Why Science?

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The thought of teaching science to a class of eager students has always filled me with slight dread. This is partly due to having little experience of science throughout my own primary experience as well as lacking any confidence surrounding science knowledge and experiments.

I decided to engage with this module in the hope that through learning about the theories behind science pedagogy my confidence and subject knowledge would grow. Not only have I learned masses about certain scientific areas, I have also gained better confidence in planning and delivering lessons.

Going into our first group teaching lesson I was slightly apprehensive as this would be the first time I had taught science and the thought of teaching my first lesson to experienced primary 6 pupils was daunting. I believe that working as a group provided ‘strength by numbers’ but also gave us the opportunity to share knowledge and ideas. Having the support of other students was also a confidence boost as it allowed us to step in and support each other in any areas of weakness.

For our second group lesson again we were in a group. I felt much happier about the thought of teaching science to a group of primary 7’s. As a teacher it is my responsibility to make sure that I have a secure subject knowledge. when we were first shown the list of topics we could cover I knew that I would have to do a lot of research, however this was extremely beneficial as it meant I was engaged with the learning process and also helped me to judge how much of a topic we could cover in the given time and also how complex we could take the concept. After reflecting on my contributions to the first group lessons, I identified areas of personal weakness which I hoped to develop and improve on.

Firstly, I believed that it was important to have a set of questions prepared in order to assess learning throughout the lesson. Although we did have a set of pre-prepared questions it was also important for us to acknowledge and answer the questions presented by the children throughout the lesson.

Throughout my time at university I have repeatedly heard lecturers mention the “hook”. A way of sparking interests in a lesson and gaining instant engagement. This is something we struggled with in our first lesson as we had a more mundane experiment compared to some of the others surrounding us. However, by incorporating fly-sticks in this lesson we instantly had pupils hooked on our concept and managed to keep their attention throughout the lesson. As a teacher it is simply not enough to have a good opening, we must be able to explain the idea and the science behind it.

I believe our second group lesson flowed well as we each presented a different experiment based on the concept of static electricity. Again, the benefit of teaching with peers was that if any questions were presented that one person did not know the answer to we could rely on each other to fill in any gaps of knowledge.

By engaging in this module I have not only learned a huge amount about science, I have also gained a greater insight as to creating educational vlogs. I have never made a video before and was apprehensive of filming and producing videos which would form part of my assessment. However, as technology becomes an ever-expanding part of society it is important that as a teacher I engage with learning about how technology can be used in the classroom. Vlogging in this sense was a great way of exploring and sharing our own personal findings however this idea could be easily used in the primary classroom. It would also be reasonable to suggest that vlogs and voice notes could be featured as a form of teacher/peer feedback.

This module has improved my knowledge of both the science curriculum and methods of teaching which in turn has created a newfound sense of confidence in myself and my teaching abilities which I hope to put into practice on my next placement.

A Visit to The Famous Grouse Distillery

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After visiting the Famous Grouse Distillery I created a video based on my findings. I thoroughly enjoyed the visit however had to cut back on the amount of information included in this video as I felt it was more important to focus on explaining the main process – fermentation.

I believe that using diagrams provides pupils with a clearer understanding as they can visualise the concept. Although the process of fermentation presents some complex concepts, it would be reasonable to suggest that some of these can be briefly mentioned. However, in order to explore fermentation pupils must have a profound understanding of solids, liquids and gases. They must be able to build upon this knowledge to then explore chemical changes.

 

Fermentation relates to multiple Experiences and Outcomes. It also provides a great context for cross-curricular learning. The Scottish drinks industry has a huge historical background which could be explored by children. Whisky in particular plays an important role in Scottish heritage which could provide multiple opportunities for research projects within the classroom.

Science

I have participated in practical activities to separate simple mixtures of substances and can relate my findings to my everyday experience. – SCN 2-16a

By investigating common conditions that increase the amount of substance that will dissolve or the speed of dissolving, I can relate my findings to the world around me. – SCN 2-16b

Social Studies:

Learning in the social studies will enable me to:

  • develop my understanding of the history, heritage and culture of Scotland, and an appreciation of my local and national heritage within the world

  • Having explored the variety of foods produced in Scotland, I can discuss the importance of different types of agriculture in the production of these foods. – SOC 1-09a

References:

The Scottish Government, (2009). Experiences and Outcomes: Social Studies. Available at:

https://www.education.gov.scot/Documents/social-studies-eo.pdf

 

The Scottish Government, (2009). Experiences and Outcomes: Sciences. Available at:

https://www.education.gov.scot/Documents/sciences-eo.pdf

What is Germination ?

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Nature is all around us and I personally feel that the prominence of nature provides a relevant context for learning as well as providing multiple opportunities for children to engage in outdoor learning.

Plants provide the early years with the opportunity to classify and sort plants into categories and justify their answers. This type of learning is mainly based on qualitative observation. However as pupils become more confident with the different parts of plants, they can begin exploring the different factors which affect plant growth. This is a topic I have briefly touched upon within my video. In hindsight, I feel that it would’ve been beneficial to suggest methods of measuring and recording results. However, research does state that children should be actively engaged with their learning and come up with solutions to problems (Cross and Bowden, 2014). It would therefore be reasonable to suggest that pupils should have some autonomy in choosing the best methods for recording their data.

Learners have been described as visual, kinaesthetic or auditory (Hastings, 2005). Visual learners will engage more when a teacher makes use of videos and diagrams (Hastings, 2005). I considered it important to include both a diagram in my video as well as a real butter bean as I believe that this worked as a way of breaking down learning as well as being appealing to visual learners. I personally find diagrams useful in building firmer understandings which is possible one reason why I have tried to include them throughout my science videos. However, it is important that although pupils may have one preferred learning style they are not categorised as one type of learner (Cremin and Arthur, 2014). Teaching should be creative and appeal to each learner within the class.

Viewing this as a learner myself, I believe that through making a video I myself was encouraged to research and build upon my own understanding. This module has encouraged me to develop sound pedagogical knowledge whilst providing me with more confidence. By becoming more confident in my own understanding of a concept, I believe that I am developing new ways to portray this information to children.

