Category Archives: My educational philosophy

Profound Understanding of Fundamental Mathematics

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 “Teachers must have a profound understanding of fundamental mathematics.” – Liping Ma, 2010

009To teach maths, you must first understand maths. To understand maths you have to be fully engaged and willing to put yourself in your pupils’ shoes and learn. Liping Ma states that this is one of the most important factors in terms of enhancing teachers’ knowledge of, and ability to better teach, primary mathematics.

However, having a concrete profound understanding of the fundamentals of mathematics is much more than being able to understand primary mathematics. You have to make sure you have a sound knowledge of the overall theoretical structure and basic attitudes of mathematics. By having this, you will then be able to use this as a foundation in order to teach your children effectively and inspire them to want to learn maths for themselves and not because they have to. It is very important to have a conceptual and procedural understanding – to know how and why we do something – that is deep, broad and thorough.

In order for yourself and your pupils to meet what Liping Ma states as a profound understanding of the fundamentals of mathematics you have to make sure that you can identify and understand the four principles that are essential in being able to meet this ultimate goal.

The first of these principles are (inter) connectedness. This refers to being able to see connections between concepts and procedures. Meaning that children can see why there is a need to have elements of maths that connect together in order to be able to use at other points of your mathematical education. This could be as simple as letting the children understand that in order to move on to understand and describe two dimensional shapes they first have to know the properties and characteristics of two dimensional shapes. This will then help to ensure learning is not fragmented, but viewed instead as a unified body of knowledge.

The second principle is multiple perspectives. This is having the ability to comprehend and also appreciate the different approaches you can have to one specific mathematical problem. This therefore encourages a more adaptable way of thinking and is therefore not restricting any child as it is not focused on one learning style. Teachers who have the ability to develop multiple perspectives for every topic within mathematics will have a better sound knowledge of the fundamentals of maths overall.

Thirdly, Liping Ma talks about basic concepts and having a full awareness of all the central ideas that surrounds primary mathematics. It is important that the basic ideas that recur throughout maths are constantly revisited until they are fully reinforced and have created a solid foundation in order to move forward onto future concepts. Without basic concepts, we would not be able to move forward and enhance our mathematical ability.

The last feature is longitudinal coherence. This is having a full awareness of the entire mathematical curriculum and how one basic idea or principle can be built upon another. What is taught today becomes the base for future knowledge, just as current mathematics teaching builds upon students’ previous knowledge, however fragmented that knowledge may be. This allows for there to be much more understanding and flexibility in terms of where learning is headed as lessons can be tailored with this in mind.
With this profound understanding of fundamental mathematics, we as teachers will be able to teach students more successfully. I fully agree with everything Liping Ma says and believe that I will definitely work to this model in order to teach mathematics to the best of my ability to my pupils in future.

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Ma, L. (2010) ‘Knowing and teaching elementary mathematics’. London: Routledge.

 

Lets have fun, lets do maths!

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One of the most important factors for me to have children engage with mathematics at a level that they want to learn and more important understand what they are learning is to make sure they enjoy what they are learning. In order for this to happen it is up to us, as teachers, parents and careers to make mathematics enjoyable and allow them to see that maths can be used whilst playing.

As an adult being able to play during a maths input put a smile on my face. I loved it. Being able to physically get to grips with what we were learning through the use of building blocks, games and other various maths resources that can typically be found in an everyday classroom and most home environments was so much more refreshing than a boring PowerPoint.

007Allowing children to play is an extremely central factor in their overall holistic development. It allows them to make connections to their learning, especially when they are in a relaxed environment. It empowers them to experiment and encourages creative and flexible thinking.

The National Scientific Council on the Developing Child recognises that child development is the key to the future success of a society.  They define the core concepts of development as including “cognitive skills, emotional well-being, social competence, and sound physical and mental health” They also stress that if these areas of development are nurtured in the early years through quality learning environments, positive relationships, and engaging social interactions, a foundation will be laid for future successes that everyone wants for every individual child. Some of these successes that the NSCDC describe as things such as; positive school achievement, future economic productivity, as well as responsible citizenship.

005A simple thing such as the building blocks we used within our input are small but so effective. They can help a child start there numerical experiences by counting one by one, moving onto addition and subtraction and then can be used further up the school for more challenging lessons such as cubic centimetres. We take for granted as adults how easy counting actually is. We do not remember the stress and anxiety that we had to go through when learning the simplest fundamentals of mathematics. This step is one that has to happen though; Liping Ma states that we have to be aware of the basic concepts of maths and these concepts have to be reinforced and revisited before children have the foundation to deal with future concepts and can then move onto more complex mathematical problems.

