Maths in Computer Games

Introduction

Before this input, I knew there was a huge amount of maths involved in computer games. However, I hadn’t  given this much thought as I assumed this was far beyond anything I would be able to understand with my knowledge of maths. So my question is: which elements of fundamental mathematics do I need to  help to understand complex mathematics used in computer games?

Counting

Number systems and counting are of clear importance when it comes to computer games. I have a deeper understanding of this based on previous experiences in this module. We learned that base twenty system was used for counting due to having ten fingers and ten toes. Learning of the Mayan’s using a base twenty number system encouraged me to think of the differences made when the base is changed. Lumen (undated) states ‘the Mayans used a base-20 system, called the “vigesimal” system. Like our system, it is positional, meaning that the position of a numeric symbol indicates its place value’. This means that a base twenty number system is also positional in the same way that our base ten system is.

Image result for mayan number system

Although I do understand what base ten number system is, I decided to explore it further to deepen my understanding. Killian (2012a) states ‘the process repeats over and over, and eventually you get to 99, where you can’t make any larger numbers with two digits, so you add another, giving you 100’. So if this explains the system when counting, what happens when it comes to large numbers? Smith and LeVeque (undated) state ‘when it became necessary to count frequently to numbers larger than 10 or so, the numeration had to be systematized and simplified; this was commonly done through use of a group unit or base’. Therefore, as maths grew more complicated, our number system had to be adapted to become easier to work with.

Binary

Computers use a base two number system as they work in a different way but an understanding of number systems allows for understanding this process to become much easier. Killian (2012b) states ‘ while everyone knows binary is made up of 0s and 1s, it is important to understand that it is no different mathematically than any other base’. This made the idea of binary seem more approachable as someone who has no previous knowledge on the subject. I had a grasp of the concept of binary but in order to have a thorough understanding I looked into comparing binary to our number system.

Therefore, binary operates on a very small base 2 number system, this means that computers can only tell if a wire is on or off. Binary also operates in eights which makes the process much clearer to me. This has simplified for me a process which I previously thought would be highly complicated. This has highlighted for me the importance of independent research in order to deepen my understanding. With a better knowledge I will feel less intimidated when exploring different and interesting areas where maths can be applied with my pupils.

Image result for scratch

Now that I have this knowledge, I will be able to provide a much richer experience in practice. On my first placement, the pupils were using a programme called ‘Scratch’ in their ICT lessons. I saw the basic idea that they were programming their own games but did not understand much deeper than this. I feel that now I would be able to provide sufficient explanations and make connections with maths in ICT which could bring this to life.

Conclusion

Therefore, the list of mathematical processes involved in computer games is endless. However, a huge part of this is number, number systems and place values. Having an understanding of this can simplify understanding a topic which may otherwise seem too complex. I think that if pupils if teachers can explain the maths behind a topic such as computer games, they will be more engaged and motivated.

References

Killian, J. (2012). ‘Number Systems: An Introduction to Binary, Hexadecimal, and More’. Available at: https://code.tutsplus.com/articles/number-systems-an-introduction-to-binary-hexadecimal-and-more–active-10848. (Accessed: 9/11/18).

Lumen (undated). ‘The Mayan Numeral System: Mathematics for the Liberal Arts’. Available at: https://courses.lumenlearning.com/waymakermath4libarts/chapter/the-mayan-numeral-system/. (Accessed: 9/11/18).

Smith, E, D, LeVeque, J,W. (2012). ‘Numerals and numeral systems’. Available at: https://www.britannica.com/science/numeral. (Accessed: 9/11/18).

Images

https://en.wikipedia.org/wiki/Maya_numerals

https://scratch.mit.edu/

Taking Maths Outdoors

Introduction

The concept of taking learning outdoor is something I am familiar with. However, I would associate this with subject such as language, gym or science. I have given a lot of thought to thinking beyond the classroom in maths but i had not considered the benefits of physically taking maths outside. So my question for this post is, which elements of fundamental mathematics can be developed effectively outdoors?

Image result for outdoor maths

Angles

After doing some research and thinking back to my first placement, measurement and angles stood out in particular. There are multiple ways to include variation in the teaching of angles within the classroom. However, it is important to think creatively, something I have discovered in previous posts. Haylock (2007, p. 266) explains that ‘when teaching about angles, do not always draw diagrams or give examples in which one of the lines is horizontal’. This further explains this idea that angle should be taught in a multitude of ways.