Reflecting on previous classroom experience I understand that it is important for ‘Learning Intentions’ and ‘Success Criteria’ to be made explicit to children at some point throughout the lesson. It would have perhaps been of benefit to include a learning intention relating to the science experiment so the viewer had a clearer understanding of what skills they would be developing.

The Curriculum for Excellence Sciences Experiences and Outcomes (2009a, p2) state that biodiversity and interdependence state:

“Learners explore the rich and changing diversity of living things and develop their understanding of how organisms are interrelated at local and global levels. By exploring interactions and energy flow between plants and animals (including humans) learners develop their understanding of how species depend on one another and on the environment for survival. Learners investigate the factors affecting plant growth and develop their understanding of the positive and negative impact of the human population on the environment.”

Exploring nature is clearly a huge topic that requires a large amount of time. However, through enquiry based learning pupils develop transferable skills such as problem-solving, measuring and recording data. Seeking patterns is also linked strongly to art and mathematics. Through engagement with this module and other education modules, I believe that as a teacher it is vital to make these connections explicit to children. By doing so, children can see the relevance of their learning as well as creating their own links as to how they can apply their skills in their everyday lives.

The benchmarks (Scottish Government, 2009b) also explore how pupil’s learning can progress through exploring nature:

  • Pupils can observe, collect and measure the outcomes from growing plants in different conditions, for example, by varying levels of light, water, air, soil/nutrients and heat.
  • Structure a presentation or report, with support, to present findings on how plants grow.

The benchmarks present yet another opportunity for cross-curricular learning, by suggesting that pupils create a presentation or report there are key links to language and literacy and also ICT. I have no reason to doubt that pupils would be capable of creating videos to show their findings given the right support and resources.

References:

Cremin, T., and Arthur, J. (2014) Learning to teach in the primary school (Third edn) New York: Routledge.

Cross, A., and Bowden, A. (2014) Essential primary science (Second edn) Maidenhead: Open University Press/McGraw-Hill Education.

Hastings (2005). Learning Styles Available at: http://www.tes.co.uk/article.aspx?storycode=2153773  (Accessed on 23rd October 2017)

The Scottish Government, (2009a). The Curriculum for Excellence. Sciences: Experiences and Outcomes. Available at: https://www.education.gov.scot/Documents/sciences-eo.pdf (Accessed: 13 October 2017)

The Scottish Government, (2009b). The Curriculum for Excellence. Building the curriculum 4, skills for learning, skills for life and skills for work. Available at:

http://www.gov.scot/resource/doc/288517/0088239.pdf (Accessed: 12 October 2017)

Reflecting on Our Group Science Lesson

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Our lesson was based on the separation of water and oil. It was important for us to assess the class knowledge at the start of the lesson in order to structure the lesson to suit each group’s needs.

Each group brought new ideas, different levels of knowledge and importantly different questions. Children’s questions are central to science and enquiry. It is important to encourage children to ask questions which they can find solutions to. Providing a context which excites children and engages them is central to learning. One problem we faced was being surrounded by experiments which involved acid and alkali reactions. The excitement surrounding these experiments somewhat took away from the engagement with ours. In hindsight, as a group I believe it would’ve been beneficial to communicate with our peers and gain a better insight as to what other groups were doing. This perhaps would’ve helped us assess how to best put our ideas into practice.

Having prepared questions is also key to good assessment and learning. In hindsight this is something as a group we should have considered more closely. In our plenary we introduced the word emulsion which left children slightly confused. It would have been beneficial to introduce the word at the start of the lesson as a plenary should sum up learning. Assessing group work can be difficult, and what works for one group may necessarily not work for the next. In a situation where you are unfamiliar with the children and their preferred learning styles it may be of benefit to have more than one prepared method of assessment. Assessment should not only tell a teacher what a pupil has learned, partly learned, and not learned at all. It should also identify areas of teacher improvement. By assessing our own performance we have the ability to adapt and improve our lesson for the next group, meaning that by the time the last group arrive our lesson should be well polished and clear.

Central to the constructivist theory of teaching and learning is social interaction. Children should be encouraged to share their thinking and ideas with their peers through talk. It was hard to engage all children in talk as they were unfamiliar with us as a group of teachers. Finding other ways to engage pupils in talk, breaking the ice or perhaps asking them to share ideas with a partner instead of the whole group would have possibly worked better. However, without knowing the children it was hard to plan for these uncertainties.

Identifying areas of weakness, as well as  areas of strength, will help my future practice. The issues raised from today’s lesson should help inform my planning for the next group lesson. This lesson has also contributed to building my confidence as a science teacher as it was a good experience having other contributors to the lesson to learn from and create a wider knowledge base.

 

Putting theory into practice

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The most recent science TDT asks us to explore and research one learning theory and consider and reflect upon how we might use this in practice. I decided to research the work of John Dewey.

 

I created a lesson plan based on butterflies as I felt this is something that would excited and interest an early years class. Dewey states that learning should be a balance between teaching knowledge and teaching what children want to learn and I feel like this can be reflected in picking a topic like butterflies.

 

Return To Science

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I decided to select this module due to my lack of experience and confidence in the subject. As a teacher, I feel it is important to challenge yourself and gain subject knowledge in order to produce successful lessons. The thought of going into a primary classroom and conducting a large-scale science experiment is extremely daunting to me. I hope that through engagement with this module my subject knowledge will greatly increase alongside my confidence.

Today was our first lecture in the Science elective. This input consisted of a short introduction followed by our groups conducting a small science experiment. As part of this elective, it is a requirement to vlog our findings. I have decided to make a short video detailing today’s experiment and findings.

On reflection, as a group, there were a number of things which we could have done to improve the accuracy of this experiment.  Cross and Bowden (2014) state that the key to any investigation is fair testing. Our experiment therefore could be considered flawed as we did not accurately measure the water in each of the boiling tubes meaning that the solids had different volumes of water to react with. When experimenting, there are many variables which can be changed, in this instance the variable was the solid. Although it is unlikely to have affected the outcome of the experiment, it could be argued that by using the same spatula for each substance cross-contamination could have occurred therefore altering the reaction/outcome.

