Monthly Archives: September 2016

Ett, två, tre…

100_6431This week we looked at the Education System in Sweden and other Scandinavian countries, which has been long praised and admired. Before joining this course, I had never really considered the starting age of school in this country, as it is the norm that I have grown up with. However, upon looking at research and other systems across the world, I am questioning exactly why our children start school at 5, sometimes even 4.

Why do our children start on or around their 5th birthday?                                                           What are the issues surrounding children starting school before 6?                                      Are there drawbacks to starting formal education so late?

Below is a clip from 2013 discussing whether children, as in Scandinavian countries, should start school age 7:

The clip raises some interesting arguments, pointing out the importance of play in the early years. While children are highly intelligent (as one woman points out), it is good for them to learn through play, developing skills that they will need for further education – and life in general – such as communication and cooperation with others. This informal learning means children will be motivated to learn – a type of motivation that does not come from being told to sit down and complete a worksheet. Fun and exploration are crucial at this age, and denying children this right is, potentially, killing their desire for learning and school in general.

Why do you think Swedish children are attaining higher literacy skills?

The above video raises two possible conclusions about why Scandinavian children perform so well: their later starting age; or the higher qualified teachers.

In these such countries, it is necessary for teachers of any level to have a masters degree. classroomHowever, I do not believe that you need a masters degree to be a successful teacher. I believe that teaching is a natural talent which can be developed and polished through a degree, but is ultimately an intrinsic skill.

I believe that Scandinavia’s success is more likely to be because of their later starting age. Children have longer to develop social and personal skills through play at an early age, meaning that they are ready to start school and concentrate more on their learning.

Assessment – do we over assess our children?

I believe that they way teachers must assess children is totally against the type of culture we are trying to promote in schools. I understand that is useful to keep written assessment pieces, especially in upper years of primary, however, children at such a young age cannot be assessed as often this way. Teacher observation and actually communicating with the children is a much better way of gauging where the children are at in terms of their academic development.

But Why?


Our internal monologue is programmed to make judgements and connections about the world around us. We almost create stories in our head about what people are doing and why. These “causes” that we create are called attributions. These attributions that we assign to different situations are what decide how we react and interpret behaviour, either our own or the behaviour of others.


There are many different aspects of attribution theory, and Weiner describes 3 different dimensions:

  • Locus – the location of responsibilitypicture1
    • Internal – believes self to be the cause
      • genetics etc
    • External – believes cause lies in the environment around them
      • family, luck etc
  • Stability – duration
    • Stable – fixed, unchanging situation
      • outcome likely to stay the same
    • Unstable – changeable, not constant
      • outcome likely to be different
  • Control
    • Controllable – has ability to change behaviour
      • personally accountable
    • Uncontrollable – unable to change/affect what is happening
      • blames other people or luck etc

The above image is a simplistic model, but explains the correlation between these factors quite well. For example, if a person believes they are what affects test scores (internal) and that their test scores are always similar (stable), then they believe the cause of this is a natural ability for maths. However, if a person believes that other people are the reason for their success or failure (external), and their results are often varied (unstable), then the person will put their success or failure down to luck (or lack of it).

These attributions often correlate with one’s emotions, or affective responses. 

captureThis table shows how both internal and external attributions can affect how we feel about our success or failure, for example, if we feel that we have cause our success then we feel proud of ourselves and confident for future attempts. However, if we feel that we have ourselves caused failure, then we feel guilty and unlikely to have a positive outlook on future experiences. Using experiences and attributes in this manner is called expectancy beliefs – where our motivation for future attempts is affected by the outcome of our current attempt. A feeling of confidence in out ability at this stage will motivate us to try further activities.

Motivation plays a huge role in attribution theory – the attributes we give behaviours can affect how motivated we are to repeat these behaviours. This is often linked to the perceived vs the actual attributes of a situation i.e. how a person themselves sees the situation.

Motivation is split into two strands: intrinsic and extrinsic. Intrinsic motivation is the type we should try to instill into our pupils – a desire to do something for the goal of achievement and knowing you have completed the task. Extrinsic is the opposite of this, where reward systems are put in place, so the goal of a task is to complete is to get the reward. It is often this type of motivation that is seen in schools through the use of sticker charts and points systems. The motivation we have, and ultimately the students in our classes have, determines how we approach future tasks.


