Discovering Mathematics- Reflection

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At the very beginning of the Discovering Mathematics module I was quite anxious about maths as a whole however I had the intentions of getting the most out of the module and hopefully changing my attitude towards maths going forward in my teaching career. This module has definitely changed my outlook on the subject and my learning will without a doubt support me in the teaching and learning of mathematics in the future.

When first introduced to Liping Ma’s four key elements of profound mathematics in the very first input I must admit that I didn’t quite understand how these elements actually fitted in with the everyday mathematics we teach in our primary classrooms.

Now, at the end of the module I can safely say that I have a much deeper understanding of the four elements of (inter)connectedness, multiple perspectives, basic principles and longitudinal coherence and just how they will support me in the future. Ma (2010) states that:

“PUFM is more than a sound conceptual understanding of elementary mathematics- it is the awareness of the conceptual structure and basic attitudes of mathematics inherent in elementary mathematics and the ability to provide a foundation for that conceptual structure and instil those basic attitudes in students” (Liping Ma, 2010, page 106)

Ma also speaks about the depth, breadth and thoroughness of understanding that an individual with PUFM will have. They will be able to make links between individual pieces of mathematical knowledge and understand the connections between them.

Therefore, it is vital that we, as prospective teachers, are aware of PUFM and gain the confidence and competence needed in order to teach our future pupils mathematics in a way in which will benefit them in the future.

I would say that this module has helped me tackle the insecurities I had about teaching maths and going forward I feel as though I am much more comfortable with the prospect of teaching maths in the future. The module has really opened my eyes as to just how much mathematics plays a part in society around us each and every day. I will take forward this knowledge and use it in a classroom environment in the future as I feel that by linking maths to other areas of society, it makes it a more accessible subject for all and perhaps will engage those children who suffer from the ongoing issue of maths anxiety.

References:

Ma, Liping. (2010) Knowing and Teaching elementary mathematics: teachers’ understanding of fundamental mathematics in China and the United States New York:

Maths, Games and Puzzles

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In our final maths input we looked at the maths linked to puzzles and games. There are many games in which maths is involved and I feel as though it is a great thing to bring into the classroom in order to engage children with maths in a fun and interesting way.

The first puzzle we spoke about in the input was sudoku. Even though sudoku may seem complicated to some children, if they were to play this game they would be putting basic maths principles to use, e.g. addition. Sudoku is extremely accessible and is a great way to get children doing some basic maths but having fun at the same time.

There are also many board games which include some mathematical principles. A stand out game in particular is monopoly. The game of monopoly is very much based on money, therefore in a game of monopoly the players are learning about how to spend money and the player who plays as the banker will also put mental maths to good use in order to distribute change correctly.
Another example is battleships, this game involves the concept of co-ordinates and so would be a great way for students who are learning about co-ordinates to consolidate their knowledge in a fun and engaging manner.

Using games and puzzles in connection with maths will definitely be something I will take forward into classes in the future as I feel more children would enjoy and feel comfortable with maths if they associated it with enjoyment and something they find fun.

Maths, Supply Chains and Logistics

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In a recent workshop we explored maths and the links it has with supply chains and logistics. This is something that I had next to no prior knowledge about however I left the lecture feeling very informed on the topic.

A supply chain is the processes involved in the production or distribution of a product. Many companies use maths all the time in the process of supply chains. Particular examples we touched on in the workshop was the use of maths when shipping products. We discussed certain products in particular and the best way we think would be to transport them from place to place. It was this discussion that made me think just how many principles of mathematics are involved in processes like this. There are so many things to be taken into consideration such as the mass of the products, the shape, how many need to be transported and many other factors. Problem solving will also likely be involved since it is unlikely that the first method of which a product was transported was the best and most appropriate method that could have been used.

In the workshop we were given the opportunity to try out some demand planning. Demand planning is the process used to “forecast” customer behaviour and demand and helps an organisation know how much of, and what they need to order to enable them to meet customer wants and needs.