 

This experiment was based on observation. Observations are qualitative changes which are easy for people (pupils) to understand (Cross and Bowden, 2014), after grasping basic observation skills pupils can progress to measuring the qualitative changes.  Personally, I lacked any knowledge as to what the substances could be and was unable to explain why they reacted with water in the certain ways. As a teacher, it would be fundamental to have a solid knowledge of a topic before explaining it to the children.

 

However, it would have been of value to predict what each substance was and what reaction it might have when placed in the water and comparing this to the observed result. Cross and Bowden (2014) stress that predictions are important as they allow us to focus on the results.

 

This experiment was centred around soluble and insoluble substances. BBC Bitesize (2017) states that “soluble” describes a substance that will dissolve and “insoluble” describes a substance that will not dissolve. Although at the time this seemed to make sense. I decided it was important to research what makes substances soluble and insoluble.  Through research I have learned that it is the molecules of a substance which determine whether or not it is soluble or insoluble. Water is a polar molecule, one end is positively charged and the other end is negatively charged. Substances that do not dissolve in water are non-polar and do not interact well with water molecules.

 

To further progress pupils’ learning, this experiment could be extended to explore factors which affect solubility, these include: temperature, pressure, polarity and stirring speed.

 

References:

BBC (2017). BBC Bitesize – KS2 Science – Soluble and insoluble materials. [online] Available at: http://www.bbc.co.uk/education/clips/zx7w2hv [Accessed 24 Sep. 2017].

Cross, A. and Bowden, A. (2014). Essential primary science. 2nd ed.

 

The Maths Behind ‘Connect 4’

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In a recent task assigned by Richard we were asked to explore the fundamental mathematics of a game. I have decided to investigate the mathematics involved in the seemingly simple game of ‘Connect 4’.

Connect 4 is a game with relatively simple rules (Victor Allis, 1988):

  1. Each player in his turn drops one of his checkers down any of the slots in the top of the grid.
  2. The play alternates until one of the players gets four checkers of his colour in a row. The four in a row can be horizontal, vertical, or diagonal.(See examples).
  3. The first player to get four in a row wins.
  4. If the board is filled with pieces and neither player has 4 in a row, then the game is a draw.

There is no set rule which states who takes the first turn, this is ultimately left to the players to decide. This decision may be crucial in deciding who wins the game…

screen-shot-2016-11-27-at-22-22-42

There are several different ways in which this game can be approached. By creating a simple rule player 1 (black) can ensure they win or draw every game. The rule is: Suppose n is even. Group the columns in pairs, giving pairs of columns 1 & 2, 3 & 4, …, (n-1) & n. Each time White plays in one column of a pair of columns, Black plays in the other column of the pair. For n is odd, groups are made in the same way, leaving the n-th column as a single column. The same rules apply to this position. Only if White plays in the n-th column, Black plays in that column, too.

Fundamental mathematics can be found in Connect 4 as the principles of probability and prescription are apparent. A player must attempt to predict where their opponent will place their next move. They must estimate the probability of their opponent predicting their next move and try to prevent them from making a move which will trap them and make them lose.

In relation to Liping Ma (2010) a player must have multiple perspectives when playing connect 4. This means that a person must be able to see the game in various ways and must be able to approach it in multiple ways. They must be aware that their opponent may have various moves available and they must be able to prevent any moves which will result in them losing. A person must also be able to take into consideration not just their opponents next move, but the next few moves they could make in order to guarantee a win. This could be done by recognising patterns they make.

When I played this game when I was younger I would try my best to place my counters in such a way that I create multiple opportunities for winning. For example create two lines of three meaning my opponent can only block one of my potential wins and leaving me with a guaranteed win. I would do this by considering possible patterns of play, trying to predict where my opponent would place counters to block mine but in some wscreen-shot-2016-11-27-at-22-22-01ays it could be argued that the game is somewhat down to luck. For example your opponent may get distracted and miss an opportunity to win or fail to notice your plan.

 

 

Reference:

Victor Allis (1988), A knowledge based approach to connect-four, Available at:

http://www.informatik.uni-trier.de/~fernau/DSL0607/Masterthesis-Viergewinnt.pdf  (Accessed on 27th November 2016)

Re-discovering Mathematics

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Why choose maths?!

I guess I chose this elective as I enjoyed mathematics all through primary school and always felt particularly confident with the subject when it came to testing. My positive attitude towards maths remained with me until I decided to sit Mathematics at higher level. In one sense, my attitude changed simply because I did not like the teaching style my teacher used, I found she
took any enjoyment we had previously developed away from us. Another difficulty with Higher Maths was7cd05c2267bceac7ba2101dc4624d14d having two teachers who split our maths time between them. This resulted in us learning two completely separate topics at the same time which at such a high level was very confusing.

On reflection, I struggled to see the relevance of what we were learning. I constantly thought to myself when am I ever going to need this information again? In relation to Liping Ma (2010) I could consider myself as not having a profound understanding of mathematics as I struggled to see the connectedness betweeimages-2n the two topics we were learning at the time. I also found it confusing when one teacher would explain something in one way and the other would
introduce a completely different strategy, I found that I liked having one way of approaching something and achieving a set answer. Reflecting back on this, I also lacked Liping Ma’s multiple perspectives as I was unable approach problems in multiple ways.

Although I put in a lot of hard work and still managed to achieve an A at higher, I still feel like the problems I faced in my last academic year of maths left me slightly anxious at the thought of teaching mathematics to the upper years. I know the importance of showing positive attitudes towards a subject as a teacher’s attitude highly effects how pupils view a subject’s importance. Liping Ma (2010) also discusses the theory that a teacher with a profound understanding of mathematics has a greater impact on students as to produce effective learning you yourself must have a specialist knowledge of the subject. This highlighted to me the great importance it is for me to deepen and broaden my own understanding of mathematics so that in future I can answer question and explain all curricular areas clearly and with confidence.

