# Have I discovered maths?

Today was our last input for discovering mathematics. Throughout this module I have discovered a few things including mathematics. This journey of discovery hasn’t been easy but I can officially say I understand fully the fundamental ideas of mathematics.

Essentially, I have discovered: what the fundamental ideas of mathematics is, different aspects of mathematics within the classroom and how a teacher can accomdate this in the classroom.

At the beginning of this module I believed maths to be counting, equations, sums and dread. The idea of maths always brought fear and anexity to me, however this module has changed the way I think about maths and consequentially the way I will teach in the future.

Essentially, Liping Ma (2010) devised an idea to teach children mathematics through the idea of profound understanding of fundamentals mathematics. This is essentially through four main ideas: basic ideas and principles, interconnectedness, longitudinal coherence and multiple perspectives. To achieve success in primary and secondary mathematics these four ideas must be applied. The idea of basic ideas and principles suggests that all stages of maths should be broken down and applied in a simpler way and then built up into a more complicated way, without this children may get confused and begin to disengage resulting in poor mathematical skills. With this scaffolding children can link ideas and find easier ways to complete a question/sum. Furthermore, children should appreciate interconnectedness throughout their learning. Linking ideas together can make problems easier and can allow children to break things down. By showing children interconnectedness in their learning this will allow them to begin to appreciate the links between real life and maths, for example my previous blog on statistics. Showing children this link can help promote engagement and motivation within the classroom. The idea of longitudinal coherence refers more to the teacher to track progression throughout learning to show children improvements and things to work on, by doing so children can work on their progress points and track improvements. As well as know where they are within the class – doing well or not. Finally, children must have the ability to have multiple perspectives. This relates to the way the teacher teach the class, providing them with different ways to reach the same result, by doing so children can opt for the way they find easiest and guide their learning on their own preferences. By applying all four ideas children have the ability to progress within their learning journey and find their own personal success, however none of this will be done without the scaffolding of the classroom teacher this is something I have learnt throughout my discovery of mathematics.

Within the classroom children have all different ways to learn mathematics which the teacher must accomodate for this is to optimise the attainment within the classroom, throughout this discovery I have learnt that learning can be fun and active a few ways that I have learnt is;

• art to teach thirds
• outside work to optimise distance
• science to incorporate maths

Without this module I would be more hesitant to deliver a maths lesson and this has made me so much more confident in my maths skills. I believe that I have fully discovered maths and I will be taking my knowledge into my future teaching, applying these fundamental mathematics and showing children an easy way to approach a difficult problem. This module has opened my eyes and enlightened me with ways to teach maths.

References:

Ma, L., (2010) Knowing and teaching elementary mathematics New York: Routledge.

# Maths that help

Everyone knows that mathematics can help children in the classroom and academically however, how can they help in real life?

In a recent input we discussed how mathematics is involved in medicine specifically, how statistics can help. This is something that has really interested me in the sense that the NHS can be reliant in this mathematics at times.

According to NHS England (undated) ‘statistics are used to create debate, inform decision making and research both within government and by the wider community.’ This suggests that without statistics research within the medical world would not be able to take place.

This is supported by Annekld (2016) where they believe that statistics are vital to medicine and in specfic nursing and they way they interpret and understand the data they have been presented with. Medical statistics allow nurses to make quick decisions and act on outcomes they have been presented.

Essentially, statistics is an integral part of nursing and the medical profession, this is due to the direct impact it has on the wider community and society. This can effect individuals on a wider scale being without statistics people could be prescribed wrong dosage, or not be prescribed the essential medicine.

According to Caplan (2012)  statistics are used in medicine for a number of reasons most importantly for blood pressure accuracy, this is devolved around statistics – what is healthy and what needs attention. This suggests that statistics are needed to test the healthiness of the patient and allow everyone to achieve the ‘norm’.

SO… what does this mean for us as teachers?

Well, this has certainly opened my eyes to the power of mathematics, without this people have the ability to deteriorate in health and in worst case scenario have a fatal outcome. This statistical values allows people to keep on top of health as well as correctly preform a medical procedure.

