Author Archives: Kaylan McAtear

maths and games

Todays input was on the math behind gaming. Myself and another classmate decided to look into the game rock paper scissors and surprisingly found out quite a lot.

First of all we looked a little into the history of the game and discovered that it was created in China, as far back as the time of Christ. The game then stayed in china for many years after that and then made its way into japan around the 1700s, which it then just kept travelling worldwide. In chinese it is called a Ken game.

The rules behind it are simple.

  • Scissors beats paper
  • Paper beats rock
  • Rock beats scissors
  • 2 players

The game only has 4 possible outcomes.

  • A tie
  • Rock beats scissors
  • Paper beats rock
  • Scissors beats paper

 

We thought about the math behind it. When actually playing the game it is statistically said that most people go for scissors first. Though realistically it is clear that the game relies on luck or perhaps pyschology.

Although the results show us that there is a very simple math behind it.

The probability of getting a certain outcome is ¼, 0.25, 25%.

It also highlights the use of chance within math and would be a very fun way for children to see this. It also shows that something so simple like a game of rock paper scissors has math within it and shows how crucial math is within our education system and the importance of a teacher with great confidence in teaching it.

The maths behind demand plannin in buisness.

When I first noticed we had a three hour slot of math today I was absolutely dreading it. However the three hours actually went buy so quickly. We were looking into demand planning and how it is used in businesses and the math behind it. I have worked in the hospitality industry before, therefore have had the opportunity to look into stock and how it works, and it was not until now that I realised the huge amount of math that is actually behind it and ensuring it is done correctly.

In the input today we were given the chance to work in pairs and “run our own business.” We were in charge of the order of stock for a whole year. The rules included that we could only buy 5 types of products at a time. Because of this we had to look at the time of year and decide what type of products we thought would sell the most, therefore earning the most money. for example in December we bought selection boxes, and in July we bought ice cream wafers.

After we made the decision with the products we had to find out the percentage of them that sold and calculate this to see how much of a profit we made. It required a lot of concentration and few of us did end up quite frustrated however the math behind it was countless and this was not made clear until after the first month of doing it.

In the end we got to see how successful we were through our overall profit starting from £5000.

This exercise I felt was a tough one, though it is one that I would like to do again. It is the perfect exercise I feel to show how math is used within the wider world and also how different topics within math are connected. It is also good for the repetition used throughout it as you are constantly having to do certain equations over and over again, therefore reinforcing them.

On a whole, I feel like this input today was very beneficial and actually quite shocking on how much math was used within this one simple task.

Image result for demand planning

The use of maths within music.

Music has always been a huge part of my life and not only because of my love for listening to it. Related imageI have grew up a dance so I have, from a young age, had to learn to count music and hear it. I then had to learn to read music as I began playing violin, guitar and percussion. I then took music as a subject in school for my whole six years of being there in which I was allowed to discover and learn about musical theory. Though despite this being such a huge and influential thing in my life, I have never seen any connection between math and music as subjects.

“Rhythm depends on arithmetic, harmony draws from basic numerical relationships, and the development of musical themes reflects the world of symmetry and geometry.Image result for music  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)

When reading this quote from Sautoy, it actually makes sense that math is used within music. There are many more examples on how music is used within math, those of which include; notevalues, tuning, scales, sequences and many more. Though it even goes back to basics such as counting and how it helps us in music.

In our lecture today we done an exercise in which we were split into groups and had to clap a different rhythm each whilst everyone else was doing theres. It took a few attempts for us to  get correct and it wasn’t until everyone had their counting correct that it actually worked. I feel like was such a simple example that was used but is one I would love to use in the future within my classroom teaching.

We then looked at note values and how each note has a different length, for example a crotchet is one beat and a quaver is half a note. For someone to be able to read music, it is Related imageessential that they understand all of this and therefore have to have a basic knowledge on the math behind the notes.

Overall there are many examples of how music is used within math. It is something that is actually incredibly important and I feel should be taught more about in schools. It is possible that it may actually help increase children’s positivity towards math as children seem more than likely to enjoy studying music in school, especially at a young age as it is perceived as being fun.