We were given templates in which we had to decide which things we thought we would need to order at certain times of year, we had to take into account what customers would want at the time of year given to ensure that we made a profit. By the end of the activity we had made a profit however many others in the group seemed to have made much more money than we did. Why? Because many people had the idea of bulk buying a product such as baked beans which are sure to sell all year round and do not go out of date quickly, this meant that any products they did have left over could be carried over onto the next time period and eventually all of the beans were gone!
This shows that companies use maths to keep them in business, they do the maths to ensure that they have the correct amount of the correct products in order to make a profit and keep the company alive.

I feel like this kind of activity would be excellent for a middle/upper stages class. This would give them the opportunity to feel responsible for their own little business while performing some basic principles of mathematics. I feel as though the children would really enjoy an activity of this type and again, it would be a way of engaging children who perhaps aren’t so confident with maths as a subject however may find it more accessible in a fun way like the above and working as part of a group.

Maths and Sport

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Maths and Sport have very strong links, most of which I had no idea even existed until our input on the subject and further research afterwards.

One very obvious link between the two is the use of different scoring systems in various sports. Some scoring systems are quite simple such as the one used in football- each goal scored by a team is counted as one and at the end of the game the team with the highest number of goals win the game. Other scoring systems such as the one used in tennis is a little more complex, in a game of tennis the scoring system usually consists of points, games and sets. All three link as you have to accumulate points to win games and accumulate games to win sets. Although slightly more complex maths is used in the scoring system for tennis than in games like football, maths is always at the heart of sports and is vital to ensure that the running of games is efficient.

John Barrow, a professor of mathematical sciences researches many different ways in which maths and sport are related and links these to particular formulas and even has mathematical theories in which it can be determined which events are the easiest to score in when participating in a decathlon.

The video below explains some of the links between sport and mathematics, examples being fluid dynamics being used to tailor and design swimsuits and a maths model being made to determine whether there is actually a limit to how much an athlete can push themselves. The main point that I have taken from this particular video is just how much mathematics is involved in the design and manufacture of sporting venues. Routes and structures are carefully analysed by mathematicians to ensure that the building/stadium etc can withstand its purpose, maths is also used to ensure that the structure can withstand various weather conditions including rain, wind and snow. Maths is used not only to predict what the needs are for the building, but also to predict the behaviour of the people who will be inside the building to ensure not only that the structure is appropriately designed for purpose but also that it is safe.

https://youtube.com/watch?v=QGC5yTAZSQ0%2520frameborder%3D0%2520allowfullscreen

In our maths and sport input, we decided to look at the rules and the sport of taekwondo and how maths comes into the sport and how we can adapt the sport in relation to the maths involved. In taekwondo a game consists of three 2 minute rounds with a break of 1 minute between each round and the contest area is a 10m square mat. Like most sports, the game can be won by scoring the most points. The scoring system in taekwondo is fairly simple and does not involve complex mathematics- one point is scored for a strike to the body and two points are scored for a kick in the head. Another mathematical link to the sport is the weight divisions in use. By dividing people into categories depending on weight this allows the competition to work more fairly and allow competitors to have an equal chance at victory.

We, as a group decided to take the maths involved in taekwondo and adapt it to create our own version of the sport. We decided firstly to focus on the actual design of the ring the sport is played in, we suggested decreasing the size of the ring after every round- this means that the competitors will have less space and so the competition would gradually become more difficult at the beginning of each new round. We also decided that we would introduce a height division as well as the weight division that is already in place. This would again, ensure a fairer fight if the competitors were more mathematically matched in terms of their height as well as their weight.

Now that I am much more aware of the links between maths and sport I will now take my knowledge forward and hope to share this knowledge with the children I will teach in the future, in this way those who perhaps feel like maths isn’t a subject for them may find alternative ways to engage with the subject through other subject areas which may be of more interest to them.

