Probability in Mathematics – to gamble or not to gamble…

Personal opinion

Having never been a gambler myself I felt this was an interesting topic to cover in the Maths elective as I have always thought that the bandit/casino/dealer always wins. I have always said that I would only gamble if I had money to throw away and up to this time in my life I have not had excess cash to waste gambling.

My theory (having watched people gamble and from my dads advice) that the casino/bandit/slot machine wins is backed up by Bellos (2011) in Chance is a Fine Thing chapter where it starts with the explanation of machines in the US making ‘$25 million dollars’ after they have paid out the winnings. This shows that maybe one person might drop the jackpot in every few hundred people that play it but the gamblers don’t actually win in the long run.

Lottery

Gambling takes many forms but the probability of winning depends on what you play. Likes of the lottery the probability of winning the Jackpot is approximately 1 in 14million but this does not discourage people from playing it as there is a very small chance. Stefan Mandel proved that he could win the lottery in Virginia with every possible combination bought from stores which was a very laborious task and took a huge team of people to do this. The video below shows how his system worked.

Probability of a dice

Dice have 6 sides and if rolled could land on 1, 2, 3, 4, 5 or 6 – there is a 1 in 6 chance it will land on one of these numbers. But to roll two 6s with two dice changes the odds to 1 in 36 as there are many other options which could be rolled. The table below shows all the possible combinations that can be thrown with two dice which equals 36.

1	1	2	1	3	1	4	1	5	1	6	1
1	2	2	2	3	2	4	2	5	2	6	2
1	3	2	3	3	3	4	3	5	3	6	3
1	4	2	4	3	4	4	4	5	4	6	4
1	5	2	5	3	5	4	5	5	5	6	5
1	6	2	6	3	6	4	6	5	6	6	6

Roulette

Roulette has several ways of gambling – numbers, odd, even and colours – the table is shown below. People can bet on which number they think will come up and there is a screen which shows what numbers have come up which may influence peoples decisions to bet on different numbers. In the input on this particular area there was a video showing how Derren Brown wanted to beat the roulette table and memoriesd like a computer how to win it. This is a very difficult thing to do and takes many years of training to complete.

As mentioned at the start of this, I am not a gambler but after reading Bellos (2010) Chapter 9 has opened my eyes to what probability is and how it can capture people into thinking they can win. The odds for gambling and slot machines are set to make it impossible for the casino to loose in the long run as they are mathematically calculated.

Bellos, A. (2010). Alex’s Adventures in Numberland (Chapter 9). London: Bloomsbury

http://lottery.merseyworld.com/Info/Chances.html

http://datagenetics.com/blog/july12015/table.jpg

Investigating Volume – Regular and Irregular shapes

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Volume Definition – The amount of space that a substance or object occupies, or that is enclosed within a container.https://en.oxforddictionaries.com/definition/volume

Having enjoyed mathematics at school and knowing how to calculate volume it was interesting to find out today not just how to do it but also practical methods to show the children how to work it out. Calculating the volume of a cube is done by the formula length x breadth x height = volume (cm3) but there are many practical ways to do this with visuals to so how this works. We were asked to create a cube out of squared paper, scissors and sellotape. This was then used to fill with 1 cm cubes which shows how many fit into the cube looking at the volume. The picture below shows that I created a cube which was 5 x 5 x 5 which makes the volume 125cm3.

Allowing the children to make their own cubes with squared paper (a reasonable size – 3x3x3) and collecting enough cm cubes to put inside to count the volume will broaden their knowledge of what volume is and not just a formula. This is a great way to introduce volume as many find it a difficult concept but progressing on to using the formula is important as it would be near impossible to create a cube 100x100x100 and fill it with the cubes.

We then looked at the volume of a complex object such as plastic elephants which are used for counting, patterns etc in the early years. This is a whole different concept but children further up the school in P6/P7 may be able to grasp this. It involves water displacement and as shown in the photos when the elephants are added to the water the water rises in the beaker.