The clip below outlines attribution theory and looks at it from a teacher’s perspective:


A Sixth Sense

Piaget believed that children were born with no cognitive understanding of mathematics, or “numerosity” – the ability to understand small quantities (Marmasse, Bletsas and Marti 2000). However, more recent research has shown that children of just a few months old understand very small quantities, distinguishing between 2 and 3 items, but not between 4 and 6, showing their understanding is not fully formed (Starkley et al 1990).This ability proves that infants are born with an innate number sense. 

file0002003501002There are many different number systems, outlined in the article by Marmasse, Bletsas and Marti (2000), dating back to prehistoric times. When writing was invented, there became symbols which represented this ability to count. These symbols we call tags. The easier these tags are, the easier it is for children to learn to count. For example in China, 15 is spoken as “ten five” and in French, 92 is spoken as “four twenty twelve” (as in 4 times 20 and then add on 12). This system is helpful when it comes to teaching children place value.

Marmasse, Bletsas and Marti’s (2000) article also describes the 5 principles of counting, outlined by Gelman and Galistel (1978). It is these principles that young children must grasp in order to count accurately:img_2922

  • One to One
    • one counting tag for each item
      • One, Two, Three NOT One, Two, Two.
  • Stable Order
    • counting tag order must be repeated and consistent (not as below)
      • Counting 3 items – One, Two, Four
      • Counting 4 items – One, Four, Three, Five
  • Cardinal
    • last tag represents the cumulative amount of items
      • If counting the apples, you know that once you have counted 10, that the ten applies to the total of the apples, not the specific last apple you counted.
  • Abstraction
    • anything can be counted
      • from age 2/3 children can count groups of mixed items
  • Order Irrelevance
    • doesn’t matter where you start counting from (left, right, top, bottom)
      • This skill doesn’t emerge until age 4/5

file1321335630826Early counting involves using manipulatives i.e. fingers or toys. This then progresses onto verbal counting, removing these prompts with children counting in their heads, and eventually being able to recall facts from memory. For example, we all know that 3+7 = 10 without actually having to count on 3 from 7.

The part of the article that particularly resonated with me was where they discussed different teaching approaches. Marmasse, Bletsas and Marti discuss the two different teaching approaches as “traditional” and “constructivist”. These two approaches are much the same as Skemp’s instumental and relational teaching (as discussed in my previous blog available at

It is clear that, while Piaget was partially correct in saying children are not born with any mathematical ability, numerosity is both innate and developed through learning experiences. There are some principles of basic mathematics that cannot be developed until around age 4/5, however, Piaget’s belief that it is not until age 8 that children develop a mature number sense has been clearly disproved by theorists such as Starkey. This is an important factor to consider in the classroom, and I will take this forward in teaching maths in school. Children are more capable than they are given credit for in mathematics, and I intend to use this knowledge and try more complex lessons and mathematical discoveries in future.


Marmasse, N., Bletsas, A. and Marti, S. (2000) Numerical Mechanisms and Children’s Concept of Numbers. Available at (accessed on 1/12/16)

Starkey, P., Spelke, E.S., and Gelman, R. (1990). Numerical abstraction by human infants. Cognition, 36: 97-127.


There’s Been a Murder!


In the clip below, Dan Walton (Teacher of the Year) is teaching his class Pythagoras. My memories of pythagoras at school mainly involve textbooks, much like most other maths topics in high school. We were taught the rule and how to apply it (instrumental understanding) and given textbook work to consolidate our knowledge. However, Dan’s approach to teaching this topic is very different.

Pythagoras is the rule that the squares of the shorter two sides with equal the square of the shortest side – a²+b²=c². Rather than simply teaching this rule to his class, he has them find out the answer. Some of the children simply draw the triangle to scale, giving them the correct answer, others must work out the rule using numbers. This is giving the children multiple ways to solve the problem and they then realise that the formula is more efficient than drawing triangles every time. By having the children investigate this rule for themselves, Dan instantly has the children engaged in the lesson.

captureBy using a real life example (golf hole), Dan is showing the children the context of this learning in the world outside of the classroom. He gives them the option to solve the problem any way they want, allowing them to choose between the two methods they have explored. All of the children opted for the formula method, showing their ability to select an appropriate method for solving a problem.

