Monthly Archives: November 2017

Millennium Mathematics Project

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Following on from my previous blog post which was about maths in sport, during my research and reflection for this blog post i came across the Millennium Maths Project. The Millennium Maths Project is an education initiative designed for children aged between 3 and 19, created by that mathematics and education departments of The University of Cambridge. The main focus of this project is to increase mathematical confidence, enjoyment and understanding by using  imaginative and creative approaches to maths. Between 2015-2016 the website received 43 million page views from users worldwide, as well as 15,000 pupils and 4,000 teachers getting involved with face to face event and activities.

Maths and Sport

Originally to celebrate London Olympics 2012 the Millennium Maths Project created free online resources and activities for their maths and sport project. These resources include rich mathematical activities, articles and video challenges which are aimed at students from ages 5-18, and are arranged based on the 5 key stages within the English curriculum. These activities are designed to develop problem solving and mathematical reasoning in a creative and fun way. There is also a collection of activities based on maths in football which are in collaboration with arsenal football club.

Here are a few examples of activities aimed at children in stage 1(5-7 years) and 2(7-11 years).

After looking at how maths is applied within sport, and how this can then be used to teach or develop maths within the classroom, these activities look very useful for doing so. Also after finding out more about this project and what it aims to achieve, i think this is a great, useful and engaging resource that i will certainly consider using in future placements and once i have my own class.

The Millennium Maths Project also has various other divisions such as the maths and sport project, these include:

  • NRICH – this provides free mathematics enrichment resources for age 3-19 as well as teachers, which are designed to build confidence,  mathematical reasoning and initiative through problem solving.
  • Plus– this is a free magazine online, aimed at readers age 16+. This covers a variety of topics and theories such as do parallel universes exist, as well as uncovering the hidden maths behind headline news stories and mathematical research news.
  • Wild Maths– this aims to encourage mathematical creativity, curiosity, exploration, discussion and discovery. It involves identifying patters, making connections and looking at things in new ways based on what you already know. This provides rich and open-ended resources – mathematical activities, games and investigations aimed at 7-16 year olds.

I feel like this project ties in to a lot of the things we have discussed and looked at throughout the discovering mathematics module, such as creative maths and sports in maths. Both of which i have discussed in previous blog posts ‘can maths be creative?’ and ‘maths and sport’ (Dillon, 2017). I am very interested in the aims of this project and feel very strongly that using creative approaches to maths can help to develop understanding and confidence, so i feel like this resource could be extremely helpful to use within classrooms or to help develop these skills as well as enjoyment while teaching and reinforcing maths.

Resources 

Dillon, R (2017) ‘Can maths be creative?’, Rebecca’s Teaching Blog, 21 November. Available at: https://blogs.glowscotland.org.uk/glowblogs/rdeportfolio/2017/11/21/can-maths-be-creative/

Dillon, R (2017) ‘Maths and Sport’ Rebecca’s teaching blog, 27 November. Available at: https://blogs.glowscotland.org.uk/glowblogs/rdeportfolio/2017/11/27/maths-and-sport/

University of Cambridge (2017) Millennium Mathematics Project. Available at:  https://maths.org/ (Accessed: November 2017)

Can Animals Count??

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In a recent input with Richard we were faced with the question “do you think animals can count?”, after a few moments of silence and deep thought this sparked a very interesting discussion on whether or not we thought animals have any form of numerical understanding. Some of us making suggestions like “my dog knows to wait for a count of 3 before he gets a treat” or “if your cat knows exactly when you will get home every night, is that an understanding of time?”. All of these questions left me unsure of my opinion on the question, but as am very big animal lover myself I would love the idea of my cat being able to do times tables or being a secret maths genius, but I was sceptical. The issue came up in discussion that animals probably don’t have the same mathematical understanding that humans do but perhaps just are just trained by owners to appear to understand simple mathematics. For example a dog can just be trained to know that after the sound “one, two, three” this is when they are given a treat rather than being aware this is counting. We then went on to look at a few studies of animals who appeared to have the ability to count.

