary Mathematics: Teachers’ Understanding of Fundamental Mathematics in China and the United States. 2^nd ed. New York: Routledge.

Can Animals Count ?

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In a recent maths input I was asked the question, ‘Can animals count?’. Straight away I laughed and responded with not a chance, but after the input and doing some of my own research, I am now unsure of my answer.

The first piece of information which made me doubt myself was down to a horse called ‘Clever Hans’. In the 1900’s it was believed that Hans could count. Apparently when the horse was asked maths questions involving addition and division, it would answer by tapping out the answer using its hoof. It turned out that infact Hans couldn’t count and instead of understanding maths problems was understanding commands from his master ‘Van Osten’. Through experiments and observations it was discovered that instead of the animal quickly doing the sum in his head, he was responding to his owner’s movements to know how many times to tap his hoof (Jackson, 2005).

At this point in my research I was feeling pretty confident with my response of animals cannot count, however further into the input we looked at chimpanzees and ants understanding of maths which were the most convincing examples of all.

Over 30 years ago a professor created a study to demonstrate how Amuyu the chimp was a very intelligent animal and could respond to mathematical problems. The study showed Amuyu getting shown 9 numbers randomly placed across a screen for 60 milliseconds before they disappeared. He then was able to click the numbers in the correct order of what he had previously seen. After I had a shot and failing at this exact test I was amazed to see (in the video we were shown), the speed of which the chimp completed the task and also how when numbers were missing he was still able to remember the order they were in. This ultimately suggests that chimps can engage with mathematical skills, however I am still unsure if I’m convinced or believe this was down to Amuyu having remarkably good memory skills (BBC, 2017).

Something I didn’t know before this module was how clever ants were. When ants leave their nest to go and get food they remember the distance they have travelled by apparently counting the number of steps they have taken in order to get back to the right place. This should then mean that ants have an understanding of numbers and counting…….

Researchers Martin Muller and Rudiger Wehner decided to investigate this theory and find out if that is the case. One of the tests they done was shortened the ants legs and the other was increasing the ants legs by adding match sticks to them, in order to see if the variables would affect the ants ability to calculate the distance they have travelled back to their nests. The researchers concluded that the ants with the longer legs continued to walk past their nests and the ants with shorter legs stopped before their nests. This was put down to the ants having internal pedometers, meaning that the ants do in fact count how many steps they have taken from leaving their nest and then take the exact amount of steps back. So by having longer or shorter legs, the ants still counted their steps back to their nests but just travelled a shorter or longer distance (Carey, 2006).

From the studies I have researched I still cannot pick a side as to whether animals can count or not. I do believe animals can understand the concept of counting (proven by the ant investigation), however I’m not sure if they can count as they cannot talk meaning they don’t have words for numbers.

In the future this would be a topic in which I would be interested in researching some more in order to have an answer. I believe this would be a great topic to look at with my future class to demonstrate how maths can be fun and associated with topics they are interested in (animals).

Can animals count ? The research continues…..

Refrences

BBC. (2017). Super Smart Animals – Ayumu – BBC One. [online] Available at: http://www.bbc.co.uk/programmes/profiles/31n3tMPHkZ8sQgxS5ZjdzN/ayumu [Accessed 6 Oct. 2017].

Carey, B. (2006) https://www.livescience.com/871-ants-marching-count-steps.html (accessed: 27 November)

Jackson, J. (2005) http://www.critical-thinking.org.uk/psychology/the-clever-hans-effect.php (accessed: 27 November)

Muldertn (2008) Chimps counting. Available at: https://www.youtube.com/watch?v=0cKg9D4QKCM (Accessed: 27 November 2017).

Maths in Music

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Music has always been a subject which I love but have never been very good at, after TRYING to learn the violin (we wont talk about that today) I discovered I was never going to be a musical genius. I love nothing more than listening to a bit of Taylor Swift or watching a good musical. Sadly, that’s as far as my musical knowledge goes.

A recent maths input, which I very much enjoyed, was discovering the links between maths and music. At the beginning of the input, we were asked to think of as many links as possible, my list consisted of rhythm and beats in a bar. After being proud of coming up with 2 links you can imagine how amazed I was to discover the list is pretty much endless. Some links, which I wasn’t aware of included:

Note values
Tuning/pitch
Counting songs
Fingering on music
Time signature
Scales
Fibonacci sequence
Patterns and repetition

Patterns and Repetition

In any piece of music, pattern and repetition are usually involved in order to create a rhythm, which is a regular repeated pattern or sound (Rhythm, 2017). According to Professor Peter Schickele, the reason for this “is that regularity of pattern builds up expectations as to what is to come next”, thus making the piece more exciting and memorable. However when composing a piece of music it is essential to create the right balance of repetition as too much can make the piece boring and predictable (Schickele, 1980).

Fibonacci Sequence

The Fibonacci sequence, according to Elaine J. Home (2013) is “a series of numbers where a number is found by adding the two numbers before it”. For example, the sequence starts like 0,1,1,2,3,5,8,13,21. Lets take the number 8, this number belongs in the sequence as the two numbers found before it equals 8 (3+5+8).

In music, a chord is made up of the 1^st(the root), 3^rd and 5^th note on a scale. These are all Fibonacci numbers. Fibonacci numbers also re appear in the octave and multiple scales too (Meisner, 2012). The video below demonstrates how the Fibonacci sequence appears visually in a musical context.

The ‘music in maths’ input was one of my favourites as, even though music is something I listen to on a daily basis, I had never associated it with maths. This highlights the idea that maths is a common theme in many aspects of our lives. In the future, I would be interested in having a second go at trying to learn an instrument. After this input and with a basic fundamental mathematical knowledge, I might have more luck this time as I will be able to look out for the links!

References

Elaine J. (2013). ‘What is the Fibonacci Sequence?’ Available at: https://www.livescience.com/37470-fibonacci-sequence.html (Accessed 17 November 2017)

Meisner G. (2012). ‘Music and the Fibonacci Sequence and Phi’ Available at: https://www.goldennumber.net/music/ (Accessed 15 November 2017)

Rhythm. (2017). In: Oxford Disctionary, 1^st ed. Oxford University Press.

Schickele P. (1980). Symmetries. Symmetry in Music, p.238.