# Think 182

Prior to studying discovering mathematics I believed maths to be only about numbers. However following the module, I now understand it is much more than that, it is everything and it is definitely an art form. Mathematics is prominent in many aspects of music such as beats in a bar , notation value ie crotchets and semi quavers etc, tempo and in tablature, the list is infinite.

For those who are unfamiliar with tablature or tab it is a form of musical notation that refers to instrument fingering rather than musical pitches (big guitar , no Date) . For example:

This picture shows musical notation indicating pitch and so requires the guitarist to know where each note is represented on the guitar fret. However the bottom line is the tabs. Tablature tells the individual where to put their fingers so the first note would be open first string as it tells the reader no fingers on fret but to play open first string once, the second note would then be first finger first fret first string played once.

I used to believe those who played tablature to play music were much like artist whos work was made using dot to dot. I didn’t think it required much if any understanding of music. However I recently decided to try playing tab and I think it is possibly the best decision I have made in terms of my musical progression. I already had a conceptual understanding of music or so I believed I recently tried to learn hotel California on guitar however there are quite a lot of sharps and flats in the music and I was struggling to remember it all so I tried using tabs and found it be alot easier. I didn’t need to keep reminding myself where the sharps were as the notation told me where to put my fingers. I learnt to play the song reasonably quick after this I just needed to perfect the pace.  Which brings me to my next point; pacing.

A disadvantage of tablature is that because there is no notes without truly knowing the song or understanding the notation above it indicating the pitch you have no way of determining the speed of the song or the dynamics (how loud a note is played) . However, as I learned to play music before I did tablature I used the notations to help me determine the speed of the song. I also knew that by looking at the start of the music where it tells me how loud to play the song using something I believe could be defined as algebra.

These letters represent more than just their face value they dictate a song massively (Angela ,2018). I believe that the understanding and appreciation of pupils learning about dynamics will increase their appreciation of the beauty of algebra.

In addition to this I used to believe that the f note was first finger first string just because it just was however after comparing the notation to the tablature I noticed the links between the two. I used to wonder why the  g note  was third finger first fret first string and not first finger second fret first string after all G does follow F in the alphabet ?  Tablature has helped me understand by comparing the two it is because there is a semi tone between f and g which Is f sharp and that Is why the second threat first string is f sharp not g.

So this begs the question so what?

I believe that by learning tablature my horizons have been broadened in terms of music as having an understanding of both tablature and notation I have developed a conceptual understanding of music, understanding not only the how but also the why of music. Learning music through the use of numbers have furthered my understanding of a mathematician and a musician and I would love for pupils in my future classes to have the opportunity to experience this and so I will to the best of my abilities ensure I teach maths and music together in hope that both experiences are enlightening and enjoyable for pupils.

# my sixth year personal essay

Following an input on attribution theory i was reminded of my personal essay that I  wrote for my advanced higher English portfolio. The essay was completely my own and i did not allow for any of my teachers to see it until the day before it was meant to be turned in. I wanted it to be completely my own.  I hope you enjoy reading it.

P3r50na1 355ay

“Do not judge me by my successes, judge me by how many times I fell down and got back up again.”
Nelson Mandela

School life has not always been easy for me; I guess you could describe me as a “late bloomer”. Personally, I do not believe this to be representative as I feel that no-one should define which stage a child should be, or indeed when, in their development. We are all individuals who mature, learn and process information at different rates. From an early age, it was apparent that I struggled with English, especially reading, and as a result of this I was stuck into the euphemistically named “Red Group” which even my slightly naïve eight year old self could work out was the dreaded…bottom group. Even though I coped with the demands of working out the three bold words on the page using the pictures as clues, simply being in the bottom group shattered my confidence, leading me to believe, that I was one of the “dunces”.

Never making it out of the Red Group throughout my entire seven years of primary school left me believing that I was less intelligent than the other children in my class. Due to this internal belief, the consequences were demonstrated externally. The mere thought of having to answer a simple question in front of the class would result in the feeling that my heart would leap out of my chest. The endless silence followed by a sea of little eager faces awaiting a response was too much to bare. I developed extreme anxiety about answering questions in class – not because I wasn’t willing to offer a response but simply because I feared getting the answer wrong and confirming my class mates’ beliefs that I was vacuous.

