Category Archives: Discovering Maths

Reflecting on Discovering Mathematics

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I can’t quite believe that first semester is drawing to an end and that the Discovering Mathematics module is now over. I can truly say that I have thoroughly enjoyed my time and have learned a great amount about the world of maths surrounds me. I have also learned the extreme importance of having a profound understanding of fundamental maths, which I will ensure I have before I complete university. So that when I have my own class, I can give the children in my class the best opportunity to reach their full potential.

 

From learning about how Fibonacci’s golden sequence and ratio occurs in many aspects of nature, music, art and I am sure, many other things… To learning about the history and mathematical concepts behind logistics, sport, statistics and even gambling! I will be sure to use many of the different activities we took part in through out the module in my own lessons. All the workshops were engaging and encouraged us to research and discover even more!

 

At the beginning of the module I was very worried about my maths anxiety holding me back with my teaching, however, this module has not only given me the confidence in my own abilities but it has also made me realise that teaching maths isn’t all about the complicated maths equations that scare me! I look forward to continuing my maths journey throughout university and beyond.. I will forever be reminded about this module with all the maths I see in my everyday life!

 

I can tell I won’t be very popular when I keep asking people… “did you know there’s actually maths behind that?!”

 

But what can I do when mathematics really is EVERYWHERE!!

What do you mean there is maths in music?

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Music has always been a special part of my life. Ever since I was born I have grown up surrounded in the wonderful world of music. My grandad was a trombone player, conductor and music teacher, my uncle is currently a professional trombone player for the RTE orchestra in Dublin and of course the biggest influences in my life; my mum a horn player and my dad a principle cornet player in a championship brass band. My whole childhood I was taken along to band practises, concerts and contests… I was always blown away by the talent of the people sat in front of me but sadly I never took an interest in playing an instrument myself, one of my biggest regrets! I always wonder “why?” but after seeing the time and commitment my parents had to put in, it must have put me off which is a shame because the reason they were so committed and hard-working, was because of the love and passion they had for playing music. “ Oh, well.. Jacqueline is the singer and dancer of the family” my mum always told her friends from band when they asked why I wasn’t playing an instrument yet. I really did love singing, oh and I can’t forget my attempt at playing (more like memorising) the keyboard for my higher music exam, they managed to bag me an A (I hope it was more the singing!), so I couldn’t have been too bad! I can’t forget the help my mum gave me with the theory either, she wouldn’t be happy if I never mentioned that!

 

So, even after having so many encounters with music, when I was told we had a lecture on maths and music, I questioned it. How much maths is there really in music? Well, a quote we were given in the lecture was a revelation! Connecting music and maths finally made sense to me:

 

“Rhythm depends on arithmetic, harmony draws from basic numerical relationships, and the development of musical themes reflects the world of symmetry and geometry.  As Stravinsky once said: “The musician should find in mathematics a study as useful to him as the learning of another language is to a poet.  Mathematics swims seductively just below the surface.”  (Marcus du Sautoy, 2011)

 

There are many connections:

 

  • Note values/rhythms –
  • Beats in a bar- being able to divide bars in to numerous fractions of beats in a bar
  • Tuning/Pitch
  • Chords
  • Counting songs
  • Fingering on music
  • Time signature
  • Figured bass
  • Scales
  • Musical Intervals
  • Fibonacci sequence

 

Many of these actually have quite an obvious link with maths when you really think about it.

 

 

Music and ‘golden sequence’:

 

Another, perhaps less known, but important, link between maths and music is the ‘Fibonacci sequence’. The Fibonacci sequence is a special series of numbers formed by using the sum of the previous two numbers to get the next number within the sequence. The sequence looks like this: 0,1,1,2,3,5,8,13,21 and so on…

 

If we look at a piano keyboard we can see that the chromatic scale consists of 13 notes. The diatonic scale is composed of 8 notes and the pentatonic scale, 5 notes. In addition to this, the basic chord structures used in music consist of a triad of notes. These are the first, third and fifth notes in the common ‘diatonic’ scale.

 

I thoroughly enjoyed the mathematics and music workshop… firstly because it reminded me of my love for music but, more importantly, it taught me that something that I have been immersed in my whole life has, in fact, got a lot to do with music which I had never really thought about until that point! It made me consider all the other things in my life that probably has some sort of maths behind it that I haven’t discovered… yet! I am looking forward to teaching music in the future with enjoyable activities where the children can really see the impact maths has on music.