Image result for types of angles primary school

I also think that this can be related to one of the CfE defined principles of relevance, Scottish Government (2017). If children are only calculating angles in a textbook, they may struggle to see the relevance of angle in the real world.

Measurement 

The points made are similar when it comes to measurement, creative teaching is also key. Hansen (2006, p. 104) states ‘children begin to form an idea naut length when objects can be matched and compared’. This will be far easier to do if children can compare and contrast different objects or buildings outside. An example of this on my first placement was when the pupils went outside to calculate the perimeter of the school. This brought their previous learning to life.

Outdoor Learning

Outdoor learning can be an effective means of teaching maths. NCTEM (2015) states ‘getting out of the classroom facilitates authentic or experiential learning (the engagement of learners with the world as they actually experience it)’. Throughout this module I have realised the importance of valuable experiences in maths. Therefore as a teacher it is important to enrich the pupils learning by providing experiences such as fun outdoor lessons. A change of environment could also be refreshing for the class. Maynard and Waters (2007, p.260) states ‘while the teachers indicated that they were unsure whether or not they should change their pedagogical approach when working outside, several indicated that they felt more relaxed outdoors’. Therefore being outside could be a nice change from learning in the classroom. I  have also considered maths anxiety a lot throughout this module and learning outdoors could be a means of creating a more relaxed and positive attitude towards maths. Pupils could begin to see the real life maths and have less anxiety out with the confines of the classroom.

Image result for maths outside

It is particularly important to make use of the materials outside, as opposed to conducting a lesson created for indoors outside. Bilton (2010, p. 4)  ‘quality outdoor provision would incorporate this type of practice, but merely taking indoor equipment outside does not constitute quality outdoor provision’. This could be implemented by basing the lesson on objects outdoors or buildings. For example calculating the diameter of a tree or perimeter of a building. This could also involve using materials found outside, this will encourage pupils to discover for themselves and find innovative ways to use maths outside.

Conclusion

Therefore, angles and measurement are key fundamental maths skills that can be explored outdoors. However, materials outdoors can be used to create lessons in any area of mathematics. This can bring a change of scenery for peoples which could engage and motivate them. It will also highlight the relevance by bringing mathematics out of the classroom and making fun activities outdoors.

 

References

Education Scotland (2017) What is Curriculum for Excellence? Available at: https://education.gov.scot/scottish-education-system/policy-for-scottish-education/policy-drivers/cfe-(building-from-the-statement-appendix-incl-btc1-5)/What%20is%20Curriculum%20for%20Excellence (Accessed: 8/11/18)

Hansen, A. (ed.) (2006). Children’s Errors in Mathematics. Understanding Common Misconceptions in Primary Schools. London: Learning Matters Ltd.

Haylock, D. (2007) Mathematics Explained for Primary Teachers. London: Sage Publishers.

Maynard, T,  Waters, J. (2007) Learning in the outdoor environment: a
missed opportunity?. Available at: https://www.tandfonline.com/doi/abs/10.1080/09575140701594400#aHR0cHM6Ly93d3cudGFuZGZvbmxpbmUuY29tL2RvaS9wZGYvMTAuMTA4MC8wOTU3NTE0MDcwMTU5NDQwMD9uZWVkQWNjZXNzPXRydWVAQEAw. (Accessed: 6/11/18)

 

National Centre for the Excellence of Teaching Maths (2018). Numicon. Available at:https://www.ncetm.org.uk/public/files/266859/Sue_Rayner_Resource_Sheet_A.pdf. (Accessed: 7/11/18).

Images:

https://www.tts-group.co.uk/maths-outdoor-grab-and-go-foundation-kit/1002001.html

https://www.pinterest.co.uk/pin/2251868538674324/

What are the Chances?

Introduction

When I think of learning about probability, all I remember is discussing the chances of rolling each number on a dice. Although this is an effective way to teach probability, my question for this week is: what are the methods that can be used to teach probability?

Gambling

I knew that gambling was all about statistics but I had not considered the fact that games in casinos are probability on a large scale. Akusobi (2010) states ‘all events in gambling games have absolute probabilities that depend on sample spaces, or the total number of possible outcomes’. This means that professional gamblers constantly asses the risk and chances of certain outcomes. This highlighted for me an application of probability that is widely used in casinos all over the world.