As teachers we should always emphasise the importance of mathematics within the real world and consequently this is a big one. This can allow children to further engage with their academic studies as well as show them there is a life of maths outside of the classroom. This links to Ma (2010, pp.22) where she states children should have interconnectedness within their learning in maths, how does this impact on them in the long run and how can they grow up to change the world from maths. This gives them a goal to achieve and a dream to set, to change the medical world through the impact of maths.

Us as teachers need to encourage these goals and plant the right seeds for children to fall in love with maths and see it as so much more than just counting and sums.

References:

NHS England (undated) Statistics[online] Available at: https://www.england.nhs.uk/statistics/category/statistics. (Accessed on: 11 November 2018)

annekld. “What are the uses of statistics in nursing?”, 29 Jan. 2016, https://www.enotes.com/homework-help/what-uses-statistics-nursing-361410. (Accessed 11 Nov. 2018.)

Lorraine Caplan. “What are the uses of statistics in nursing?”, 22 Sep. 2012, https://www.enotes.com/homework-help/what-uses-statistics-nursing-361410. (Accessed 11 Nov. 2018.)

Ma, L., (2010) Knowing and teaching elementary mathematics New York: Routledge.

# Is maths beautiful?

Maths makes our portraits beautiful.

Recently, we had an input surrounding maths and art. This is something I really enjoyed, after this input I began to think about how much mathematics is actually involved in life, even art.

So, how does maths make us beautiful?

To explain, I think I should firstly show you some art I have done in a recent input. The left side of the picture is free hand drawing, of a person put up on the board. The right side of the picture is using maths, the difference that using maths made was amazing.

it is hard to believe that those two faces has been drawn from the same picture.

So how did I turn that awful drawing into that better drawing?

# MATHS!

I followed some mathematical steps from this link.

To break it down:

Step 1: Similarly draw a circle in the middle of the page. From the middle/top of that circle draw a vertical line to below the circle. From this join up the line and the circle with straight lines to make a jawline.

Step 2: Draw guidelines to the right of the circle. This is the mathematical part. Take a ruler and line it up to the right side and make a vertical line slightly longer then the entire face outline. Calculate the length of this line, e.g. 14 cm make 7 equal horizontal lines coming from the vertical one, e.g. every 2 cm make a horizontal line.  Label them beginning from line 4.

Line 4 – Centre Line

Line 5 – 1

Line 6 – 2

Line 7 – 3

Line 1 – A

Line 2 – B

Line 3 – C ( As seen in the picture above)

Step 3 -Draw the eyes on the centre line, this is half way down the face. Half of the eye above the line half under giving the ideal eye shape. Centre the eyes half way between the vertical line and the edge of the circle.

Step 4 – Draw the nose. From the middle of the eyes made a vertical line down to horizontal line 3. Add nose features between lines 1 and 2.

Step 5 – Add the eyebrows on line C. Use short lines to create the hair effect.

Step 6 – Draw the mouth. Draw a triangle from line 2 – 3 just below the nose. Draw a vertical line from below the eyes to line 3 and shape the mouth between the triangle and the vertical lines.

Step 7 – Add the ear of the centre line, on the same line as the eyes. And then add other personal feature e.g. hair, freckles or glasses.

So using mathematics, I was able to present a better proportioned face and a more life like drawing. So why does this matter? Maths is involved in every aspect of daily lives. Arts use maths in most of their drawings, above is just an example of how maths can be applied and how I used it personally but artists use mathematics to create perceptions, and dimensions.

A piece of art which is centralised around mathematics which many people don’t know is  the Mona Lisa. This painting is drawn according to the “golden ratio.”  This is 1:0.618 and it is named this as it is satisfying to the eye.  This pleasing proportion is simply a rectangle with dimensions that show the golden ratio, this painting has lots of rectangles to make the painting  The Mona Lisa has many golden rectangles throughout the painting to make it look better.   If the  rectangle is divided on her forehead with a line drawn across her eyes, we get another golden rectangle, this shows that the  proportion of her head length to her eyes is ‘golden’ .