 

Mathematics and creativity?

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Maths AND creativity??

I know! two words you would never normally put together. Maths is usually a subject people associate with lessons that involve worksheet upon worksheet where your answer can either be right or wrong. Where is the fun in that? No wonder so many children hate maths when they are stuck doing the same boring lessons. But maths CAN be fun and creative! This was proven in the two workshops we had in the discovering mathematics module that focused on the creative side of maths.

In Eddie’s workshop, we looked at teaching creative maths in geometry. For example, teaching about shapes by using tessellation. A tessellation (or tiling) is a repeating pattern of shapes that fit perfectly together without any overlaps or gaps. There are different types of tessellations: regular, semi-regular, and then other tessellations of circular, curved, irregular shapes that mathematicians cannot agree on how to name. Tessellations of CONGRUENT shapes, are called monohedral tessellations. The word monohedral basically means ‘one’ – mono and ‘shape’ – hedral.  Regular tessellations are made up of only one regular shape repeated, whilst semi-regular tessellations are made up of two or more regular shapes tiled to create a repeating pattern. The regular shapes that tessellate are: squares, hexagons and equilateral triangles. ALL triangles and quadrilaterals also tile but they are not ‘regular’ shapes and often have to be rotated to make them fit together.

Tessellations are a great for connecting maths and art together. Many historic paintings were made using tessellations and by showing some examples of these to a class, it would be a great way to engage the children in the lesson immediately. They probably wouldn’t even think it was a maths lesson! I thoroughly enjoyed this workshop and creating my own tessellation with Caitlin. Creating patterns with the different shapes and colours whilst also making sure everything fitted together perfectly was a fun challenge and is a lesson I will use in the future. It allows the children to fully experiment with 2D shapes instead of just looking at them in a textbook.

 

Getting into the child-like spirit with paw patrol plates and colourful paints!

The beginning of our masterpiece! figuring out how we wanted our tessellation to fit together and what pattern we wanted it to create.

The final product! unfinished and not very neat.. but I love the way it would have been if we had more time to finish it.

Type 1 diabetes, maths and me 

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Maths is my life. And no, this isn’t me saying that I love maths, sitting myself down to do Pythagoras equations or algebra every day. What I really mean by this is: Type 1 diabetes.

Rewind back exactly three years. After weeks of a vigorous cycle of drinking>peeing> constant sleeping and in the end, fainting, I finally went to see my GP to get blood taken to find out what was wrong with me (this might be a good time to add how much I despise blood and needles!). Also, I had been in complete denial and actually quite proud that I was drinking more fluids. Three days later, I received a phone call telling me to go immediately back to the GP to find out my results. At this point, I was still unsure of what it could even be. It’s not like it would be anything too bad, right? Wrong! The doctor did a few extra tests and when the result came back she sat in silence for ages (well, what seemed like ages) and then told my mum to take me straight to A&E.

Little did I know when I walked myself into hospital on Thursday 23rd of October 2014 that I would never walk out ‘recovered’. My first night could be considered to be the worst night of my life. I cried so much I was literally unrecognisable due to how swollen my face was. I had two drips inserted in the inner joint of both my elbows which meant that I could barely move, let alone sleep. On top of this, every hour I had someone prick my finger to find out my blood sugar (I was surprised I had fingers left to prick), I was also hooked up to a heart monitor and blood pressure monitor that squeezed my arm constantly making it feel like it would fall off! Oh, and don’t forget to add into the equation all my previous symptoms, a few drunk people in A&E and a terrified 17-year-old in hospital for the first time and… voila! As I said, the worst night of my life.

After my very long night, the diabetes consultant came to pay me a visit and gave me the ‘present’ of officially diagnosing me with Type1 diabetes. Now, remember that fear I had of blood and needles? Well, I had to conquer that fear ASAP. The doctor informed me that I would have to check my blood sugar at least 7 times a day and inject myself insulin on average 4 times a day. So, what was the first thing I did? That’s right, I cried even more. I even made the doctor cry for the first time when diagnosing someone… quite impressed with that one, to be honest!