The beaker started with 100ml of water in it and when 6 small elephants were added it rose to 150ml of water showing that 6 elephants = 50ml so 1 elephant would = 8.333ml/cm3. This video shows measuring the volume of an irregular object. Using videos in class may also help to explain new concepts to children.

I felt that the importance of this lecture was to show that it is crucially important to us different methods for children to learn and make maths fun for all. Textbooks are useful for practice but learning different concepts most children will learn better hands on. This has been proven by many theorists who have done vast research in the field. Jo Boaler looks at this in her writing where she investigates instrumental and relational understanding in primary school through mathematics. My understanding of instrumental understanding is that it is learned by writing and following a procedure whereas relational understanding is learning what to do but also why you do it. This is key in maths and problem solving but actually in life as it is important that children learn what and why they are doing something and not just following a procedure.

https://en.oxforddictionaries.com/definition/volume

Boaler, J. (2009) The Elephant in the Classroom: Helping Children to Learn and Love Maths. London: Souvenir Press Ltd.

‘Stand and Deliver’ – Mathematics Films

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Inspired by the introduction of Discovering Mathematics I felt intrigued to watch the film which was suggested for TDT number 1. I enjoy watching films for leisure but also having a reason to watch this film and take some notes during it made me enjoy it even more. Stand and Deliver looks at the journey a very determined teacher who teaches a class with lower ability Calculus (an advanced level of mathematics using lots of different formulas).

At the beginning of the film, the class were disrespectful towards the new teacher as they tested his boundaries and methods. I found it very interesting how Jaime Escalante didn’t put up with any poor behaviour and gained the respect of his class very quickly.

The simple examples which he started with such as visuals bringing in apples and cutting them at the front of the class captured the attention of the students.

Notes which I observed from the film:

Explaining positive and negative numbers by using the beach and digging a hole – actually allowing the students to visualise how numbers work and not just the answer
Using repetition – e.g. negative x negative = a positive – the whole class repeated this after him many times, this could help store different methods in their memory. At the end of the repetition, he then asked the question WHY? This is showing that there is a reason for calculations.
Escalante was very encouraging and wouldn’t settle for second best – ensuring his pupils felt valued
Very determined teacher and not willing to give up but fight for his classes rights even though his health was suffering.
Built up a professional but also a personal relationship with his class and took interest in all his pupils.

The overall message which I got from this film was as a teacher it is crucial to build up a solid relationship with the class and show that you are working hard for and with them. It is also important to make math’s real life so the class can visualise what you are trying to teach which they may not get with examples in a text book.

This video shows the repetition of the class and teacher:

Design Technology – MA1

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The Design technology inputs have been very interesting this year in semester 2 of MA1. The first one involved simple manipulative skills such as using scissors and making a ladybird which could be done in many different age groups and classes. For each ladybird to be different the child can make their own templates which then ca 16930719_10209629972120930_1942021203_o n be cut out and attached with a split pin. These can be created to make show me boards if laminated, have different numbers or calculations which the children can challenge themselves or others with. Creating learning intentions for these topics are quite challenging as they have to relate to the skills being used and not the actual activity. 16936072_10209629972480939_1986658517_o

Learning Intention – We are learning to use scissors correctly

Success criteria – I can hold scissors correctly, I can hold the paper steady with my other hand, I can cut around the line drawn…

The next input involved using hammers, hand drills, G Clamp and Browder which can all be used in the classroom with lots of different stages and improve the children’s manipulative skills, fine motor skills and control. In groups, we had to teach others how to use these items and also discuss what they would be used for.

