At the beginning, I was unsure if this module would be beneficial for me. This was because during the first session we were asked to put up our hands if we have maths anxiety. For me, this is something I had never really considered as I loved maths throughout school and I started to feel like I had picked the wrong module. However, I was wrong.
This module has opened my eyes to the world of mathematics. I always knew maths featured in the real world but hadn’t ever really been taught that. In school, it was all about textbook work and learning to pass exams rather than how these methods can be applied to the real world and the history of mathematics and how these topics came about. It had also never occurred to me that we need to have basic knowledge of mathematical concepts in order to understand further mathematics topics and make these links to our daily lives. From medicine to playing hockey, playing Monopoly to making a patchwork quilt, it is undeniable that mathematics features in many places.
As a trainee teacher, I believe it is important to consider Liping Ma’s ideas on the key processes to make a good mathematics teacher. These are [inter]connectedness, multiple perspectives, basic principles and longitudinal concepts as previously discussed in my blogs. By making these key processes a part of learning and knowing the mathematical concepts ourselves, we are able to successfully and effectively educate the future doctors, artists and teachers of this world. By grasping basic concepts early on, pupils are able to progress into more complex processes and discover the importance of these basic areas to explore further mathematics. If pupils are able to make links between mathematics and their daily living, they are more likely to find mathematics an enjoyable and worthwhile subject which is not limited to textbooks and exams but extends to infinity and beyond!
For me, this module has truly opened my eyes and encouraged me to look for mathematics everywhere. I had never thought about the mathematics behind taking a photo, tuning a piano or the formation of plants. It is incredible that no matter where we look, there will be mathematics nearby. I believe it is important for children to learn this at an early stage and hope to be a teacher who encourages the exploration of mathematics both inside and outside the classroom on a daily basis. I want to have pupils come up to me and tell me of their new mathematical discoveries from playtime and home as well as in the classroom.
Before clocks existed, many people relied on nature to grasp the concept of the passing of time. For example, the movement of the sun across the sky would indicate day and night. It is believed that in the past, ancient people divided the sun’s cycle into different timekeeping periods. For example, the ancient Egyptians built tall obelisks that would cast shadows to help divide the day into sections (Wonderopolis, 2017). We watched an interesting video on an elephant water clock in class (Luppino, 2015). I was fascinated by the mechanics and level of maths behind this to make everything work at the right time.
Whenever I was younger, I used to think that the whole world was at the same time of day as me. Obviously, I later discovered this was incorrect. The idea of time zones is just amazing and very relevant for me. I have several family members in Canada including my brother and friends in places such as New Zealand. It is therefore necessary for us to consider each other’s time differences before we Facetime. This is especially strange with Kiwis as they are 13 hours ahead which means they are often a day ahead in a sense.
Maths is crucial in timetabling as you need to schedule different lectures for different times and ensure that no room or lecturer is double booked. This is a complex process and something I don’t think I could do! The idea of sitting with pages of names, subjects, rooms and lecturers to sort into a timetable just freaks me out! Would it be easier to use computer timetabling to get an automatic timetable for all students and lecturers? Whilst it would probably be a lot easier and quicker, there would be a lack of personal touch in that nobody wants a 4-5pm lecture on a Friday! Furthermore, a lecture could finish at 11am in the Tower Building and the next one start at 11am in Dalhousie. There is no way you could make it to lectures on time if this was the case.
Whilst at school, I studied A level Applied ICT. This involved creating a game, another aspect of computing that requires maths. The idea of direction was crucial in my game as it was a maze game. The number of coins that were collected needed to be calculated up and the character needed to only be able to move within the game path. I also used the programme Scratch where I created Sprites. This involved programming the sprite to move X steps in a particular direction and turn different angles. This is something I would definitely consider using in the classroom to allow children to see basic maths in action within gaming.