Image result for casino

A game such as roulette has an element of subjective probability. Investopedia (undated) states ‘it contains no formal calculations and only reflects the subject’s opinions and past experience’. For example, if it has landed on black six times in a row, a person may take the subjective probability approach and assume it will land on red next. This is based on the past experience of several of the same colour in a row. There would be no calculations in this, instead it is a logical assumption. Looking into the mathematics behind gambling brought forward the relevance and applications for me. I think that it is therefore important to make it relevant for the pupils I will teach.

Tossing a Coin

We experimented with tossing a coin in class to explore the probability. We first wrote down our predicted results without tossing a coin and then compared this with results when using a coin. We found that nobody had written the same outcome more than five times in a row. I think this was an example of us applying subjective probability. We all assumed that the chances of the same outcome appearing several times in a row was small. This is because we know that there are only two outcomes and would assume that the number of times for each outcome would be relatively equal. McCluskey and Lalkhen (2017) further explain ‘common sense tell us that, provided the coin is unbiased with heads just as likely to fall as tails, the ratio of heads:tails should be 1:1 and therefore the ‘expected’ outcome after 20 tosses would be 10 heads’. This confirms this idea that we all made an assumption based on the probability that we thought was most likely using common sense.

Image result for tossing a coin

Rolling a Dice

Starting with the most common example when teaching probability, the dice. Probability is the chance or something happening and in this case, what the chances are of rolling each number. BBC (undated) states ‘there is one way of rolling a 4 and there are six possible outcomes, so the probability of rolling a 4 on a dice is 1/6. This is called the ‘theoretical probability’ – in theory, if you roll a dice six times then you should roll a 4 once’. It is therefore important to highlight to pupils that this is simply a theoretical probability. However, I think that of we were to explain this to pupils, they may not fully understand. I think it is important to let pupils explore and discover this theoretical probability for themselves. For example, rolling a dice for themselves and recording results. Exploring this concept independently will give the pupils a more thorough understanding of probability.

Image result for roll a dice

Terms

Now that my own knowledge of probability is better, I have realised the concept does not need to be taught in isolation. I think it could be effective to teach probability within other activities. For example, when the pupils are playing games. The pupils could explore what the odds are of winning or losing. This could promote discussion about maths. Pupils should first have an understanding of the terms. MCA Online (2017) explains the terms as impossible, unlikely, even chance, likely and certain. I think it would be effective to encourage pupils to identify the probability of different situations using these terms. This will encourage a consideration of the application of probability in daily life.

Conclusion

Therefore, my experience of learning about probability made it a far more interesting concept for me. It has also allowed me to see the applications of it elsewhere. This means that I have a much deeper understanding of the topic. This has also shown me that I must provide the same experience for pupils. They should also have the opportunity to learn in interesting and engaging ways in order to build a positive relationship with mathematics.

References

Akusobi, C. (2010). ‘Should You Bet On It? The Mathematics of Gambling’. Available at: http://www.yalescientific.org/2010/02/should-you-bet-on-it-the-mathematics-of-gambling/. (Accessed: 30/10/18).

BBC (undated). ‘Probability’. Available at: https://www.bbc.com/bitesize/guides/zsrq6yc/revision/2. (Accessed: 30/10/18).

McCluskey, A, Lalkhen, G, A. ‘Statistics III: Probability and statistical tests’. Continuing Education in Anaesthesia Critical Care & Pain. Volume 7, Issue 5. Available at: https://academic.oup.com/bjaed/article/7/5/167/534620. (Accessed: 30/10/18)

Victoria University (2017). ‘Basic definitions and concepts’. Available at: http://www.staff.vu.edu.au/mcaonline/units/probability/procon.html. (Accessed: 31/10/18)

Images

The Traveller’s Guide to the Best Manchester Land-Based Casinos

https://www.thoughtco.com/thmb/lvjed7xsmt0LaJWwoYxg-GadMNc=/768×0/filters:no_upscale():max_bytes(150000):strip_icc()/TwoDice-58bddad45f9b58af5c4aa0d4.jpg

http://math.ucr.edu/home/baez/games/games_9.html

Counting on Technology

An abacus is used to help solve maths problems. After researching and teaching myself how an abacus is used, it prompted my question for this week; are mathematical tools as effective as technology today?

Abacus

Lumen (2018) explains ‘the idea of number and the process of counting goes back far beyond history began to be recorded. There is some archeological evidence that suggests that humans were counting as far back as 50,000 years ago’. It is important to have an understanding of the history of our maths and number systems in order to have an appreciation for it. It can also allow us to see how counting has progressed over time. This can be useful to highlight to pupils as it can give them a more broad view of mathematics if they can see where concepts originated and progressed.