I spent the rest of the weekend trying to get my head around my diagnosis and being taught the ins and outs of controlling my blood sugar. I was amazed watching the nurses and doctors calculating how much insulin was needed in order to bring my blood sugar back down to a normal range. I was discharged on the Monday and, although the original symptoms were no longer there, I was still walking out of that hospital with a condition I would never live without. Something I still struggle to come to terms with.

You are possibly wondering what I was thinking when I was diagnosed. Firstly, what is diabetes? Let’s get something straight. I didn’t cause it by eating too many sweets! There are many forms of diabetes and I am sure you have heard of at least one. Type 1 and Type 2 are most common. Here are the basics: Type 1 is an auto-immune disease, where the body’s own immune system destroys the insulin producing beta cells in the pancreas and is normally diagnosed in children or adolescents. People with Type 1 have to inject themselves with insulin to compensate for the ‘death’ of their pancreas. Type 2 can be caused by many things including lifestyle and is characterised by the body losing the ability to respond to insulin, often medication is enough to help. Both types of diabetes can cause serious complications if not treated properly.

Secondly, what exactly is insulin? Insulin is a hormone produced by the pancreas which converts carbohydrates into energy, when the pancreas stops making insulin it causes the blood sugar to rise dramatically. As the body is no longer getting energy from carbs, it starts to convert fat into energy. This is extremely dangerous as it develops ketones, which is a breakdown of fatty acids in the blood. Most Type 1’s are diagnosed when they are in ketoacidosis, myself included. Ketoacidosis can be fatal and can end with the person in a coma. I am so lucky to have been diagnosed just before it got that far.

 

So, where is the maths?

 

As I mentioned earlier, my life with diabetes is surrounded in numbers, ratios and equations. Let’s start with numbers. As a ‘T1D’, I have to inject insulin in order to keep my blood sugar between the ideal range of 4-7mmol… but it’s not as easy as it sounds. I must take insulin whenever I have a meal with carbs (normally 3 times a day) but depending on how many carbs I have in each meal, I have to adjust the number of units of insulin I give myself.

So, many foods (and drinks) have different amounts of carbohydrates and it also depends on how much of that food you are eating! For my injection’s I have a ratio which is 1 unit of insulin to every 10 carbs I eat (1:10). Basically, if I had a meal with 50 grams of carbs I would inject 5 units. Having to measure the amount of carbs is the tricky part as it means using the nutritional information which is normally given in carbohydrates per 100 grams of food or sometimes per serving. This means I often have to do an equation to work out how many carbs I am going to eat by adding up the different types of carbs on my plate e.g. rice, potatoes and vegetables. On top of this, some foods with carbohydrates can easily put my blood sugar into the 20’s, which means if I calculate my food wrong I could end up much too high and having to do another injection to bring my blood sugar back down. This means a correction ratio is given, for example 1 unit of insulin drops me 2 mmol (1:2). Something that makes taking insulin even more complicated is If I go below 4mmol I am in danger of having a hypo which means I do not have enough glucose in my body to fully function. This can make me feel shaky, confused and sweaty. When I have a hypo, I need to take some fast-acting carbs (something sugary) to bring my blood sugar back up quickly as if it goes too low it can cause a seizure. Keeping blood sugar between 4-7mmol is a complete balancing act when so many things other than carbs can also contribute to it rising and falling including exercise, hormones and stress. This makes Type 1 diabetes a total roller coaster of highs, lows, carbs and of course, maths.

The Discovering Mathematics module has completely opened my eyes to the fact maths is all around me and reminded me that I use it every day of my life! I am so thankful to have a profound knowledge of fundamental maths as without it, I would not be able to physically keep myself alive.

Example of a slightly bumpy roller coaster day! Mostly kept within the range which is what is important.

To date, in the three years of living with T1D, I have on average, given myself 4,380 injections and pricked my fingers 6,570 times to find out my blood sugar. Type 1 diabetes is a condition that affects me physically and mentally. In fact, only recently have I felt more in control of my diabetes and it is all because of my new blood sugar monitor. A new technology that allows me to scan a sensor on my arm to find out my blood sugar instead of pricking my poor fingers and also traces my BS continuously for me to see (let’s not get started on the maths that must be involved in that!). I am so lucky to have the love and support I receive from my friends and family who make sure I never feel alone in my life journey.