The follow up to this lesson was creating an item for a play park using a selected mechanism such as cams, pulleys, levers, pnumatics, hydraulics etc. For this design project, we were split into groups of three and had to create a new piece of equipment with hammers, nails, wood, and the above mechanisms. Allan, Liam and I created a climbing frame with a pulley system to take sand from the sandpit and take it to the top of the climbing frame to make sandcastles there. We were happy with our creation and felt that it could be used with a middle or upper class in school over several lessons.
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Reflection on Semester 1

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An eye opener which struck me and I feel that I can reflect on in semester 1 is the working together module and visit to Dundee Children and Families Social Work Department in Lochee. This was a very impacting visit and I feel even though I am not naive to the world I didn’t realise to the extent of child neglect in and around Dundee. With a fantastic group of 10, we all worked together to come up with questions for the department visit. The manager, family support worker and newly appointed social worker all talked to us about their role in the area and also about why it was so important to work together with schools, social work and CLD to create a collegiate society all with the child in the centre.

Reflecting on this visit it was a fantastic opportunity to get a real insight into what happens day to day in a children and families social work department. As I am studying primary teaching it was interesting for me to see a different occupation and the importance of it in Dundee. The passion from our speakers was also very evident throughout the 2/3 hour visit and they were very descriptive and enlightening.

With the Working Together module being multidisciplinary I was able to work alongside trainee primary teachers, social workers and CLD students. We shared our opinions and listened well as a group with equal contribution and felt we clicked as a whole group. With the visit, we had to create a presentation as a group to highlight key areas for discussion and we worked hard together and managed to get a good result.

Overall a fantastic visit and experience working together to improve our understanding of the importance in future career to have the child at the centre. Also the importance of working alongside many different people to create a safe, healthy, achieving, nurturing, active, respected, responsible and included (SHANARRI) environment for the children in our care and in the community around. (word press representing good team working)

Drama TDT 1

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With very little knowledge or experience of drama before completing this TDT, I firstly had to research what conventions in drama were and also look at the experiences and outcomes in expressive arts to familiarise myself with them. Conventions otherwise known as techniques are the ways in which you work and move to create a desired dramatic effect or style. Woolland (2013)

Having researched this, I was then able to watch and evaluate the video given in the TDT.

The lesson which was being delivered to primary teachers in a CPD (Continual professional development) style showing them different ways in which to teach their classes. The structure was very clear with rules at the start showing the expectations of the tutor. This would be beneficial for the children as well highlighting to them key rules and behaviours in drama. They used the three C approach with communication, cooperation and concentration. All three were explained and there was a poster on the wall so they could be referred back too if there was any breakdown during the lesson. I thought this was an excellent idea as it builds up the expectations of the class from the teacher. This could be discussed before going to the area where drama is taking place and refreshed when in the space.

Following the rules there was then a warm up which allows the children to get ready for their drama session ahead which differentiates it from the previous lessons. Warm ups could include vocal, concentration, team working and also physical activities. After the warm up there was a stimulus of photographs of a village in India and this caused great discussion and is an effective way to start off the drama session of setting the scene. It also brings in a geography aspect which is a sign of interdisciplinary learning.

Soundscape – having the children imagine what the sounds would be like in the village with the beginning of a story (tapping on shoulders for response as the children will have their eyes shut)
Bodyscape – now moving on to making images from just their bodies from a story thought of by the teacher relating to the topic involved.
Still image – use of different levels with some standing and other lying, kneeling or sitting down portraying a image without movement directed by the teacher
Thought tracking – another way of gaging what is going on in the children’s mind by selecting a few children to share what they are thinking during a still image relating to the topic
Performing – this doesn’t have to happen every drama lesson but it is good to have the children being an audience but as well as showing their work during the lesson to the rest of the class. Some children will love to perform where as others will shy away but it is all about learning
Evaluating – must be done at the end of each drama session to make it meaningful and also so the teacher can see what the children have learned and their feelings about the class. The evaluation time will also allow for the children to calm down after an active and exciting session.

The benefits of the structure of this lesson is that it is very progressive starting with an image on a piece of paper and then having a still scene created by groups of children by the end. Voice is also used by creating the sounds of the village in this case but depending on the topic could be anything. I thought the conventions which were used in this clip were Structure and Story as they used still image and at the end were given a short script which they needed to act out.