(Natasha Glydon, undated)

Okay, so how can we apply math to modern life art? Instagram.

By using something called the rule of third you can make Instagram pictures more appealing. I tried it out. This is an original picture that I took. Its not very attractive right now:

By applying the rule of third I have made a third chairs and 2 thirds grass with the central person off centre. This can make the image much more interesting to the eye. This makes the picture a lot more creative and beautiful.

So what is the point of all of this?

Mathematics has the ability to make art beautiful, so does that mean maths is beautiful? By opening your mind to the application of mathematics it can show you much beauty and relevance it has in the real world. If you accept that maths is beauty then why not begin to see why you need it? This links back to Ma (2010, p.22) theory of profound understanding of fundamental mathematics that by applying the main principles including interconnectedness, by showing children the connections between maths and other aspects of live it has the abilty to find mathematics more relevant and applicable to their own individual lives. Some children might not believe they are good at maths but they might believe they are good at art, show them the connection.

Therefore, maths is beautiful.

References:

Ma, L., (2010) Knowing and teaching elementary mathematics New York: Routledge.

Natasha Glydon (undated) The Mathematics of Art Regina: Pacific Institute for Mathematical Sciences

Darlene Nguyen (undated) Learn to draw a face in 8 easy steps: Beginners Available at: https://rapidfireart.com/2015/12/07/how-to-draw-a-face-in-8-steps/#

# Stereotypes/myths and Maths Anxiety

Does maths stereotype and myths lead  maths anxiety?

Okay so, we have all heard the common”I can’t do maths,” “maths is too hard,” or “I’m not a maths person, I’m better at language.” But are these all true? The answer is NO.

Okay, to be fair I have said these once or twice in my life but now through the development of my academic career, throughout this module and my own education I have learned it is not as scary as it seems. Honestly, my mum decided she wasn’t a maths person this is where I decided I wasn’t too. However, I have a twin sister that is wonderful at maths so she was known as the ‘one’ who was good as maths and I was known as the ‘one’ who was good at language. Thats always how it has been, but why…

So when I was thinking of this I asked my sister what she thought of maths in primary school, her reply was: “I loved it, my favourite subject.” Whereas when I thought of this question I reflected on my maths experience as painful and difficult. As my sister began to dig deeper into her maths experience she quickly realised that the only reason she received a A in Higher Mathematics was due to her love of maths.

So this made me think, maths stereotyping and myths actually can lead to maths anxiety and hatred and this is where my blog starts.

So essentially, no child can just diagnose themselves as bad at maths or not a maths person. However, their environment and role models can inform their decision making around this. This is particularly seen in older children opposed to younger children. So role models, what do I mean by that? This could be siblings, parents, grandparents, sport instructors even teachers.

“…mathematics anxious teachers may serve to foster the early development of mathematics anxiety among their students” Arem (2010, p.30)

All these people can act as role models or influencers for that child and if they begin to say ‘oh, maths isn’t my thing,’ then the child may begin to think that that is the same for them, although this is not the case.

Everyone is, whether they know it or not, capable of learning maths.

Inheriting these negative stereotypes may stop the child from opening their full potential in mathematics for the rest of their lives.

Okay so how do we get this across? Firstly, children must understand every mistake is a lesson and that if they don’t achieve the correct answer for one sum thats fine, they must just pick themselves up and start again and continue to preserve in their mathematic journey. Simple things like these have the ability to boost children mathematical confidence.

Okay so what is maths stereotypes and myths? Well to name a few…

• The maths gene myths – some people inherit maths skills
• You don’t need maths myths – how is this relevant to my life
• The drill and repeat myth – repetition makes you good at maths
•  The Right way myth – there is only ever one solution
• The memory and speed myth – basically just memorising and writing what you have remembered down quickly in a test/exam

(Teachers Professional Resource, undated)

Okay so can this cause maths anxiety? I believe yes.
These stereotypes and myths may induce children’s fear of mathematics and develop a strong math anxiety for the child.