I chose Discovering Mathematics to re-discover my own enjoyment of maths and develop my understanding to improve my future teaching.

How did I find Discovering Maths?

I must admit I left multiple lectures feeling totally confused but in the best way possible. There were multiple lectures where I sat thinking ‘WOW, I did not know that’ and some where I had no idea what was going on. Through additional reading and blogging I feel like I have developed my understanding in the areas where I was slightly more puzzled. I honestly had no idea how much maths surrounded us. It was obvious to me that maths was all around us, but I had no idea of the degree to which we use maths in our everyday lives.

I particularly enjoyed how this module was organised. By bringing in guest speakers we were really getting a deep insight into how maths is used in different sectors. I found the lecture on data and statistics in health and medicine very eye-opening. One thing I took away from this lecture is to stop taking information as the truth, so many graphs have flaws that we seem to never question. Maths is key to improving the health of our nation and our ability to make measurements, predictions and calculations all contribute to our healthcare.

My favourite lecture was the input on logistics and supply chains. This was a great example of how to make maths fun and active, although it did bring out a competitive side in some of us! The aim of this lecture was to make predictions and calculate the probability or risk of an item on our list being sold. Using the probability that the item would sell we had to decide how much of the product to buy, taking into account the time of year, and whether we had perishable items etc. This highlighted to me that maths is apparent even in supermarkets and there are people dedicated to predicting how much of an item will sell and when these items will sell best. This is done by using previous data, forming graphs and using this to make accurate predications. (The lady in the video clip shown takes into account a bank holiday which she believes will influence sales.)

This module has also opened my eyes to the history of maths. I have never really thought about where maths evolved from or how we got to the stage where we are. I now know that our base system is based upon the fact we have 10 fingers (therefore it makes perfect sense to use them to help us count). There is a huge amount of history in maths that I was blind to before, I have learnt about the Babylonian base systems and the Ishango bone which shows that maths is over 20,000 years old! I have also discovered that there is maths in both music and art which I had never ever considered.

I can truly say that this module has brought back my enjoyment in maths. The enthusiasm and knowledge our lecturers (particularly Richard) showed throughout the module has modeled to us the attitudes we should have in the classroom. The positivity from lecturers definitely affected my feelings towards the module in the best way.

How will this impact me in the future?

Although this course has not made me a mathematician, it has made maths and the thought of teaching maths a lot less daunting for me. It has definitely shown me multiple fun ways to introduce and develop maths in the classroom and the importance of relating the maths we learn to real life situations. I hope to continue to improve my understanding of maths in future and foster the enthusiasm that our lecturers displayed to create a positive learning environment in my own classroom!

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Risky Business

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After reading Alex’s Adventures in Numberland I was made more aware of the different types of risks we take in everyday life. This chapter explores the risks people take when gambling, or playing games involving money. It is clear that there is a huge money making opportunity bas

Slot machines are a huge profit maker in Casinos

Slot machines are a huge profit maker in Casinos

-ed around the risks people are willing to take to make easy money. Bellos (2010, p) states that:

 

“slot machines make $25 billion dollars per year (USA) after paying out prizes.”

Clearly, there is a huge market for exploiting people’s willingness to take risk. But what does this mean?

The Oxford Dictionary (no date) defines risk as: “A person or thing regarded as likely to turn out well or badly in a particular context or respect.” Taking a risk means we are taking a chance on an unpredictable outcome. The outcome may result in something bad happening but there is a chance that something good may arise from the risk we have taken. In order to understand risk

many people dream of winning big money, but at what risk?

many people dream of winning big money, but at what risk?

properly we must be able to calculate the probability of an outcome. Probability is the study of chance and with a mathematical approach unpredictability becomes very predictable. (Bellos, 2010) Casino games and bets require the player to have an expected value, this is their expectation of what they can get out of a bet. For example a £10 bet could be calculated as: (chances of winning £10) x £10 + (chances of losing £10) x-£10. In casinos players should expect to lose money, but the chance of winning big means there is a great desire to take risk for an unpredictable outcome.

Probability can be used to calculate the probability of throwing a certain score on dice. When you throw a die there a 6 possibilities (1,2,3,4,5 or 6). BBC bitesize explores this further and states that there are three ways of getting an odd number (1, 3 or 5).

So the probability of getting an odd number = the number of ways of getting an odd number / total number of possible outcomes. = 3/6 = 1/3 or 0.5 or 50%.

Here there is a connectedness (linking back to Liping Ma’s (2010) definition of PUFM explored in the essay and other blog posts) as to understand what these numbers mean, a person must know fractions, decimals and percentages. They must also have the understanding of equivalent values. By calculating the outcome of probability when throwing dice, a person is able to calculate the risk that the die may/may not land on a number they have betted on.

 

Why is probability and risk important in our everyday lives?

In our everyday lives we take many risks. Risks may arise on simple tasks like crossing the road, being able to calculate the speed of the car across the distance you need to travel. You may decide that it is highly probable that you will get across the road safely but there is always an element of risk as you cannot control the drivers speed, the driver may not stop (unlikely but profit-loss-riskpossible). Risk in our everyday lives may be about calculating danger but can be as simple as sending a text that may have a negative response. In my job as a lifeguard I am constantly aware of risks in the workplace and thinking about the likelihood of an accident arising. Being able to identify risks in the workplace means you need to be able to identify what may cause harm to people and deciding if action is necessary to prevent incidents from happening.

The law states that businesses should carry out risk assessments. A risk assessment means a worker is taking measures to control or limit the risks in the workplace. This means that workers must have a basic understanding of mathematics in order to calculate the risk and work out the probability of an accident happening. Another example of risks in our everyday lives could be revising for examinations. There is an element of risk in revising that you may miss out key information, or you may look at past papers and work out the probability of certain questions coming up in the exam, meaning you only study for these questions. Again, maths would need to be understood in order to calculate the likelihood of a question being in an exam paper. The risk in this would be that exam questions are often random, and there are simply somethings in live that we cannot predict. By limiting revision to questions that you have predicted will come up, you have taken a risk. The risk may be that although highly probable, the questions you predicted were not in the exam and everything you revised is of little use. This could also relate to Liping Ma’s (2010) PUFM as she explores a person having the ability to look at things with multiple perspectives. In risk and probability you must be able to approach a problem with multiple views as there is often more than one outcome. A worker needs to be equipped with the mathematical knowledge to allow them to evaluate and calculate risk in the workplace in order for a business to thrive.