High School; a fresh start. An opportunity to shrug off the label that had been assigned to me in primary school. An opportunity to rise above the mediocre expectations that had been set for me. Unfortunately, I was terrified of my own shadow back then so the thought of shrugging off and rising above anything was going to be quite the task. I was intimidated by the stature of the school and those around me, thankfully I had someone, other than my really embarrassing older sister, to look out for me. I was firstly introduced to my Guidance Teacher, Miss Duncan. I did not know it at the time, but later on in my school career, she would become the most influential factor in my decision to become a teacher.

I found it difficult at first to acclimatise to my new school environment. I was not used to travelling from class to class, and as a result of this I found organising my school work to be a challenge. I was placed in a small class with another twenty pupils. It became apparent to me that we had an extra teacher in the room. At the start, this did not bother me as I really enjoyed having someone else to talk to and having someone who would help me with my organisational skills, whilst also aiding me in attempting to conjure up a Victoria sponge cake in Home Economics; which, to this day, I still require assistance to make. It soon became apparent to me that this teacher was in class specifically to see if I was coping with the demands of the school work, specifically in English.

Shortly after my arrival at high school, I was tested for Dyslexia. The results came back positive. Word soon spread through my English class, as I began to arrive to class with the dreaded “Alpha Smart” which was basically a glorified calculator but for words instead of numbers. I did not mind people knowing I was dyslexic but what I did mind was the constant questions. Can you spell this? Can you read this? And the worst of all – it’s not fair, why does Cameron get to use the computer? I decided that the best way to stop these questions was simply not to use my Alpha Smart anymore. I viewed the Alpha Dumb as an opportunity for my peers to re-label me as the class “dunce” rather than a way to aid me in my studies. I decided that the best way to get people to stop speaking to me as if I was inferior to them was to beat them at their own game. I set myself the goal of being the best English student in my year. No mean feat for a boy who needed a sheet of yellow film to stop the words from jumping off the page. Aspirational, huh?

At the start of third year, I was placed in a new English class and, for the first time ever, the top set. I had finally reached the pinnacle of my school career. I dreams and aspirations had finally been fulfilled. I was still rather shy, so I sat at the back of the class in order to avoid drawing attention to my presence. I had a severe case of Imposter Syndrome: an inability to internalise my accomplishments; and a persistent fear of being exposed as a fraud. I kept waiting for the Head of English to come and drag me, literally and metaphorically, back down to the bottom class. The teacher arrived; silence fell. We all knew Miss Duncan was someone that you did not wish to get on the wrong side of but I had always had a good relationship with her. She noticed immediately that I was sat at the back of the class in the left hand corner, and she offered me a re-assuring smile. Her belief in me sparked my love for the subject. Despite the protestations of the class, we studied Shakespeare, more specifically we studied the Scottish play “Macbeth”. I instantly fell in love with the play, not just for its storyline but for the way we were taught it. Miss Duncan showed me that words have a deeper meaning than what is first presented. Miss Duncan and I became close and I aspired to be like her, as she presented herself to me not only as a teacher but also as a friend. We shared many similar interests not only our love for English but we are both also “die hard” Manchester United and Dundee Football Club supporters. I would hang back and speak to Miss Duncan at the end of every English period. This was five minutes where I could have a conversation with someone without feeling like my views and opinions were invalid. This helped me grow in confidence and enhanced my academic abilities, as I had finally found someone who had faith in my abilities.

In order to repay Miss Duncan for the support and guidance she had given me for all of third year. I began to make essay plans for my upcoming third year exams and studied two hours a night for two weeks. I sat the exam and got full marks on my “Macbeth” essay. Whilst many believe it is simply third year tests that do not count towards anything. I believe the opposite these tests that “ meant nothing”, meant everything to me as it was the first time I had seen myself progress and it also gave me an opportunity to prove to Miss Duncan that all the time and dedication she had spent on me had paid off.