I understand mathematical anxiety to be children who have a genuine fear of maths so much that they dread the time of the day where maths is about to be taught. It gives them a sense of failure and unhappiness in their abilities. Hembree (1990, pp.45)  describes this further as  “a general fear of contact with mathematics, including classes, homework and tests.” Okay so I was right, it is a general fear of mathematics but why? This, amongst many other reasons is due to, maths stereotyping and myths.

Skemp (1989, pp.25) again describes maths as a  “conditioned anxiety stimulus.” Again another person relating maths to anxiety.  Okay, so what can we tell from this? Maths anxiety does exist and it is appearing in a number of young people today.

So how can we solve maths anxiety?

• Positive reinforcement – stop the myths and stereotyping!!
• Extra learning/teaching on the area the child struggles at
• Reframe anxiety – have children write down what they are worried about and set a challenge to overcome it
• Make maths more interactive, have group activities

(Oxford Learning, Undated)

So now we have established the links, if we reduce the amount of people stereotyping and producing myths to children at a young age they may grow up to have a love for maths, just like my sister. She was positively encouraged and reassured her maths skills was excellent and she went on to great things even has choose a degree area in university surrounding this. So this helps us to understand, if we stop the negativity surrounding maths positive outcomes may blossom.

Heres an interesting video I found to help overcome maths anxiety  that I would like to share with you:

https://youtu.be/KZNdBxdNGIE

Does maths stereotype and myths lead  maths anxiety? I believe it strongly does, without these myths being planted into children ears of maths being difficult children would experience maths in their own way and this could turn into something beautiful.  The Conservative newspaper (2013) has produced a article which explains that their is strong links between stereotyping and anxiety. It also states that a classroom without these educational barriers is a classroom without fear, essentially stop stereotyping and telling children myths. Experiences that have happened to one person may not happen to another.

References:

• Hembree, R. (1990) ‘The nature, effects and relief of mathematics anxiety’, Journal for Research in Mathematics Education,21, pp.33-46.
• Skemp, R. R. (1989) Mathematics in the Primary School. London:Routledge.
• Arem, C. A. (2010). Conquering math anxiety: A self-help workbook. Belmont, CA: Brooks/Cole.
• Teachers Professional Resource, LLC (undated) 5 Common Maths Myths Available at: https://www.teachersprofessionalresource.com/5-common-math-myths-parent-tips/ (Accessed on 23/10/18)
• Oxford Learning (undated) What is Maths Anxiety?  Available at: https://www.oxfordlearning.com/what-is-math-aniexty/ (Accessed on 23/10/18)
• Available at: https://youtu.be/KZNdBxdNGIE (Accessed on 23/10/18)

# Maths Ability Groups

A good thing or a bad thing?

This is a topic which interested me so much I decided to find out for myself what does this actually do to children and their learning/development?

Obviously, we all know that maths is a complex concept which many children have difficulty understanding within the classroom as it is without the pressure of being in the highest attainment group.  This is something I saw often in my own placement. Are we right to arrange children in ‘ability’ groups? Does this change children’s perception of mathematics? Does this encourage children to give up? I believe that arranging children in different ability groups has the ability to boost confidence but also to drop confidence.

Okay so what are ability groups?

My understanding of this is being arranged in groups according to academic strategies, which is not always your academic preference. Take me for example, in school I was in the bottom group for language and the top for maths, but I too HATED maths, but I now ask myself was that because I was in the bottom group? Was I not getting pushed enough?

However, Hallinan et al. (2003, pp. 95) suggests that the theory of mathematic ability groups is to ideally get full potential out of all student learning and development but realistically does this happen? I would agree with Hallinan et al no.

In reality this is not the case. It can also be shown that Hallinan et al believe that assigning children in different ability groups highly restrict learning opportunities for children. So how are children supposed to find mathematics easy when their learning in the classroom is significantly narrowed due to the group they have been assigned?