Example of ideal blood sugars at certain times of day, the ’58’ is different way of measuring BS and is the healthiest average over three months.

 

additional information:

https://www.diabetes.org.uk/In_Your_Area/Scotland

Maths anxiety in children

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Maths anxiety

Heart beats faster and faster. Sweaty palms. Puzzled and confused. Everyone has some type of fear or anxiety. Imagine how you would feel when being faced with a maths question that leaves you in this state, the cause? Maths anxiety.

What is maths anxiety?

Maths anxiety is defined by Mark H. Ashcraft (2002) as ‘a feeling of tension and anxiety that interferes with the manipulation of numbers and the solving of mathematical problems in ordinary life and academic situations’. This shows that people not only suffer from anxiety when faced with a maths question, but due to the maths affecting aspects of our everyday lives, it can affect some people constantly. Now, of course everyone can have a different level of anxiety and it doesn’t always stop some people from doing well in maths. It is also possible to conquer maths anxiety and I will mention some of the ways teachers and parent can help children who suffer from it.

Does maths anxiety affect performance?

Well to this I ask: What came first, the chicken or the egg?

Random question, I know! But this theory can be applied to maths anxiety and performance in maths. And of course, there isn’t a clear-cut answer for this either. What came first? Ma (1999) provides evidence that people who suffer from maths anxiety are more likely to perform more poorly during assessments than those who do not suffer from it. Where it gets confusing is that we don’t know which caused which. Anxious thoughts could be what causes poorer performance in maths or it could be that struggling with maths causes anxious thoughts about mathematics. I personally feel it is my difficulty with maths that has stemmed my anxiety and this can be traced back to primary as there are some fundamental area of maths that I never got to grips with which meant anything that was built on top of these area as I got older I was anxious about and had no confidence. However, others may experience it the other way around for example if they go to school with a fear of maths from listening to people at home being negative about it, this may affect the from the start.

 

How will I defeat maths anxiety in my future classes?

 

Involvement: Ensuring parents are actively involved in helping their child with maths is proven to improve children’s success with maths. If a child sees their parent has a good relationship with maths, this will help them to have a better perception of it.

 

Positivity: As a teacher, I will ensure I use positive language surrounding maths and children’s abilities. Making sure children are not under pressure to answer questions they may not be confident about in front a whole class so that anxious feelings and loss of confidence never happen. I will also make sure to celebrate improvements and give assurance for any struggles they may have.

 

Fun and relevant lessons: Making lessons fun and relevant will allow children to realise that maths isn’t just a subject you need to learn for school. Highlighting that it is all around us in our everyday lives will motivate children to put more effort in to learn. Active lessons eg. groups competing against one another are great ways for children who are less confident working individually to learn from their peers. As there are no specific children in the spotlight it allows them to enjoy the activity without worry. Even adapting lessons around specific children’s interest eg. football or dancing, will engage them more and make them want to learn. Making sure to eliminate gender stereo types for future jobs by showing both genders achieving any many professions.

 

 Building knowledge slowly: Rote learning is often looked down on these days, however, I am someone who wishes I did learn some of the basics by rote to ensure they were instilled in my mind. Timetables were always an aspect of maths I never knew ‘off by heart’ and it caused to struggle with many other aspects of maths that depended on confidence with times tables. Therefore, with my class I would ensure that children are confident in fundamental maths so that building further knowledge isn’t daunting. Going slow doesn’t mean a child is bad at maths but it ensures they have thorough understanding before moving on which will, in the long run, make them more confident.  

 

Mistakes are allowed! Children must realise that maths is not all about getting every answer correct all the time. The process of solving the problem is just as important. My maths exams in school are what taught me about the importance of this, as one maths question could be worth 5 marks and within those 5, the correct answer was only worth 1 mark. Maths is about being able to process problems and being able to apply these skills to many different questions within maths or even real-life situations. The more pressure a child puts on their self to always be right, the more anxious it will cause them to be. It is also a good way to show all the alternative ways there are to find an answer to one question and all of them are correct if it leads you in the right direction.

