Today was our last input for the module, Discovering Maths. At the beginning of the module my understanding of mathematics was just the basic sums and problem solving skills that I was taught in primary school, however this module has taught me so much more!

From the tuition in Discovering Maths, I have discovered that maths really is the foundation of most aspects in life.  I have truly explored the fundamental properties of mathematics  and just how important they to almost every life situation in which we encounter. Liping Ma (2010) supports the idea of the importance of the fundamental principals of mathematics, and states that the four three fundamentals of mathematics are (Inter) connectedness, multiple perspectives, basic ideas and principles and longitudinal coherence. Curriculum for Excellence (undated) further highlights the importance of teaching the fundamental principals of mathematics from a young age. Curriculum for Excellence (undated) says that the fundamentals of mathematics are extremely important and useful when it comes to everyday life, and so, it is important that students are introduced to these principals from a very young age.

From studying this modules, I have come to realise that mathematics is a subject that relates to almost every situation and problem that we face in the world. Maths plays a huge part in a range of different aspects in the world, music being one. Sangster, p (2018) further develops the idea of maths playing a huge part music and uses a wide range of examples to back this statement up, including: rhythms and time signatures.

Overall, I feel that this module has had a huge influence on my developing of mathematics and will have a positive impact on how i choose to teach the subject. I really enjoyed this module as it has influenced me to dig deeper in mathematics and explore different uses and concepts of  maths. Discovering maths has taught me that there is mathematics in almost every situation, thus highlighting the importance of being able to pass on my knowledge to further, upcoming, students.

References

Curriculum for Excellence (undated) Curriculum for Excellence: Mathematics, Principals and Practice , Available at: https://education.gov.scot/Documents/mathematics-pp.doc (Accessed: 24th October 2018).

Ma, L., (2010) Knowing and teaching elementary mathematics (Anniversary Ed.) New York: Routledge.

Sangster, P. (2018) Discovering Maths: Music and Mathematics [MA2 Discovering Maths Lecture] ED21006: Discovering Maths. University of Dundee

From a recent workshop, I truly have found how maths makes us beautiful! Through linking maths and art together, I discovered that maths helps to make the beauty of the human face. I can back this up with the picture below…

The drawing on the left is my first attempt. To create this drawing we copied an image and drew free handed. However, the picture on the right is how we should be taught to draw in education. To create this image, we copied a step by step guide which explained the different fractions of the face and exactly where each facial feature should be placed. Using measurements, I created this drawing. We new the exact fractions and proportions of the face and this helped to make a clearer, and more attractive, facial drawing. The difference is clearly visible! True beauty, right?

Bourne, M. (2018) backs up the idea of maths bringing to beauty to individuals. Bourne, M (2018) explains how the human face depends on ‘the golden ratio’ and particularly focuses on the mathematical concept of symmetry. The golden ratio comes from the idea of the Fibonacci number sequence (explained in a previous blog of mine). Bourne, M (2018) explains that this idea is followed when it comes to the positioning of eyes and also the length of the nose.

To conclude, this workshop really opened my eyes to the thought that maths stretches to beyond numbers and calculations. I feel that it was this workshop that got me thinking to how mathematics plays such a huge part in our lives. I have now began to make connections between mathematics and other concepts, and no just number orientated problems. I feel that in school I was also taught that maths was linked to numbers and calculations and so I feel that it is extremely important that we are introduced to ideas like this at an early age. Thus, widening students knowledge of mathematics.

References

Bourne, M. (2018) The Maths Behind The Beauty , Available at: https://www.intmath.com/numbers/math-of-beauty.php (Accessed: 5th November 2018 ).

Maths was always a favourite subject of mine at school, however I suffered from maths anxiety. I only ever begun feeling anxious towards maths when i studied both national 5 and higher mathematics. I used to think that there was only one set way of doing each type of question and the only way i knew was they way that my teacher taught. I suffered from anxiety during my exams as I am a perfectionist and so I put a huge amount of pressure on myself to learn the exact method I was taught. I truly believe that I was not the only one, therefore I feel that it is important that teachers make students aware that there is not just one right method!

The University Of Cambridge (2017)  defined the term ‘Maths Anxiety’ as “a feeling of tension and anxiety that interferes with the manipulation of numbers and the solving of mathematical problems in … ordinary life and academic situations”. I agree with this statement! Going to maths classes used to make me anxious and this was a barrier when it came to the learning of maths. I used to believe that I was not born with a ‘maths bairn’ and so this always stood in the way of my success. Kapner, L. (2017) states that J Boaler, a Standford Professor, believes that there is no such thing as a ‘math brain’. Kapner, L. (2017) further describes that by believing the math brain myth, this lowers students academic performance in mathematics. I truly believe that my under performance in mathematics in first to third year was due to thinking that i was not born with a maths trained brain. However this changed in fourth year! Lets have a look at how I changed my ways of thinking…

In order to overcome the maths brain myth, I used positive reinforcement. Willis, J. (2017) describe how enjoyment a positivity are essential for learning to effectively occur. It is further explained that by having a stressed mental state, this limits how focused you are on the task and restricts your learning ability. By changing my mindset towards maths completely, I felt that I was more open to learning different approaches to questions. By allowing myself to do this, I feel that this helped to relax me when dealing with maths problems and I could use a few different methods to approach the question.