My initial concept of maths has completely changed in the few weeks that I have being doing the Discovering Mathematics elective and I feel this is due to the fun that has been incorporated into lessons and inputs. By being able to work with friends to solve problems or to play maths based games brings out feelings towards maths that I never knew I had. As a student teacher, this is one of my main goals when teaching maths to my pupils. I personally feel that I will move away from the old games and resources, as good as they were, I used them 17 years ago so they are a bit outdated. But with all the technology we have now a days and how easy it is to access different resources I hope to let all my pupils know that maths does not need to be hard, stressful or boring… Maths can be fun. 006

Haylock, D. (2010) Mathematics explained for primary teachers. 4th edn. London: SAGE Publications

Ma, L. (2010) Knowing and teaching mathematics: Teacher’s understanding of fundamental mathematics in China and the United States. 2nd edn. New York: Taylor & Francis

Earn it

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College was the first time I had heard of B.F. Skinner and his theory of operant conditioning. Straight away I took an instant interest in it and decided that I would work around his theory of positive reinforcements to complete my graded unit.

My graded unit consisted of me investigating an area of my choice within the classroom and reporting back on my findings in detail in a form of a report.

Straight away, the idea of reinforcements for behaviour got me thinking about children and one 052child in particular that I worked one-on-one with. This specific child, lost his golden time almost every week. He had different behaviour management strategies in place however told me that he did not find the need to behave as he always lost golden time anyway. After having this conversation, I researched low self esteem in schools and the highest trigger for children with low self esteem was due to the children constantly getting in trouble. So, I discussed in depth with my teacher the idea of changing golden time from the norm of losing it, to every child starting with none and earning it for a week.

At first, the teacher felt that the children would not like the Golden Time changed however, after I discussed with the children what would be happening, I allowed them to vote independently wither or not to try the new Golden Time procedure so that it was the children’s decision and not mine. The results came back and the majority of the class voted to changing Golden Time to earning. The teacher was very surprised with this but was also excited to see my results after the week.

As I based my project on the theories of, Skinner, Rodgers, Maslow and Erik Erikson I learnt a great deal on children’s behaviour overall. I agree with Skinner in a lot that he says about positive reinforcements and my investigation reiterates that what he was saying actually has a major factor of truth.

After everything was researched and the ‘Golden Rules’ that the children came up with collectively as a class was put in place, I allowed the children to then earn their golden time over a week. After the week was over, I gained feedback through a carousel method and found 051that the children found earning golden time a better method to use as they could work as a team and it made them feel better knowing their positive behaviour had gained a reward.

I would love to have done this with the child that gave me the inspiration to put this investigation into place. I feel that it allowed children who may feel discouraged to improve their behaviour due negative reinforcements to have a clean slate and try to turn their behaviour around by working together with their peers. By also physically seeing the rewards for their good behaviour by receiving golden time the children’s self-esteem will also hopefully increase overtime.

The Big Five

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Everyone has a personality, there is no disputing that. Everyone’s personality is also very different. However, it is something that I have to say, I have never really thought about until now.

I found todays lecture surrounding personality very interesting, especially the five different dimensions that your personality can be broken into.

I had never heard of, ‘The Big Five’ before and thought that I would do some of my own research into finding out more detail on each of the sections themselves. Whilst doing this, I came across a website that allowed you to take a personality test which would then give you back in a percentage what your personality scored.

This is a snapshot of my personality test which I have to say, did surprise me.

050 Most of the traits were scored quite close together and I do agree with a few. I feel that I do go out my way to please others and I do feel that I may come across as shy in certain situations. However, I was very surprised to see that the score for Neuroticism was very high at 81%. I know that I have experienced some situations that arise negative emotions but I wouldn’t say that it was any more than anyone else. Due to this, I feel that I need to look at myself and take consideration in the way I may or may not react to everyday situations to see if I subconsciously experience negative emotions without myself even noticing.

If this test is something that also interests you and you would like to find out what your ‘Big Five’ say about you, this is the link here.

The Road to Becoming an Enquiring Practitioner

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Are you someone who is proactive? Are you responsible for maintaining and enhancing your own professional skills? Do you do this to enhance your own pedagogical development? If so you may just be on your way to becoming a very good enquiring practitioner.