So why did counting systems evolve is they previously were non existent? Lumen (2018) states ‘as societies and humankind evolved, simply having a sense of more or less, even or odd, etc., would prove to be insufficient to meet the needs of everyday living’. This can highlight the relevance of counting as a part of maths as it was needed for everyday living. Emphasising the relevance of concepts in maths is becoming a common theme as I progress through this module as I find myself searching for the real life contexts.

Therefore, if tools such as an abacus were created in order to meet the needs of daily living, it would make sense for them to still be of use today. Although technology may solve problems faster or more easily, physical tools can still provide an effective learning experience for children.

Counting Tools Today

These methods made me think about a tool used in maths today called Numicon. When using this on my professional practice, I found that children engaged with it much more positively as they found it interesting and enjoyable. NCTEM (2018) states ‘when Numicon patterns are arranged in order, pupils begin to notice important connections between numbers for instance that each number is one more than the last and one fewer than the next, odd and even numbers and place value’. Pupils who would otherwise refuse to engage with mathematics would thoroughly enjoy activities using these tools. This was because they perhaps felt as though they were not doing maths, or what they perceived it to be. This highlighted for me that it was not maths itself that caused the pupils to be reluctant but their attitudes to traditional maths learning. This further reinforces the idea of relevance that is essential in maths understanding. This also answers my question as to why tools such as these are still used in place of technology. These number tools are also versatile and perhaps this is why they have adapted with the times and are still relevant.

Calculators 

Forrester (2003, p.8) proposes the idea that it is more effective to have children use a calculator to discover how many ways to make the number ten as opposed to using a calculator to solve a series of problems. This is an example of children gaining a deeper understanding of mathematics and using tools to discover and investigate for themselves. Forrester (2003, p. 8) also states ‘a class set of graphic calculators allows each pupil to have a simple ‘mini-computer’ at their own desk, available when required without a trip to the school computer suite’. This means that using calculators in class provides pupils with a small piece of technology that is easily accessible and can be used within the classroom. This could mean more opportunity for solving maths problems in less traditional ways and more chance for pupils to investigate maths for themselves.

Technology

Forrester (2003, p.2) explains it is important as teachers to constantly be aware of changes in technology in order to provide an effective learning experience. This means that as part of continuing professional development, teachers should keep updated with implementing technology to teach maths. Forrester (2003, p. 3) states ‘teachers have now been struggling for many years to integrate calculators and computers effectively into their day-to-day teaching’ this means that although some teachers may be capable of bringing new technologies into the classroom, they are finding it difficult to implement this. I therefore think that it is important to continue to be creative and inventive in teaching mathematics in order to implement tools and technologies effectively.

Conclusion

Therefore, physical tools and objects are still useful in classrooms today. These tools such are versatile and provide a different learning experience for pupils, stepping away from traditional methods. It also allows them to develop a deeper understanding through their own investigation. Technology today is also a useful tool in mathematics but in order to be effective, teachers should take the responsibility to stay updated and be creative.

References

Lumen Learning Mathematics for the Liberal Arts (2018). Early Counting Systems. Available at: https://courses.lumenlearning.com/math4liberalarts/chapter/early-counting-systems/. (Accessed: 17/10/18).

National Centre for the Excellence of Teaching Maths (2018). Numicon. Available at:https://www.ncetm.org.uk/public/files/266859/Sue_Rayner_Resource_Sheet_A.pdf. (Accessed: 17/10/18).

Way, Jenni, and Toni Beardon (2003). ICT and Primary Mathematics. England: Open University Press.

The HEV Project. (2013). Abacus Lesson 1: Introduction, Proper Technique and History of the abacus.(online video). Available at: https://www.youtube.com/watch?v=SkUdjlQy3rk. (Accessed: 23/10/18)

 

The Art of Maths

When this concept was explained in our lecture, I did not fully understand. I feel this may happen many more times throughout the module as I familiarise myself with maths again. I decided to remain positive towards maths and explore the idea for myself until I both understood the how and the why. I think that I understand that there must be some element of mathematics within art. However I did not fully appreciate how interesting this is or exactly how it works. I have aways found maths intimidating and daunting. So my question for this week is; can I find the beauty in maths for myself?