References:

BBC, Bitesize Revision, Probability (no date) Available at: http://www.bbc.co.uk/education/guides/zxfj6sg/revision/6 (Accessed on 8th November 2016)

Bellos, Alex (2010), Alex’s Adventures in Numberland

The Oxford Dictionary, Definition of Risk, no date, Available at: https://en.oxforddictionaries.com/definition/risk (Accessed on 8th November 2016)

Ma, Liping (2010) Knowing and Teaching Elementary Mathematics: teachers’ understanding of fundamental mathematics in China and the United States

Musical Mathematics

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It seems that there is virtually no escaping maths. In a recent lecture with Anna Robb we
imagesexplored the idea of maths in music. Although I have played violin and piano for a large part of my life, I have never really appreciated the large amount of mathematics found in music.

 

When I first began playing violin I was taught about time signatures and the values of different

Learning note values and equivalent values is important in music.

Learning note values and equivalent values is important in music.

notes. For example a crotchet is one beat, a minum two and a quaver is half. To understand this basic concept I must’ve had an understanding of fundamental mathematics as I could understand the value of each note and how to count to that value. Even being able to associate notes to which finger to put down on the fingerboard required some aspect of maths I was unaware of at the time. I knew that on each string the higher the note required to play meant the higher number of finger to use. (e.g. playing a G on the D string uses the 3rd finger which is a note higher than F which uses the 2nd finger) It all seems more complex trying to explain in words.

 

Different music also required different speeds. The speed was dictated at the top of each piece of music by stating a note (mainly crotchet) and a number which represented how many beats were to be played per minute. ( crotchet = 128 bpm, or quaver = 140 bpm, the higher the number generally the quicker the pace of the music. This can also be put into a metronome which produces a sound at the speed requested allowing you to play music to the correct speed whilst keeping to the beat.

Time signatures also dictate how many beats are in a bar and the value of the beat. More maths! 4/4 is the most basic and most used timesignature in music and consists of 4 crotchet beats per bar. This tells the musician that there are four beats in the bar and also that when to play the downbeat. 3/4 is commonly used in Waltz as it is a simple 1,2,3 1,2,3, 1,2,3. In music exams you are also required to identify how many beats in a bar are in certain pieces of music played by the examiner, this means you must have a basic knowledge of maths as you need to know the value of the beat and count.

Patterns and repetition are also apparent in nearly all music. A composer often repeats the violin_piano_pair_by_sinenombre3same pattern, or creates a pattern to invert, mirror or play at a different pitch. Patterns are often recurring. We have already discovered the mathematics behind forming patterns so patterns in music is another example of maths. Music can take different form, ABA, ABCD, ABACAD. Each letter has a different theme or pattern. In ABA, the A is the repeated pattern.

Today’s lecture also showed me that there is a concept in maths, firstly which I had never heard of, but secondly that I would have never associated with music. This is the Fibonacci sequence. The Fibonacci sequence is a series of numbers where a number is found by adding up the two numbers before it.(Hom, 2014) Starting with 0 and 1, the sequence goes 0, 1, 1, 2, 3, 5, 8, 13, 21, 34 (the rule for this can be expressed as xn = xn–1 + xn-2 ). It is interesting to note that in music a chord is made up of the root (1st note of a scale), the 3rd and the 5th. These are all Fibonacci numbers, infact Fibonacci numbers are apparent in

An example of Debussy's work where is a clear pattern of Fibonacci numbers.

An example of Debussy’s work where is a clear pattern of Fibonacci numbers.

the octave and multiple scales too! In a previous post I discussed the use of the Golden Ratio in Art. I have now discovered that the Golden Ratio is also closely linked to music and is infact used when designing instruments like the violin. (Something I will be investigating when I am reunited with my own violin). The Fibonacci sequence is used in many melodies and harmonies as the pattern of notes is most pleasing to the ear and can be heard in many of Claude Debussy’s compositions (Shah, 2010). Although when listening to music it may be hard to pinpoint exactly where the sequence is present, when reading the music itself this becomes slightly clearer. (I have uploaded a picture of an extract from Debussy’s work where the notes, 1,2,3,5,8, and 13 form the main melody).

Music in maths is something I found very interesting as even though music is something I play or listen to everyday I don’t tend to associate with maths. It reinforces the idea that maths is crucial to our understanding of multiple aspects of our lives. Music provided me with so many different opportunities and experiences, my favourite being touring Italy with Perth Youth Orchestra.  I can’t imagine a life without music and it seems absurd to me that if I didn’t have a basic knowledge of fundamental mathematics I wouldn’t have been able to progress this far in music.

http://www.perth-youth-orchestra.org.uk/lord-of-the-dance/ – Link to one of my favourite performances from my time at PYO (skip to 3:48)

References:

Elaine J. Hom, 2014, What is the Fibonacci Sequence? Available at: http://bit.ly/2dtNlVm (accessed on 9th November 2016)

Shah, Saloni, 2010, An Exploration of the Relationship between Mathematics and Music. Availabble at : http://eprints.ma.man.ac.uk/1548/01/covered/MIMS_ep2010_103.pdf (Accessed on 9th November 2016)

Maths in Art?!

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With the upcoming deadlines for essays fast approaching, today I found myself procrastinating… Again! Often I find myself scribbling down patterns and shapes without even thinking. Art to me is a good escape as there are no right and wrong answers, unlike maths which can seem very rigid. Today after I finished my scribbling, I realised that without my conscious knowledge at the time, throughout my drawing I had been considering numerous maths concepts.

