# What is Time?

Time is one of the most important mathematical aspects which we use every single day. Time is something that is linear and can only move forward. As time is made up of years, months, days, hours and seconds, we can only move through each of these at a certain pace and can’t travel back.

The study of time is not only important to us humans, however, to animals also. This is due to many animals hibernating or migrating at certain times of the year. As this is seasonal, animals must be able to tell the time right? Or is it just the sudden changes in temperature when summer fades into winter? Seasons aren’t the only times animals must tell the time, but day and night. Nocturnal animals must know when to go to sleep and when to wake up. Or do they guess it’s time for bed when dawn breaks? Either way, animals are able to sense the time whether it’s through the sun and moon or temperature change.

Continuing the discussion on day and night, full days are made up of 24 full hours. This is based on a theory from ancient Egyptian time. During this time, Egyptians calculated 10 hours of day (light) and 10 hours of night (dark). They then estimated 2 hours each for dawn and dusk. This then linked together in order to create a 24 hour day.

However, how were people even able to tell an hour had passed before the invention of mechanical clocks? They managed this through the creation of sundials or obelisks and water clocks. Sundials and obelisks were used in order to track the movement of the sun throughout the day. Water clocks on the other hand were used to measure time through the regular flow of liquid in or out of a container then measured.

Even though people were able to tell the time, it wasn’t until 1700/1800s that standardised time was introduced. This is when all countries were synchronised to the same time. However, it eventually became confusing as countries were working with the same time although areas of the world were in darkness and others in daylight. GMT was then adapted by the US and the rest of the world in order to solve this issue. This is also described as different time zones.

Another factor that is important in everyday life that involves both time and mathematics is timetables. Timetables in the university or school setting are extremely useful as they show dates and times for each class and what room specific lessons are in. You can also find timetables for busses and trains which allow you to see exactly where they stop in order to travel on the correct route.

Overall, time and timetables are extremely important in everyday life. Time in particular is an important topic within mathematics that young primary children learn within school. As a teacher, I must make sure that children understand units of time before teaching how to read analogy and digital clocks. Being able to tell the time is important for the children to use every day throughout their lives and I, as the teacher, must make sure my lessons are adapted to suit each stage in order for their learning to be successful.

# Longitudinal Coherence – Two Definitions

During the process of writing my assignment, i came across two different meanings of longitudinal coherence which caused me to become slightly confused.

The mathematical term of longitudinal coherence, stated by Liping Ma, is described as the layering of the subject. This can be like the curriculum and how there are layers of various stages in each topic area and what each ability should be learning and implementing. Ma describes that the teachers must be aware of all levels and areas of the curriculum and not only the stages they are teaching or have taught. This, therefore, means that the teachers understand what their students have previously learnt and what they’ll be learning in the future in order to lay the right foundations for future lessons.

On the other hand, when I was searching for other definitions of longitudinal coherence, i found that this term also has a different scientific meaning. Within physics, this term is defined as the “distance over which two waves from the same source point with slightly different wavelengths will completely dephase”. As I have never understood physics, I don’t understand exactly what this describes. However, relating it to the assignment, I believed that it was explaining how two different topics may cross over or link as they contain basic areas which can be used within both or multiple topics. As this is very similar to interconnectedness, it caused confusion. However, i never realised that there are two completely different meanings for longitudinal coherence and the scientific definition, therefore, has no relation at all to the topic being discussed within my assignment.

Although the scientific meaning of longitudinal coherence relates in no form to the mathematical definition, i found it extremely intriguing. I believe the scientific meaning in a way, of what i understand, can in fact be an interesting description of how subjects or topic areas can be totally different, however, have similarities.

Segre, C. (2010) ‘Longitudinal Coherence’. PHYS 570: Physics. Available at: http://phys.iit.edu/~segre/phys570/10F/lecture_04.pdf (Accessed: 20 November 2016)

# Logistic and Supply Chain

The logistic and supply chain is describing the managing of planning, implementing and controlling the process of the shipment of goods. The best storage method during shipment must also be considered during this process in order to arrive safely to the supermarkets in order to meet the consumers’ requirements.

Food miles can also emphasise a way that mathematics is used in everyday life. These miles describe how many miles your food has travelled before arriving on your plate. This includes the distance from the producer to the supermarket and finally to the consumer. Food miles are a good example of mathematics. These miles can be broken down into kilometres, meters, centimetres and eventually millimetres. This can be broken down further by the description of number recognition and sequences. This emphasises the fundamental principles of mathematics as it can be broken down in to the most basic concept.  Food miles are important in everyday life and are used to encourage people to buy locally as the miles are often calculated through the pollution that was caused during the journey.

