in our recent input on mathematics in business, Richard set us an apprentice style   business simulation to demonstrate the mathematics in demand planning. As someone who watches the apprentice religiously every week, I was extremely excited at the opportunity to pretend I was one of the candidates trying to impress Lord Sugar (well in this case Richard) and on reflection I maybe took it a little too serious. After lots of deliberation Me and Gillian came up with Team Sparkle (because who doesn’t love sparkles?).

 

The Rules:

• Each team started with £5000
• The year was split into 4 quarters and we could only order 5 different
• products per sales period (each quarter).
• Any stock left from one sales period could be taken over to the next quarter (except items such as milk and bread which go off very quickly.)

 

April-May-June

When deciding initially what to order for the first quarter we had to consider a few different things. First, we considered what would be popular at this time of year, so straight away obviously ruling out any Christmas themed products- because who really buys a selection box in June? We then considered which produced appeared to make a higher profit, we were initially drawn to the champagne which are sold for double the price we would pay, as well as the beans sold for 8x more than we would pay!!! Along with these we decided to chose products which we knew sell consistently and regularly.

 

As you can see from the image above, all the products we chose to purchased sold reasonable well and managed to make us a reasonable profit, doubling our original £5000. To work out the money we made we had to do a series of mathematical calculations. First we had to work out how many of the units we ordered that were actually sold, by multiplying the quantity ordered by the percentage sold. Then to work out the sales value generated we had to then multiply the units sold by the selling cost. Finally, we had to work out the amount of units of remaining stock which could be carried over.

By calculating the total of our sales values and adding on the money we had left in the bank, at the end of the 1^st quarter we had £10,040.

July- August-September

Again, we considered which items would sell best during these summer months again whilst making us more the most profit, we decided to order more champagne, bread and milk but this time adding on beer and soft drinks.

Again all of our products sold well with 100% of beers selling, and 90% of both the champagne and soft drink flying off the shelf. Again, by doing the calculations we were able to work out we now had £18,380 and a small amount of stock to carry over, almost doubling our money since the last quarter.

 

October- November- December

When we got to this quarter, we obviously had to consider that Christmas would be in this sales period meaning we could finally spend some of our money on selection boxes!! We decided to spend a large amount of money on more champagne as everyone enjoys a glass or two at Christmas, and for those who aren’t champagne fans we purchased 3,000 beers. We only purchased 500 of the frozen turkeys because although we knew these would sell, they were not going to make too much profit so we decided not to spend too much on these (potentially a risky move).

This round was very successful, with 100% of the selection boxes, champagne, turkeys and luxury hampers all selling. We were left with very little extra stock and we calculated our takings went up from 18,000 to 35,950. On reflection we probably could have purchased more high profit products such as the hampers or even more beans as 90% of them sold with the selling price still at 8x the purchase price.

 

January- February- March

In the last 3 months, we clocked on to the fact beans had sold consistently well through every sales period and with a consy. In this quarter the selling price for beans was 10x the purchase price!!! So we knew the key to success here was buying a lot of beans. We also decided to purchase more of the lower priced items such as milk and bread as Christmas always leaves the bank account looking bleak, so January may be a month of only beans on toast for breakfast lunch and dinner.

This month saw our earning increase majorly, with everything we had purchased selling reasonably well. 100% of beans sold meaning from the £5,000 we spent on them this brought in £50,000. In total we managed to take our starting figure from £5,000 up to £98,000, which to be honest I was very impressed with. I’m sure Alan Sugar would disagree.

Beans, beans, beans.

After completing the task and discussing our tactics with rest of the groups, we came to the conclusion that way to earn the most money throughout the game would literally be to only buy huge amounts of beans. Due to its consistently high percentage sales in each quarter and the massive increase from purchase price to selling price, if we had only spent our money on buying beans alone our earnings could have been way into the hundreds of thousands. Despite the months which it didn’t sell as well, any leftover stock would carry over to the final quarter due to large shelf life and would ultimately leave you with massive profits. If I was to do this over again, I would definitely put all my focus on beans. This maybe would have made profits that Lord Sugar would be more impressed with.

Throughout this business simulation we used various different mathematical strategies, most of which were basic concepts such as addition, subtraction and multiplication. Although this activity used basic fundamental mathematics, it also required a deeper level of understanding to be able to understand the processes and why the mathematics was being used. I think this would be a great activity to bring into the classroom. As it is based on basic maths processes, it could be easily made simpler or even harder by changing the amount of money that you begin with or the number of products you are allowed to purchase in each quarter. This would be a great way to show pupils a real-life application of mathematics, and encouraging them to develop problem solving skills and think critically. I thoroughly enjoyed the activity and I feel like it would be a fun and engaging way to explore maths with a class, because who doesn’t love the idea of making lots of money.

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].

 

 

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)