I believe that giving children different attainment groups will begin to make the children may begin to feel discouraged in their mathematic abilities and begin to give up therefore reduce their confidence and growth mindset in maths. This can encourage children to have a certain feel about mathematics that they can’t do it or it’s too hard. This is commonly seen in lower ability groups in maths.

The BBC News tried to unpick the issue of maths ability groups. The article entitled “Should young children be grouped by ability?” (2017) Something that really touched my heart in this where a child quoted ‘I really hoped to be a doctor like my mum but that changed when I have moved down a group” Should children really have to change their dreams due to their math’s ability group?

From my personal experience of maths grouping I would agree with this statement, as bad as it sounds I once changed a dream due to my academic success in maths. When I was little I wanted to be a lawyer, just like members of my family and that dream ended in secondary school where I was put again in the lowest maths class, is that right?

So what does this do to children? Do they begin to feel like a failure? Or that they aren’t getting pushed enough? Personally… I believe yes. Why?

Well, due to the fact that some groups are being taught differently and more important different stuff. From my experience of primary school, children are given different work for their individual topics depending on what group they are in. By the end of the topic children in the lower groups hadn’t covered nearly the same stuff as children in the top groups, personally I believe this is profoundly unfair. But why do they do that?

This is supported by Pritchard (2012) as they believe that maths ability groups does not allow children to achieve the full benefit for the curriculum due to the groups varying the different aspects of maths. Not all children achieve the same education as others.

Right okay, so maths ability groups are sounding bad at the moment.

However, it’s not all doom and gloom…

I came across a very interesting document produced by the Dr Marks, NCETM (2012) that shows the pros of having maths ability groups. The thing I found most interesting about this document is that it give children a sense of identity and a feeling of being apart of something with in the class. I found this really quite touching, this gives children the chance to make friends and relationships within their class and even grow confidence in their learning.

Furthermore, maths ability groups allow children to have a group discussion and allow help from other members of their groups which are working at the same level/work as them. This may in fact boost confidence for maths knowing they are not going through it alone and can seek help from peers as well as the teacher.

Okay so, after this research I have came to the conclusion that I believe that maths ability groupings has pro’s and cons. It is something which I have speculated upon a lot and have decided that I agree with maths ability groupings to aid all children in work through discussions etc however, I believe all children should be initially taught the same material where they then choose how far they wish to progress with it, this is something I will choose to do in my future teaching.

References:

• Hallinan, M.T et al. (2003) ‘Ability Grouping and Student Learning’   Education Policy (6) pp. 95
• ‘Should you children be grouped by ability?’ (2017) Available at: https://www.bbc.co.uk/news/education-42154013 (accessed on 23/10/17)
• Pritchard, R. (2012) The Influence of Ability Grouping on Math Achievement in a Rural Middle School New Jersey, USA: Seton Hall University
• Marks, R (2012) Well-meant intentions: ability-grouping in primary mathematics King’s College, London: NCETM

# Chance and Probability

What is the odds that you’ll win a toy playing the ‘claw’ arcade game?

First of all we should probably consider what is probability and chance. So what is Probability?

Basically probability is how likely something is to going to happen. Lots of different things can be said to be probable to happen for example, the common phrase ‘it’s probably going to rain today.’ This is the common phrase of deciding if something is going to happen. I can better explain this through the common tossing of a simple coin. As you toss a coin there can only ever be two results, either heads or tails. The probability of getting a head is ½ and likewise with tails. This is just a simple way of explaining what probability is.

Okay so now we understand probability. What is chance? Well, chance is similar to probability in the sense that chance is the likelihood that a particular outcome will occur.

So now we understand these definitions… let’s get into some real life situations of chance and probability. When I was sitting during this lecture, I began to think deeply about chance and probability and I began to think of the important question I ask myself every time I lose at the arcade. What is the chance and probability of winning the claw toy arcade game?

This here is an example of the machine I am referring to. And now everyone is asking their selves the same question. HOW DO WE WIN THIS?

Well I’m glad you have asked because I have done some research for this and have calculated the chance and probability of winning.