During the journey, a variety of other mathematical factors must be considered. When shipping the products, the correct method of packaging must be considered in order to carry the biggest amount of goods possible at once. This includes thinking about the weight, size and temperature requirements for each of the individual products. The shelf life must also be calculated through how long it took the food to travel to the supermarket and how long left it has left on it’s sell by date. All of these factors are influenced by mathematics whether it be amounts in a variety of forms or simple calculations.

Before any of the products even make their journey to the supermarkets, the businesses must demand plan. This is when the supermarket plans exactly what products they want and how much of each. This can be done by looking at the previous years data that was collected in order to judge whether they need more or less and what to get at certain times of the year. A good example of this is pumpkins. This is because buyers are usually only interested in them around the time of Halloween. During a clip from BBC1’s Supermarket Secrets (‘Autumns Supermarket Secrets’, 2015) it’s stated that “no one wants a pumpkin a day after Halloween. And the stores can’t run out too early.” This is a great example why supermarkets must look back at the data they collected on how much pumpkins were sold previously and on which particular dates as they don’t want to buy too many or too little.

In the future, this will help me develop my own health and well-being lesson on these areas. I believe it is important for children to understand how their food was produced and how far it’s travelled before they were able to buy it from the supermarket. Using food I bring into class, I will have the children calculate the food miles of each product through using the ‘Food Miles Calculator’ – accessible from https://www.foodmiles.com/. Although this information has gave me lesson ideas for when I’m teaching, I have learned how mathematics is needed throughout the logistic and supply chain which will be useful for me when ordering a number of resources for my classroom.

‘Autumn’s Supermarket Secrets’ (2015) Supermarket Secrets, BBC 1 London, 25 October. Available at: https://learningonscreen.ac.uk/ondemand/index.php/clip/27113 (Accessed: 20 November 2016)

# Data and Statistics

Data and statistics are an interesting area within mathematics which can be used widely within different subject areas. Data is defined as the collection of any facts and information, whereas statistics is specifically collecting and analysing numerical data.

It is known that the use of data and statistics reaches back to 35,000 years ago. At this time, the oldest mathematical tool, the Lebombo Bone, was used in order to collect and record data by bushmen in Namibia. This was similar to tally marks and was carved into the piece of bone – often the fibula of a baboon. This method of recording information was found to be used near the Border Cave in the Lebombo Mountains between South Africa and Swaziland. As it had 29 markings, it is believed that it could have been used to track the moon phases, menstrual cycles, or simply as a measuring stick.

This finding emphasises how long data and statistics have been around for and how it has developed over the years. Thousands of years on, we are now using software on computers to withhold information for us. We are able to create tables, whether on paper or within the computer, and input the data or statistics in order to collect all the information together.

Within the public health department, doctors must be numerate every day. This includes working out the doses of medication for individual patients or organising money for new drugs. Workers within this department also frequently use data and statistics to track the health of their patients. Graphs are used regularly in order to plot the rate a baby is growing within the womb, so they can track whether they’re growing at a healthy rate or not. They also use graphs to plot a patients height against their weight to be able to work out whether they’re under weight or obese for their height.

To conclude, data and statistics have been around for many years and is used within many subjects and vacations other than mathematics. Children learn how to collect data and statistics within maths, however, will use it within different areas such as topic work or ICT, etc. and will find it useful in the future. As a teacher i must make sure my lessons are effective and are stage appropriate in order for the children to learn successfully. I will also use data and statistics when teaching in order to note and calculate when assessing children. I will also use data with the class register as it will include the children’s full names, date of births and whether they have any additional support needs. Overall, data and statistics will be used regularly during my teaching career.

# What is Mathematics?

To a lot of people, mathematics is only about numbers and calculations. They also believe that, apart from the basics, a lot of the more difficult areas taught are pointless and will never be used outwith maths class. It’s emphasised that mathematics is all about finding the one correct answer and has been stated to be all about “remembering and applying the correct rule when the teacher asks a question; and mathematical truth is determined when the answer is ratified by the teacher” (Lampert, 1990, p.30). However, maths does not only consist of numbers but is made up of rhythms, sequences, patterns, time, etc. Marcus du Sautoy considers maths to be in the world around us – nature and man made.

