Category Archives: 3.1 Teaching & Learning

Discovering Mathematics Reflection

After finishing the Discovering Mathematics module, I have decided to take some time to reflect upon my experiences within the module.

At the start of the module, and before it even began, my attitude towards mathematics was extremely negative. I feel this is because maths was always a subject which I struggled with at school, especially higher maths, as to do well I had to work extremely hard and put a lot of effort in. As much as I was relatively good at maths, it was not something which I enjoyed at school. I think this is mainly because the way in which I was taught mathematics, was extremely procedural. Furthermore, the teachers would make out that there was only one way to answer a question, and if you did not understand this, then you were wrong. This contradicts what Liping Ma (2010) says, as she states that teachers who have a profound understanding of fundamental mathematics should realise that not all children teach the same, and that teachers should encourage that there are different ways to solve the same question.

Before taking Discovering Mathematics, I have never experienced enjoyment in conjunction with maths. However, this module has taught me that mathematics can be FUN. Multiple lectures throughout the course of the semester have included task, or topics which I have thoroughly enjoyed. For example, one of my favourite inputs was learning about the connection mathematics has within sports. I then went on to look at maths in golf, a sport which I played for years when I was younger, and I found this extremely interesting. Moreover, another input which I also enjoyed was about whether animals can count. Prior to this input, I had never thought about this, but after studying it I have realised that animals can count. It was interesting to consider different animals like ants, horses and chimpanzees, and understand how they can all count in their own individual ways.

Finally, I feel that the Discovering Mathematics module has improved confidence in maths. Prior to this module, I was worried that when I came to teaching maths in the future, that the children would identify my lack of enthusiasm and confidence in the subject and that this would impact their experience of mathematics. However, I can now say that my confidence in mathematics, has improved and that I know this will have a positive impact on not only my teaching, but also the children’s mathematical education. Additionally, due to studying Liping Ma’s (2010) profound understanding of fundamental mathematics (PUFM), I have come to understand some of the key qualities that a successful mathematics teacher must have. I will also take some of the activities and tasks which we have done in the module, such as the Apprentice task, and include these in my future teaching profession, as I believe that children would enjoy these and see the fun and relevance of mathematics within the wider society and in their own lives.

References

Ma, L. (2010). Knowing and teaching elementary mathematics. Milton Park, Abingdon, Oxon: Routledge, pp.120-141.

Maths Games and Puzzles

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Who doesn’t love a board game?

Board games are something which friends and families across the world, join together to play. However, what many people do not realise is, that board games and puzzles are a fun and exciting way of practicing mathematics at home or in a fun, school environment. Most board games and puzzles in the current market, involve some sort of mathematics, whether it be as simple as the chance of rolling a 6 on a dice, or counting the squares as you go along in monopoly, mathematics is involved.

Today in Discovering Mathematics, each group looked into, and played, different board games such as Monopoly, Cluedo, Battleships, and my group played 5 Second Rule. In 5 Second Rule, the players are given a 5 second timer and a topic, such as; “Name 3 things you find in the sky” and the player has to answer the question within the 5 seconds. This game involves the elements of time and categorizing, which are fundamental to the understanding of mathematics.

Furthermore, mathematics is also involved in the game of Cludedo, which is a murder mystery board game. In order to find out who committed the murder and in which room they did it with which weapon, the players use a process of elimination, another fundamental mathematical concept. Another group also played Battleships, which involves co-ordinates, rows and columns, and positioning, which are all mathematical skills.

However, the game of Monopoly, which is one of the most popular board games around the world, involves many fundamental mathematical concepts and skills. Some of these include; the chance when rolling the die, the role of the banker, who must able to add, subtract, multiple, divide etc. in order to give out the correct amount of money, counting spaces as you go along, working with money and working out which properties are the best to invest in or trade.

It is interesting to see the connections which mathematics has within board games, especially since they are something which many people enjoy, I know that I do. Board games are therefore, an interesting and exciting way to practice maths with children, whether this be in the classroom or at home with parents, family and friends. This also allows for parents to be involved with their child’s learning and mathematic growth and development, as it has been shown that parents play an important role in their child’s mathematic education. Moreover, board games are something which I am going to use in my professional future as a teacher, as I have seen first-hand in placement, how much children enjoy playing them, and the mathematical development that they help children to make.

Maths, Play and Stories

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“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.

Maths? Creative?

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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!

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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.

Maths Anxiety

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Mark H. Ashcraft describes maths anxiety as “a feeling of tension, apprehension, or fear that interferes with math performance” (2002, p. 181). Math anxiety is a recognized stress disorder which, according to research shown in the attached video, 20% of our population suffer from (Turner & Carroll, 1985). It ranges from feelings of mild tension to strong fear when involved with any kind of mathematics. Physical symptoms include headaches, muscles spasms and aches, shortness of breath and increased heart rate. Furthermore, math anxiety also causes psychological problems such as confusion, the inability to concentrate and incoherent thinking (Arem, 2010, p.30).

Math anxiety does not only affect children in school, but adults too. For example, suffering from math anxiety may stop adults applying for certain jobs as they have a fear of failure and lack in confidence. Additionally, adults may struggle to deal with the mathematical challenges involved with dealing with personal finances, bills and mortgages.

The shorter video attached explains what math anxiety is, but it also highlights a problem which I myself face. During school I was never bad at math, in fact I was always in the higher classes and did manage to achieve a B in Higher Maths. However, this was not an easy process for myself. Maths was always something which took up a lot of my time, as I was always working to better myself. I knew that if I wanted to do well, I would have to work hard at it. However, there is still many areas of mathematics which I struggle with, which worries me for when it comes to teaching my own class. The attached video explains how pupils can easily sense if teachers suffer from math anxiety themselves and I am worried that this will be conveyed across to the children during my math lessons. If I myself suffer from math anxiety, how am I supposed to feel confident and competent in my own mathematical skills, when it comes to teaching the children? By taking the Discovering Mathematics module, I hope to improve my confidence in mathematics, so that when it comes to teaching the children, I can give them the best mathematical experience possible.

Furthermore, the University of Dundee have also researched into ways of targeting maths anxiety. They have introduced the Online Maths Assessment (OMA) to improve poor levels of mathematics and confidence within education students (Henderson, 2010). By doing this, the University of Dundee hope to target maths anxiety in student teachers so that they do not implement negative views towards mathematics in their future classes.

References

Ashcraft, M. (2002). Math Anxiety: Personal, Educational, and Cognitive Consequences. [ebook] Cleveland, Ohio: Blackwell Publishing Inc., pp.181-185. Available at: http://www.thinkingahead.com.au/Documents/math_anxiety-consequences.pdf [Accessed 30 Sep. 2017].

Henderson, S. (2010). Mathematics Education: The Intertwining of Affect and Cognition. Unpublished doctoral thesis. D.Ed. University of Dundee.

Nuffieldfoundation.org. (2017). Understanding mathematics anxiety | Nuffield Foundation. [online] Available at: http://www.nuffieldfoundation.org/understanding-mathematics-anxiety [Accessed 30 Sep. 2017].

Turner, J.R. & Carroll, D. (1985) ‘Heart rate and oxygen consumption during mental arithmetic, a video game, and graded exercise: further evidence of metabolically-exaggerated cardiac adjustments?’, Psychophysiology , 22(3), pp.261-267.