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An enquiring practitioner goes beyond the norm of personal enquiry and reflection. They have the ability to share and discuss their own knowledge with others and also to listen and retain information that others share with them. From doing this, as a professional, you will then be able to continuously develop on your own learning.

 

Professor John Hattie stated; “The biggest effects on student learning occur when teachers become learners of their own teaching”.

A teacher who is constantly learning and can be seen as an enquiring practitioner may research topics such as teaching techniques and adapt their own ways of teaching to facilitate the best learning possible for the children within their classroom.

There are numerous benefits that come with practicing to be an enquiring practitioner. Not only does it allow us, as teachers to monitor our own practice it also allows us to critically analysis our practice and challenge ourselves to become better and more professional practitioners.

By being an enquiring practitioner, we allow ourselves to continuously develop and enhance on our own learning and teaching abilities. By doing this, we are in control of setting out the best learning environment we can to teach our children in.

Being an enquiring practitioner also means that we can work together, collaboratively, with not only our colleagues but also the pupils within our classrooms. By working closely with these people, we can see what does and doesn’t work with others practice and also know that there is a safety net if you feel that advice or guidance on specific areas may be needed.

By working together, teachers can make sure that they are all working towards the same standards and guidelines to ensure that they are working towards the Curriculum for Excellence.

Alongside the benefits; we are also faced with numerous challenges when practicing to be an enquiring practitioner. For teachers who may have been in the profession for many years, or teachers who have a lower self-esteem, the thought of changing their ways to become an enquiring practitioner may cause problems due to anxiety’s and or a fear of a change. Due to this, it may be difficult for these teachers to open up and share their own experiences and knowledge with others which then hinders them from becoming the best practitioner they can.

Although there are challenges that face practitioners becoming an enquiring practitioner; the benefits outweigh them. Due to this, every teacher should try their hardest to overcome their fears of becoming an enquiring practitioner as there are so many positive outcomes that can be gained by not only yourself but also your colleagues and your pupils within your class.

As a student teacher, we have a responsibility to also practice as an enquiring practitioner. Whilst on placement as a professional, we will be put in new situations which we may not feel comfortable with but having the ability to adapt our teaching styles and work closely with other staff members we should have the ability to therefore overcome our anxiety’s to these new situations.

Practitioner enquiry impacts on us all both as students and fully qualified teachers. We need to have the ability to have higher expectations of ourselves; have the ability to be able to adapt to new situations and surroundings and be aware of ways to improve our own learning and utilise this within our practice in the classroom.

Reflecting on reflection

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Reflection is a means of processing thoughts and feelings about an incident, or a difficult day… And gives us a chance to come to terms with our thoughts and feelings about it.

Personally, reflection for me is a key part in my learning due to my anxiety. Reflecting back on my learning allows me to identify not only my errors and weaknesses but it can also bring to light the positives of what I am actually succeeding at within my studies. By seeing my own strengths, this gives me a confidence boost and allows me to feel that I could possibly overcome the anxiety’s that I feel sometimes hinder my learning and hold me back.

I reflect on my problems and situations that I find myself in on a day to day basis. Due to this, I see myself implementing and reflecting on most aspects of my life all time, especially my academic studies. I feel that having a more focused reflection, I am able to look at new outcomes and ways of approaching and reacting within certain situations.

‘The way that we learn from an experience in order to understand and develop practice’ – (Jasper2003)

Reflection not only allows us to solve problems but also allows us to learn from past experiences and take control of our own learning. However, reflection does not just have to be looking back and reflecting on what has already happened; it is often useful to also reflect forward. By doing this we can put our past experiences to good use and plan in a way that reflects positively on our learning.

Active & Co-operative Learning

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Active learning allows us as teachers to involve our pupils more in their own learning. Active learning also hopefully lets children feel more engaged in their own learning and feel inspired and excited to learn. There are many positive factors for active learning including; the children being more active towards their learning than having a passive attitude. It also allows the child to take their learning into their own hands which I feel is a more effective method of learning as the child will be more likely to remember and feel excited about what they are learning.

There is an endless list of benefits when it comes to working co-operatively within the classroom for both the teacher and the pupils.

Personally, I feel that working and learning with my fellow colleagues is a more effective method of learning. Discussion ideas with others and getting their opinions and views enhances everyone’s knowledge that is involved within the discussion. Working co-operatively also helps to develop skills such as; time management, communication, social skills and commitment. So if we use co-operative learning within our classrooms with our pupils then this will allow the children to gain and develop these valuable skills.