These claw games are designed so the claw sporadically gets strong enabling the player to win the prize. In my research I have found that some even weaken the strength after a short time so individuals get a sense of victory before it is taken from their reach. This game actually  is programmed to ensure players cannot win this game. Unfair, right? So what is in the programme? Well, it is set to only go strong after 21 games. So you have to play 20 games before you can win the prize. Well, that’s not the only disturbing part, it can even be programmed to go make the claw weak after 10-25 seconds.

So what is the chance and probability of winning?

As I have mentioned previously, in order to be lucky in winning this game you have to play 20 games before you will hit a lucky strike and win a prize. Due to such high odds the chance that people are likely to win is slim. Some people might hit it lucky and begin the game on the 21st cycle however, other people may take at least 21 tries before becoming successful. This is a very frustrating but addictive game that everyone will have at least tried once. So why do they do this?

Phil Edwards (Daily Mail, 2015) discovered many of them are rigged for profit. With the settings being changed continuously from weak to strong, this suggests that the game down to hugely luck rather than skill. Edwards comprised a video (situated below) that explains the operator of the machines can set how often they pay out, and the strength of the claw will be dictated by how much money has been put in.

How are they rigged? Well… say a prize costs £5, and it is 20p or 30p to play each time and the operator wants a profit of 50 percent, the claw will only allow the player to win one out of every 21 games. Edwards has proven this through his careful studying of the machines.

It is important to remember: this is randomised, though, so the winning game cannot be counted or worked out.

The chance of winning is 1 in 15 people would receive a  prize from the claw machine, this is a huge profit to all arcade companies.So basically, the game is receiving 2 to 5 more money and profit because of this impossible game.

Can you increase your chances of winning?

To increase your chances of winning you should look do some research into machines with a fixed strength. Right okay, so what does this mean? Basically, the claw that grabs applies the same grip each time and then does not weaken after the prize is claimed.  You can also increase your chances by going for stuff close to the drop zone and stuff that is on top and not blocked by lots of other and heavier prizes.

So overall from my research, I have discovered that the chance and probability of this claw machine cannot in fact be measured or calculated  to ensure a concrete win. However, if you play the game approximately 21 times you will have a higher probability of winning this game.

References:

# The Resource Allocation Task – 19/09/17

On Tuesday the 19th of September we had our first tutorial. Due to the large size of the class we was split into two groups; I was in group 1 for this particular task. In this tutorial we was instructed to move into smaller groups in order to complete the task better. We was split into 5 individual groups and each given a pack which had unknown items in each, I was in group 5. When we opened our pack we had limited resources which included; a piece of paper, two posits, 5 paper clips, blue tack, pens and a pencil. With this items we was instructed to make something that would be useful for a new student at Dundee university student to use.

Our group came up with the idea to come up the an idea to make a pencil case with all useful resources in it, we did this by folding the piece of paper and sticking it together with blue tack. We used the posits to write useful emails and a personalised timetable for the new students to use and put them on the back of the paper. We then placed all remaining items in the paper and constructed a pencil case.

After this task we was given scores, group 1 was scored 9/10, group 2 was scored 8/10, 3 was scored 4/10, 4 was scored 2/10 and our group was scored a low 1/10. This confused our group as we all worked the hardest we could with we materials we was given. After the scores was given this lead into a discussion about why other groups was scored higher. We soon discovered that this was because they had more resources than what we did.

The idea of this task was to show that when people have more than others they often don’t realise that they do and will just take everything for granted and get better praise for a less amount of work. This showed us how working in a primary school may work with people having more than others getting a higher credit.

# Welcome to your WordPress eportfolio

Welcome to your ePortfolio. This is where you will document and share your professional thoughts and experiences over the course of your study at the University of Dundee and beyond that when you begin teaching. You have the control over what you want to make public and what you would rather keep on a password protected page.

The ePortfolio in the form of this WordPress blog allows you to pull in material from other digital sources:

You can pull in a YouTube video:

You can pull in a Soundcloud audio track:

You can upload an image or pull one in from Flickr or any other image sharing site.

You can just about pull in anything that you think will add substance and depth to your writing.