# Reflection post on science and maths!

What links does maths have with science?

In class, we drew graphs to plot y=x, y=x^2, y=1/x and y=1/x^2. In order to draw these graphs, we first needed a fundamental understanding of basic concepts such as numbers, the sequence of numbers and being able to understand patterns in order to compare results and see relationships. Furthermore, we needed knowledge of the measurement of the squares on the page first, we needed to know measurements as one square is 1mm therefore, 10 of them make a centimeter so we can use 1mm to represent one of somethingg out of 10. Therefore, we demonstrated knowledge of fundamental understanding of mathematics as we used basic concepts and connecting them together in order to make relationships and associations between the graphs (Ma, 2010, p.104).

Science is defined by Oxford Living Dictionaries (2017) as “The intellectual and practical activity encompassing the systematic study of the structure and behaviour of the physical and natural world through observation and experiment”. So, science involves observation and experiment and these could not be carried out without maths because in order to observe for example the magnetic forces between magnets it involves recording observations on a graph which as I have stated above involves many basic mathematical concepts. In science, you are applying your use of mathematics to study the world. However, if science is the application of maths how is it that even Einstein (1943, quoted in Letters from and to children, 2004 ) one of the greatest scientists in history said that even he had great difficulty with maths?

Through our use of maths and science together to find the relationship between distance and  forces with magnets. We found that distance and force has an inverse relationship which also links to electricity and gravity (Taylor, N. (2017). Therefore, once we understand these links we can explore what we can do more with our knowledge. For example, with electricity once this discovery was made it was used to make phones, dishwashers, washing machines, laptops, televisions and apple watches which are all everyday things that we may use in society but we don’t think about how the science and maths behind them all started out from basic concepts and relationships.

In order to develop children’s fundamental knowledge of mathematics in the future, I would need to start off teaching fundamental mathematical concepts such as measurement, how to draw a graph, the skills of observation used in science and how to plot a graph in order to show relationships between science and maths which links to connections between topics which Ma (2010, p.104) refers to as an element in developing your understanding of fundamental mathematics. Cross-curricular links could also be made to technology!

List of references:

• Taylor, N. (2017) Science and maths. [Lecture to Discovering Mathematics Year 2], ED21006: Discovering Mathematics (year 2) (17/18). University of Dundee. 20th November.

# Application of maths for a business simulation.

In a workshop, I took part in a business situation which demonstrated an application of Profound understanding of fundamental mathematics in the real world!

An overview of what was involved in this business simulation:

• We had 5,000 Euros to spend for each quarter of the year
• We had to choose a maximum of 5 items to sell for each quarter
• We had to choose what quantity of items we wanted (quantity being a basic concept which is needed to have a profound understanding of fundamental mathematics according to Ma (2010, p.104))
• We had to be careful and look at how much we were buying the item for to ensure we were not paying more for an item than it was being sold for such as the Christmas selection boxes in January.
• We had to keep track of how many items were sold and whether they could be carried over into the next quota or whether it was a ‘write off’
• We calculated how much we had spent by adding the prices together and subtracting what we had spent from the 5000 Euros or money we had to see what was left over. Therefore, through this process we were building upon each stage and adding to it over a period time which links to longitudinal coherence (Ma, 2010, p.104). Furthermore, we connected basic concepts together such as adding, subtracting, multiplying, percentages and decimals

• We had to look at multiple perspectives to see what we were going to buy and sell however, we didn’t really look at multiple perspectives from a mathematical point as we continued to use the same methods of calculations throughout the session.

However, although we tried to be tackle by what we bought by guessing what items were more likely to be bought around a certain time of year, we could have looked ahead and seen that for January there was a sale price mark-up which mattered more. For example,  beans only cost 25p to buy but they were being sold for 2.50 euro and 100% were sold. Therefore, there was a ten times mark up. Consequence, if I was to do this again i would pay more attention to the price per unit that we were buying it for and the seasonal price in order to make a bigger profit.

In the future, I would like to use this activity or at least one similar to further pupils understanding and application of fundamental mathematics in the real world or in the wider society. Therefore, they could connect and link various topics together for a meaningful purpose (Ma, 2010, p.104). It would be a fun and creative task or game for the children to do and could potentially due to the relevance of the task, it could give them an interest in business as a future career. However, in order to improve this activity I would like to further gain the children’s interest as well as emphasis the relevance by having the packaging of the actual items out on desks to further emphasise the relevance.

References:

• Ma, L. (2010) Knowing and teaching elementary mathematics: teachers’ understanding of fundamental mathematics in China and United States. (Anniversary Ed.) New York: Routledge.

