All About Me

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Me
I am Katie Doyle, in the University of Dundee studying for an MA (Hons) in Education.

I have always wanted to go into teaching, as far back as I remember. Back then it was because I saw teachers everyday and admired them as role models and wanted to be a role model for children myself when I grew up. In recent years, however, I have worked with children and been able to reflect on the experiences which shaped my plans up until I began the course.

In my journey to teaching, I spent two years as a peer mentor for the Ripple Project, a community hub in Edinburgh. I found the whole experience very challenging, while I was there and dealing with the kids, but it was also difficult to deal with on a personal level. I found it hard interacting with the children, knowing their backgrounds and details of their personal lives. One child in particular who was ‘my’ child, was dealing with problems which I genuinely thought only happened in ‘Tracy Beaker’. It made me reflect upon my own experience growing up and how different my childhood was to hers. I had never experienced any real difficulties at all: my parents are still happily together; I’ve never wanted for anything, money, clothes, food etc; and I have never experienced violence or conflict in my home. Her life is so different to mine, and that makes me sad, but it also makes me determined. Determined to take full advantage of every opportunity offered to me, to study for the career I really want, and determined to use that career to make a real difference to the children that I work with.

Throughout my primary years, I found school very difficult. Often, I simply could not keep up with the rest of the class academically. I was always in the ‘Extra Spelling’ or ‘Extra Maths’ class, and was always in the bottom set of these classes. For me, this used to be very demoralising. I have considered my experiences more recently, and my goal in teaching is to look into helping struggling individuals similar to myself, as I know what a horrible feeling it is to struggle in school like that, something I would very much like to prevent future generations of children from experiencing in school.

I went through the private school system and I had both access to and the benefit of academic tutoring throughout my school career. While I am very grateful for these opportunities, I do not think that my parents’ financial situation should have dictated whether or not I had access to academic resources and private tutoring. I believe that all children should be able to access a high quality education, and my ultimate goal is to leave this course qualified to provide just that.

Having completed 1PP1, I have seen education from a different side, that of a teacher as opposed to that of a pupil, and it has given me an appreciation for the amount of effort that goes into being a teacher. I spend the whole time exhausted, eating at odd times and getting an average of 5 hours sleep, and all that was on my mind was the class I was working with. I was obviously doing significantly less work than that of a full teacher, which shows me just how much they do! The amount of work that they do is incredible! I also had the benefit of working with a very good teacher, who was very willing to put in a lot of time with me and also allowed me a lot of freedom within the class which made me very motivated and gave me the chance to really use my own skills, and I am very grateful to her for such an experience.

 

 

 

 

 

My Educational Philosophy

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Children should know that their thoughts and feelings are valued by adults, and that they can think and speak for themselves without worrying about being wrong or of anyone making fun of them. Education should be for developing self confidence and self worth in order that children feel comfortable with themselves whilst in the school environment.

The aim of school should be to produce well rounded individuals who have a creative and critical way of thinking. I believe that high quality teaching is the most effective way to achieve this. From the 1PP1 placement, I found that as long as children are interested in the lesson, then they are learning, so we should all be making sure that what we teach is interesting to the children we work with.

Education should always be inclusive of all learners. If somebody is making an effort to turn up to school, then they deserve to be included fully in the education system. Saying this, if children are not, or do not want to make the effort to come to school, then we should look to the education system and see what may have disillusioned the learner and look to make changes as opposed to blaming the learner. I believe that school should promote a disciplined approach to education. I do not think it is a massively important point to make, of course teachers should be aware of behaviour management techniques, but they should not be a main focus.

Schooling should offer as many subjects and experiences as possible. The aim of education, in my opinion, is to produce well rounded individuals. I think that the best way to do this is to give them knowledge and experiences. They should study the basics in order to understand the more exciting specific subjects, ie. should be able to read so that they are not focusing on the reading but engage with what they are actually reading. In my opinion, the Curriculum for Excellence  does this really well, the idea of one topic spanning several curriculum areas is a really positive one. I think that all children can benefit from such a system.

Teachers were some of the best role models for me throughout school, I always admired them for the way they seemed to know everything. Despite this, I remember one occasion while I was in high school when somebody asked the biology teacher a question and he answered it, but the next lesson he told us that he had given us an incorrect answer and that he had asked another teacher and found out the correct answer. I remember this as, I can imagine, being a teacher it must be difficult to admit to not knowing an answer, and certainly to come back having made an effort to find out the correct answer was admirable to me. This particular teacher, to me, was an example of a teacher who is willing to go the extra mile and therefore was a role model to me.