In a recent lecture with Wendee we discussed the presence of mathematics in patterns. We discussed shapes, repetition, turns and drops. All of which seemed somewhat important in art but which artists may not necessarily deem as maths. It was clear to us that maths is extremely important in art as it allows you to calculate spacing, angles, patterns or sequences, this is something I have never considered before. To me, maths has always been a subject which was completely set aside from others.

When drawing today I found myself calculating which angle was best to hold the pen in order to achieve thinner or thicker lines. I also had to consider the spacing between the lines in the drawing itself as I wanted to keep them as parallel as possible (again, had I

Who knew there could be so much maths in a simple drawing?!

Who knew there could be so much maths in a simple drawing?!

not had a basic understanding of fundamental maths I would not understand the concept of parallel lines, or angles). The speed I moved the pen at also impacted the thickness of the lines and the accuracy of the lines which is something I had to consider more closely when the spacing of lines reduced. More maths!

 

I even found myself using maths when trying to make a random pattern. I wanted the small dotted pattern to seem random, this would imply that I did not think about how many dots I was putting in each square. However, I found myself counting the amount of dots and trying not to repeat the same number too often. I am genuinely amazed at how much mathematics can be found in even the simplest of drawings.

In a recent lecture with Anna Robb we were informed about ‘The Golden Ratio’. This is something I have never heard of until now, but on reflection used multiple times throughout my time doing standard grade then higher art in high school. The Golden Ratio is also known as Divine Proportion and is determined by the number 1.618 (Phi). The Golden Ratio is often used in art when artists are creating portraits, by distancing the facial features in relation to the golden ratio an artist considers their work to be seen as beautiful (this is often why we see artists stepping back from their work and using their brush to check proportions). A person who’s body is in proportion to the golden ratio is also seen as beautiful (unfortunately for me, I do not fall in this category). One website I came across when researching divine proportion in art describes it as (http://bit.ly/2ecAsw1)    “the most mysterious of all compositional strategies. We know that by creating images based on this rectangle our art will be more likely to appeal to the human eye, but we don’t know why.” I find it fascinating that we have an innate sense to the golden ratio and are more drawn to liking this that use divine proportion. It is even suggested that the Egyptians applied the golden ratio when building the great pyramids, as far back as 3000 B.C. Clearly, mathematics plays a fundamental role in both art and architecture which to me is extrodinary as I feel this is something we perhaps take for granted.

So far, this module has really opened up my eyes as to just how much we use maths, sometimes without knowing. I feel that because I have a firm knowledge of basic maths I don’t often think about when I am using it. Just simply being able to tell the time and calculate how long it will take to walk to a lecture means I am able to leave my flat at a suitable time. This is something I have never really considered as ‘maths’ as to me it comes as second nature. Liping Ma

Time = A basic concept we take for granted everyday

Time = A basic concept we take for granted everyday

describes having a fundamental understanding of basic mathematics as being able to identify connectedness between mathematical concepts. In my art I was able to connect the speed of the pen to the spread of ink on the paper, resulting in the thickness of the line. Moving the pen faster resulted in a thinner but less accurate line. Interconnectedness is also apparent when calculating what time to leave. You must know the distance you are travelling, the approximate speed you walk at and be able to calculate the time it will then take you to cover the distance. Although often taught together, speed distance and time are three separate yet basic concepts in maths that to be able to understand fully must be learnt together.

 

 

Maths is all around us, there is no escape!

Maths... There is no escape.

Maths… There is no escape.

Baffling Base Systems

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The Base Twelve-System

I found binary much easier when adding the place value at the top of each column.

I found binary much easier when adding the place value at the top of each column.

Trying to forget what everything you have previously understood about maths is extremely challenging. This was the case when we attempted to understand the dozenal-base system. When 12 means 10 and 13 means 11 we were overwhelmed. Our understanding of maths has been built using the base ten system, which actually restricted our learning of the base 12 system. Although to us the dozenal-base system seems extremely confusing, it actually has some advantages over the base-10 decimal method of counting. 12 is a highly composite number — the smallest number with exactly four divisors: 2, 3, 4, and 6 (six if you count 1 and 12). This means that using fractions is much easier, diving into halves, thirds and quarters is much easier using twelve. (½ = 6, 1/3= 4, ¼ = 3) where as diving 10 into fractions is much more complex ( ½ =5, 1/3 = 3.33, ¼ =2.5). The dozenal system is exceptionally friendly to computer science, in fact the dozenal system is all around us. George Dvorsky explores this and says:

“a carpenter’s ruler has 12 subdivisions, grocers deal in dozens and grosses (12 dozen equals a gross), pharmacists and jewelers use the 12 ounce pound, and minters divide shillings into 12 pence. Even our timing and dating system depends on it; there are 12 months in the year, and our day is measured in 2 sets of 12.”

12 equals 10?!

12 equals 10?!

 

This course has taught me that there is so much more to maths that meets the eye. Before this, I had never explored different number systems. One benefit of the base 10 system is that it is extremely easy to count due to humans having 10 fingers and 10 toes. Zero serves as the placeholder in the base-ten system.

Binary

Another number system we have explored recently was described as the most simple number system, Binary. Although it had been described as simple, understanding the concept of base-2 system proved more than difficult to us as again our knowledge of the base 10 system restricted our learning. It wasn’t until we started writing down the system on a piece of paper that it actually began to click. This also reminded me that teacher’s should explore a topic in several ways as what works for one child won’t work for others. I think the reason that I personally struggled with this was because we were using the numerals 1 and zero which have different values in the binary and base 10 system. Perhaps if I was to ever explore this with children I would use letters to begin with. Richard spoke to us about the English schooling system and how primary aged pupils learn binary and are tested on this. The teaching of binary is important as it is the system used in computing and technologies. I found binary much easier to understand when writing it out myself with the place value written above each column.

I think it is important to explore different base systems as it can deepen our understanding of the world. Binary helps us to understand codings in computing systems, the base 60 system is used in time and the base 12 system is used in bakeries and calendar months.