# Statistics can save lives!

From the lecture presentation I developed my understanding of the fundamental mathematics behind statistics as statistics couldn’t be understood without starting with fundamental basic mathematics. Also, statistics are an example of longitudinal coherence as they give a full picture and can be broken down to basic concepts that were built upon each other which Ma (2010, p.104) states is a profound understanding of fundamental mathematics. In primary school, you are taught how to do tally and other sorts of graphs. The knowledge gained of recording and creating these graphs is built upon in order to create charts for medical reasons. Thus, a profound understanding of fundamental mathematics has major implications, having this knowledge can keep people alive or it can be fatal as child can be poisoned if too high of dose is given to a child (Hothersall, 2016). These drug doses are given per kg.  Therefore, children are weighed so the drug doses can be worked out. Here is a basic concept in maths that is required for use in medicine, weight which involves measurement and this is applied or links to medicine to save lives (Ma, 2010, p. 104).

Furthermore, junior doctors are expected have a profound understanding of fundamental mathematics as they are to know ratios and statistics to do with for example, the risk and probabilities of what one single cigarette can do to you (Hothersall, 2016). Therefore, this part of medicine involves several basic concepts of mathematics such as probabilities, ratio, change and recording (Ma, 2010, p.104). Even breaking your leg requires knowledge of the basic concepts as it’s due to forces and the angle, the speed that something might hit your leg at to break it (Porta, D.J).

However, maths should be taught in a fun and relevant way as it’s important to show the relevance of maths and helping them see that maths in science. So, when you are doing a fun experiment in class, help them see its fun. Maths is fun so inspire their love and interest in maths. I also want to help develop pupil’s knowledge of profound understanding by demonstrating this example of longitudinal coherence to them. The importance and relevance of statistics or why we learn the basics in maths like making graphs. I know that when I went to school I was learning how to draw tan graphs but I saw no point in learning it because I was not told the relevance.

An interesting point is that statistics links to social media. For public health reasons, there is an “Ailment Topic Aspect Model” that has prior knowledge of ailments. This model the analyses tweets to search and track sickness or illness over a period of time by “…measuring behaviour risk factors, locating illness by geographical region, and analysing symptoms and medication usage.” (Paul and Dredze, no date, p.1). However, a weakness of using twitter for statistics is that surely many people don’t tweet seriously, they may exaggerate their problems, they could be lying for a laugh or attention seeking. Furthermore, many account are private so how are all the tweets from these accounts accounted for in their data? What if the majority of information about a recent illness is on these accounts? Additionally, the symptoms that people might state on twitter could potentially be too vague.

A drawback should be noted about statistics. Although they can be useful and save lives, they are not always correct. There is such a thing as bias statistics especially in advertisement. For example, Colgate toothpaste claimed that 80% of dentists recommended Colgate but this was misleading as dentists were given a list of options to choose which toothpaste in comparison to the other competitors (Derbyshire, 2007). Therefore, fundamental mathematics can be used in a negative way in wider society. Therefore, In the future I would like to teach children that they need to critically evaluate statics and use multiple perspectives to look at the different ways statistics could be looked at as different perspectives can tell you different things (Ma, 2010, p. 104).

The video below gives some examples of negative uses of statistics (TED-Ed, 2016).

In conclusion, statistics are an example of how fundamental mathematics such as longitudinal coherence can be applied to wider societal issues.  A drawback to statistics is that they can be misleading however, they can also help save lives and this is why learning mathematics is important!

List of references:

Derbyshire, D. (2007) ‘Colgate gets the brush off for ‘misleading’ ads’, The Telegraph, 17 January. Available at: http://www.telegraph.co.uk/news/uknews/1539715/Colgate-gets-the-brush-off-for-misleading-ads.html (Accessed: 15 November 2017).

Hothersall, E. (2016) ‘Numeracy: Every contact counts (or something)’ [PowerPoint presentation]. ED21006: Discovering Mathematics (Year 2) (17/18) Available at: https://my.dundee.ac.uk/webapps/blackboard/content/listContent.jsp?course_id=_56905_1&content_id=_4941433_1&mode=reset (Accessed 9 November 2017).

Ma, L. (2010) Knowing and teaching elementary mathematics: teachers’ understanding of fundamental mathematics in China and United States. (Anniversary Ed.) New York: Routledge.

Paul, M. J., and Dredze, M. (no date) You Are What You Tweet: Analyzing Twitter for Public Health. Available at: http://www.cs.jhu.edu/~mpaul/files/2011.icwsm.twitter_health.pdf (Accessed: 9 November 2017).

