Number Systems

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In our number systems lecture we were exploring patterns, sequences and similarities. In particular, we were asked to consider why we have numbers? Of course there were multiple answers to this:

money ~ pocket money, buying products, banking figures
counting ~ shopping, people, stairs
weight ~ baking/cooking, scales
time ~ bed time/bath time, appointments
shape ~ tiling cans, pictures
angles ~ stairs, picture frames

We don’t always think about numbers but realistically they are all around us. We need to have an understanding of numbers for the majority of our day-to-day activities. Without this understanding our mathematical thinking would be non-existent.

Numerals

Next we were asked to consider different types of numerals. Numerals are defined to be symbols used to represent a number.

As we know, there isn’t just one numerical system present. There are many different systems throughout the world. Here are a few examples:

After exploring some of the other numerical systems in the world we were asked to create our own, new, numerical system. Here is what I came up with:

Within my numerical system I began with straight forward lines then advanced onto shapes. I’m not entirely sure how this process would work after 20 but it looks understandable up until now!

Maths Anxiety

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“Maths anxiety, a feeling of fear about maths, is believed to affect about a quarter of the population.” (The Guardian, 2012)

Throughout Primary School I had a great passion for mathematics. For us, maths wasn’t a set subject, we incorporated maths into as many daily activities as possible. All this being said though, the most active our learning ever became was using the ‘show me boards’.

I chose this elective in order to develop my fundamental understanding of mathematics. To find new and exciting pedagogical methods for introducing and teaching mathematics that I can incorporate into my classroom.

During my years at high school, 4 out of 5 years I had a truly inspirational mathematics teacher who would take the time to reinforce what had been taught to enable us to feel confident enough to use our learning in other contexts.

However this all changed in my final year when my maths teacher wasn’t interested in the subject themselves. They would go over one example on the board and then we would be left to our own devices.

Being in that position I can truly say I will never follow the footsteps of that teacher. I know and understand that children need to have a steady foundation to be able to develop further with their mathematical skills. Once the solidity is there, the children can then progress onto more difficult tasks but because of the initial understanding they will be able to interpret these tasks into a meaningful and positive way.

Mathematics ~ Teaching, Understanding, Thinking

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In the Scottish Primary Schools we aim to teach the curriculum using the guidelines to aid our teaching strategies.

As teachers we are aiming to teach mathematics in a fun, engaging and motivational way. We can do this by incorporating active learning into our lessons. By using active learning the children will be enthusiastic to learn as we are providing learning contexts that are relevant to their own interests. By using subjects/matters that the children are interested in we will enable ourselves to communicate mathematical understanding in a successful way.

This following video goes into a primary maths lesson to explore their learning techniques.

The children at this Primary School are “learning without knowing they’re learning”. The are learning through songs, dances and actions. They are learning through the associations made with their actions. They also create their own wrap linked to mathematics. Using the reinforcement methods of repetition and questioning the children are learning continuously but may not realise exactly to the extent of what they are learning.

We are encouraged to make maths intriguing. To issue children with a confident understanding of each concept yet to have the children being challenged by their questions.

The two main aspects of learning to look into are two understanding methods: relational and instrumental. Having a relational understanding of maths means that you have good, solid foundations that allow you to explore ideas further. On the other hand, instrumental understanding is when you don’t have a full understanding therefore struggle to make the appropriate connections where required.

To enable an appropriate competence in maths we need to consider the steps that you process to think mathematically. Below is the grid that we came up with during our “Intriguing Maths” Lecture.

Additional to our Mathematical Thinking Process we also added in a conjecture. This allows us to take a prediction of what we think the correct method would be and then after we have checked this for validity we can then reflect on our initial thinking.