When Dan then moves on to working out the length of a shorter side, he has a small piece of paper showing the rules of pythagoras, but does not tell the children anything about what they have to do. This investigation and discovery really has the children engaged and involved in the lesson in a way that a textbook cannot do. The children are working out what they must do – they are taking control of their own learning. By giving the children the opportunity to do this, Dan is helping them with long term problem solving skills. The children learn that the answer is not going to be given to them, they must work it out themselves.

The climax of the lesson, drawing on all the pythagoras they have learned, is a murder mystery file000814023043problem. There are multiple pythagoras questions which they must solve in order to find out who the murderer is etc. This is an incredible way to find out if the children have taken in all that has been taught. If the children can find out the answer, then they understand the rules of pythagoras that they have been taught. Dan even hides some of the questions around the school to bring some energy and movement to the lesson. There is no doubt that this is substantially more rewarding for children than sitting at a desk with a textbook.

While pythagoras may be a more advanced topic than those of primary mathematics, I believe that many lessons can be learned from Dan’s lesson. Children should be encouraged to explore numbers and mathematics, rather than being told a rule and applying it. If they can work the rules out for themselves, not only are they much more likely to remember it, but they are more likely to enjoy this learning. While we cannot allow primary children to run around the school looking for questions, it is important that we allow them to have active maths, even taking them outside as a class into the playground to solve some problems will be much more engaging and exciting than a normal maths lesson. Dan also does not share the learning intention with the children at the start of the lesson, again, promoting discovery and exploration. I believe that this is even more important in a primary classroom as allowing children to find out what they are learning themselves shows that they have actually understood what is being taught.

In my future maths lessons, I want to incorporate some of these techniques, especially taking learning outdoors. Maths does not need to be sitting in front of a textbook. Maths should be a wonderful, exciting discovery of the whys and hows of numbers – an idea all too often overlooked in the primary classroom.

Lost in Number Translation

Skemp suggests that there are 2 types of understanding: instrumental and relational.

Instrumental understanding – Not quite about playing the piano, but I think the analogy applies. old-piano-keyboardInstrumental understanding is like knowing the notes to play, but not knowing the tune – in maths terms, it is about knowing the rules, formulas and processes to get an answer, but not knowing the underlying concepts. This method is easier to understand and children get to see the results of their learning quicker, giving them a sense of success that children, like all of us, are excited by. These reasons are why it is understandable that teachers use instrumental understanding in the classroom. If there are upcoming tests or exams, it is quicker and easier to teach this way if it is a subject they simply need to know. A teacher may also feel that the children have not developed skills that are needed to understand relational thinking, the other type of understanding described by Skemp.

above_londonRelational understanding is a more complex affair, however, the long term effects are substantially worthwhile. It is about knowing why you are using a certain rule and the concepts beneath the strategy, i.e. why two negatives make a positive. This approach is more adaptable to new tasks and is easier to remember in the long term. Relational understanding is knowing all of the connections across mathematical topics.


Skemp uses the analogy of a town to explain the difference between these two approaches. You can walk through town knowing your route from A to B and a few other routes nearby to get to the essential places you need (instrumental) or you can create a “cognitive map” of the town in your head, knowing all the routes and which is best for your journey (relational). If you can master the second approach, then you will never be lost.


Skemp, R. (1976) Relational Understanding and Instrumental Understanding. Mathematics Teaching. Available at (Accessed 23/09/16)

Clever’s New Friends

Stories are a great way to introduce new concepts or feelings to young children, especially in file000129746402Early Years (primary and nursery). Children may recognise the feelings of the main character in the story as feelings they have felt in their lives, however, young children struggle to communicate their feelings – emotion words are often learned last. Stories provide children another land to get lost in as they follow the main character and find out how they deal with their problems. The child, knowingly or not, will be able to take messages from the story and use them when they find themselves in this situation.

There are lots of different “social stories” that target specific issues children may be having such as loss/grief, anger issues or loneliness. There are also stories like this for children with Autism and other learning difficulties, which may help them cope with problems they might have in daily school life.

The below clip shows a social story about using polite words and being nice to others:

In the story Clever’s New Trick, we see the story of Clever the fox who has problems with his temper. This leaves him lonely as no one wants to play with him. Jerome the Gnome teaches captureClever a trick to help with this – Stop and Think. He uses this trick with some of the other animals, practicing controlling his temper and playing with his new friends successfully.