School should offer the opportunity to achieve academically, but for me there should be more to it than just passing through a system and come out the other end with a certificate of exam results. Of course children should learn some academic skills, they should have developed language and mathematics skills, and plenty experience of RME, Social Subjects, Technologies, Expressive Arts, Health and Wellbeing and Science. They should be able to experience so much more from their time in school: experience success, critical thinking skills, creativity and social skills. They should be directed, but be given enough space to develop in their own way and at their own pace.

Maths Anxiety: What is it and how can we deal with it?

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Maths Anxiety

Maths anxiety is about the way we feel when faced with everyday mathematical problems, for example adding up shopping; splitting the bill in a restaurant; or working out how much flour to put in a cake recipe. It’s not about ability in mathematics, one could be highly competent but struggle with the most basic mathematics. David Robson, writing for bbc Future is a good example of this, he says:

“I have a university degree … in mathematics. Yet somehow, advanced calculus in the privacy of my own room was a breeze compared to simple arithmetic under the gaze of others – or even remembering my building’s security code.”

You could not possible claim that he is ‘bad’ at maths, but he struggles with very basic mathematics, why? Maths anxiety was researched in Stanford University, where was shown that then people with maths anxiety are exposed to mathematics, their brains react in the same way as a person who had a phobia would react to seeing their phobia. We should take from this that maths anxiety is not about ability, it’s not a label for people who struggle academically. It goes deeper than that, just as you would not chase an arachnophobic person with a spider to cure them, you cannot throw mathematics in a high-pressure situation at a person with maths anxiety as it will not help.

Something that we should also be aware of is that girls may be more likely to occur in girls, especially if their teacher is also female. Even in my own experience, women are more likely to shy away from mathematics, however the Department of Empirical Educational Research, University of Konstanz found in a study that girls did have more maths anxiety than the boys, but that both had similar abilities when tested.

What can we do about maths anxiety? One suggested method is to have pupils with maths anxiety write about their fears, the idea being that they can see their feelings about it written down and not see them as insurmountable. It is also thought that pupils should be taught to approach mathematics in a completely different way. David Robson suggests looking at maths more as a challenge than a problem, to try to do it and not be put off because its maths.

As a teacher, we should remember that children will pick up on the way that we feel about maths. If we act as if we are nervous or scared by maths, then children will think that there is something to be scared of, which there is not. They also may not fully trust us to teach them properly and they may not get as much out of the lesson as they should. I think that teaching style may be important here, making sure to spot any pupils who may have maths anxiety and giving them the necessary support, allowing them to work through mathematics, without any need to be anxious.

I decided that I would find out for myself if I have maths anxiety, the test I used gave 10 questions and I had to rate how much I agreed on a scale of 1-5. The results suggested that I am ‘fearful’ about maths but not that I have maths anxiety. This is useful to be aware of, as I would hate to pass such fear on, and it is part of the reason I am taking this module. I think that

Goetz T, Bieg M, Lüdtke O, Pekrun R, Hall NC(2013) Do girls really experience more anxiety in mathematics?. Available at: http://www.ncbi.nlm.nih.gov/pubmed/23985576 (Accessed: 14 October 2015)

Robson, D (2015) Do you have ‘maths anxiety’?. Available at: http://www.bbc.com/future/story/20150619-do-you-have-maths-anxiety (Accessed: 14 October 2015)

Freedman, E (2006) Do You Have Math Anxiety? A Self Test. Available at: http://www.pearsoncustom.com/mdc_algebra/math_anxiety_material.pdf (Accessed: 14 October 2015)

www.theguardian.com/education/2012/apr/30/maths-anxiety-school-supportBrian, K (2012) Maths anxiety: the numbers are mounting. Available at: http://www.theguardian.com/education/2012/apr/30/maths-anxiety-school-support (Accessed: 14 October 2015)

The Ishango Bone – What does it mean to us?

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Ishango Bone

 

 

After a lot of internet research, all searches for prehistoric maths seem to come back to the Ishango Bone. It was discovered in the Democratic Republic of the Congo in 1960 and is thought to be around 25,000 years old. At a first glance, it’s just a stick with some lines on it and they don’t make any sense.