Clever Hans

The First animal we looked at and discussed was a horse names ‘Clever Hans’. In the early 1900s Clever Hans was touring with his owner Wilhelm Van Osten who was claiming the horse had the ability to count, he claimed he was able to teach it basics sums including addition, division even square roots. Hans would be able to give the answer to any question by signalling the correct number with taps of the hoof , in fact 86% of the time Van Osten asked Hans a question he was able to give the correct number of taps. It really does sound quite incredible, doesn’t it. Well after many scientists became sceptical of the horses knowledge, they began to test the legitimacy of this in various ways. One way they used to test if the horses knowledge was real or whether it was to do with something the trainer was signalling, was they made it so that the horse was unable to see Van Osten when he was asking the question. This test along with others in fact found that the reason the horse was able to tap its hoof the correct amount of times was that its owner with giving it very subtle ques of when to start and stop tapping its hoof in order to get the correct answer. So rather than being a mathematical genius Hans was simply following commands given by his owner, much like a dog being told to “sit”.

Ayumu the Chimpanzee

After Clever Hans’ unsuccessful attempt at convincing us that animals can understand numbers, we then looked at some other examples including; ants, lions, chicks and bees. Yet all of these were still unable to provide me with an answer to the lingering question “can animals count?”, but potentially the most convincing of all of these was the example of Ayumu the chimpanzee.

This study showed that when shown numbers from 1-9, the chimps were able to put them in order(to be rewarded with a peanut if they were correct). Although this initially seems to be very impressive, I then began to think surely if the chimp was just able to remember the correct order of the visual symbols they click when they receive a peanut, this doesn’t really have anything to do with the numbers or values the hold. It then goes on to show that when the numbers are flashed and then covered up quickly, the chimps can still remember and correctly order the numbers from 1-9 (this particular chimp Ayumu only got this wrong once!!). Again I was very impressed by this, but I still don’t see how this proves mathematical understanding rather than just an extremely good memory. The last test they did on Ayumu and the other chimps is what had me almost convinced, in the final test not all of the 9 numerals were shown and were covered up the same as the previous test, again the chimps were able to put the numbers in the right order despite there being some missing. This is what has me more convinced that these animals may be able to understand numbers or the idea of counting, when their is some missing it proves that the chimps are aware that some numbers always come before others .. so does this count as being able to count?

Even after looking at this within the class input and then also further in my own time, as much as I wanted to believe it I still am not quite sure if I’m quite convinced that animals can count or understand maths the way in which us humans do. I feel “can animals count?” would be a great question to ask a class of children, allowing them to use their mathematical understanding to discuss and share their own opinions and come to their own conclusions about if they think animals can understand maths, whilst still being a fun and light hearted way to approach mathematics.

 

Can maths be creative?

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To me the obvious answer to this question was no. When I look back to my time learning maths in school my memories mainly consist of textbooks pages, worksheets, and more textbook pages. For most of us this was, and still is our experience of maths within the classroom.

According to the ‘Trends in International Mathematics and Science Study’ (IEA, 2008), 72% of Scotland’s P5 pupils were taught using a textbook as the primary resource. Also, the most common type of maths activity given in classrooms throughout Scotland is based on pupils “working quietly own your own” and from a textbook. 50% of the P5 pupils surveyed said that during most lessons they are told to work silently and individually, and 55% of children in P3 agreed (Scottish government, 2009). These figures very clearly show there is a lack of creativity in the maths lessons being taught in our classrooms.

In my experience of both being the learner and during my time on placement last year, when a lesson is not engaging, or you are not interested, it makes it very difficult to concentrate to what is being taught. If a teacher is simply standing at the front of the class explaining a new concept, the moment you lose concentration or engagement in what is being said, you then immediately shut off completely. By shutting off completely this is very likely to result in gaps in knowledge and understanding, this then leads to a cycle of losing increasingly more engagement and becoming gradually more and more lost or confused. Over time this lack of engagement and therefore lack of understanding can lead to anxieties and hatred towards the subject. I feel this can is one of the main causes of maths anxieties, which I discussed in my previous blog post.

Lampart(2009) identifies the main believes towards mathematics. Some of these include: the idea that maths problems only have one right answer, that there is only one way to solve a problem, and that most students do not expect to understand the mathematics but simply need memorise it and apply it to each question. The idea that an answer to a maths problem is either right or wrong and that you can only solve it in one way, I feel is one of the main reasons why the subject can appear to lack any creativity or room for imagination.

So how can we make maths creative and fun?