Mathematics can be found in various areas throughout the man made world. It can be seen in shops and supermarkets through the use of prices, amounts or weights, VAT, or even calculating the total and change due. It can be found in buildings or building plans through the number of windows and doors the building consists of, if the building is symmetric, or even the use of the golden ratio in order to create sizes for rooms – without mathematics, architectures would not be able to create successful structures. Artists have also used the golden ratio in order to create proportionate artwork or interesting designs and spirals.

The golden ratio can also be found in nature within the spiral of sea shells and plants. Other ways mathematics can be seen in the world around us is through patterns created within plants and flowers or even the hexagonal shapes within the honeycomb of a bees nest.

Overall, mathematics is not only about numbers but holds many other components which can be seen and used within everyday life. Mathematics can’t fully be used everyday, however, basic aspects can such as number, sequence, pattern, etc.

Lampert, M. (1990) ‘When the problem is not the problem and the solution is not the answer: Mathematical knowing and teaching’, American Research Journal, 27(1), pp.29-63.

# Why I Chose to Discover Mathematics.

During  my first year placement within a primary 6/7 class, i found myself finding the maths lessons very difficult to teach. The highest maths group were learning about problem solving using decimals. For some reason i was finding this extremely hard to break down and explain. I then realised that i was finding some simple things difficult in order to understand, let alone how to explain it effectively to the children.

I couldn’t get my head round why i was finding simple maths questions so difficult and i was too embarrassed to admit it and ask for help. I then realised through a conversation with the class teacher that I wasn’t taught the basics effectively during primary school due to asking for help and getting told to “sit down and work it out myself”. This wasn’t helpful. This advice caused me to often sit for the rest of the lesson, stuck on the same question. I’d then get into trouble for not finishing the page. How was this method of teaching fair? Due to a teacher being bored of me asking for help too often, my missing knowledge is now effecting me in later life.

This is why i have chosen this elective. I don’t want to be that teacher who sat behind her desk and didn’t see a child was struggling and needed extra help. I want to be able to be confident whilst teaching maths and be able to assist the children effectively. I don’t want my pupils being effected in later life due to my non-existing support as i myself didn’t have a full understanding on the topic.

What’s the point in becoming a primary teacher when you can’t be bothered with your pupils asking questions or get annoyed when they approach your desk more than once. Teachers are in place to support children throughout their time at primary school and make sure they have the key skills and knowledge to prepare them for later education. Hence why I want to make sure I enhance my knowledge within maths in order to ensure my pupils get the correct information and support.

# Blobs in a Bottle

‘Blobs in a bottle’ is a great science experiment to do with children in order to explore the term molecular polarity and what it means.

To begin the experiment you must pour 200 millilitres of water into a clear 1 litre bottle of water. Afterwards you must add 700 millilitres of vegetable oil. After a few minutes, the oil will settle and will sit on top of the water with a clear separation. This is called molecular polarity. This term basically means that the two substances can not mix; The water molecules are attracted to the other water molecules and the oil molecules are attracted to the other water molecules. Due to the structure of the two different molecules, it does not allow them to bond together hence the clear division of the substances.

To make this experiment more interesting for the children, you can add any colour of food colouring into the bottle – I found red to be the best as it was a strong colour. The food colouring will drop through the oil and will mix with the water. After the colour is as strong as

you want it, you can move onto the next step and add a fizzing tablet, i.e. an Alka Seltzer, into the bottle. When the fizzing tablet dissolves it creates a gas. As the gas bubbles rise, they take some coloured water with them. Once the blob reaches the top, the gas escapes and the coloured water then sinks back down.

This process looks just like a lava lamp which can look even more effective if a light is placed underneath the bottle. This is a great experiment for kids as they are creating something they may have at home while learning about molecular polarity and how their home-made lava lamp works. This experiment will effectively engage the children in their learning as it’s something they will enjoy doing at home or within the classroom.

# “Under the Sea” – Dance Lesson Plan

I based this lesson plan on the class having taken part in previous dance sessions built around the theme and song from “The Little Mermaid”, ‘Under the Sea’. The previous lessons consisted on the children learning how to travel, i.e. swimming movements, and twist to represents sea creatures and underwater plants.

Working towards outcomes of a Curriculum for Excellence

Inspired by a range of stimuli, I can express my ideas, thoughts and feelings through creative work in dance. EXA 2-09a

Learning Intentions

To successfully use their bodies to imitate sea weed swaying within the water.                                                To successfully move loosely to emphasise how the plants move within the waves.