References

Du Sautoy, M. (2011).  ‘Listen by numbers: music and maths’ Guardian.  Available
http://theclassicalsuite.com/2011/06/listen-by-numbers-music-and-maths-via-guardian/

Can animals count?

Can animals count is one of those questions that to me, is alongside can animals talk? Well it certainly was until after leaving a recent input on the question. It seems ridiculous to say that animals can count although upon further research I think it may seem ridiculous to say that they have no number sense at all.

imageThe clever hans effect is something that we came across in today’s input. This input is all to do with a horse named hands who’s owner, believed that they had trained him to add, multiply, subtract, understand fractions and other mathematical things. He would be asked a question by his owner and would respond his answer with the tapping of his hoof. Scientists were amazed at this discovery as It was observed through experiments that hans would answer correctly 89% of the time which is a pretty amazing figure for a horse.
It was then found upon further tests and discoveries that hans in fact was not responding to the maths question but to his owners reactions. He knew when to gradually slow down the tapping of his hoof and to eventually stop.

Although not responding to the mathematical questions, this was still a very clever horse as he knew what was expected off him and how to react to things. This though put a doubt into mind wether I think animals can count or not.

When I came home I then read into an article on the BBC website as to wether or not animals can count and found out some interesting stuff.

An interesting read I found was that Serengeti lions and their ability to look at smaller and large groups and know what one is the biggest. This ultimately is a basic maths skill as it is something that we teach within a classroom. We teach children to look at quantities and to know which one is largest and smallest.

Another interesting read within this article was about animals when they mate. It can be difficult for animals to mate as many of them look very similar. Frogs as an animal, help find a mate by the pulses in their croak. They need to count the number of pulses in their croak and can do so in phrases of up to 10 notes long. It is believed that they measure the volume and length of the others croak.
Again this shows that animals do have a sense of numeracy and maths.

For one I am still dubious as to my answer on this particular subject, although the after some research I am swaying more towards believing that they can. Is has been a to
If that has very much interested me and is something that I would again, look into in the future.

Finger Counting?

As a topic, this has always been one that I am willing to debate. It goes without saying, all of us will probably have been told off once or twice for using our fingers to count. But why is this an issue?
As an adult I still find myself from time to time using my hands for maths, hiding my hands under the table trying not to get embarrassed by it. Personally, I believe that as teachers we should be encouraging the use of hands in maths. They are tools that we have right in front of us, so why not!
For some, the use of their hands in maths is a sort of comfort zone. It helps with confidence levels in ensuring that they are doing their maths and counting correct. It can also make maths easier for people.
The above video was something I found recently, and had never in fact seen or heard of before, and I certainly wish I had. The six, seven and eight times tables were always ones that I struggled with in school and now wish I knew this trick to help me with them. It is so easy and simple to use and takes less than a minute to do. This could make so many children’s life’s easier and boost their confidence in maths. It also makes maths seem even so slightly more fun.
This is not the only trick out there we can do with our fingers in maths. Simply type in finger counting and millions come up on YouTube. It should be essential that teachers teach and utilise these within their lessons as it may just make a difference to some of their students. They would certainly have made a difference to myself.

 

Before discovering mathematics

Before doing the discovering maths module this year, I was feeling worried about beginning it. Maths has never been my strong point nor will it probably ever be. It has also never been something that I have enjoyed whilst being at school. This is the reason behind me choosing to do is module as as an aspiring teacher I feel that my views have to change on the subject. I also feel that it is essential that I break down the front I put up in relation to maths as a subject.

As a student in school I was always told that maths was not my strong point and to stick to other subject such as English an expressive arts. This I feel, created my views and attitudes towards maths and ultimately affected my ability to do well in the subject. I was always doubted as a “mathematician” therefore I doubted myself.

When applying to do teaching at university I hesitated. How could I possibly ever teach someone how to do maths? I was encouraged by my teachers and family that this attitude I have will change throughout my studies and that I would soon learn to love maths as a subject.

Coming out of first year at university, I would not say my views on the subject have changed greatly. However it has been so encouraging for me as an individual to see that I am not the only one with these views and worries.