Maths and art

In one of our recent workshops with Eddie we were looking at how maths can be explored creatively, specifically through art. We discussed in this session various ways throughout history that artists have used mathematical concepts such as symmetry, tessellation and proportion to create works of art. For example, the importance of renaissance painters working out the proportions of the persons facial features in relation to face and body size by calculating mathematical ratios, the most famous painting of all time the Mona Lisa was created using these mathematical techniques.

During this input we also focused on the Islamic art technique of tessellations, and how these can be used to creatively teach geometry within a classroom. A Tessellation is a pattern of repeated shapes that fit perfectly together with no gaps spaces or overlaps. Regular tessellations are made up of only one regular shape repeated, whereas semi-regular tessellations are made up of two or more regular shapes to create a repeating pattern. Regular shapes that tessellate include: squares, hexagons and equilateral triangles. Regular shapes are those which have all their sides the same length and all the internal angles the same size, the reason these tesselate is that when all vertices meet they create a 360 degree angle.

                  

In this input we had the chance to see how this could be done within a classroom and made our own tessellations. We were given sheets with various shapes on and were able to choose which shapes we would like our piece to consist of, we then cut these out and stuck them onto a coloured piece of card making sure there was no gaps, spaces or overlaps between the shapes and the pattern was able to be continuously repeated. We were then able to pain our shapes and make them look as colourful and creative as we wanted. I really enjoyed this activity and found it strangely relaxing, in no way did it feel like we were doing a maths task. I feel like this would be a great way in a classroom to introduce or develop geometry, as for those who dread the idea of a maths lesson or opening up a textbook this can make learning maths much more enjoyable and less terrifying. It also provides children with the opportunity to see how maths surrounds us, rather than the idea that you will never use it again once you leave school.

This workshop really opened my eyes to how maths can be made creative, and the impact this can have on the engagement of the learners, because I actually found myself enjoying a maths activity which I honesty i don’t think I have said many times in my life. Looking forward to my further development towards becoming a teacher, I think this will effect the way i look at and aim to teach mathematics in the coming years. I must continue to look for creative applications and ways to incorporate maths into the classroom that will engage and excite learners, and prove that maths really isn’t always textbooks and worksheets, it surrounds us in everything we do.

 

References

IEA (2008) Trends in Mathematics and Science Survey 2007. Lynch School of Education, Boston College: International Association for the Evaluation of Educational Achievement.

Lampert, M. (1990) ‘When the problem is not the problem and the solution is not the answer: Mathematical knowing and teaching’, American Research Journal, 27(1), pp.29-63

Scottish Government (2009) 2008 Scottish Survey of Achievement: Mathematics and Core Skills. Available online at: http://www.scotland.gov.uk/Publications/2009/04/02133043/0 [Accessed October 2017].

 

 

Maths Anxiety

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I’m sure most of us can relate to the overwhelming feeling of distress and confusion when being asked a maths question and knowing you are going to get the answer wrong, or when staring at a set of questions in a textbook and being completely clueless of where to start, sending your brain into panic mode. What exactly is this feeling? Although many of us experience this throughout our time in school, most are unaware that Maths anxiety is a recognised condition which can be overcome and prevented.

What is Maths Anxiety?

Maths anxiety can be defined as “as a feeling of tension, apprehension, or fear that interferes with math performance.” (Ashcraft, 2002) or “a general fear of contact with mathematics, including classes, homework and tests” (Hembree, 1990).

In 2012 it was found that a quarter of the UK’s population were effected by math anxiety, and 2 million children in England alone (Brain, 2012). Not only does maths anxiety effect huge numbers of children within our classrooms, many of today’s school teachers also suffer from some degree of anxiety towards mathematics.

There are various Psychical and Physiological symptoms associated with Maths Anxiety, some of which include:

  • Headaches
  • Increased heart rate
  • Shortness of breath
  • Confusion
  • Mind blanks
  • Inability to concentrate

What causes maths anxiety?

Maths anxiety can be caused by various different factors, and each individual who suffers with this will have their own reasons why. For many people anxieties are due to environmental factors such as school, home life parents and teachers. For some, their anxiety stems from parents attitudes or fears towards maths, if a child is brought up in a setting in which a parent has a negative attitude or feeling towards maths, it I extremely likely this will be passed on, and the child will then go into maths with the same negative attitude and concern. This is the same as if a class teacher feels negatively or has insecurities with maths, children are able to sense when a teacher is not confident with what they are teaching, and if basic principles are not taught correctly this can lead to children then lacking fundamental knowledge and confidence, leading to anxieties. Also in terms of within the classroom and the class teacher, many children’s anxiety comes from the idea of being wrong and the embarrassment of doing badly, if a child is asked a question in front of a full class and gets its wrong, this embarrassment is likely to lead to a massive loss of confidence. Children within a classroom should be made to feel comfortable in that they can always attempt a question and if they are not correct the first time this is not something they should feel ashamed off, the way to success is by making mistakes and learning from these.