Porta, D.J. (no date) Biomechanics of Impact Injury Available at: http://eknygos.lsmuni.lt/springer/659/279-310.pdf (Accessed: 9 November 2017).

TED-Ed (2016) How statistics can be misleading – Mark Liddell. Available: https://www.youtube.com/watch?v=sxYrzzy3cq8 (Accessed: 15 November 2017).

# Maths causes major happiness!

There’s a link between music, maths and our emotions. How can this be and why do major chords in songs make us happy? This is what I am going to explore in this blog post!

The links between maths and music:

• beats (the value of each note)
• timings
• rhythm
• string numbers
• if you are changing key, you go up or down
• scales: scales follow the same pattern, no matter what note
• tempo: speed of the music (metronome)

Music makes us happy. I don’t know about you but I love listening to music and it makes me feel better no matter what mood I’m in. Kim (2015) states that the Feel Good Index (which is an equation itself) is the “… sum of all positive references in the lyrics, the song’s tempo in beats per minute and its key.” Having a fast tempo in a song makes us want to dance, we want to move and it makes us happy. Apparently this is because “Beats automatically activate motor areas of the brain.” Fernández-Sotos, Fernández-Caballero  and Latorre (2016) also agree that the tempo impacts whether the music makes us happy or sad.

However, sad music can make us happy. Sometimes I’ll be in the mood to listen to sad and slow songs but they make me happy however, this contradicts what is said above? The lyrics are sad, not pleasant. This is because whilst the emotion of sadness is seen as negative, in artistic form, sadness can be felt, sensed or understood differently. Therefore, songs that are in a minor key which are identified as being sad songs do not always cause a negative emotion (Kawakami et al. (2013, pp. 1-2). Personally I think the reason for this is more than just the links to the maths behind the music such as a slower tempo or a minor key. It’s also because we connect with the feeling, the emotion through the song or lyrics and this connection is pleasant to us (Nield, 2016). The emotions are caused as the music brings back previous experiences that can make us happy or sad. (Konečni, 2008, cited in Hunter, Schellenberg, and Schimmack, 2010, p.54).

Additionally, why do certain pop songs in the charts make us feel happy because their tempos are fast, around 116 beats per minutes and have a major third musical key (Kim, 2015)? You might be thinking, what does music have to do with maths? Well, music is made up of “…pleasurable patterns of rhythm, beat, harmony and melody” (Gupta, 2009). If you are still asking what do tempo and beats have to with music well, according to Fernández-Sotos, Fernández-Caballero and Latorre (2016),

Tempo is “…the speed of a composition’s rhythm, and it is measured according to beats per minute.”

“Beat is the regular pulse of music which may be dictated by the rise or fall of the hand or baton of the conductor, by a metronome, or by the accents in music.”

So, what makes a pop song catchy? Why do we enjoy hearing the next new hit song on the radio and want to sing and dance along? The University of Bristol asked the same questions. They formed a mathematical equation to work out what makes a popular song popular. They created a diagram to compare pop songs patterns. The coloured parts of it represented beats and the connections seen in the diagram were sections of music that join. What they found was that many pop songs had a very similar pattern Seeker (2014).

A drawback to the equation that The University of Bristol developed (which they recognise themselves), is that it will need adapted as what becomes popular changes since, over time the songs that have become popular are ones that are getting louder (University of Bristol, 2017). Why is it that what is popular changes over time?

Why do these pop songs make us feel good? In one of my previous posts (Noble, 2017), I talked about how according to Burkeman (2011) gambling is satisfying as we are addicted to the potential of getting a reward and the satisfaction is due to the chemical dopamine being released (How the Brain Gets Addicted to Gambling, 2017). This same chemical is released when we listen to these pop songs therefore, making us feel satisfied, please, happy and feel good. However, why do we not get bored of these songs? In the video linked below it demonstrates how a lot of the famous pop songs are repetitive, they use the same four chords (random804, 2009).

So, we seem to be  satisfied by the same types of songs. These songs that are popular, are popular because they fit “[I]mplicitly learned patterns…” or their patterns only differ by a slight bit (Wheatley, no date, cited in Hughes, 2013). This slight difference must be what keeps us satisfied as we would be bored if it was the exact same every time.

Critically, maths can be non-existent in music according to Sangster (2017). For example, every pitch has a different frequency but a piano note can’t be tuned to the exact frequency that it mathematically should be or it doesn’t sound right musically. This is where maths cannot be applied to music. This video below demonstrates why it’s impossible to tune the piano notes to the exact mathematical frequency although it demonstrates why this is so using maths (Minutephysics, 2015).