References

Barrow, J. (2013) Decathlon: The Art of Scoring Points– Available at: https://sport.maths.org/content/decathlon-art-scoring-points-0 (Accessed 27th November 2017)

Holme, R. (2017) “Maths of Sport” [powerpoint presentation] ED21006:Discovering Mathematics (Accessed 27^th November 2017)

Maths and Music

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Music is something that I have always had a strong interest in and I studied the subject throughout my time at high school. Little did I know just how many links there were between music and maths. I was always very aware of the simple mathematical concepts that were involved in music such as determining how many beats were in a bar or the different note values. However, after the maths and music input and further research into the topic I am now much more aware that there are many more links between the two subjects than meets the eye.

There are many basic links between maths and music, these links include: pitch, beats in a bar, note values, chords, intervals and sequences and patterns.

Wiggins (2012) states that pitch is something that can be related directly with mathematics as we can measure pitch. A musical skill such as tuning a piano makes use of mathematical concepts.

Also, by having an understanding of maths principles, it is then easier to have a more theoretical understanding of music and musical concepts. An example of this is the formation of chords. There are 13 notes in an octave, a scale, however, is formed of 8 notes and the 5th and 3rd notes in this scale form a basic ‘root’ chord. By understanding the intervals between notes and the numbering of the notes, this would allow a musician to be able to form the root chord of any note asked of them without really having to think about it.

Below is a video of a prime example of mathematics being used by extremely famous composer Beethoven, who was actually partly deaf and used his mathematical knowledge to create music that was so widely popular with listeners.

https://youtu.be/zAxT0mRGuoY

Besides mathematical and musical concepts being very closely linked, I was also interested in further reading about if the connection between maths ability and musical ability has actually been proven or if it is, in fact, just a myth.

In the article The Enduring Myth of Music and Maths (The Independent, 2011) it is stated that there is no evidence to back up the supposed “Mozart Effect” in that a group of children who have been exposed to music by Mozart are said to be more intelligent in subject areas like maths than children from a control group.

From my research I have found that there are in fact many links between music and maths that I did not know existed however there does not seem to be much evidence to prove that abilities in the two areas are linked. You do not necessarily have to be mathematically talented in order to acquire musical skills and knowledge.

I will take forward my knowledge of the links between the subject and hope to share them with those I teach in the future as music has always been a subject I have been passionate about but I never quite realised just how much of my mathematical knowledge I put to use throughout my studies of music. I feel that this may be a good way to help pupils who suffer from maths anxiety to put maths to use without actually realising it and hopefully improve their confidence along the way.

References:

Gowers, T. (2011) “The Enduring Myth of Music and Maths”, The Guardian, 5th July, no page given.

Sangster, P. (2017) “Music and Maths” [powerpoint presentation] ED21006:Discovering Mathematics (Accessed 17th November 2017)

Maths Anxiety

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Throughout my school life I had always just accepted that I was more talented in the area of languages than I was in maths. It wasn’t that I couldn’t do maths, it was simply that I felt more confident and comfortable in other school subjects.

The above is one of the reasons why I jumped at the opportunity to study the Discovering Mathematics module when it was offered as one of the second year electives. Already, I can see the positive impact that my learning from this module will have in my future career. I know that in order to teach maths and make the children in my class feel at ease with the subject then I must be confident in my own abilities and approach maths in a very open-minded way.

The Guardian article “Maths Anxiety: The Numbers are Mounting” spoke of a particular example of maths anxiety. A young girl called Flora had significant difficulties with anything related to maths however her struggles seemed to go unnoticed at school. Shortly after moving to a new school, Flora’s difficulties were noticed by her teachers and suspected that she may have dyscalculia which is a kind of dyslexia with numbers as her maths was observed to be very poor. After referral to an educational psychologist however, it was found that Flora’s problems were not down to ability but actually down to her anxiety towards maths as a subject.

Maths anxiety is extremely common and is said to affect around a quarter of the population which equates to more than 2 million school children in England alone, along with thousands of teachers.

The concept of maths anxiety was first discovered in the 1950s, however the significant effect it has on performance has only newly become evident.

