Monthly Archives: October 2017

Maths, Play and Stories

Leave a reply

“Play allows children to use their creativity while developing their imagination, dexterity, and physical, cognitive, and emotional strength” (Ginsburg, 2007).

Friedrich Froebel explains that a child does their best thinking and learning whilst they are playing. Play within education is fundamental to a child’s holistic development. It helps to make connections in their learning in a relaxed environment as it enables the children to experiment within their own learning and apply it to contexts which they are familiar with. Furthermore, Susan Isaacs also valued play based learning as she saw the value of play as a means to enable children the freedom to balance their ideas and feelings.

There are various types of play which can be involved within play based learning. These involve; symbolic, creative, discovery, physical, technological, games, environment and through books and language. During quality play within mathematics however, children are involved with making decisions, imagining, reasoning, predicting, planning, experimenting with strategies and recording (Lewis, cited in Pound, 1999). Playing around in maths allows the children to know and understand early maths language involved with basic mathematical skills such as measurement, time, shapes, spaces, positions, early numbers and order and patterns. One way to help children practice their new mathematical skills through play, is by learning number rhymes and songs such as; Five Currant Buns, Ten in the Bed and One, Two Buckle My Shoe. These are fun ways for children to connect with maths in a playful and exciting manner.

Play within learning encourages creative and flexible thinking, and is something which parents can get involved in. However, parents who are afraid of maths or dislike it, will pass this onto their children (Furner & Duffy, 2002). Therefore, it is important that when parents are encouraging maths in the home, that they promote positive mathematical experiences. Susan Isaacs, alongside Friedrich Froebel, has valued the importance of parents as educators. Parents of preschool children especially, are essential in their child’s early development (Pound, 2003). It is important for parents to encourage play based learning in their home as this will help to develop the learning of the child. Parents can be involved with helping children have fun with simple mathematical concepts such as numbers, shapes and measure. It is crucial however, to have a balance between child initiated play and adult initiated play. It is important to ensure that children are regularly at the forefront of their learning, as this is when the child will learn best. This can easily be done by allowing the children to create their own rules or their own games.

I have attached a picture which explains different ways in which parents can help children when learning maths.

Another way in which children can learn maths is through stories. Stories allow children to make sense of both the real world and the imaginary world. A mathematically themed story can be shared either on a 1-to-1 basis or also within a group or classroom environment. Stories could be read aloud at home by parents to their children, or teachers could use stories to support their pupils’ mathematical learning and understanding. Furthermore, the pictures within a story book are also a good stimulus for the development of mathematical discussion. However, it is important to ensure that the questions asked and discussions had, are relevant to the children’s stage of mathematical development. If this is not the case, the children will not benefit from the story and instead this may confuse them. Using story books within mathematics can also support other areas of the curriculum too. For example, the children could act out the stories, linking to drama and performing arts, and place emphasis on the mathematical language or concepts involved in the stories, and how this links to what they are learning at the moment in class. Furthermore, reading story books to help support maths, will also improve the children’s language skills and influence their love of reading and language.

I have attached a video of a mathematical story book being read aloud, which is a perfect example of the kind of story books which could be used to assist mathematics for children.

References

Ginsburg, K. (2017). The Importance of Play in Promoting Healthy Child Development and Maintaining Strong Parent-Child Bonds.

Pound, L. (2003) Supporting Mathematical Development in the Early Years. Buckingham: Open University Press.

Pound, L. (2008) Thinking and Learning about Mathematics in the Early Years. Oxon: Routledge.

Skwarchuk, S. (2009) How do parents support preschoolers’ numeracy learning experiences at home? Early Childhood Education Journal, 37(3), pp.189-197. Doi:10.1007/s10643-009-0340-1.

Can animals count?

1 Reply

I must admit, I have never properly thought about whether animals can count or not. I always knew animals like chimpanzees and apes were particularly clever, but I never focused on the mathematical aspect of their intelligence. This is mostly likely because when I think of maths I always think of equations and algebra. I forget that maths includes problem solving and basic counting, a skill which scientists have discovered that some animals possess.

Jason Goldman (2012) suggests that even though animals may not be spending their time doing algebra or trigonometry, “mathematical ability is widespread in the animal kingdom”. This all began back in 1891 with Clever Hans. Clever Hans was a horse whose owner believed could count and give answers to basic mathematical calculations, in which he gave the answer by stomping his foot. However, it appears the horse was reading body signals and cues from his owner, which allowed him to know when to stop stomping (Heyn, 1904). Although this horse may have been highly intelligent, he was not using any mathematic skills.

However, there has been successful case studies which have proven that certain animals can perform mathematical skills. According to Goldman (2012), Ants are the math geniuses of the animal kingdom. When ants leave their nests in search of food, they must remember their way back. The ants do this by calculating the distance they have walked, by counting their steps, known as “path integrate”. Researches Martin Muller and Rudiger Wehner decided to investigate how ants do this and if different variables would affect it. They attached stilts to the ant’s legs to see if this would affect the distance the ants would walk on the way to and from their nests. Each individual step was made longer than it would’ve been without the stilts, as they overestimated the distance (Goldman, 2012). They also did the same investigation with the ants, but this time they decided to cut the legs of the ants shorter. The ants were able to mathematically calculate that they needed to take more steps, clarifying Goldman’s statement that ants are the “real Math wizards of the animal kingdom”.