When it finally clicked

When it finally clicked

Narrow-minded Maths

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Our recent lecture really got me thinking about how narrow-minded we can be when considering mathematics. Before 2000px-babylonian_numerals-svgtoday’s input I had never really considered how our number system came about or in fact where maths in general came from. I found that discovering other number systems extremely interesting and creating our own was good fun too. This was also an opportunity to use some mathematical knowledge with creativity. Like many other groups in the class we tried to create a number system that symbolised the value of the number itself (1 dot for 1, 2 dots for the number 2, etc.), to us this seemed very logical. However had we placed our number system in front of someone from the Babylonian era, they would be completely baffled by our sense of logic.

After reading ‘Alex’s Adventures in Numberland’ I have discovered that the Babylonians were infact the first people to introduce a place holder. The Babylonians used a base 60 system (which is much different from our base ten system). The first column is for units, the second was for 60s, the next for 3600s. Comparing this to our system, (1, 10, 100, 1000) I feel like we have certainly developed a much more easily understandable system.ishango_bone

I have never really paid much attention or thought as to where maths originated from. Nor have I spent anytime researching ancient maths techniques and systems. After the lecture I decided to further research the Ishango Bone.

The Ishango bone was found in 1960 and is suspected to be more than 20,000 years old. Research claims that the bone is the fibula of a baboon and it was found on the shores of Lake Edward in the Ishango region. On first glance it looks like the bone is covered in tally marks, but there is clearly more to this artifact than simple tallies. Scientists believe that these marks are more than tallies, they are infact an indication that the Babylonians had a much deeper understanding of mathematics. Some scientists suggest that these marks follow a mathematical succession, others interpret the marks as some form of rule. What they can agree on is the fact that maths existed 20,000 years ago. This I find fascinating and extremely eye-opening as I’d been so narrow-minded in terms of maths believing it was something that had evolved and that all countries use a similar system.

Reference:

Bellos, A. and Riley, A. (2010) Alex’s adventures in numberland. London: Bloomsbury Publishing PLC.

Can animals really count?!

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It seems that many pet owners claim that their animal can count. This is not a new idea, it seems the idea of animals counting goes back centuries. In the late 1800’s Wilhelm Von Osten came forward with the proposal that his horse, later named ‘Clever Hans’ had the innate ability to count. When Osten spoke a number, for example, the number seven, Hans was able to tap his hoof seven times, seemingly without any guidance. People were in awe of the animal’s ability to count out numbers up to ten and the horse travelled country to country showing off

Clever Hans: Image from https://upload.wikimedia.org/wikipedia/commons/5/57/Osten_und_Hans.jpg

Clever Hans: Image from https://upload.wikimedia.org/wikipedia/commons/5/57/Osten_und_Hans.jpg

his apparently extremely rare talent. However when animal experts and psychologists analysed both the horse and owner’s behaviour it soon became apparent that the horse wasn’t counting, merely just tapping until receiving some sort of signal from his owner as to when to stop tapping. Leaving the question still unanswered, can animals really count?

 

 

Clever Hans is just one example of an animal associating a word with an action. When Hans heard certain words (1-10) he knew to tap his foot, just like most dogs associate the word “sit” with the action of sitting. All of this training is done through positive reinforcement.

More recently however the question of whether animals can count or not seemed to be answered when ‘Maggie the Counting Dog’ appeared on American TV screens in 2008. To me it seems crazy that a Jack Russell can count as I can barely get my five-year-old Jack Russell to sit or roll over. Nevertheless, owner Jesse had every confidence in her seven-year-old dog’s ability to count she pits her against a class of seven-year-old children for a maths test. (As seen in the attached clip)

Like Hans the clever horse, Maggie seems to have the ability to tap out the correct answer to a number of questions. Not only can Maggie seemingly add two numbers together, she can multiply, subtract and divide! She left the class stunned as she got over ten questions correct, however, left me slightly sceptical. As with Hans, Maggie’s behaviour conveyed the idea that her owner was giving a subtle signal as to when to stop tapping.

Jesse and Maggie also featured on an episode of Oprah (an American talk show) where Jesse claims that Maggie did not need taught any maths. In fact, she claims   that Maggie was born with an innate ability to count and just needed some positive reinforcement. Like Hans, animal behaviour experts were sceptical of Maggie’s supposed counting ability so conducted several experiments to test this claim. The scientist used white sound to blur out any possible secret sound signals that Maggie was receiving, this proved that there were no sound signals so the theory that Maggie could count still seemed possible. The owner was then asked to hide her hands and covered her eyes with sunglasses, again, Maggie the counting dog answered the equation correctly. Questions were then raised when Jesse left the room and Maggie was unable to give a correct answer to several questions. It was then concluded that Jesse was infact giving Maggie some sort of clue as to when to stop tapping and although the dog couldn’t count she was deemed extremely clever with her ability to pick up subtle clues.

Several other experiments exist where scientists try to prove and disprove whether or not animals can count. Some argue it is simply a memory test for some animals, or the ability to associate and action with a word, while others argue and try to prove that animals do have an innate ability to count. it does seem that certain animals have some understanding of numbers, such as mothers counting their young, this could also be disputed as to an animals ability to smell, sense or estimate how many young surround them. Although I am slightly torn on the answer to this question it does seem that animals are extremely clever individuals and their list of talents seem to be endless. Whether or not we will ever get a conclusion to the answer remains to be seen.

Full clip of Maggie’s interview with Oprah available at:  http://www.oprah.com/oprahshow/maggie-the-dog-does-math

Online Assessment Reflection

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Today I completed the Online Maths Assessment and must admit I am quite shocked with my results. I decided to tackle the assessment after reading Liping Ma’s theory that where there is a gap in teacher’s knowledge there will be gaps in student’s learning. I wanted to reinforce my belief that I had a firm grasp of the basics in mathematics but in actual fact this test highlighted to me that although I understood the questions and got the correct answer for 80% of the test, I couldn’t explain why I came to the answer or the reason for my working out. This is important as to have a profound understanding of fundamental mathematics you must first be able to do the maths and be able to explain how and why you came to your conclusions. I clearly have some mathematical knowledge however I could not yet describe my knowledge as profound. Exploring different theories, mathematical ideas and teaching points, and in turn developing my own knowledge of fundamental maths will result in me becoming more confident, and a more competent teacher in the future.