Mark Warner (2015) discusses the idea that digital roots can provide a visual representation of the multiplication tables. As a visual learner, I found this helpful as I can link a mathematical concept to something almost artistic. I think that in the classroom, pupils who may struggle with the traditional learning methods of maths may find an exercise such as this helpful. I also now see the importance as it could be of benefit to children should they be able to identify and create patterns. This could bring forth the relevance of mathematics for children which is essential if they are to have the motivation to learn. Not only can I now appreciate how the digital roots work but I also can appreciate how clever it really is. Exploring times tables in this way would be an enjoyable and different experience for children whilst deepening and broadening their understanding of maths.

The National Centre for Excellence in the Teaching of Maths (2011) explains that creating art with maths must begin with an understanding of shape. My experience of observing shape taught was solely classifying and memorising the properties of shapes.  This is a good basis for understanding but should be explored further. Haylock (2007) explains ‘this process of classifying and naming leads to a greater confidence in handling shapes and a better awareness of the shapes that make up the world around us’. Exploring shape through art can bring relevance and a real life context which can solidify this learning for pupils.

Being able to tie together mathematics with art will highlight for children the importance and relevance of maths in daily life. I think it is important when learning maths to occasionally detach the concept from their traditional exercises and relate them to real life situations. Education Scotland (2018) highlight one of the key principles as relevance meaning this is essential to the curriculum. It is also a word I heavily associate with maths, bringing forward the relevance is key in my personal experience in order to give me the motivation.

I decided to explore interesting ways of intertwining art in maths to highlight the relevance of maths in what we see around us.

Architecture

Image result for pretty architecture                                            http://prettyarchitecture.tumblr.com

Using the example of architecture can show pupils how amazing maths and its uses can be. This is something I did not think about for myself but so much architecture is beautiful and would not be possible without maths. David Mumford (2006) states ‘the beauty of mathematics is very similar to the beauty one finds in abstract art or architecture, or in music’. Images such as these illustrate the beauty of mathematics. I think that making pupils feel inspired by mathematics could be a step in the direction of creating a more positive attitude towards maths.

Islamic Art

Creating Islamic art in classrooms can also be an interesting way of exploring maths. Salim Al-Hassani (2007) explains that ‘Girih designs feature arrays of tessellating polygons of multiple shapes, and are often overlaid with a zigzag network of lines’. This gave me some context for the concept of tessellation and an example of its use. I think that for teachers to have confidence and competence to teach maths, it is important for them to appreciate  the relevance of maths for themselves.

Image result for islamic art

The Maths

It is all very well that I now can appreciate the maths in art but i still wanted to understand.

0 , 1 , 1 , 2 , 3 , 5 , 8 , 13 , 21 , 34 , ? , ? , ?..

I first of all wanted to know where the Fibonacci Sequence came from. Tyler Clancy (undated) states ‘first derived from the famous “rabbit problem” of 1228, the Fibonacci numbers were originally used to represent the number of pairs of rabbits born of one pair in a certain population’. Therefore a number sequence was used to tackle a real life problem. This gave me an idea of the importance of the Fibonacci Sequence. However, I was still thinking, why would this be important for me to know? Dan Reich (undated) further describes that the sequence spans so much further than it’s original purpose as it can be used in so many other contexts. This means that perhaps understanding the sequence could give me a wider and deeper understanding of mathematics which is an aim I have for myself throughout this module.

Fibonacci in Nature

The Fibonacci Sequence can be used to highlight patterns in nature. Dr Ronn Knott (2016) explains ‘on many plants, the number of petals is a Fibonacci number: buttercups have 5 petals; lilies and iris have 3 petals; some delphiniums have 8..’. This provides a basis for many lessons which can give maths a real life context. This also further develops a point made in my previous blog post about the necessity of highlighting relevance in maths. I can also see a positive to this as it can encourage exploration of maths and number. This is important in itself as I wanted to have a more positive attitude towards maths.

Image result for fibonacci in nature

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Fibonacci in Art

Expanding on this point about encouraging children to explore the maths in the world, another example is art. This is all down to the ‘golden ratio’. Elaine Hom (2013) explains ‘The Golden ratio is a special number found by dividing a line into two parts so that the longer part divided by the smaller part is also equal to the whole length divided by the longer part’.

Image result for fibonacci in art

e497361febd1b367305101943598c634.jpg

Looking into images and seeing them as more than they are can motivate children to think deeper about maths and make discoveries for themselves.

Conclusion

I am beginning to see development of a deeper understanding as a key theme in the module. My own experience of mathematics left me with a profoundly surface level understanding of maths and I wish to give my pupils a richer experience. My research for this blog post has given me a new appreciation for maths and all of the beauty around us that would not be possible if not for maths. I also feel motivated to become more confident in the subject for myself because the love of maths in the future begins in the classroom.