Due to the result I got in my third year exams, and also the guidance given to me by Miss Duncan, I began to become more confident in my work and also within myself. I became more sociable and now had the confidence to put up my hand in class without fear of being subjected to ridicule by my fellow classmates. Luckily for me, Miss Duncan was my teacher in both fourth and fifth year. During my fifth year at school, I ensured that my love and enthusiasm for English did not fade, even though my peers had become increasingly distracted by other aspects of their lives. I continued to work extremely hard and pushed myself to the limits, something that previously I would not have done. My prelim results were a testament to my hard work as I was later presented with the English Dux medal as I had received the highest mark in the year; ninety per cent to be exact. And whilst many people have attributed “Dyslexia” as the reason they did not succeed in school, I have found the complete opposite to be true. I have used the diagnosis of Dyslexia as a catalyst for my success. I refused to be defined by my disability. Having a learning disability, only too often, can lead to a lack of faith in them to do well. This contributes to the self-fulfilling prophecy. Most people are unaware that Dyslexia is not solely about having difficulty with spelling and reading but it also affects time management skills, brain processing and organisational skills. Whilst these seem like negatives, people with dyslexia are actually more inclined to being able to see the bigger picture and allow them to think outside the box. I believe this enhanced my abilities and allowed me to progress further in English.

As I matured and began to consider my options for the future, I looked at those around me for inspiration. I was unsure about my future aspirations, I had previously desired to be an accountant; I probably only wanted to be an accountant as the lavish lifestyle and extraordinary high annual salary seemed appealing. But life as an accountant was harder than I first believed. I acquired work experience at Murray Taylor accountancy firm in Arbroath. What can I say? The dry lifeless office environment is not for everyone, and is certainly not me. After endless months of procrastination, I finally set my goal of being a primary school teacher. However, in order to do this I knew that I would require valuable work experience at a primary school. I arranged to do this experience at Longhaugh Primary School at Whitfield in Dundee. This is one of Dundee’s most deprived districts and at first I was hesitant to go as I feared the pupils would be too challenging and would put me off wanting to be a teacher. However, they did the complete opposite. I learnt valuable lessons whilst at Longhaugh; the kids there were inspirational, the level of poverty was incredible, yet these children would still continue to come to school and do their very best to ensure that, when they are older, they will not have to continue to live like this. I formed many strong friendships and relationships with the children whilst at Longhaugh. During my time there, I had learnt the true meaning of being a teacher, it wasn’t about the pay cheque at the end of the month or ensuring a child was a straight ‘A’ student. It was about making a child feel needed and wanted and to instil in them the belief that they can be whoever they want to be regardless of their background and certainly regardless of any learning difficulty that they may have. Due to my experience at Longhaugh, my desire to have a “monumental” impact on someone’s life has become my new goal.

Counting down to my last few weeks of school, I occasionally imagine what life will be like out with the constraints of the school gates. A life where I no longer need to follow the “one way system” as I am now free to determine my own journey. A life where I no longer have to utter the question “Please Sir, may I go to the toilet?” A life where I am free to be whoever I want to be, without fear of being judged by others. I also wonder what will become of me and my friends. Will we still remain in contact even though we are no longer available cell mates, confined within the breeze blocks of the classroom walls? Whilst the future may be unclear and frightening, I am without doubt excited to see what the future holds for me. Will I be someone Miss Duncan’s? I strongly believe that being a teacher is about more than ensuring your pupils get the results required to go to university but it is more about ensuring each and every pupil meets their full potential. Despite a rocky start, my overall experience of education has been positive. Even though there have been many obstacles to overcome, I know that without them I wouldn’t be where I am today. And now those same pupils no longer ask can you spell this? or can you read this? They now ask me did you get the English Dux medal? or can I have your essay plans, please? How ironic, I say. “what’s that?”  they ask. And I laugh.