References

University Of Cambridge (2017 ) What is Mathematics Anxiety? , Available at: https://www.cne.psychol.cam.ac.uk/math-memory/what-is-mathematics-anxiety [Accessed: 20th October 2018].

Kapner, L. (2017) The Myth of the Math Brain , Available at: http://giftededucationcommunicator.com/gec-spring-2017/the-myth-of-the-math-brain/ (Accessed: 22nd October 2018).

Willis, J. (2017 ) Busting math myths to create math-positive attitudes, Available at: https://npjscilearncommunity.nature.com/users/20252-judy-willis/posts/20852-busting-math-myths-to-create-math-positive-attitudes (Accessed: 23nd October 2018).

To many individuals, maths and play are not connected at all. When it comes to maths many people describe it as ‘boring’, ‘torture’ or ‘something which was compulsory’. This is a devastating matter as, in reality, this should not be the case (Early Years). The Curriculum For Excellence has a huge focus on using active learning in order to help children engage with a range of different materials and also apply different concepts to real life situations. By introducing maths through play, this will help to get rid of the stereotypical views of the subject and will help students to understand how maths is a useful subject and relates to everyday life. Toys, games and other materials used to learn mathematics can help to relieve the pressure and intimidation of maths (Early Years).

It is seen that babies immediately react to the different shapes that make up the human face (Nursery Resources, 2018). This shows that the learning of maths starts from a very early age and is being learnt through simple activities.   Both sand and water are another two aspects which are used to enhance aspects of maths at a young age. Through playing which these features, children can begin to develop the idea of some mathematical concepts and language and also look at different patterns and shapes in which they can make using the materials (Early Years). This concludes that maths can be learnt through play in a variety of settings and not just at pre-school and school.

“Play gives children a chance to practice what they are learning.” (The Strong National Museum of Play,2018). I feel that this quote summarises how important it is that active learning is used during learning, in order for the children to understand what is being and learnt and also to allow the children to link their findings to everyday life.

Through my time at Primary School, I feel that my learning actively, this really helped to engage me in my learning and helped to change my overall opinion of Mathematics from a young age. To me, active learning was an important part of my learning and helped to me feel the enjoyment of maths and helped me to learn the basics of mathematics. Now, looking from a teachers point of view, I feel that it is important that a number of maths lessons are done actively as this will help to engage all children.

References

Early Years () Maths Through Play , Available at: http://www.early-years.org/parents/docs/maths-through-play.pdf (Accessed: 22nd October 2018).

The Strong National Museum of Play (2018) Play Quotes , Available at: http://www.museumofplay.org/education/education-and-play-resources/play-quotes (Accessed: 22nd October 2018).

Nursery Resources (2018) Maths and Numeracy in Early Years , Available at: https://www.nurseryresources.org/post/maths-and-numeracy-earlyyears (Accessed: 22nd October 2018).

The Fibonacci Number Sequence is a number sequence that creates a beautiful pattern. The sequence starts with 0,1,1,2,3,5,8,13,21,34… and so on! The number sequence was first introduced to Western European Mathematics by Leonardo Pisano in 1202 (Anirudh (2015 )). The sequence was also named after Leonardo as he was also known as Fibonacci.  Before his finding of The Fibonacci Number Sequence, he studied the Hindu-Arabic Arithmetic system as he was growing up in North Africa.

Now how do we work the pattern of the sequence?

Easy!

All we have to do is add the two numbers before together in order to identify the next number in the sequence.e.g. –> 0+1 = 1, 1+1=2, 1+2=3, 2+3=5 etc. We now then take the answers to our simple calculations and form a number sequence: 0,1,1,2,3,5…

The Fibonacci Sequence doesn’t quite sop there… we can transfer the sequence into a spiral! By drawing squares with the dimensions of the numbers, a spiral can be formed.

  E,J. Hom (2013)

(Benjamin, A. (2013))

References

Anirudh (2015 ) 10 Facts On Leonardo Fibonacci And The Fibonacci Sequence, Available at: https://learnodo-newtonic.com/fibonacci-facts (Accessed: 3rd October 2018).

Benjamin, A. (2013) The magic of Fibonacci numbers , Available at: https://www.youtube.com/watch?v=SjSHVDfXHQ4 (Accessed: 3rd October 2018).

E,J. Hom (2013 ) What Is The Fibonacci Sequence? , Available at: https://www.livescience.com/37470-fibonacci-sequence.html (Accessed: 3rd October 2018).

Last week we had a fun and exciting lecture which focused on tessellations and their link to Islamic Art. . Firstly, a tessellation is a pattern of flat shapes which is repeated. When the pattern is repeated the shapes fit perfectly together in order to cover a surface, with no gaps between the shapes. You can get a variety of different tessellations, some of which are regular and some are semi-regular. Regular tessellations are repeating patterns of a regular polygon.

The image above are the three regular tessellations. There are only three possible regular tessellations.

Semi-regular tessellations are patterns which are made up of two or more regular polygons. There are only 8 possible semi-regular tessellations;

The history of tessellations

The creator of the first tessellation still remains unknown and so the credit for the wonderful designs was first given to a Dutch artist named M. C. Escher. Escher experimented a range of different ways and patterns to create tessellations and this is where he came to the realisation that tessellations following one repeating pattern.

In Islamic Art, tessellations are used. In many of the mosaics which helped to to create tiles and floors in Roman buildings, tessellations were using in order to create a repeating, and symmetrical, pattern. Below is an example of a tile in a Roman home;