We started off the lecture by considering a restaurant which had 2 choices of starter, 3 choices of main and 2 choices for dessert and how many different combinations the restaurant could serve. I worked this out by giving names to each dish e.g. Tomato soup, steak and chips and chocolate fudge cake. I then wrote out each starter and completed the meal by changing the main and dessert each time. I concluded that there could be 12 different combinations. This would be a good starter activity in the classroom to get children thinking about the probability of getting a certain selection of dishes.
In the counter intuitive maths lecture, we considered this idea with socks- 4 black, 4 red and 4 blue and how many socks you would need to make a pair. The answer is 4 as you only need 1 more sock than the number of different colours. Again, this is something which could be explored in the classroom.
A die is one of the most commonly used objects within probability and is used a lot in gambling. It is unlikely I will use gambling as a main tool to teach probability, however, I will use the idea of rolling a die. Some activities could include getting children to record what they roll for a certain number of throws or asking them to calculate the probability of rolling certain numbers e.g. the chance of rolling a 5 on a 6-sided die i.e. 1/6. They could then look at throwing a 5 on both 6-sided dice i.e. 1/36. The probability of this happening is actually calculated by subtracting the probability of it not happening away from 1. I have explained this below:
Before this input, I would not have known that this can be used in gambling and slot machines to work out the chance of winning or losing. Maths is used when designing the likes of slot machines as the probability of an outcome multiplied by the pay-out/prize for that combination will never equal to 100%. This means that slot machines will always win and earn a profit, never the player. Additionally, this can be ‘weighted’ so that bigger prizes or frequent smaller prizes are paid out, resulting in more money for the casino (Holme, 2017).
There is more to gambling than just luck, there is fundamental mathematics behind it. For me, I don’t think that gambling is worth the time or the money unless you are crazy and rich enough to do as Mandel did. However, a lot of countries have now banned this technique so it’s probably not worth your while really! I think I will keep to the likes of rolling dice and flipping coins to explain chance and probability in my classroom!
As someone who does not consider themselves musical, I hadn’t really put much thought into how maths is needed in music. I love listening to music and find it a great way to relieve stress whilst belting out a song! However, I studied music in school and absolutely hated it. I would dread walking into that classroom to be asked to play the Eastenders theme tune yet again on the recorder or be asked yet another music related question that I had no clue how to answer and to be frank didn’t care about! I knew of the basic elements of music e.g. tempo, rhythm, dynamics but I didn’t fully understand how maths held such a great purpose in music. After our input with Paola, my eyes have been opened!
In pairs, we had to think of as many links between maths and music as possible. Megan and I came up with quite a few including the note values, beats in a bar, the actual making of an instrument and counting songs. Other ways in which maths and music link include tuning instruments, figured bass, scales and even the Fibonacci sequence! This is because there are 13 notes in an octave e.g. from C to C. A scale is composed of 8 notes. The 5
I have always known that there must be some level of mathematics behind medicine and health care, however, I did not realise just quite how important it is in the world of medicine. As the daughter of a nurse, friends of medical students and someone who considered nursing as a career, I have a basic knowledge of the aspects of maths involved in medicine.
I went to the Royal Belfast Hospital for Sick Children for a week where I spent time in the Infectious Diseases ward, Oncology and Haematology unit as well as exploring the other aspects such as renal dialysis and lumbar puncture. During this time, I experienced maths in medicine by doing rounds of observations. This involved taking the oxygen saturation levels, blood pressure, respiratory rate, temperature and heart rate. All of which are mathematical measurements which need to be recorded to determine a score on the observation chart. As observations need to be on frequently e.g. every 2 hours, you can easily compare whether the patient is getting better or deteriorating as it forms a line graph. In primary schools, often charts are made from a tally of cars that have drove past. This is quite irrelevant as a topic, however, the skill of creating and reading graphs is developed through this which is a key skill in medicine for not only doctors but also paramedics and nurses.
A further example of using charts in medicine is for measuring a baby during pregnancy. If there is sudden growth noticed in the chart, this will be cause warning bells in the doctor’s head. They will want to get the pregnancy checked out in a scan to see if there are any complications.