 My experience with maths anxiety

For me specifically, maths anxiety was never something I suffered with or experienced throughout my time in primary school, it was a subject area which I thoroughly enjoyed and felt like I was confident in, up until secondary school maths was something I found enjoyable. It wasn’t till around my third year of high school that maths began to become an issue for me personally.  As the difficulty of what I was learning increased to much more challenging concepts and areas of maths, my confidence in my own ability severely went downhill and all enjoyment I once felt for maths was lost, walking into the maths classroom began to be the most daunting part of the day. Despite this growing stress, I chose to continue maths to Higher level, this was when maths anxiety became a massive problem for myself. One thing I remember very vividly to have affected me in terms of my confidence in maths was is being told “you will need a miracle to be able to get a pass in this subject” by my teacher at the time. From that point on I was convinced I was completely unable and therefore completely shut off and lost all concentration in the subject to avoid the distress it was bringing me. Much to my surprise I passed (luckily being over the pass mark by only 1 mark), although I was shocked and proud to have proven my teacher wrong, this result was a massive disappointment in comparison to the A I had gained at national 5 level. Due to this, the moment I stopped studying maths I was convinced I no longer needed to think about it and tried to shut it out of my life as much as possible, but due to this I now feel like I have lost most of the knowledge and ability I once had, now even relying on a calculator for simple maths sums.

Overcoming maths anxieties

According to Lee (2017), there are 6 ways as a parent or teacher that you can help a child to overcome their maths anxieties:

  1. Playing maths games – playing maths games or games centred around numbers is a great way to get children much more involved and interested in learning maths, by putting it into a fun context which they will enjoy rather than dread.
  2. Be aware of your own attitude towards maths – children are watching and learning from you, if you are expressing or giving off negative feelings towards maths rather than talking about the fun and positive applications and importance of maths, children will be aware of this and will therefore be at a disadvantage.
  3. Practising with the child – The best way to improve confidence and skill when it comes to basic maths principles is by ongoing practise. By bringing maths practise in to daily life or into other areas of the school curriculum this can significantly improve the child’s performance without explicitly doing maths.
  4. Get rid of the idea “some people are not good at maths” – This is a very important part of helping a child overcome maths anxiety, the moment they feel like they “cant do” maths is when they completely give up. We must eliminate the idea that some people simply are bad at maths.
  5. Get help early– As a teacher or parent if you see a child struggling, it is best to provide them with extra help as soon as possible to try and prevent any math anxieties developing. A good example of this is by getting an out of school tutor or even an older pupil to provide extra help for the child at certain times during the school day.
  6. Help the child to shake off mistakes – One of the best things to do is assure the child mistakes are something that will naturally happen and that are positive learning opportunities, not embarrassments.

I feel that in recent years maths anxiety has began to affect me more than it ever has especially the closer I get in my journey to becoming a teacher, and I understand this is something I must constantly be trying to overcome in order to confidently and effectively teach maths in the future, I feel my engagement with this module so far has helped me to begin to overcome this and develop an understanding of fundamental mathematics. I must now continue to build my knowledge and understanding to a point where I can teach mathematics confidently to prevent any maths anxieties i once felt to be passed on to pupils, and to also effectively help pupils overcome any anxiety they feel towards mathematics and allow them to reach their full potential.

 

References

Ashcraft, M. (2002) Math Anxiety: Personal, Educational, and Cognitive Consequences.  Available at: http://journals.sagepub.com/doi/pdf/10.1111/1467-8721.00196 (Accessed: October 2017)

Brian, K. (2012) ‘Maths Anxiety: the numbers are mounting’, The Guardian, 30 April. Available at:  https://www.theguardian.com/education/2012/apr/30/maths-anxiety-school-support (Accessed; October 2017)

Hembree, R. (1990) ‘The nature, effects and relief of mathematics anxiety’, Journal for Research in Mathematics Education, 21, pp.33-46.

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: October 2017)