After having learnt about the discovering maths module, I was certain that this module was for me. Throughout this module I hope to break down the barriers that are stopping me from enjoying maths, and perhaps fine a true love for the subject.

image

science literacy

According to the Programme for International Student Assessment (2006): “Scientific literacy is the capacity to use scientific knowledge, to identify questions and to draw evidence-based conclusions.” In other words scientific literacy can be defined as the knowledge and understanding behind a range of scientific concepts and processes that we use in day-to-day life in varying contexts. According to NWS (2011) students are scientifically literate they are aware and have an understanding of various scientific concepts which apply to their life within society. Furthermore these pupils will be able to read articles and then evaluate the quality of the information through applying their previous understanding. Another aspect that a pupil who is scientifically literate will be able to undertake is pin pointing specific scientific issues that influence local and central government. The term scientific literacy can therefore be referred to as an umbrella term as it refers to a number of areas.

 

For those who do not have a good grasp of scientific literacy it can be hard to make sense of news articles and reports, journals and even published papers which often include scientific jargon incomprehensible to the ‘everyday’ person. And so when articles and papers are published containing ideas which people cannot fully understand the instinctual response is to follow what others are doing in reaction. This is exactly what happened with the MMR scandal. A paper published by Andrew Wakefield stated that the MMR vaccination could have potential links to autism, and therefore giving your child this vaccination would increase their chance of becoming autistic. This paper was held with high regard due to the credibility of its author and publisher. For many people this paper would be far too advanced to unpick and evaluate without appropriate scientific literacy and so newspapers began to publish articles in a simpler language for people to understand. However this paper published by Wakefield was later found to be biased and based upon unfair testing and untruths. And so in fear, provoked by media pressure, many parents chose to withhold the MMR vaccination for their child, therefore putting their child at a higher risk of contracting measles, mumps and rubella. This was caused by a lack of scientific literacy allowing an informed decision to be made and this is why being scientifically literate is so important.

 

When doing a science experiment in a classroom it is crucial to do the test fairly to get the best possible results. Fair testing is the process of changing a different factor of the experiment and keeping the rest the exact same in order to achieve the most reliable results. There are multiple ways in which you can conduct change factors in an experiment in order to receive the best and most reliable results. Examples of the different things you could change whilst conducting science experiments could be changing the PH levels, the amount of a specific factor, the volume of a specific factor or the materials used. Fair testing in science can teach children multiple things. For example after a fair testing experiment has been carried out, it will allow the children to write up an effective conclusion about the experiment as they will have the evidence to do so. Fair testing links to science literacy as it has the children thinking and discussing the most effective ways in which to carry out an experiment

 

Scientific Literacy is not just having the knowledge, but is also having the understanding of scientific concepts. Meaning, that a person has the ability to explain and predicted natural phenomena. National Academy Press states; “A literate citizen should be able to evaluate the quality of scientific information on the basis of its source and the methods used to generate it.” Enforce the notion that a person who is scientifically literate should be able to explain how just the how but the why. All of this portraying the thought that you would need to know everything about science in order to be scientifically literate. However, this is false. “You can be scientifically literate without knowing how a superconductor works at the atomic level, what the various species of superconductor are or how one could go about fabricating a superconducting material.” This quote from Hazen. H and Terfil. J indicates that in order to be scientifically literate you do not need to know everything about science, but have a basic understanding of the matter being discussed.

Reference List:

Greenslade, R. (2013) “The story behind the MMR Scare” 25th April. Available at: http://www.theguardian.com/society/2013/apr/25/mmr-scare-analysis [Accessed: 13/02/16]

H Hazen. H & Trefil. J (2009) Science Matters: Achieving Scientific Literacy. United States of America.

National Academy Press (1998) National Science Education Standards. United States of America: Washington, DC.

NSW Department of Education and Communities: What is Scientific Literacy? Available at:

http://www.curriculumsupport.education.nsw.gov.au/investigate/ [Accessed: 13/02/16]

PISA Programme for International Student Assessment: Scientific Literacy. (2006) Available at:

http://www.pisa2006.helsinki.fi/oecd_pisa/pisa_in_a_nutshell/scientific_literacy.htm [Accessed: 12/02/16]

Jessica Murray, Megan Gowens, Amy Louise Burnett, Kaylan McAtear