In the future, I would like to apply my knowledge and understanding of how maths underpins music to teach pupils about maths. Pupils could make their own short songs, using their maths skills such as counting, timings, rhythms and beats! This would be a fun activity showing the relevance that maths has in the wider environment and in everyday society.

In conclusion, maths is behind music. Music is composed by using basic concepts in maths such as the speed of the music, timings and counting the beats per minute. In order to count beats, people need to know how to count in a sequence, and how long a minute is. All these basic concepts are put together and built upon to make music over a long period of time. All of which relate to what Ma (2010, p. 104) says are the principles of fundamental mathematics. Furthermore, the type of music that is produced from using and building upon all these basic mathematical concepts can have an affect on peoples emotions, making them either happy or sad and formulas can even be created to determine or predict what songs will be big hits!

List of references:

# Reflection on maths in sports!

Previously, it hadn’t occurred to me about maths in sports. If I was playing a sport, my main aim and line of thought would be to try and score, or win, along with using some tactics. Therefore, today’s workshop about maths in sports really opened up my eyes to see how the fundamentals of mathematics can be used to help people in everyday life activities such as playing sports.

Prior to today workshop, I researched about the maths in the sport Cricket. Interestingly, I found that even the weight of the bat can affect your performance in the game, the angle at which the ball hits the bat, the vertical bounce of the ball, the speed the ball is bowled at, the mass of the ball and even the ball spin (Physics of Cricket, 2005). Angles, weight and speed are all basic concepts used in mathematics which links to what Ma (20 10, p.104) refers to. All of these basic concepts link together, can be tested over a period of time and thus, the game performance can benefit over a period of time, by building upon the results and doing research. (Ma, 2010, p.104).

In addition to maths and cricket, today in workshop we redesigned the football league table from 1888-1889 by including the goals against, goals for, goal difference, points, games played, games won, games drawn and games lost. Below is an example of the original football league table.

We decided to order the football clubs from top to bottom according to the most points a club had won. We used basic mathematical principles (Ma. 2010, p. 104) of counting to find out how many games each team had won, drawn or lost. To work out the goal difference we used the basic mathematical concept of subtraction, subtracting the goals against from goals for.

After creating our new football league table, we discovered that we could have used simple  algebra to work out the points if we multiple the wins by 2 and add the draws.

Winn x2 + draws = the points (simple algebra).

We could have designed this table differently by taking at the average of the goals scored (goal average)  and sorted them that way.

Next, we designed our own sports game and looked at how maths was applied to the sport. Our sport was called Smack-ball. It was based on the memory of a game many people have played. This being, when you have a balloon you try and keep the balloon up in the air by hitting the balloon as it comes back down and you can’t let it touch the ground. So, essentially, smack-ball involves using a ball that is the size of your hand-span and it weighs 196 grams. The court will be rectangular, 10m by 5m, the shorter walls are the goals, there are three players on each team and the game lasts 10 minutes. The aim is to try and smack the ball (involving passes to your other team members) towards your teams wall without letting the opposite team intercept the ball.

Applying maths to our sport:

• using Pythagoras to try and perfect the perfect pass (Tohi, 2016)
• force and distance for hitting the wall
• when is the best time to intercept the ball out of someones hand
• ball spin and speed

Reflection point:

In the future, I would like demonstrate to pupils how basic mathematical principles can be applied to sport! Pupils could choose one of their favourite sports therefore, creating interest and they could play the sport whilst others record results to illustrate how speed, distance and points are all relevant to sports. Demonstrating how maths can link to their interests, making maths enjoyable and relevant (The Scottish Government, 2008, p. 30)!

In summary, maths can be used to help benefit peoples performance in sport and can actually help people win! Many fundamental basic concepts were involved to create a league table and to look into how to improve in sport such as examining size, weight, position, location, counting, adding, subtraction, multiplication, simple algebra, force, distance, speed and time (Ma, 2010, p.104). Therefore, the fundamentals of mathematics can be used to help people in everyday life activities such as playing sports.

# Mathematics is in everything!

List of references:

• Ma, L., (2010) Knowing and teaching elementary mathematics (Anniversary Ed.) New York: Routledge.
• Physics of Cricket (2005) Available at: http://www.physics.usyd.edu.au/~cross/cricket.html (Accessed: 5 November 2017).
• The Scottish Government (2008) curriculum for excellence building the curriculum 3 a framework for learning and teaching. Available at:  http://www.gov.scot/resource/doc/226155/0061245.pdf (Accessed: 6 November 2017).
• Tohi, K. (2016) Maths in Field Hockey. Available at: https://prezi.com/3mk2gu_u74ph/maths-in-field-hockey/ (Accessed: 6 November 2017).