CfE experiences and outcomes for Expressive Arts

I have chosen two which I feel relate to this lesson if delivered to children:

I use drama to explore real and imaginary situations, helping me to understand my world

(EXA 0-14a)

I can create, adapt and sustain different roles, experimenting with movement, expression and voice and using theatre arts technology (EXA 2-12a) Scottish Government (No date)Overall with a fantastic input 1 on drama and an interesting

Overall with a fantastic input 1 on drama and an interesting TDT I feel a lot more excited about teaching drama to my pupils in the future and also to further drama inputs.

Reference: Scottish Government (no date) Curriculum for Excellence: Expressive Arts Experiences and Outcomes. Available at: https://www.education.gov.scot/Documents/expressive-arts-eo.pdf [Accessed: 24th January 2017]

Wooland, B. (2013) Teaching Primary Drama. USA:Routledge.

TDT Health and Wellbeing Relationships

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With watching the videos suggested in the Health and Wellbeing lecture, it has been brought to my attention that babies are born prematurely in their development, unlike other mammals and animals. This is due to the vaginal canal being too narrow to give birth to a fully formed head. As the baby is brought up, many different factors can affect and influence its development. Unfortunately, every child may not have a significant person in their life who they can trust and rely on to make a safe and nurturing environment at home. This is where teachers and other adults can become the significant other who they can trust and feel safe around. It is essential in the role of a primary and nursery practitioner to be caring, nurturing and understanding.

Not one family is the same and the ‘Ideal’ family with a mum, dad and children is not the general norm nowadays. This does not mean that a single parent cannot raise their child the same as an ‘ideal family’ or step parent family. The problems start to occur when there is violence and potentially domestic violence in the families which can affect the babies, toddlers and children’s development. Suzanne Zeedyk, a lecturer in phycology at Dundee University explains how there is a stress hormone which may be over produced in the brain if violence is present in their home setting. This can create a barrier in children’s minds where they are setting up barriers to protect themselves in other settings. This can be apparent if a child is coming into school and is not able to concentrate or sit still as they are not used to the calm and reassuring atmosphere which a classroom should have.

Interestingly, I was not aware of the science behind this and it has broadened my thinking to behavioural management and techniques which may work with some children and not with others. An example of this is shouting in the classroom. If the teacher is shouting at the children, they may be used to this at home and put up their barriers and not feel safe with this teacher. After a lecture in voice control in the classroom, it is clear that the teacher should not be shouting in the class and vary their voice according to the situation. Shouting can be a signal for the children to turn off and not actually listen to any of the instructions from the teacher resulting in no response and a teacher with a sore voice. An authoritative voice tone is appropriate if the children are not responding but this is developed through practice and on the job training. It is also shown that even just smiling can create a safe atmosphere in your classroom. Happy teacher, Happy Class!

Overall, I am very interested in this theory and will definitely make me think deeper. Relationships between the class and class teacher are essential and the more positive the better. Allowing time for all children and ensuring they all feel safe in the school environment will be an essential job for me as a training professional teacher and eventually in the role with my own class.

Dance in the Primary School

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With very little experience in teaching or partaking in dance, this was a daunting experience. With only an hour class to start off, it was interesting how similar to PE dance is as there had to be a warm up and cool down then the main activity. Actually taking part in a lesson that would be taught to the children it turned out to be good fun, even if it was embarrassing! It was clear to me after having this hour tutorial and also reading the suggested document:

(http://www.creativescotland.com/__data/assets/pdf_file/0004/26149/GSDLitReviewv2.pdf)

which looked at the improvement and importance of creative dance relating to the commonwealth games and many other factors, I felt slightly less scared.

I am very passionate about ceilidh dancing and feel that this is an important part of being a child in primary school in Scotland. This is one genre of dance and there are hundreds more including examples such as; Irish, Jazz, African, Street and Contemporary. The general idea of introducing more dance to the Curriculum for Excellence (CfE) allows for children to be expressive and creative but can also improve their health, mental health, physical health and emotional health. All of these areas are crucial when looking into the wellbeing of children and if dance can benefit these then it is an excellent tool for teachers to use.