Co-operative learning gives the children a common goal to work towards as a group. This therefore allows for the children to work closely with each other to get the best results out of the task together, rather than individually so therefore, making it a more effective learning method. As well as allowing the children to develop team working skills it also allows for them to develop respect for their peer’s opinions and views which is a valuable lesson.

Timeline of Neuroscience

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Carrying on from the input on Brain Development today with Will, I found that there is a large array of events that took place in the subject of neuroscience… As there as far too many to write I have just selected a variety that interested me within the 20th century.

  • In 1909, Harvey Cushing is first to electrically stimulate the human sensory cortex.

Studies involving severe epileptics has shown us that using weak currents, investigators found that the usual responses when stimulating the individuals included, numbness, tingling and feelings of electricity and all these feelings where on the contralateral side.

  • The disease, Alzheimer’s, was named by Emil Kraepelin in 1910.

Kraepelin, who was a german psychiatrist that worked closely with Dr. Alzheimer, first named the ‘Alzheimer’s disease’ in the eighth edition of his book, Psychiatrie.

  • The intelligence quotient, or QI, was first developed in 1912 by William Stern.

He felt that by investigating the individuality of a person he could then uncover real principle of personality and intelligence. He developed the idea of expressing intelligence test results in the form of a single number, the intelligence quotient.

He looked at individual test scores and focused on “mental ages” which could then be compared to actual ages which could then relate to their intelligence ability. To get the intelligence quotient, he took the mental age and divided it by the chronological age.

  • In 1916, Shinobu Ishihara published a set of plates that were used to test colour vision.001

The colour test is called, ‘The Ishihara Test’. The test consists of a number of coloured plates which are called Ishihara plates. These plates contain a circle of dots appearing randomised in both colour and size. Within the dots, there are dots of another colour with represents a number or shape visible to those with normal colour vision. However, if you have a colour defect, these numbers or shapes will be invisible or difficult to see.

  • B.F. Skinner publishes ‘The Behaviour of Organisms’ in 1938 that describes operant conditioning.

The term, ‘operant conditioning’ was invented by Skinner. Roughly, it means to change the behaviour of a person or animal through the use of either positive or negative reinforcements. If the subject is shown to be doing the desired behaviour, then this is when the reinforcement is given.

  • In 1953, Eugene Aserinski and Nathaniel Kleitman describe rapid eye movements (REM) during sleep.

Kleitman and Aserinsky discovered there to be rapid eye movement while a child was sleeping. This led researcher into believing that sleeping involves some sort of learning process.

  • In 1956 Rita Levi-Montalcini and Stanley Cohen isolate and purified nerve growth factor.
  • The treatment for depression was introduced by Fluoxetine in 1987.

Eli Lilly and Company discovered Fluoxetine. This drug is used for a number is disorders including; major depression, obsessive compulsive disorder, bulimia, and panic disorder. In some cases, it has also been used to treat trichotillomania, a condition where the individual feels the need to pull their hair out, if cognitive behaviour therapy has been unsuccessful.

  • 1990 was declared the ‘Decade of the Brain’ by U.S. President George Bush.
  • Arvid Carlsson, Paul Greengard and Eric Kandel shared the Nobel Prize in 2000.

These men were awarded this prize for their discoveries of signal transduction, which is the message being sent from one nerve cell, to another through a chemical transmitter.

 

Personal and Professional Presence on Social Media

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What challenges/opportunities may you be faced with when marrying the personal vs professional presence on social media?

There are many factors which may be seen as challenges when trying to find an appropriate balance between personal and professional life with regards to social media. One of the most important challenges for professionals I feel is making sure that everything you post on social media sites is done so in a professional manner and that none of the information or comments that are posted are seen as inappropriate.

In my opinion; I feel that either using a name in which isn’t yours or using a completely different account to keep your personal and professional life separate is the best conclusion when dealing with social media online. This way you can make sure that either pupils or parents cannot have access to any of your personal details. This way you can also make sure that you are still able to engage with issues that can relate to your professional life in an appropriate manner.

Currently, all of my social media settings are turned to private. This means that only friends that I allow on my social media sites can see what I post, comment on and also what I may be tagged in. I feel that this has been the most appropriate choice for me up until now however, I am now thinking that I may open separate accounts to separate my professional life.