References

Al Hassani, S. New Discoveries in the Islamic Complex of Mathematics, Architecture and Art. Available at:  http://www.muslimheritage.com/article/new-discoveries-in-islamic-complex. (Accessed: 27/9/18)

Education Scotland (2017) What is Curriculum for Excellence? Available at: https://education.gov.scot/scottish-education-system/policy-for-scottish-education/policy-drivers/cfe-(building-from-the-statement-appendix-incl-btc1-5)/What%20is%20Curriculum%20for%20Excellence (Accessed: 27/918)

Haylock, D. (2007) Mathematics Explained for Primary Teachers. London: Sage Publishers.

J. Hom, E. (2013). What is the Golden Ratio?. Available at: https://www.livescience.com/37704-phi-golden-ratio.html (Accessed: 5/10/18)

Knotts, R. (2016). The Mathematical Magic of the Fibonacci. Available at: http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibmaths.html (Accessed: 6/10/18)

Mumford, D. (2006) as cited in CECM (undated). Mathematics belongs in a liberal education. Available at: http://www.cecm.sfu.ca/~pborwein/pborwein_resources/Architecture.pdf. (Accessed: 27/918)

NCTEM Admin (2011)  The Art of Mathematics. Available at: https://www.ncetm.org.uk/resources/18030. (Accessed: 27/9/18)

Reich, D. (undated) The Fibonacci Sequence, Spirals and the Golden Mean. Available at: https://math.temple.edu/~reich/Fib/fibo.html. (Accessed: 6/10/18)

Warner, M. (2015). Available at: https://www.teachingideas.co.uk/number-patterns/digital-root-patterns. (Accessed: 28th September 2018).

 

Afraid of Maths?

‘Maths Anxiety’

Mathematics is a subject area that is often highly associated with negativity and anxiety. Much of this occurs in adults and stems from previous experiences. Haylock (2006 p2) states that “there are widespread confusions amongst the adult population in Britain about many of the basic mathematical processes.” This misunderstanding creates a negative attitude and thus formulates anxiety amongst student and qualified teachers. It is vital as a teacher to have understanding and confidence with mathematics. Haylock (2006 p1) states “one of the best ways for children to learn and understand much of the mathematics in the primary-school curriculum is for a teacher who understands it to explain it to them”. The key elements here are understanding and explanation. Teachers have a responsibility to the children they teach and a part of this is to have a sound knowledge of subjects in order to explain and enrich the pupil’s learning experience. A solid basis of understanding will mean that teachers can ensure that pupils are appropriately progressing through the curriculum.

My Anxiety with Maths

The day of the first input on Discovering Mathematics, I found myself feeling extremely anxious and questioning why I had chosen the module in the first place.

To my surprise, most others in the class appeared to have the same mindset. With either a lacking confidence or general dislike for mathematics. During the input, the question was raised; can you actually dislike maths as a whole? Mathematics covers so many bases that to dismiss the entire subject is quite a statement. This encouraged me to question my own supposed dislike of the subject.

My Relationship with Maths

In the 4 years since passing my higher maths, I have had an admittedly negative and dismissive attitude to the subject entirely. If the word ‘maths’ or anything related pops up, my immediate response is to exclaim how much I hate maths. Thinking deeper, I don’t believe that I hate maths. I think perhaps I have just complaisant and accepted that I have little confidence in maths. Until now, it has been easy enough to say that I don’t like maths and move on. However, I think this is a mask for my lacking confidence.

Hopes?

I think this module will teach me new and improved approaches to the teaching of mathematics. In turn hopefully boosting my confidence to appear in front of a class and teach maths well. After just one week, I can see the importance of encouraging enthusiasm and confidence with my pupils. I also am hopeful that this module will rebuild my personal relationship with maths.

My aim for this module is to deepen my understanding and break down the personal barriers I have with mathematics. I think this all begins with a willingness to change my attitude towards a subject I have never really enjoyed and this elective is a positive step in this direction.

To end, I discovered this video. These children are commenting on their feelings towards mathematics. This really hit home for me as I realised that i have made every single one of these comments myself as an adult. So I want to improve my maths-esteem.

References 

With Maths I can. (2016). With Maths I can. Available: https://www.youtube.com/watch?v=sLPFaOvhlKw. Last accessed 16th September 2018

Haylock, D. (2006) Mathematics Explained for Primary Teachers. London: Sage Publishers.