While this teaches the lesson of controlling their emotions, it also teaches the children that everyone is learning things – nobody is perfect i.e. Snowy Owl is still learning how to fly well. This story could be used in Early Years quite easily with the right preparation.

There are some words in the story that young children will not know i.e. hesitant and remorseful. As children will be fixated on these new words, it would be useful to use these words prior to telling the story, a few hours or days before. This that the children are still learning these new words, but can still focus on the story. It is also important to have questionscapture to ask the children throughout the story, such as asking them to predict what will happen next. This involves children in the story telling process, stopping them from simply being passive listeners. It is essential to plan these questions in advance, as it is unlikely that suitable, high-level questions will be thought up on the spot. It is also important that children have the chance to ask questions of their own. This consolidates their learning and allows them to fully understand the story, which is especially important if there are follow up activities based on the story.

Stories are essential in the classroom, and are often overlooked as something to do to fill in time, or to calm the children after playtime. While stories can relax the children, it is important not to simply use them as a filler activity. Story time should be planned as much as any other lesson in order to get the most out of them and to develop key literacy skills in children such as prediction, analysis and merely an enjoyment of stories and reading.

“So please, oh PLEASE, we beg, we pray, go throw your TV set away. And in its place you can install, a lovely bookshelf on the wall.”

Reading is often an important step for children, and parents. Children are pushed through school reading books and literacy programs, sometimes losing the enjoyment they may have once had for reading and language itself.


Early reading for children is not so much reading, as recognition, usually of signs, logos, and other environmental print around them.

There is some debate as to whether children should start reading sooner or later. One study in support of children reading earlier is Kraus’ 2015 study where they had devised a test which could predict a child’s language ability and even whether they may have trouble reading in the future (News article of study available at

While this study may help to draw attention to those who may need assistance in language, I worry that it will isolate those who do well in the test. If a parent knows that their child will not have any difficulty in language and reading, I believe that it will make them less likely to prompt their child and support them at home in a way they may have before. If a psychic tells you that you will meet your soul mate aged 25, would you bother looking for love aged 20?

There is much research against this study, saying that we should be starting children reading courtneyhollidayreadingimagelater, not earlier. Laura Grace Weldon writes about “Reading Readiness” and how we should be giving children more opportunities to learn from life, to learn from exploring rather than from sitting at a desk reading (article available at  She notes that children have 25% less free time than they had a generation ago (taken from We have children sitting in school all day, and in many cases sitting doing homework or reading school chosen books at night. While reading does unlock a lot of other subjects in school, I agree that there is a lot of pressure on children to read certain books in order to achieve reading success. This attitude can actually be detrimental in affecting the attitudes of children towards reading. If children are being pushed into books they do not want to read, then they will have no motivation to read them, and, eventually, no motivation to read.

readingThere are some studies that actually argue that children do not need to be taught to read – they will simply teach themselves. Gray (2010, available at looked at non-teaching schools and particularly the reading ability of the children. He found that children were able to teach themselves to read. They all appeared to have their own strategy, with no correlations showing between students. This method ensures that children are learning in the best way for them and are able to choose their own books with no reading scheme to follow.


I find myself leaning more towards the argument of Laura Grace Weldon. Young children do not need to sit at a desk in order to learn. Children learn from feeling, doing, exploring. The great outdoors has a mass of teaching opportunities for young children, and I believe that teachers are not taking advantage of the wonder that lies outwith the classroom walls. During my teaching career, I would love to be able to explore this more and show children that they do not need to have their nose in a book to be learning.

I want a pig for breakfast!

While Chomsky believed that children are born with an innate capacity for language, other theorists such as Bruner and Vygotsky believed that language was developed in social situations, by interacting with others. This begins early on in the child’s life, talking to parents/carers and other family members, before the child then goes to school and develops their language skills even more by talking to peers, an experience they may not have had at home. Adults therefore play a huge role in affecting the language development of children, especially in the early years.