As well as the numerous challenges presented by social media, there is also an array of opportunities. It allows children to have experiences on different uses of technology that they may not have the opportunity to do so outside of school. Different forms of social media can have many different effects within the classroom. For some, it could be very effective in tying home and school together as social media will most likely be something that the majority of pupils use actively in their life outside the classroom.

As social media grows, it becomes a much more important tool to implement within classrooms. Due to this, the GTCS have very specific guidelines. These guidelines allow us as teachers to know the correct and appropriate way to use these sites in order to present ourselves as professionals and also to stay safe whilst online.

How are the challenges/opportunities afforded by social media framed? How will you frame things – positive of deficit viewpoint?

I most definitely have a very positive view point of technology and social media. Because of this, I will frame social media in a positive way when I am a teacher. I personally think that people feel that children are growing without a proper childhood and are using technology and social media instead of playing outside like we used to. However, with this ever changing society, we have to come to the conclusion that this route that our culture is taking and we should embrace this positively. I feel that we should use social media as a great advantage to help with education and embracing the children that we teach.

 

The Virtues of Teaching

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Teachers need to have the ability to display a variety of different virtues and ethics all the time within their professional career.

I have chosen to focus on five main traits, which I have went into more detail about below. However, I am not saying that these are any more important than other traits. It all primarily depends on the individual circumstances at the time and how you as a teacher feel would be the best way to handle that situation.

Patience;

Patience, I feel is one of the most desirable traits for any individual however, for teachers I feel it is essential. This trait is most definitely vital while working in a classroom setting. As a patient teacher, I feel you should have the ability to adapt and try new learning styles and approaches when children aren’t responding or grasping certain things you are teaching. Not every child will be able to understand and learn the same way which then results in you as a teacher being able to remain patient and calm whilst finding another method that the child or children can understand.

Patience is also very important when it comes to a child’s behaviour. I feel as soon as you lose your patience with a child due to their behaviour then you have lost control of the classroom and everything you have learnt in how to teach. I fully believe that every type of behaviour displayed by every child can be chipped away down to the root cause of why this child is behaving in the way. However, to find the root cause requires patience on the teacher’s behalf. Without patience, you may find that you just write the particular child off as a ‘trouble maker’ when in reality there is a deeper cause and meaning for the behaviour being displayed.

Respect;

I feel that, respect is one the most important traits for a teacher to possess. Without respect present within the classroom both towards the teacher and the children then it is not an environment in which anyone is going to benefit from learning. If a teacher is respected by his or her class, it will create a learning environment where everyone feels comfortable to be and to learn in.

To gain respect, one must show respect; I feel that this is very important within the classroom and that some teachers need to realise that children should not just respect you because you are the teacher, the children should respect you because you respect them. Respect is a two way relationship and I feel that if it is met by both parties then everyone will benefit.

Empathy;

In order to be the best teacher you can, you have to have the ability to display empathy towards your students when necessary. By being able to do this, you will be able to make an almighty difference in the learning of the pupils’. By being able to bring yourself down to a child’s level and fully show that you understand and empathise with what the child is going through, that child can then see that you are a trustworthy and important character in their life, that they will feel comfortable to approach. Without empathy within the classroom, pupils may not feel safe or happy. There may be a lack of confidence in the teacher from the children and they also may feel that they cannot trust them.

The key to being empathetic is to be realistic and realise that every individual is different, with completely different circumstances both within school and outside. To be able to empathise with the different circumstances that you may be approached with you have to be able to be aware of what is going on around you and also to be an approachable figure to every one of your pupils’.

Fairness;

Preconceptions and expectations should be left at the door when you as a teacher enter your classroom. Fairness within the classroom is essential for every child to be able to learn within the classroom at the best of their abilities. Without fairness, teachers may dwell on matters such as: class, gender, race, family etc. which could result in you as a teacher not being able to look at that pupil and see their actual qualities, abilities and potential.

Teachers should also not show or have any favouritism towards pupils within their classroom. Every child should be encouraged and taught to the best of their abilities to achieve their potentials.

It should only be fair that within a classroom, the teacher should make sure that every child has the same opportunities to progress and blossom throughout their education to then reach the best of their abilities later on in the future.

Compassion;

As a teacher, you have to have the ability to be compassionate. The reasoning for this is due to the vast variety of different children from different backgrounds that you will be working with. I believe that due to this, compassion is very appropriate to show the pupils that not only are you human but that you are a means of support and an approachable individual in that child’s life for when they may need it.