Success Criteria

How to loosen up their bodies and be successful when using loose movements                               How to successfully do a body roll and understand how the movement can be seen as the same as sea weeds movements when the waves cause the plants to sway.

Resources

CD player or docking station                                                                                                                         A variety of music including “Under the Sea”                                                                                             A large empty space, preferably the school gym hall

Setting the context/ Beginning the lesson (Introduction)

Introduce the lesson by recapping on the previous dance sessions encouraging the children to share what they have previously learned. Make sure the children check their l
aces are tied before beginning the warm up. Make sure I’m aware of any injuries the children may have in order to adapt the moves in order for the child to be comfortable.

Octopus Tag

One person (the tagger) stands in the middle of the gym hall. The rest of the children line up at one end of the hall and when I shout go, they all run to the other side. Whoever the tagger tags, they must stand where they got tagged and become an octopus. The octopus cannot move from their spot but must move around their arms in order to help the tagger tag the other children.

Quick stretch of the muscles the children are going to be using in order to learn the specific dance moves i.e. their arms, shoulders, neck, back and abdominal.

Teaching the learning intentions (Development)

Before starting the main lesson I will have the children find a space where they’re able to move freely. I will also check whether they are able to see me clearly through using the method of ‘if I can’t see them, they can’t see me’.

Begin by getting the children to sway lightly from side to side with lose movements.   Encourage them to follow their shoulders allowing their arms to dangle by their sides.                               Then have the children imagine that someone is pulling them by their belt which has their loose upper bodies follow their hip – Do this movement over, while counting in eights, until the children are successful with the movement.                                                                                     Now, encourage them to allow their arms to swing without them controlling the movement too much as this will cause them to tighten up.                                                                           Throughout this process, I will have music playing in order for the children to learn how to move loosely to the beat while counting in eights.

After the children have managed to loosen up their bodies and do simple loose movements, I will move onto firstly telling them what the name of the move they’ll be learning – a body roll.     I will then show the children an example of this move before talking through it step by step.   Start by rolling my head back, telling them to imagine someone pushing against their foreheads, then rolling the movement down to their neck, shoulders, chest, tummy, hips, then legs (demonstrating as I speak through each rolling movement).                                               Then have the children join in, slowly rolling each body part I am naming and imitating my movements (counting in 4s for this section).           Have the children try it on the own allowing them to speed up with practice.                                           I will walk around the hall observing the class and assist any children who are struggling.

Once I see that most of the children are becoming confident with this move, I will switch the music to “Under the Sea” and have them pretend to be sea weed within the water using the new body roll they’ve just learned.                                                                                                              I will encourage the children to other movements they have learned from previous lessons by shouting out their names and demonstrating them at the front of the hall for all the children to see.                                                                                                                                                          Count in fours for this song.

Ending the lesson (Plenary)

For this I will have relaxing ocean sound effects in order fit the theme of ‘Under the Sea’.

For the cool down, I will have the children and myself stand in a circle, having them hold hands in order to do this quickly.                                                                                                                             I will get them to drop hands once everyone is in position.                                                              The cool down will consist of having the children take deep breaths, raising their arms when breathing in and dropping them when breathing out.                                                                     After this, I will have the children lay down on the ground, close their eyes and listen to the calming music for a few moments in order to allow me to prepare for heading back to the classroom.

My next steps

During this lesson, as the children have been introduced into how to move their bodies loosely in order to successfully do the body roll, the next lesson will consist of more loose movements such as the arm wave which will represent the waves within the sea. For this lesson I will watch Youtube videos in order to give me ideas on how to break down the move and explain it step by step.

# What is reflection?

Reflection is when you look back and analysis an occasion or situation in a critical manner. This allows us to learn from our experiences and understand what we can do differently the next time. Questioning yourself such as, what did I do well? What did I not do so well with? Are great with helping you manage how you would deal with something for a second time. Reflection is important as it’s about exploring what you thought and felt instead of only thinking about what happened.

As a student I’m completely open to receiving feedback from my peers as I know that it will help me understand my situation with tasks better. It also helps me with realising things I maybe didn’t notice I had done wrong which I could go on to fix. Positive feedback for peers can also make me feel confident knowing that they believe I had done something really well. Refection is really important as a student teacher within a classroom. Everyone makes mistakes and doesn’t always get things right first time. Reflection allows us students to look back on the event and analysis ad understand what went wrong and what we could do differently next time.