Reflection of MA1

As we have heard in many of our lectures, ‘a teacher’s work is never done’. I also think that a student teacher’s work is never done because there is a responsibility for constant personal and professional development. I am the type of person who likes to be organised and always on top of my work. However I think it is also important to accept that this isn’t always possible. In semester one I discovered a good balance that meant I could enjoy the experience of university but also prevent myself from becoming stressed. I found starting university to be a big change. I was very worried about writing the assignments as I felt as though I it was a big essay to tackle. However, I decided to start very early in order to give myself time and be less stressed. In the first few weeks I hadn’t learned enough on the topics to begin the essay so I started by breaking down the question and planned the essay and built on it as the weeks went by. So I think I can apply the way I wrote my first essays to writing this semesters assignments. In turn this will take some pressure off of semester two. In a more general way I can also plan ahead because I know if I let work build up it effects how I feel. I think that often we reflect when things go wrong in order to adapt for the future but thinking over the positive can also be useful. If we discover a technique that works it is good to reflect on this to carry it on into the future.

Second semester really solidified for me that I had made the right decision and this was the path for me. I took what I had learned from semester one to improve my assignments. I believe I did well in my semester one assessments, but I think for continued professional development, it is crucial to know that there is always opportunity for improvement.

Professional practice was an experience unlike any other. Due to my nature of being well organised, I really enjoyed the challenge of the folder.  it also gave me my first experience to really be a ‘professional’. The teaching practice itself was an extremely valuable and enjoyable experience. I know that I am lucky to have had a positive experience and I really appreciated the support I was given.

First year of university has diminished any anxieties I had about my choice and given me the motivation to continue to develop and do my absolute best throughout the rest of university and into my career.

Scientific Literacy (MA1)

Scientific Literacy and Education

Scientific literacy is becoming a prominent feature within education. In the Science Principles and Practice section of the Curriculum for Excellence (CfE) (2010) there is an emphasis on this area and that we, as teachers, should be developing scientific literacy within our pupils.

When first being introduced to scientific literacy our thought was that it was based upon knowing a range of scientific language and being able to use them appropriately, but that is the complete opposite of the true definition of scientific literacy. After doing some reading (W. Harlen and A. Qualter, 2009), it was clear that scientific literacy is more than simply understanding scientific language. The definition of scientific literacy is connecting the knowledge children have in science to real life events, so they can analyse and evaluate science based articles to ensure what they are reading is scientifically accurate. Therefore, they will be able to understand that they should not always believe what they read about science in the media. This is a very important aspect we should be teaching children as previous media reports have shown how the public can be easily led by “scientific based” news stories.

The knowledge of scientific literacy is extremely important, especially when you look at examples of when the lack of knowledge has been proven to be dangerous in society. In 1998, a doctor named Andrew Wakefield released a paper on the research he had been doing about the link between the MMR vaccine and autism. As this research was released by an extremely respected medical journal, Lancet, editors and members of the public started to panic. Suddenly anti-MMR stories started to be printed by many other newspapers as people were coming forward with their stories. The country begun to think they had been lied to by the medical authorities and turned to the government for reassurance. The press asked the prime minister at the time, Tony Blair, what his thoughts on the vaccine were and if he would give it to his son, Leo. He refused to answer and this lead to many stories on the MMR scare being about his son in 2002. Thankfully, an investigation in 2004 led to Lancet coming forward and admitting that the research by Andrew Wakefield was improper and inaccurate. Unfortunately, even after all of this, people still doubted the vaccine and this is all down to the lack in knowledge of scientific literacy. If the public had been scientifically literate, they would have been able to analyse

the article and realise for themselves that it was based on inaccurate research and was an unfair experiment. Therefore, it is important to teach scientific literacy within school, through teaching things like fair testing.

Fair testing in science is the process of carrying out a controlled investigation in order to answer a scientific question. Children need to understand that a test is only fair if only one variable is changed during the experiment. Pupils will experiment in science the whole way through school. Therefore, they will develop their skills and knowledge of fair testing and why it is important. It is essential that teachers understand fair testing themselves so as to explain the terminology and concepts of a scientific experiment to pupils. (The School Run, 2018). Scientific literacy is not knowing lots of scientific facts. It is instead an understanding of how science actually works. It is important for children to have good scientific literacy as they progress through school and into further life. Practicing fair testing during school will help them explore science rather than simply learn and retain facts. It is therefore essential as pupils will learn the proper ways to test in science and will be encouraged to answer questions and discover for themselves. Using fair testing through experimentation could create a more positive attitude towards science and improve pupils’ scientific literacy through enjoyment (Durant, J. 1994).