Here is an example we worked through in class:

Professional VS Profession

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Professional vs Profession

Professional

An expert in some skill or field of knowledge (google)
Have a particular ethical or moral character (Carr)
Require a high degree of individual autonomy (Elsevier)
Engages in a specific activity as a paid occupation not an amateur (Google)
Enhancement of status (Elsevier)
Responsibility
An activity which one is paid as opposed to doing voluntarily (Elsevier)

Profession

A vocation requiring knowledge of some departments of learning (google)
Provide an important public service (Elsevier)
Wants to be part of society
Requires organisation and regulation for purpose (Elsevier)
Oldest profession – prostitution
Level of skill applied (Carr)
Competent in chosen sector
Improvement in the quality of service (Elsevier)
Keep working at it, CPD
Formal Qualifications: certificate/higher degree
Prolonged training
Commits to behaving ethically

Teaching is a profession laden with risk and responsibility that requires a great deal from those who enter into it (John. I. Goodland)

The Moral Base for Teacher Professionalism (Hugh Sockett, 1993)

Hoyle (1980)

Professional ~ Focus is on the quality of a person’s professional practice
Profession ~ Status of the occupation
Professionalism ~ community, knowledge, accountability & ideals

Bruner (1974) “Foundations of any subject can be taught to anybody at any age in some form”

Sockett (1993) “Professionals believe in the purpose of their profession”

The Role of the Teacher (Hoyle, E. 1969)

The Criteria of a profession ~ “Profession isn’t a precise descriptive concept, it’s an evaluative concept”

* A profession performs an essential social service

* A profession is founded upon a systematic body of knowledge

* A profession requires a lengthy period of academic and practical training

* A profession generates in-service growth

Discovering Mathematics

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“One of the best ways for children to learn and understand much of the mathematics in the Primary School curriculum is for a teacher who understands it to explain it to them” (Haylock, 2010)

During this elective I am personally hoping to raise my confidence levels in mathematics by focussing on enhancing my profound understanding of fundamental mathematics. To have a profound understanding I will research and explore topics in a deep and thorough way.

The four main fundamental principles of mathematics are; connected, multiple perspectives, basic ideas and longitudinal coherence. To my basic knowledge I will explain my understanding of these concepts so far.

Connectedness. When we are making connections for mathematical concepts and procedures to ensure that we are providing and constructing an appropriate level of understanding.
Multiple Perspectives. Providing the opportunities to use various approaches to solve one solution. Being able to provide the correct explanations to these approaches by having a flexible understanding.
Basic Ideas – Having a foundation of basic concepts/principles to use during all aspects of mathematics. For example, basic equations can be used even when getting more difficult formulae as you can substitute the required information.
Longitudinal Coherence – Having achiveved a fundamental understanding of the whole maths curriculum to enable you to explore multiple different experiences.

Liping Ma (2010) explains the four key elements.

Connectedness – ability to relate topics to one another so that you can build on prior knowledge to work through new processes and ideas.
Multiple Perspectives – ability to use a variety approaches to solve mathematical problems. If you are successful in doing this, then you have complete knowledge of that topic.
Basic Ideas – ability to identify the basic mathematical ideas which are prominent throughout maths topics and use these ideas to inform future processes.
Longitudinal Coherence – what we learn from the start of our mathematical journey influences our current mathematical status regardless of how fragmented our previous knowledge may be.

Fundamental Mathematics Basics

My Educational Philosophy

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A personal teaching philosophy that will be implemented in my future classroom will take into account; the teacher I mean to be, how I’ll support my pupils, what my classroom will involve and the type of education I mean to deliver.

I intend to be an influential teacher, I’ll instill a love of learning in my pupils and share my own love for learning with them. I will be willing to go that extra mile, to be open-minded and to do the unexpected. I will equip children with the information needed to make intelligent choices whilst I have balanced and unbiased views.

I believe that every child should be treated as a unique individual. Pupils will be my key concern as will listening to their thoughts and opinions. I will help them to realise their full potential by helping them discover who they are. As pupils grow and mature I will be preparing them for life society by challenging them, leading to developing together.

In my classroom children will discover for themselves through active learning. This will be done through a safe learning environment with an inclusive classroom which encourages social and interaction skills. This will also allow for freedom of expression and creativity.

Finally I plan to run a child-centred education. This gives the children motivation to work on their chosen aspect and also engages them in lessons. I will plan lessons that have clear expectations and that are interesting and meaningful – relevant to life experiences.

I do believe that my philosophy and teaching style may change throughout my teaching career as I will learn from experiences but also from the children I teach and the colleagues I work with.