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Teaching dance opens it up to some children who cannot afford private dance classes which can be very expensive. Off course, there will be children who are very excited and engaged in the dance lesson but there will also be many who don’t enjoy it as much. The role of the teacher in this circumstance is to encourage enthusiasm and be a good role model with showing little embarrassment and having fun. Dance allows for personal expression and also group working, coordination, fitness and enjoyment.

As I am not very confident in teaching dance I feel it would be very important to have a well researched and planned out lesson so there is less likely to be hiccups. Having music organised and allowing the children to help with the decision of what music they would like to dance too. Challenges I will have to overcome is being shy and embarrassed about dancing in front of people which I think will come with experience. To develop professionally I think I would benefit from watching dance teachers teaching classes and also in schools. So to improve myself I think I should speak to dance teachers and ask if I could potentially observe their class and potentially take part in dancing myself.

dance-colour

Animation – Fantastic engaging tutorial

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After having lecture after lecture introducing us to the different curriculum areas as well as the pedagogical unit (all very important and informative I must add) I was excited to have a hands-on workshop in ICT. During the two hour tutorial, I was able to be creative and work within a group as well as individually to create different animations. Starting with flip art using just paper and a pen we brought to life a person or a snowman or flowers depending where our imaginations took us. Then onto the computers with PIVOT making very simple diagrams come to life using frames etc. All tasks were progressive and could be used with a primary group over several classes. Unfortunately, in schools, the time in an ICT suite is normally very limited.

The lecturer took the role of the teacher explaining the different parts of the animation task adding in music and using behavioural techniques whilst in an ICT suite. An example of a behavioural technique was if anyone touched their mouse while the teacher was talking then all computer screens go off.

The final part of the animation included plasticine models, backgrounds, mic’s and group work to make an animation linked to a subject area. This included adding a title screen, music, credits at the end and creating a story for the characters in the middle. This could be done over several different lessons and use many areas of the curriculum for excellence. Art could be used for creating the backgrounds and plasticine models and Language and literacy for the story line which the children could write and practice themselves.

Working as a group is also very beneficial for the children as this happens from early years right through life. Also using their imagination and enhancing their ICT skills will set them in good stead for future in school and also further education.

The animation my group put together used plasticine characters of three sheep, a tree, Farmer

M and a wolf. The title, Three Little Sheep relates to The Three Little pigs as the farmer scares the wolf away to protect his sheep. Adding sheep noises and a victory song at the end to celebrate getting rid of the wolf. Hopefully, the below file works and you can see our final animation.

On reflection, it is clear from the short animation that the background sound effects the quality of the animation. This could be potentially addressed with the use of small groups working with a classroom support or teaching assistant or whole class is quite during recordings of sound. This could work well with children who are interested in ICT and I think with the new technologies constantly changing it is important to create lessons to get the children’s attention.

ICT to enhance learning is the Experience and outcome in Technologies, which highlights the children’s progression through the stages.

Back to University after a months break

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During the December break I have been working hard to save some money to pay for university next year. Working 8-12 hrs daily was stimulating and doing different jobs has kept me going for the past month. Quite a shock to the system having to get back to uni with over an hrs drive there and back where I was driving 5 minutes to my work.

Very interesting lectures today with the introduction to Teaching Across the Curriculum with Curriculum for Excellence, Numeracy, Mathematics, Literacy, Language, Science and Technologies. I am thoroughly looking forward to specific lectures on these subjects with the lecturers who are very passionate about their chosen field.

With placement in the next couple of months, I am very optimistic about going into the classroom again on placement and I am excited to have a local school close to where I live. Having looked online at the school’s website, I have observed that it is a newly built school like many in the Angus area.

Looking forward to a busy semester with lots of positive learning and starting reading from day 1!