Thus, a focus upon scientific literacy must be emphasised within schools to ensure a new generation of scientifically literate children who do not believe everything they read. This can be done through teaching fair testing and making science relevant to real life.

References

Durant, J. (1994). What is scientific literacy? European Review, 2(1), 83-89. doi:10.1017/S1062798700000922

The Scottish Government (2010) Curriculum for Excellence: Sciences principles and practice. Available at: https://education.gov.scot/Documents/sciences-pp.pdf(Accessed on: 8th February 2018)

W. Harlen and A. Qualter (2009) The Teaching of Science in Primary Schools. 5th edn, London: Routledge What is a Fair Test? (2018) Available at: https://www.theschoolrun.com/what-is-a-fair-test (Accessed on: 10/02/18)

Thinking Deeper (MA1)

We had a workshop this week that really made me think.

What does it mean to be homophobic?

We watched a clip from a video and the part we focussed on was stating that we are all at least a little bit homophobic. I think at first everyone felt a bit defensive. Nobody likes to be accused of being or doing something. I never would have thought of myself as homophobic- and I still don’t. However I do understand the point being made. We all notice if someone is ‘different’. We might even judge them for it. That’s not to say you would necessarily voice those thoughts. I think that certain ideas are engrained in our heads from a young age based on society but more heavily, the media. So it is difficult to have entirely independent thoughts on every subject.

I found a short clip of people in the crowd at a sports event. Had it been on television whilst I was in the room I may not have paid attention and many people may not take notice of what is said by the commentator. But I think this is an excellent example of the statement that everyone is a little bit homophobic and that people say offensive things, without intent or even realising it.

What do I say..?

The topic of gender has become increasingly heated as of late. I knew that there was no longer binary ‘boys or girls’ anymore but I was not entirely sure of the details. I have found out that gender holds no scientific basis. It was interesting having a discussion on the as people had stories of their own experiences and examples from the media. I didn’t know that some shops were getting rid of labelling clothes as either ‘boys’ or girls’. I found this really interesting. I am still a little unsure about this whole topic. I find myself feeling wary of what I say. I never thought using the words ‘boys’ and ‘girls’ could become so serious. It has been really eye opening.

Perceptions on Race, Ethnicity and Discrimination (MA1)

Perceptions on Race, Ethnicity and Discrimination

Before the input and reading, my thought and perceptions about race, ethnicity and prejudice were somewhat vague. I know in general what these terms meant and could give examples of what I thought each one entailed.

After learning more, I have found that race as a concept is extremely complex. I was under the assumption that ‘race’ was the term for the physical variations of people in the world, depending on their roots. However, now I know that ‘race’ is almost dismissed by scientists and scholars as they do not think there is any basis for the concept. On the other hand, many people would argue that race has meaning for some people. So it is more of a social concept that people hang onto.

I thought previously that a person’s ethnicity was a ‘proper’ term to describe their cultural and geographical background. I have now learned that it is in fact an entirely social in meaning. It is used in society to describe differences in people based on culture. People also associate certain ethnicities with particular characteristics (which could be inaccurate perceptions). I also found out that sociologists prefer to use the term ‘ethnicity’. This is because ‘race’ is sometimes linked to incorrect scientific facts.

I had a pretty good idea of what discrimination and prejudice were as they are terms I have heard lots about. What I didn’t entirely know, was the distinctive difference between the two. I knew that prejudice was a person having certain thoughts about others based on word of others or the media. I found that the line between this and discrimination was that to discriminate is to act or behave in a particular way towards others based on how you think. So I see now that, essentially, prejudice is a thought and discrimination is an action. I saw examples of this on the Padlet resource. There were articles about events that had happened and I was able to see how certain aspects were discrimination as opposed to prejudice. It was also clear that those who had certain opinions about groups of people saw no flaw in their views. With the example of a Scottish lawyer who was accused of plotting the recent attacks in Barcelona. People blamed him based on the fact that he is a Muslim. He received abuse for apparently planning the attacks when the fact of the matter was that he just happened to be in Barcelona that day. I was able to understand better why people reacted in this way. It was because an aspect common in prejudice is being reluctant to look at the actual facts and to try and see other perspectives or opinions.