Furthermore, it has been discovered that Chimpanzees also possess mathematical attributes and skills. Professor Matsuzawa started a study of chimp intelligence over 30 years ago, in which Amuyu the chimpanzee has proved to be a highly intelligent animal. He lives at the Primate Research Institute of Kyoto University Japan (BBC, 2017). Amuyu took part in a test in which he had to remember the position of nine numbers randomly displayed on a computer screen, which were only on screen for 60 milliseconds (BBC, 2017). In this test, Amuyu outranked the human, not only doing it better, but completing the test and doing so quickly. This proves that Amuyu could engage with mathematical skills such as ordinality, the order of numbers e.g. 1, 2, 3, and cardinality, analysing the amount of numbers in a test. Overall, proving that chimpanzees can do maths.

References

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

Goldman, J. (2012). Animals that can count. [online] Bbc.com. Available at: http://www.bbc.com/future/story/20121128-animals-that-can-count [Accessed 4 Oct. 2017].

Heyn, E. T., (1904) ‘Berlin’s wonderful horse; He can do almost everything but talk – how he was taught’ The New York Times [Online]. 4 September. Available at: http://query.nytimes.com/mem/archive-free/pdf?res=9E02E2D91F3AE733A25757C0A96F9C946597D6CF (Accessed: 6th Oct 2017).

Maths? Creative?

Leave a reply

To me, maths was always equations, algebra, volume etc. It was a class which I dreaded going to in school. In the first half of the lesson, we would be taught something new and then in the second half we would be putting what we have just learnt into practice by doing textbook work. If we didn’t finish the work in class, it would then become additional homework. This was an ongoing cycle. We never did anything exciting or never applied what we had learnt in class into different contexts. This was probably where my lack of enthusiasm for maths began.

It wasn’t until I had taken the Discovering Mathematics module, that I realised just how creative maths can be! Most likely due to my own experience, I had never thought of having a creative maths lesson whereby you can combine the skills which you have learnt in the classroom, to other subjects such as Art.

Throughout history, artists have used symmetry, tessellation and proportion, which are all mathematical skills, to create their works of art. Ancient Greek architects and sculptures, would use the Golden Ratio which allowed them to ensure that buildings like the Parthenon in Athens were visually appealing. Furthermore, portrait painters during the Renaissance period would have to follow specific mathematical procedures to ensure that the proportions of the subject’s head and facial features were in proportion to the size of the rest of their body. Such mathematical procedures were used to paint the world-famous Mona Lisa by Leonardo da Vinci.

In our Discovering Mathematics class however, we looked into Islamic art. Islamic art is heavily reliant on tessellating geometric shapes and represents a spiritual vision of the world. Geometry is considered to be at the heart of nature and as such at the heart of Islamic design. We looked into creating our own Islamic art, in which we used the three fundamental shapes in Islamic art; equilateral triangle, square and hexagon. However, 6, 8, 10 and 12 pointed stars are also often used in Islamic art.

I thoroughly enjoyed this class as it allowed me to be creative, something I never had the chance to do whilst I was learning maths in school. I did not have much time to create my own piece of art work, so mines is pretty basic. However, I can definitely see myself looking into either Islamic art, or something similar in the future, whether it be for my own benefit or with a future class. I have attached my own piece of Islamic art.


Maths is everywhere!

Leave a reply

Maths has been described as “the language with which God has written the universe” (Galileo, 1564-1642).

During my time at school, I probably would have turned my nose up at this quote and disagreed with it. Although, this was probably because I hated maths at school, but didn’t everyone? After taking the Discovering Mathematics module this year however, I have noticed that mathematics truly is at the heart of everything that we do. Whether it is as simple as telling the time or as complex as working out the sale price of a pair of jeans in Topshop, we constantly use maths in our everyday lives.

The Scottish Curriculum for Excellence (2016) states that “mathematics is important in our everyday life, allowing us to make sense of the world around us and to manage our lives”. Furthermore, the Curriculum’s principles and practice documents also explain, that mathematics is crucial because it is implemented and used throughout the whole curriculum. For example, in art and music you use patterns, sequencing and symmetry and in science you are often using graphs and charts when it comes to experiments. Moreover, maths is also used in health and wellbeing, modern languages, design and technology, and ICT (CfE, 2016). In addition to this, Haylock (2014, p286) states that “mathematics provides us with knowledge and skills that are valuable not just for their own sake but because we can apply them to situations in real life and across the curriculum”. It is therefore crucial that we as teachers encourage children to engage with maths in all its purest forms. It is important that children not only learn maths within the classroom, but also outside the classroom.

Education through play is a great way for children to take the mathematical skills which they have learnt in the classroom, and use them in their everyday lives. Edwards (1998) states that both children and adults learn better when they are interested and motivated to learn, as this makes learning a purposeful and pleasurable experience. She goes on to state, that the presentation of mathematics through play is a great way to sustain the motivation and interest of the children. In my MA1 placement class, they had active maths once a week, where the children used the mathematical skills which they had learnt recently, for example percentages and decimals, and applied them to game like situations. I was in charge of organising and creating the games during my placement. I would create my own board games and crosswords etc. for the children. Doing this highlighted to me the importance of play involved with learning, especially within mathematics as it helps the children to put the skills which they have learnt into real life situations and contexts.

The following TED Talk by Jim Patrick, a budding mathematician at the young age of 6, explains the importance of maths and how we use maths in our everyday lives.

References

Curriculum for Excellence: Mathematics Principles and Practices. (2016). [ebook] Education Scotland, pp.1-4. Available at: https://education.gov.scot/Documents/mathematics-pp.pdf [Accessed 13 Nov. 2017].

Edwards, S. (1998). Managing effective teaching of mathematics 3-8. London: Paul Chapman, pp.2-7.

Haylock, D. and Cockburn, A. (2014). Understanding mathematics for young children. 4th ed. Los Angeles [u.a.]: Sage, pp.286-291.