Gibbs’ Model of Reflection (1988)

# Bowlby’s Theory of Attatchment

Bowlby’s theory was based on his beliefs and examinations on the attachment between mothers and their babies. He believed that if the attachment between the mother and her baby didn’t happen at early stages, it would negatively affect the child’s behavior and learning. Bowlby researched and experimented in order to support his theory. While he worked for a mental health clinic for troubled youths, he conducted an experiment with 44 of the children who had emotional problems and 44 who had been convicted of theft. Within the 44 young people who had emotional problems he found that only two of them had been separated from the mother before the age of five. However, within the 44 thieves he found that 17 of them had been separated from their mother before they were aged 5. Bowlby’s research using the lives of the young people within the clinic helped support his theory of how the mother and babies attachment is an important relationship and if it’s non-existent, it can disturb the child’s behaviour . Bowlby also believed that the absence of this attachment also effected the child’s cognitive and emotional development. He believed that the distress from being separated from the mother can decrease intelligence and can cause depression and aggression. However, Bowlby’s research can be criticised through his choice of a small group of young people as his findings may have been different through the study of a larger group. His theory can also be incorrect as the troubled young people’s behaviour may not have been caused by the separation from the mother, but something else that may have disturbed them within their lives. Bowlby also looked at secondary research which involved animals. Within Lorenz study of goslings, he accomplished that they imprinted on the first thing they seen when they hatched. This usually being the mother, they would stay close to her and follow her in order to be protected and learn how to survive. Lorenz study proved that it was necessary for the goslings to imprint on their mother in order to survive. If they didn’t imprint within a few hours after hatching, the imprint wouldn’t occur at all. This study obviously influenced Bowlby’s theory as he too believed that if the attachment didn’t happen between a baby and its mother, the baby will live with the consequences just like the gosling would.

Rudolph Shaffer and Peggy Emerson, however, disagree with Bowlby’s theory of attachment as they believed multiple attachments were possible and didn’t only include the mother. The pair studied 60 babies monthly for 18 months within the environment of their own homes. It was established that babies up to an including 4 months, have the same response to anyone who will show the love and care. It isn’t until 7 months that the baby will have the attachment to a single person and show fear of strangers. Also at this age, the baby will also find comfort and safety within the figure and show anxiety when separated. However, as the baby continues to develop, they start to become independent and show the signs of multiple attachments at 9 months of age. By 10 months old, the babies had numerous attachments including the attachment to parents, grandparent, siblings and family friends. Overall, Shaffer and Emerson’s studied was evidence against Bowlby’s theory and proved that a baby has multiple attachments and is more likely to become attached to the people who show them the correct affection rather than who they spent the most time with.

# History of Brain Development Timeline

1905 – Alfred Binet introduced new test for measuring intelligence called the Binet – Simon scale.

1949 – Walter Rudolf Hess research showed that the interbrain is responsible for coordinating the activities of the body’s internal organs.

1950 – Karl Spenser Lashley found that there is no single site for memory in the brain through experimenting on rats.

1953 – Nathaniel Kleitman and Eugene Aserinsky discovered there to be rapid eye movement while a child was a sleep. This led researcher into believing that sleeping involves some sort of learning process.

1963 – John Carew Eccles, Alan Lloyd Hodgkin and Andrew Fielding Huxley awarded for their work on the mechanisms of the neuron cell membranes as they discovered the chemical means by which impulses are communicated or repressed by the nervous system.

1967 – Ragnar Granit, Haldan Keffer Hartline and George Wald research details how the eye passes images to the brain.

1977 – Roger Guillenim and Andrew Schally honoured for discoveries concerning the production of peptide hormones in the brain. Their discoveries helped to increase the understanding of glandular disease.

1981 – Wiesel and Hubel’s research how visual information is transmitted from the retina to the brain. Sperry’s work concerns the specialization of functions within the cerebral hemispheres of the brain.

1987 – Anti-depressant drug discovered.

1991 – Erwin Neher and Bert Sakmann discover function for single ion channels which increase understanding of how cells communicate with one another.

1994 – Alfred Gilman and Martin Rodbell discover G-protein coupled receptors.

1997 – Stanely Prusiner discovers new gene of infectious agents known as prions.

2000 – Arvid Carlsson, Paul Greengard and Eric Kandel discover signal transduction in the nervous system.

# Welcome to your WordPress eportfolio

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

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

You can pull in a YouTube video:

You can pull in a Soundcloud audio track:

You can pull in a Flickr page

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