A study which is also explained in The Guardian article previously mentioned above was conducted to look further into the reasons why anxiety towards mathematics affects performance in such a devastating way. Researchers at Stanford University have used scans in order to see what goes on inside the brains of children who suffer from maths anxiety, and discovered that these children respond to sums in the same way that people with phobias may reacts to snakes or spiders which increases activities in the fear centres of the brain. Increased activity in these areas causes a decrease in activity in the areas of the brain which assist problem solving which then makes it harder for the individual to come up with the correct answers.

Although maths anxiety is extremely common in today’s society, there are still no formally established diagnostic tests to decide when simply being worried about maths becomes maths anxiety. Mike Ellicock, chief executive of the charity National Numeracy states “labelling and categorising children into those who can and can’t do maths isn’t helpful. There is nothing more certain to be a self-fulfilling prophecy… but given encouragement and the right support, everyone can meet a functional level of numeracy.” This statement shows that by simply accepting that some children will cope well with maths while others will struggle, we are doing nothing for the children. If we, as teachers, encourage and support the children who have insecurities in the area of mathematics then we can help them to strive to be an individual with simple maths skills which will help them as they go forward in life. Even if these children never go onto study complex maths, by simply assisting them to go forward and use essential maths skills such as money handling or telling the time, then we have made a real difference to their life.

The above video describes some of the reasons why people get so anxious about maths. The video mentions that anxiety is more prominent in maths than it is in other subjects. There is no exact answer as to why this is however studies have suggested that the way children are exposed to maths by their parents and teachers has a major effect on how the children view maths. If parents talk about maths as something unfamiliar and challenging then the children will also adopt this view. Teachers with maths anxiety are also more likely to pass it on to the children in their class.

Both the above video and an article from The Guardian “The Fear of All Sums: How teachers can help students with maths anxiety” highlight some of the ways in which teachers can help children feel at ease with maths and encourage and support them to be successful in the subject. It is vital to give children the time and space they need to tackle a maths problem as if they are under pressure to complete something under a given time scale then this adds to the stress and will give the child a negative experience of mathematics. It is also important to go slow, beginning with the basics of a topic then slowly progressing in order to make the increasing difficulty less daunting for the learner. It is vital to make lessons fun, playing maths games is a great way to practice maths skills without the pressure of the need to get the right answer in order to get a good mark, this allows the learner to relax and enjoy their experience. The use of positive language is a great way of reassuring learners that they are doing a great job, using praise in front of their peers or parents is also a great way to boost children’s confidence.

Overall, I now feel that I will be able to approach maths in the classroom in a more confident manner as the teacher. I now know the techniques to put in place and the best possible way to approach the teaching of maths to those children who suffer from maths anxiety in order to give them the best possible chance at success in their maths studies.

References:

Brian, K. (2012) “Maths anxiety: the numbers are mounting”, The Guardian, 30 April, no page given.

Chandran, P. (2015) “The fear of all sums: how teachers can help students with maths anxiety”, The Guardian, 17 November, no page given.

Following our recent input with Eddie on the links between maths, play and stories, I decided that this was an area I would like to research further into as I never quite realised just how much of the mathematical knowledge that our young children first acquire is through play based learning.

Maths and Play

One of the main points I learned through the input is just how many key mathematical concepts children can develop through play, whether it be time, size, shape, colour or number, children are constantly developing their knowledge and skills in these areas through the mode of learning which they are introduced to very early in their life- play.

Allowing children to learn through play based activities is extremely important as this is a fantastic learning environment in which children feel relaxed and comfortable enough to experiment, explore and make vital links within their learning. A play based environment also provides a meaningful context for the children therefore they may be more encouraged to think more creatively about the concepts they are exploring.

Friedrich Froebel viewed that parental involvement is vital for effective learning through play. He also viewed that the environment in which the children were playing in had to be appropriate in order to encourage the child to grow and develop in the best possible manner.
Susan Isaacs also valued the involvement of parents in the early education of their children. Isaacs also believed that learning through fantasy play was beneficial for young children as children can move in and out of reality and express their thoughts and feelings.