# Linears , subtractions and fractions oh Pi!

What is the most terrifying thing you can think?  Common answers may include spiders, heights or horror movies, but what about mathematics?  Many professionals such as Boaler (2009) believes that children find maths fearful. Why is this? Is that just the way it is to be? are people just meant to be afraid of numbers? Or are we doing something wrong?

Maths anxiety comes in many forms and is experienced differently by each person suffering what could be described widespread epidemic. Arem (2010) believes that maths anxiety can cause headaches, sweating, confusion and the inability to concentrate.

So why does this maths anxiety exist?

Many professionals such as Hembree (1990) believes that maths anxiety is defined as a general fear of mathematics.  Why is this allowed to occur? If children experienced this feeling whilst studying any other curricular area it would be pandemonium. So why is little being done to help children overcome this widespread epidemic in schools ? Furthermore, the Scottish government (2009) believe that the most common form of mathematical activity in the classroom is based on pupils using textbooks and working in silence and independently (Scottish Government, 2009). To this day I still remember the feeling of working from textbooks and not for the right reasons, it is the most mind numbing soul-destroying type of work I have ever done. I believe it is our responsibility as teachers to help children develop the notion that maths is fun , enjoyable and most importantly something they are comfortable and good at tackling.

I recently stubbled across a poem that I believe represents what the communication of mathematics is like for some people.

The two dead boys

1. One fine day in the middle of the night,
Two dead boys got up to fight,
3. Back to back they faced each other,
4. Drew their swords and shot each other,

5. One was blind and the other couldn’t, see
6. So they chose a dummy for a referee.
7. A blind man went to see fair play,
8. A dumb man went to shout “hooray!”

9. A paralysed donkey passing by,
10. Kicked the blind man in the eye,
11. Knocked him through a nine inch wall,
12. Into a dry ditch and drowned them all,

13. A deaf policeman heard the noise,
14. And came to arrest the two dead boys
15. If you don’t believe this story’s true,
16. Ask the blind man he saw it too!

Whilst this poem is purposely meant to be contradictory. I believe this is how some people see the learning of mathematics. For example, I remember as a child being told that when I multiply by 10 I simply add a zero to my answer. However I was extremely puzzled as to why 1.4 x 10  does not equal  1.40, even though I had been told specifically all I had to do was add a zero. Obviously, I soon learned that when multiplying by ten I move the decimal point one space to the right and when dividing I move it to the left. That’s no big deal to someone who enjoyed learning mathematics. I understand we learn from our mistakes,  but for someone who already has negative associations with maths and finds it confusing it adds additional stress and furthers their negative attitude.

Moreover the understanding of mathematics is crucial Erickson (2008) believes that as conceptual understanding decreases pupils begin to lose interest in maths . So what is conceptual understanding and how do we allow pupils to obtain this ? conceptual understanding is defined by Ben-Hur, (2006)  as a knowledge rich understanding . Therefore it is important that as teachers we ensure that our pupils develop a conceptual understanding of mathematics which will then hopefully enable them to enjoy mathematics and study maths progressively throughout there school career.

To whoever is reading this blog. I usually end my blog posts with a conclusion as to what I will do next to progress, However one of the main points I have taken from the discovering mathematics module is that it is not what I am going to do next but more what we can do next. Everyone is learning and developing as professionals and if everyone works together to ensure a pleasant and enjoyable experience for pupils whilst studying maths and every subject for this matter then pupils will enjoy coming to school and maths anxiety will cease to exist. I believe this to also be an important message to leave for pupils. It is not what I will do as a future teacher to help my pupils overcome maths anxiety but what we all can do to help each other in our learning.

Arem, C. (2010). Conquering math anxiety. Australia: Brooks/Cole Cengage Learning.

Ben-Hur, M. (2006). Concept-rich mathematics instruction. Alexandria, VA: Association for Supervision and Curriculum Development.

Boaler, J. (2009). The elephant in the classroom. London: Souvenir.

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 3rd September 2015

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

Metafilter.com. (2018). Two dead boys got up to fight. [online] Available at: https://www.metafilter.com/51472/Two-dead-boys-got-up-to-fight [Accessed 1