8 Practical Ways to Conquer Your Child

(Taken from www.MathsInsider.com)

 

As a committed, professional developing teacher at university, I am determined to work hard over the next few years and freshen up my maths skills to ensure my past and current feelings of maths anxiety do not affect the children in my classes. After writing this blog post I have already given myself an open mind and confidence in myself that I can do it! I want to teach children, the way I have mentioned above, to be confident in maths concepts and problem solving with the hopes that anxiety will never affect them.

 

References

 Ashcraft (2002). MATH ANXIETY: PERSONAL, EDUCATIONAL, AND COGNITIVE CONSEQUENCES. Current Directions in Psychological Science 181-185.

Ma (1999). A META-ANALYSIS OF THE RELATIONSHIP BETWEEN ANXIETY TOWARD MATHEMATICS AND ACHIEVEMENT IN MATHEMATICS. Journal for Research in Mathematics Education, 30(5). 520-40.

Mukisa, C. (2017). 8 Practical Ways to Conquer Your Child’s Math Anxiety | Maths Tips From Maths Insider. [online] Maths Tips From Maths Insider. Available at: http://www.mathsinsider.com/conquer-math-anxiety/ [Accessed 25 Oct. 2017].

the Guardian. (2017). The fear of all sums: how teachers can help students with maths anxiety. [online] Available at: https://www.theguardian.com/teacher-network/2015/nov/17/how-teachers-help-students-maths-anxiety [Accessed 25 Oct. 2017].

 

 

 

My struggle with maths anxiety..

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To begin with, not only do I have maths anxiety, I clearly have a case of blogging anxiety. I am a few weeks behind in starting my blog but it is better late than never! Or so I am trying to convince myself, even though I know I should have started to push myself into starting weeks ago. I am going to begin with a less professional blog on my struggle with maths anxiety as a way of easing myself into blogging.

Mathematics was definitely not my strong point in school. I was never necessarily bad at maths, but the confidence I had in myself was virtually nothing. Something I have always struggle with when I was younger was my times tables, I always found learning them by rote was very boring and it affected me a lot throughout primary is it took me longer to work out answers as I wasn’t able to remember it straight away. I wish when i was younger we had all the apps on phone etc that we do now as a feel they would have made a huge difference. When I think about my experience doing maths in primary, all I seem to remember was being very slow at getting through the work and feeling a race of panic when everyone else in my group had completed the worksheet and I was left alone. Thinking back in the eyes of a prospective teacher, was it really bad that I took my time trying to get all the answers correct when everyone else rushed through the questions and ended up with a lot of silly mistakes that they had to correct? Now of course, mistakes are never a bad thing as it is a good way of learning, however, I wish I wasn’t quite as hard on myself for being slightly behind as it put me off my work even more. I always remember my mum being told at parent’s nights that I was easily distracted in class and I think this was the perfect example. When I started high school, my confidence in maths fell further as we were put into ‘sets’ and it seemed like I wasn’t as good as maths as I had hoped.

Fast forward quite a few years and I managed to get an A at int 2 maths, something I am extremely proud of. Although it may not be higher, I worked so hard to get that grade and by that point everything id learnt so far in maths actually made sense to me. I left school with a satisfactory feeling about maths, it will never be a subject I love but when the different areas of maths began to click, it felt amazing! However, I consciously felt that my A at int 2 was as far as I could go before my maths anxiety would come crashing back down on me if I attempted higher. To this day I don’t regret my decision.

What I DO regret is not practising my maths since school as all the concepts and fundamental knowledge I learned feel as though they have disappeared from my memory. When I found out about the Discovering maths module, I immediately felt it would be a great elective to take. Although I know it is not about teaching us the maths we may have forgotten about since school, but I feel that by thinking about maths each week due to the workshops and blogs, it will spark my interest again therefor encouraging me to improve my basic maths skills and grow back the confidence I had a few years ago.

Having maths anxiety growing up is something I refuse to let affect me as a teacher. Instead, I will use the empathy and understanding I have for children struggling with maths to help them and build their confidence. If I managed, anyone can! If children grasp even the slightest feeling that their teacher ‘hates’ maths, this will begin to affect them as well. I am going to do further research on maths anxiety and how I can prevent it from happening to children in my class in the future, my next blog will be about what I discover. I am also thankful for the way the discovering maths module is giving me an insight into maths that I have never thought of before.