But how is maths related to play? I had no idea that such a wide number of mathematical concepts were explored through play yet they seem so obvious after they have been highlighted.

During quality play children are:

making decisions
imagining
reasoning
predicting
planning
experimenting with strategies
recording
(Lewis, cited in Pound, 1999)All of these concepts listed above are key mathematical skills in which children begin to develop even before they start their school life. It is vital that children are provided with a play rich environment in which they can freely explore and develop these skills.

In terms of adult involvement in play, Tucker, 2014 states that if mathematical development is to be fully supported though play then there must be a degree of adult involvement. In order for it to be fully effective then there must be a mixture of child-initiated and adult-supported play.

“While practitioner-led activity can ensure the systematic teaching of skills, child initiated learning, without adult control and dominance, can enable children to become self-regulated learners.” (Tucker,2014)

Maths and Stories

Many stories can also help develop mathematical concepts in young children. There are a wide range of books which can be used to introduce and discuss mathematical language or help develop skills such as counting, number formation, ordering, addition and subtraction.

In my opinion, stories are a great way to introduce maths to children. Stories create a relaxed atmosphere for learning in which children feel a sense of enjoyment and feel at ease and comfortable. By learning maths through story we are also developing literacy skills at the same time.

Below is an example of a story that can be used to teach young children a few different mathematical concepts.

https://www.youtube.com/watch?v=3_Fs0eyM1jw

This story in particular allows opportunity to explore many maths principles with young children. The first concept being when the characters do not know how to count but are trying to find out who has the most marbles, this could then be an opportunity to question the child or children and ask them how they think they could find out who had the most marbles.

The next opportunity for discussion in the story would then be when the characters want to know who caught the most fish. Many questions could be raised here such as “Would the same solution work again?” “Why wouldn’t it work?” then more discussion could be had about the varying sizes of the fish.

Finally, graphing is introduced as the solution to find out who had the most fish.

I thought this story in particular was a fantastic example of how story can be linked to mathematical teaching due to the variety of concepts introduced in such a short story.

Overall, through both this input and my own research I can now say I am fully aware of just how much play and story can come into use when teaching maths and it is something I will definitely value and make good use of in future practice!

References:

How stories develop maths(no date) Available at:http://www.teachingyourchild.org.uk/maths-stories.htm#How_stories_develop_maths_ (Accessed 19th October 2017)

Tucker, K. (2014) Mathematics through play in the early years 3rd edn. London:SAGE publications ltd.

Valentine, E. (2017) “Maths, Play and Stories”[powerpoint presentation] ED21006:Discovering Mathematics (Accessed 19th October 2017)

Reflective Practice

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we-do-not-learn-from The SPR section 3.4.2 emphasises the importance of reflection and the part in which it plays on professional development, I am now more aware of how important reflection will be both in my professional practice and in my teaching career.

Reflecting on semester 1, one of the most important moments of my professional development was the process of working collaboratively across the professions in the Working Together Module.

Although I have worked in groups throughout my time at school, the experience of working collaboratively across three different professions was a new concept to me however I feel as though the whole experience was a key moment in my professional development.

Throughout my collaborative practice I learned more about the three different professions and the skills and attributes each professions bring to work collaboratively, I also learned more about group working and the skills and qualities needed to work effectively in a group towards a common shared goal. This experience was a key moment in my professional development as I now feel as though I am more informed on collaborative working and this will allow me to confidently work with others both when I am on placement and in my future work. I also feel that by working with others in a school setting I will further develop my knowledge and understanding of collaborative working and gain more experience in working with others.

Following todays input on reflective practice, the process of reflection is now something I am much more aware of and conscious about. I now have a brief understanding of theorists such as Dewey and Schon and will now read more into these theorists and their ways of thinking in order to prepare myself to effectively reflect on my practice when I am on my placement.