Talking to children from birth is so important in modelling words for the children to imitate. While language acquisition cannot solely happen through imitation (this theory does not account for misuse of grammar such as “I goed”, which you can often hear children say), it cannot be denied that it is a crucial step in a child’s language development. Unfortunately, I have seen lots of new parents pushing their child in a pram/buggy with one hand, and the other hand attached to a phone. I do not judge these people, I do not know them, but in terms of a child’s development, they are missing out on crucial attention from an adult who should be helping them to make sense of the mystical world around them. This is an example of how adults can inhibit the development of children’s language.

In the clip below, we see Niaz, a 3 year old child in nursery beginning to make sense of many of the complex words and rules of the English language.


When Niaz begins playing with other children, he quickly finds that they are not giving him the attention that he wants and seeks this attention from an adult. This is because children at this age are still quite egocentric, and believe that they are the centre of the world which revolves solely around them.

The adult in this situation is a good example of how adults should support children in their language development. She uses lots of praise when talking to the children and has a clear, consistent voice that is easy for the children to understand and model. She knows that the children will model what she says – when Niaz gives Stephen some paper she says “Thank you Niaz” which the children will pick up on and eventually internalize as correct manners. Even though she has to monitor other children, the adult gives Niaz lots of attention – this will make Niaz feel more confident and want to continue talking as he feels listened to.

The adult also asks lots of prompting questions in an attempt to get Niaz talking more and answering them i.e. “What do we need the pencils for?” When she asks him this, you can hear that Niaz is wanting to say “list” but is getting stuck on the ‘l’. The adult continues to prompt Niaz which results in him being able to communicate what he is wanting to do. If the adult had given up at this point, Niaz would have lost confidence, inhibiting his language development.

When they begin writing the list, the adult uses pictures to signify objects they will recognise capturefrom everyday life – such as cereal and milk. When Niaz begins his list, he draws a pig with quite a few too many legs. Rather than correct this, the adult praises Niaz for his attempt, getting the rough shapes correct. Niaz then draws a picture of himself. The adult then tells him that then we will know that it is his list. This is the beginnings of teaching ownership and certain words such as ‘mine’, ‘his/hers’ and ‘yours’.

The role of an adult in terms of language development is to encourage children, using lots of praise even if what the child says isn’t quite correct. If an adult is constantly correcting and berating a child for incorrect pronunciation or grammar, the child will lose confidence and will eventually stop trying. We must remember that children are just beginners in language – it will take several years for them to master this complex skill. It is important that adults spend the time talking to children at this early stage. Even if you think they do not understand what you are saying, they may really be internalizing every word.

(All images are screenshots taken from the video hyperlinked above.)

“Tough guys don’t do math. Tough guys fry chicken for a living.”

Stand and Deliver (1988) is a film following teacher Jaime Escalante as he teaches a class of mainly Hispanic students in a fairly impoverished school/community. He has a radical teaching style much different from the norm of teachers across the globe, where he frequently makes fun of children and has a ‘no tolerance’ policy for anything less than perfect.

Image result for stand and deliver film

Real Jaime Escalante with Edward James Olmos, the actor who played him in the film. Picture courtesy of

Escalante, born in Bolivia in 1930, became one of the most famous educators in America, moving there in pursuit of a better life. As shown in this film, he taught disadvantaged pupils, whom some teachers had given up on completely, and managed to have a handful pass an extremely difficult Calculus test. Escalante’s success has earned him many accolades, including being entered into the National Teachers Hall of Fame in 1999.

It is interesting to analyse Escalante’s teaching style in the film as it is far from conventional. He does not accept poor behaviour, and even why one student, Angel, walks out of the class, he merely says goodbye rather than chasing after him. Escalante is more concerned about the children who want to learn and believes that it is a privilege to be in his class. The children respect their teacher and want to do well for him. While his teaching style may be considered to be scaring his pupils into working hard, I believe he does this with a true sense of compassion and care for the future of these children. This caring nature is highlighted in the scene where Escalante gives Angel 3 textbooks – one for class, one for home and one for his locker – as he did not want to be seen carrying them around. This compromise can be useful in the classroom as it encourages conversation between teacher and student, rather than a one sided lecture from the teacher, which can cause the students to disengage.

When looking at specific teaching points in the film, it is clear that there are lessons to be learned from Escalante’s teaching. For example, a quote from the film that resonates with me is “Students will rise to the level of expectation”. It is crucial that teachers have high expectations for their students as it shows a confidence in them that they may not have themselves. I hope to remember this along my teaching journey.