Initially I thought it was perhaps a primitive tally chart. This would make sense, as the people who used it all those years ago may have needed to count, for example the resources they had or perhaps something like the birth rate. It would also be a very logical way of using numbers and is nothing  like our complicated numerical system, as it seems that | =1 and || = 2 and ||| = 3 and so on, compared to our system of numerical not actually depicting the number they represent like this.

Having looked into this more, it is clear that the prehistoric people were far more mathematically advanced than we give them credit for. The Ishango Bone has lines in groups, and the groups are split into 3 rows (a), (b) and (c). (a) shows a group of 9, 19, 21 and 11. (b) shows 19, 17,13 and 11. And (c) shows 7, 5, 10, 8, 4, 6 and 3. Row (a) and (b) both add up to 60, and it is thought that (c) uses multiplication by 2. This suggests that the prehistoric people who used the Ishango Bone must have had a fairly solid understanding of these numbers and been able to use them to aid their everyday life, much like we do.

Further research tells us that more recently the Ishango Bone has been shown to have more markings on it than first thought, and it shows links to the lunar calendar. Claudia Zaslavsky, an Ethnomathematician, wrote in 1991 “Now, who but a woman keeping track of her cycles would need a lunar calendar?”. She suggests that the Ishango Bone was used by a woman or women to keep track of their menstrual cycles. If this is true, then it could mean that the first mathematicians in the world were women, using mathematics to aid them in their everyday lives. This is significant, as even a Google search for ‘famous mathematicians came up with results such as Albert Einstein, Leonardo Pisano Bigollo, Pythagoras, Archimedes and John Napier. This is of course not to take away from all of their mathematical successes, but they are all male.

From a teaching perspective, this is highly informative. I think that it is highly important to take away from this research that when teaching is that generally we see boys going into traditionally male subjects such as mathematics and girls for traditionally female subjects, such as English. However this shows that women can be mathematicians and we, as teachers, should be encouraging this through providing positive role models for them. If the class I was working with was old enough to understand the menstruation part, I would share some of this information with the class to try to encourage girls in the class to do mathematics if it interests them and not be put off thinking that it is for boys. I will also try to remember that the numerical system and how it compared to the one we use and that children will need time to pick it up and therefore not to rush them. From a personal perspective, I am going to try to keep this in mind, but also I think that to remember that the prehistoric people were not as primitive as perhaps I believed before, and I will try to convey this in my teaching if it is ever possible.

Coolman, R (2015) The Ishango Bone: The World’s Oldest Period Tracker?. Available at: http://www.thedailybeast.com/articles/2015/10/06/the-ishango-bone-the-world-s-oldest-period-tracker.html (Accessed: 7 October 2015)

Mastin, L (2010) Prehistoric Mathematics. Available at: http://www.storyofmathematics.com/prehistoric.html (Accessed: 7 October 2015)

Weisstein, E (2015) Ishango Bone. Available at: http://mathworld.wolfram.com/IshangoBone.html (Accessed: 7 October 2015)

Williams, SW (2008) Mathematicians of the African Diaspora. Available at: http://www.math.buffalo.edu/mad/Ancient-Africa/ishango.html (Accessed: 7 October 2015)

Zaslavsky, T (no date) Claudia Zaslavsky. Available at: http://www.math.binghamton.edu/zaslav/cz.html (Accessed: 7 October 2015)

Tessellation

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Following the lecture on 28/9/15 on creative mathematics, I had some idea of what tessellation meant, but had never considered it in any great detail. I decided to look it up and see what I could find out about it. I decided to investigate what shapes would and would not tessellate…

I started by choosing some random shapes to see if I could tessellate them myself. I chose an isosceles triangle (orange) [photo 1], a pentagon [photo 2], an equilateral triangle (purple) [photo 3], a hexagon [photo 4], a star [photo 5], and a right-angle triangle (pink) [photo 6]. I made copies of the shapes, cut them out and attempted to tessellate them. Now my cutting and sticking skills are not up to scratch, but think it’s still clear that some definitely tessellate while others do not.