The process of reflection now has much more of a meaning to me, I know what the characteristics of a good reflection are and how to reflect on a lesson. I feel as though the knowledge I have gained about the process of reflection will aid me in effectively reflecting whilst out on my professional practice, by considering what went well and what could be improved, considering why things may not have gone the way I had intended them to and also linking my reflection to my goals with reference to literature.

Overall, reflection is vital in my own professional development and I will continue to further my understanding of the process by reading to ensure that I can effectively reflect on my own lessons and practice in the future.

Health and Wellbeing

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As part of our most recent health and wellbeing input we were advised to watch two videos about the importance of early years, pre birth-three. One of the videos was by Doctor Suzanne Zeedyk and the other was by John Carnochan OBE.

Both videos focussed on the fact that as humans, we are brought into the world much earlier in our brain development than other species due to the size of our brains. This means that children’s brains are still developing throughout the early stages of life and factors such as relationships that they have with significant people in their life and the quality of environment around them will have an impact on their brain.

A scenario focussed on in the clips is that if a child is brought up in a home wherein domestic violence takes place, the child’s brain will then be focussed on the violent environment and the stress around the, the brain will then see the world around them as a threatening place and be focussed on spotting the next threat, this can then make t difficult for a child to concentrate in a classroom setting therefore have an impact on their learning.

Due to brain development being ongoing in the early years of a child’s life, it is important that children have significant others in their life and a safe, consistent environment to ensure that their brain development assists their learning and does not hinder it. For some children the only place that they will have this safe, consistent and supportive environment is within nursery or school.

By watching the videos I am now more aware of the importance we have, as primary practitioners to ensure that children have this safe and consistent environment available to them as many will not have it at home. I feel as though having this knowledge will impact on my professional practice as I will ensure that my classroom is a place in which my pupils feel safe and supported and I will aim to be a significant other in the life’s of my pupils to ensure I can aid their brain development and watch them grow as learners and also as individuals.

Teaching Across the Curriculum- Dance

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When I noticed that a dance workshop would take place in the second week of the semester I instantly looked forward to participating. I have danced for around 13 years now and it has always been something that I see as not only a hobby but also as one of my main strengths. I taught a dance class for younger children during my final year at primary school and have been part of a dance group for as long as I can remember, now at which I assist in taking classes for younger dancers and have done for the past 3 years.

After reading parts of “Get Scotland Dancing: A Literature Review (2014)” I now have a clearer understanding of the various purposes dance can have- whether it be to improve physical health, to portray emotion or to reflect on human behaviour in society- dance is something that has an involvement in our lives at some point or another. Also by reading the article I have become more aware in the part dance plays in our culture here in Scotland which roots from our folk history. However, research has shown that at present, a low percentage of Scottish people participate in dance regularly. Dance can be a great form of improving physical wellbeing therefore if we teach dance to our pupils with enthusiasm and passion it will then allow them to enjoy what they are participating in whilst forming a healthy lifestyle and learning new skills all at the same time.

There are many individual factors which suggest that dance may only be aimed at a certain group of people, these factors include age, gender and motivations. It is part of our job, as teachers, to ensure that every child in our class feels as though they can fully participate and express themselves with confidence in the things they do, therefore by teaching dance from a young age, this will allow the children to both grow in confidence and develop their skills.

I feel as though my own experiences and my dance background will help me in terms of teaching the dance curriculum. I still feel as though I will face some challenges that will perhaps include getting the children to have the confidence to participate or finding the enthusiasm to fully enjoy what they are being taught. My goal, as a teacher is to ensure that all of my pupils feel confident and comfortable enough to participate and enjoy the dance curriculum, I aim for a relaxed environment in which the children can enjoy their learning and gain new skills.

Although I feel as though dance will be one of the areas I am most confident in to teach, I have still set myself a goal which is to familiarise myself with the curriculum around dance and to broaden my own creativity to come up with various different ideas to use whilst teaching dance to a class.

I feel as though teaching the dance curriculum will come with both ups and downs but it is something that I am greatly looking forward to doing in the future.