Another example is how to help the children understand what he is teaching them, he uses language and problems that make sense to them – he gives the problems a sense of relevance. One example of this is when he uses numbers of girlfriends in a problem (see the below clip).

Using girlfriends instead of other objects such as apples or pens engages the children, making them laugh and therefore creating a relaxed classroom atmosphere where the pupils are confident in answering questions. Another example is where the pupils ask the real life benefit of learning these things and their teacher takes them on a trip to show them exactly how that maths is used in the real world. This idea links to the principle of relevance within the Curriculum for Excellence (Scottish Executive 2004, p15).

It is important that we teach children why they are learning things. While this seems to be an accepted part of the curriculum, maths, in my opinion, seems to miss this principle. In a broader sense, you can often hear students, especially at high school, saying “Where’s the point in this? When will this ever help me in real life?” This shows a distinct lack of teacher communication with the children about why they are learning these topics. In terms of more basic level mathematics, learners need to know what all these different rules and formulas actually mean. Pupils could be given rules and memorize them, which tends to be the case, however, they have no true understanding of why. This may be the case because many teachers themselves do not know the reason why, as they have been taught just to memorize the rules, therefore getting trapped in an endless cycle of knowing but not understanding.

I believe that I myself fall into the above category. While I enjoy maths and teaching it, I would say that I do not have a depth of knowledge in why maths happens. I hope to look into areas of mathematics in more depth in order to improve my knowledge of maths and my ability to teach it to a strong degree.

References Editors (2014) Jaime Escalante Biography. Available at: (Accessed: 15/09/16).

Scottish Executive (2004) A Curriculum for Excellence. Available at: (Accessed on 15/09/16)

A Journey of Discovery

I have chosen this elective because of my love of maths. I have had a real enthusiasm for maths and numbers from a young age and have always been fascinated by the way numbers are connected and can move and change.

In this elective I am looking forward to learning more about maths and where it comes from, and especially how maths is used in school. I have found that children in primary school have a love of maths and enjoy learning about it, in general. However, when we get older, usually reaching high school, that love is gone. Textbooks chase out the enjoyment in maths.


It’s no’ aw Haggis an’ Bagpipes

Culture is something we all accept and we are aware of the culture around us, however, it is difficult to explain or define and has been for many years. In fact, in 1952 Kroeber and Kluckhohn (cited in Spencer-Oatey 2012) listed 164 different definitions of Culture.

I see culture as social norms which affect how we live our lives. For example, a school with a culture of hard work and respect is likely to promote this traits in their pupils, which should in turn see children valuing these traits more.  Values play a huge role culture, whether that be the culture of a small group such as a family or a school, or in fact a wider community or country. I believe that in this country we have a very capitalist society, which is instilled in our minds and affects the values we have, such as hard work and an aspect of independence.

I belong to many cultures: family, friends, university, Scottish culture, and the culture associated with teaching. These different groups/cultures have shaped me to be the person I am today, however, they are quite different. The way you behave around your friends may be totally different from how you behave with your family, which may again be different from how you behave in a teaching environment. This is because of the social expectations and norms set within these groups that lead us to behave in different ways.

Scottish culture is often perceived as haggis, bagpipes, kilts and whiskey. While these are all part of Scotland’s rich culture and heritage, they are just cliches – there is much more to Scotland than people think. Scotland has a rich heritage of music and dance, dating back to Robert Burns and Auld Lang Syne, a song still hugely celebrated in Scotland and across the globe.

Scotland also has a culture of dance, which is slowly dying out in this modern world. Both Highland and Scottish Country Dancing are celebrated in Scotland, with the latter being taught in many schools in an effort to teach children about the culture of their country. However, I believe this is not taught in the best way, as many children, in particular boys, disengage from the dances. I myself have been Scottish country dancing as a hobby since the age of 5 and have seen the numbers in our class hugely decline over time. I believe that this is partially due to the way these dances are taught in schools

Scottish music can also be recognized across the globe, especially the classic image of the piper kilted up in the traditional attire. Take the time to listen to and appreciate the rich culture of Scotland and I hope I am not alone in being able to appreciate this beautiful music even after so many years.



Spencer-Oatey, H. (2012) What is culture? A compilation of quotations. GlobalPAD Core Concepts. Available at GlobalPAD Open House