I also looked at the idea of calculating drug doses during my work placement as it is different in adults and children. For adults, initially everyone is given the same dosage, no matter their age, weight or height meaning a frail 89-year-old woman would get the same dosage as a tall, obese 30-year-old man. Whilst in paediatrics, the drug dosage is calculated per kg of weight to ensure the child is administered the correct and safe dosage. Another aspect that involves maths is intravenous drips- it is important to calculate how much fluid the patient has lost and how much they need whilst ensuring there isn’t too much fluid going in that the electrolytes end up diluted.
Blood pressure is a ‘mathematical representation’ of two forces. The top number known as systolic is the force against the artery walls when the heart beats and the bottom number known as diastolic is the force against the artery walls between the two beats of the heart (this is when the heart is in a relaxed state). A blood pressure range of 110/70 to 120/80 is considered normal (Medindia, no date).
Maths is required in prescribing medications as it is important for doctors to prescribe only enough tablets to complete the planned time e.g. a course of antibiotics for 2 weeks. An example in my life is when I went to Canada for the whole summer, I needed enough tablets to do me for 11 weeks. This required calculating how many of each tablet I need each day multiplying that by 7 and then that by 11 to determine the exact quantities I would require to ensure I didn’t have to miss out on medications.
Biomechanics was mentioned during the workshop which is all about the forces required to cause fractures. We also looked at pharmacodynamics and biochemistry. This involves the amount of a medicine administered depending on how fast it leaves the patient’s body which depends on kidney function and how much the patient urinates.
Something I was not aware of before today was the value of Twitter in medicine. Twitter has been used to discover the waves of diseases e.g. the flu. People tweet about having flu like symptoms which helps the NHS to know that in a short time, there will likely be an increase in patients coming into their local GP practice with the flu due to the spread of it. I was fascinated by this as it could be used to help predict future diseases.
Maths is not only required once you are a qualified doctor, it is required even before you enter university through the UKCAT test scores, UCAS tariffs which consider your upbringing and where you live. The idea of deprivation is considered and it has been found that those from a rich area and with parents who have jobs in professional settings such as doctors, teachers, lawyers etc are the most likely to apply to medical school. However, it was interesting to see that those from a poorer background with parents in manual jobs which don’t require a degree were more likely to apply than those from a rich background with parents in manual jobs. This may be due to schemes to encourage the more deprived who are capable to attend medical school and bring in variety to the world of doctors. By having doctors who are from poorer backgrounds, it helps to break barriers as they can relate to patients and therefore the level of trust may be higher.
Statistics play a huge part in medicine and predicting future illnesses and life expectancies. Life expectancy is calculated by taking the average age of death for everyone that year e.g. if the average age of death was 76.9 in 2017, then the life expectancy for babies born in 2017 would be 76.9. It has been seen that men tend to die approximately 5 years younger than women. This may be due to men, in general, being worse at visiting the doctor and waiting longer to seek help if they have a health concern. Living in a poor area has also been shown to decrease life expectancy, particularly if you are male.
Maths in Medicine could be explored in the classroom in various ways. Role play could be used where children run a doctors’ clinic and must prescribe the correct number of tablets to each patient. Medicine could be brought into maths problems where students must determine how much IV fluid is required to keep a patient healthy. Pupils could consider the different angles required to x-ray a particular part of someone’s body. Older pupils could look into health statistics and even create their own surveys for a topic such as healthy eating or exercise within the class. They could look at the average, mean, median and mode of these figures. Maths is clearly a skill required in medicine and we need to educate pupils on this as for all we know we could be educating a class full of future doctors!
Field hockey teams usually consist of 16 players, 11 on the field and 5 reserves.
When trapping a hockey ball, a player’s stick must be at a 120 degree obtuse angle when first moving the stick in a motion to meet the ground. This specific angle helps the player have more control over the ball when first stopping it; it also gives the players more time and skill to continue playing.
Pythagoras’ Theorem relates to field hockey through the triangle passing in the sense that three hockey players can successfully eliminate their opponent through correct distance measurements.