Following what was said about the angles at the meeting points on the tessellation, I decided to check that this was true. I found that that I could measure that point and it did add up to 360°. The equilateral triangle [photo 8] and the hexagon [photo 9] had angles which were exactly the same, whereas the isosceles triangle [photo 7] and right angle triangle [photo 10] had two different angles which helped to add up to the full 360°

The star and the pentagon did not tesselate at all, so I decided to look into this a little more, and came up with this website. {https://plus.maths.org/content/five-fits}. It explains that we get convex and non-convex pentagons. Non-convex pentagons have points which are bent into the shape, see example [photo 11], and these are not included. In the example, it can be seen that the bottom ends in to the shape, which is why it is non-convex. They set out to find an irregular convex pentagon which would be able to tesselate. It appears that there are 15 pentagons which will tessellate, the most recent of which has been published this year by Casey Mann, Jennifer McLoud and David Von Derau at the University of Washington Bothell, which looks like this [I will make it clear at this point, that this is not my own work, simply a summary of research conducted by Marianne Freiberger and those she has cited]:

My conclusion from this research is that clearly mathematics is not as rigid as I previously believed. If this new ‘tessellateable’ pentagon was only discovered this year, then clearly mathematics is still  continually evolving and updating, meaning that mathematics really is all around us and there will always be new discoveries to be made. From a teaching perspective, I think that this is an important message to impart to children, that mathematics should not be done to them, but they should be doing it and trying things out and perhaps one day they will be discovering new shapes or theories, and they should be able to use the basic skills learned at school to do so.

 

Freiberger, M. (2015) A five that fits. Available at https://plus.maths.org/content/five-fits (Accessed 29 September 2015).

Math-Salamanders (2015) Shapes Clip Art Triangles & Quadrilaterals. Available at:http://www.math-salamanders.com/shapes-clip-art.html (Accessed 29 September 2015)

Wikimedia Commons (2006) File:Isosceles-right-triangle.jpg. Available at: https://commons.wikimedia.org/wiki/File:Isosceles-right-triangle.jpg (Accessed 29 September 2015)

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Could They ‘Hunt’ Me?

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After learning that the new Chanel 4 television show ‘Hunted’ [See here…] included mathematics on 17/9/15, I decided that I would investigate this further. To paraphrase, the show simulates what would happen if an individual had to go on the run from the authorities. The aim was for the 14 volunteers to go on the run and remain undetected for 28 days. While they were doing this, 30 experts would be trying to track them down as they would with a real criminal.

One pair, Sandra and Elizabeth were hunted down very quickly despite thinking they were doing well. They were hiding by constantly getting on and off busses around the South East of England, but were spotted through their use of an ATM. CCTV was able to show which busses they had been on, and from this it was shown that they were following a pattern in their travel plans. The hunters used this pattern to forecast the possible routes they would take and then found them. One of the hunters explained: “We all establish patterns just to get through the day, that’s how we work, and so it’s really hard for people to be random”. By this example we can see that she is right, we seem to have an almost innate affiliation to patterns built into us.

This got me thinking about if anyone wanted to hunt me. What would they be able to tell about me from my own routines? I think if someone observed me for just a few weeks they could learn a lot about my routines and would be able to pinpoint an exact time to catch me. Some examples include: I always leave to attend university exactly 30 minutes before the input is due to begin; I always take the same route there and my route back is always the same; I do not miss university regularly; I speak to my mum at the same time every morning; my boyfriend stays over the same nights every week; and I go back home to Edinburgh every 3 weeks. That list could easily be even longer, but it definitely shows that my daily life has fallen into a pattern, it means that I would be very easy to find if anyone wanted to – all they would really need to do so is a copy of my university timetable.

If I am honest, I was not very sure that this show included mathematics, and it did take me a long time to see any mathematics at all, but now I can see it, it is very interesting to think about. I think that it is very easy to follow patterns, it is human instinct, but I can see that the role of these experts to find the real criminals and it clearly requires a specific type of thinking. I think that this type of thinking is where mathematics comes into it, to find the criminals we would have to be able to look at the normal behaviours and routines of the individual and be able to use them to think as the criminal is and attempt to predict the moves that they will make, and their reasoning behind making them.

From a teacher’s point of view this is interesting to know as it can allow us to try to foresee events and either change or encourage them. We can try to predict what pupils will and will not understand, or perhaps we can predict an issue between pupils in the future and attempt to ease any tensions before that happens. It is also a possibility that we can identify this type of mathematical thinking and encourage children to use it to their advantage.

http://www.radiotimes.com/news/2015-09-10/what-is-hunted