A clock’s structure relates to a hockey player’s tackling structure in the sense that a player is able to successfully tackle their opponent through the following:
As with most sports, time is crucial. It is needed to ensure that the game lasts for the set time. A collegiate field hockey game is divided into two halves each lasting 35 minutes in length. Half time lasts seven minutes. At half time, the teams switch playing sides. If a game is tied at the end of regulation, there will be two seven-minute periods of play.
Many people scrunch up their face or roll their eyes when they think of maths, many believe that it is boring. I reckon it does not have to be that way- maths can be fun! I believe that we as teachers need to liven up the idea of maths and bring in cross curricular learning as well as looking at learning mathematics through play.
Research has shown that previous traditional teaching methods have not been successful as when adults were asked to explain how to solve particular problems and why we need certain mathematical concepts, they were unable to recount their learning. These rote and drill teaching methods such as handing pupils a page of calculations to complete has been referred to as shallow learning as it did not make complete sense to pupils. Parents and teachers are now worried that the maths that parents pass onto their children is not solid and accurate yet it is crucial that parents play an active part in the mathematical learning of their children particularly during the early years (Valentine, 2017). It is important for maths to be a continuous part of the home environment through aspects such as time (for cooking), money (bills) and telling the time to help encourage the learning.
Play is important because it is a major part of children’s everyday world- for them it is a familiar environment, resulting in more successful learning as it is a meaningful context. Furthermore, play helps them to develop social skills such as sharing e.g. they can use maths in a role play situation e.g. play shop. Play also allows children to learn in their own time and be independent learners. They are able to control what happens during their learning and the outcomes of it. By using play to learn maths, children are able to visualise their learning instead of using a textbook e.g. use of 3D shapes. Play allows children to experiment in a relaxed environment where making mistakes is not an issue and written outcomes are not a focus.
There are many forms of play which can be used for learning. These include symbolic, creative, discovery, physical, technology, games, environmental and books and language. Activities may include rhymes, outdoor play, songs and role play. We looked at a video on maths in literature where mathematical concepts were used in traditional fairytales and stories such as Goldilocks and the Three Bears which changed to Goldilocks and the Three Squares. Something as simple as this is a great way to introduce children to basic concepts in maths.
Tessellations of congruent shapes, such as above, are called monohedral tessellations. The word monohedral literally 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. A lot of Islamic art uses tessellations of equilateral triangles, squares and hexagons. Furthermore, in Spain there are many examples of art in tiling such Park Güell in Barcelona.
Snowflakes are another example of maths in nature. They exhibit six-fold radial symmetry, with elaborate, identical patterns on each arm. Snowflakes are made entirely of water molecules which have solidified and crystallised to form weak hydrogen bonds with other water molecules. The bonds maximise attractive forces and reduce repulsive forces, allowing the snowflake to form its hexagonal shape 
Maths is even required in photography. Many photographers use the ‘Rule of Thirds’ to set up their photos. This is where the image in broken down into 9 sections using 4 lines. The idea is that if you capture an image where the main object/focus is placed along the lines or the intersections, the photo will be more natural and pleasing to the viewer instead at the centre of the shot (Rowse, no date). Another method photographers use is balancing elements. This is similar to the rule of thirds and is simply placing a focal point off centre to create a more interesting image, however, this means there is empty space at the opposite side. This is where balancing elements comes in- you place another similar object at the other side to balance the photo out- known as formal balance. Informal balance is when you place two varying objects at opposite sides of the image (Google, no date). Leading lines are another method used in photography in which straight objects such as roads are used to draw the viewer’s eye to the image and connect the foreground to the background (McKinnell, no date). The final method photographers use is symmetry and patterns within photos to create a balanced and aesthetically pleasing image (DMM, no date).
Mathematics. One word with so much importance and relevance. One word which can either bring extreme fear or excitement. One word which is needed in society everyday yet so many people are overwhelmed when they hear it. What feeling fills you when you hear someone say “mathematics”? Does your mind fill with random equations you learned in high school but have never actually used in real-life? Or does it get ready and excited to discuss such a topic? Does your heart start racing as you think of all the exams you sat and the horrible memories come flooding back?