Liping Ma also explores the idea that Chinese teacher’s improve their maths ability through discussion with other teachers, taking on and developing ideas from students and finally practicing mathematics themselves.

Over the time of this course I hope to explore some of the theories cited in Liping Ma’s book, but also other theorists who have impacted the mathematical field.

Reference: Ma, Liping. Knowing And Teaching Elementary Mathematics. Mahwah, N.J.: Lawrence Erlbaum Associates, 1999. Print.

What really is Mathematics?

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What is mathematics?

Before today’s input my basic understanding of mathematics was the ability to use numbers to solve a problem or equation. However, maths is so much more than that. Maths involves many different key elements such as shape, size, patterns, and more which
we often overlook due to our fascination with the assumption that maths can only involve numbers.

Marcus du Satoy’s article in ‘The Guardian’ opens our eyes to the fact that maths is much more than what we perceive it to be. There is more to maths than the basic grammar and vocabulary of numbers we are taught in school and that techniques regarded as ‘core skills’ can limit our enjoyment and discovery of what maths really is. Maths to me was always quite mundane throughout school. We sat down, opened our textbooks and listened to the teacher for some of the lesson and then were suddenly expected to have grasped the new concept and begin working through questions simply by listening and watching someone else solve a problem. Du Satoy’s article makes me question why did we never challenge maths in school? When told a rule for mathematics as a class we just accepted that that was the rule and there could be no other way. We would never question why. Perhaps this dulled our perception of maths in school too, the fact that we were taught not to question what we were told leaving us very unmotivated and uninspired.

In the article du Satoy refers to a book by Hardy which states: “A mathematician, like a painter or a poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.” He suggests that maths is more interconnected with creative arts, and other curriculum areas than often we believe. In schools we often see cross-curricular working but maths is repeatedly pushed to the side. Satoy argues that there is so much history and discovery in mathematics that is often left out of the “unadventurous curriculum” when in reality the discovery of fundamental mathematical principles were crucial in key historical moments. Without maths the Egyptians would not know how much stone was going to be required to build the pyramids in Giza. I had never thought of the endless creations that would have never happened if it wasn’t for the art of mathematics. I must admit that throughout High School I was always left wondering “when am I ever going to use maths?” Maths is all around us, without a basic understanding of mathematics we would struggle to survive everyday life. Mathematics opens doors to discovery and is full of potential breakthroughs and opportunities that could make the difference to the world.

Stand and Deliver

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Stand and Deliver is an American drama filmed in 1988 based on the non-fictional story of a mathematics teacher named Jaime Escalante. Escalante becomes a mathematics teacher at Garfield High School where he faces the daily challenge of teaching an uninspired class. The pupils face many difficulties in their learning, they are well below the average grades and are deemed incapable by many of the teachers in the school. During a staff meeting Escalante confronts the other teachers’ low expectations of their pupils and sets an ultimate goal of getting his pupils through the AP Calculus Exam. Other teachers think he is crazy however his undying determination and commitment sees all eighteen of his pupils pass the calculus exam despite allegations of cheating by the Educational Testing Service. Yet again Escalante shows sheer grit and determination by defending his hardworking pupils by challenging the exam board and allowing all eighteen pupils to re-sit the exam with every pupil passing with top grades. The story is extremely inspirational as it demonstrates the ability of a strong-minded, dedicated teacher to challenge and change not only pupils’, but teachers’ perceptions of mathematics and the ability of lower-class children to succeed.

It could be argued that Jaime Escalante is different due to his unwillingness to give up on a class of ‘less abled’ pupils. He shows that he is unlike other teachers at Garfield High School by challenging their opinions of the pupils’ abilities. He uses controversial teaching points (such as making one pupil sit at the front of the class for not cooperating in the class test) to control his class. Although debateable, his techniques provide him with the capability to break down barriers and build relationships with each of his pupils. His commitment to his class was inspiring, dedicating over sixty hours a week to improving his class’ knowledge on the subject, running extra classes after school, throughout holidays and on weekends. He was determined not to let his pupils down despite facing ill health through exhaustion. Through providing his pupils with insight as to the relevance of mathematics in the real world the teacher further encouraged the students’ willingness to learn. Despite facing several challenges Escalante never gives up. He gains the respect of his pupils and their families and even goes to great lengths to keep several of the pupils in school on the prospect of them passing the exam and furthering their education. After the exam, Escalante’s hard work is rewarded through every pupil passing the exam. Not only did his hard work benefit each and every one of the pupils’ in his class, he showed the school that negative teacher mind-set and low expectations only prevents achievement. Garfield High School’s grades rose each year after Escalante’s success. His sheer grit and resolve makes him a true inspiration.

Reference:

Stand And Deliver. Ramón Menéndez, 1998. DVD.

Scientific Literacy TDT

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“Scientific literacy is the knowledge and understanding of scientific concepts and processes required for personal decision making, participation in civic and cultural affairs, and economic productivity.”
While this is a definition of scientific literacy, once you begin to look into what it means to be scientifically literate, it is easy to see that it is a little shallow. Being literate in science is about being able to question so-called science based on our knowledge; evaluating scientific stories and discoveries made every day. It is the critical analysis of science that makes us scientifically literate, not the ability to blow things up in a lab. While the UK is above average in terms of literacy rates (OECD study), the curriculum in England is beginning to put more emphasis on scientific literacy, and teachers and pupils alike are beginning to notice the change. Based more in secondary than primary education, teachers notice that while it is trickier to teacher, they believe it is more worthwhile. In terms of primary schools, the teacher is essential in building up scientific literacy among children (Shulman 1987), and therefore as training teachers, it is our responsibility to ensure we educate ourselves in terms of science as much as possible.

Analysis of an example where a lack of scientific literacy has led to inaccurate media reporting
In 1998 Andrew Wakefield published a fraudulent report claiming that he combined measles, mumps and rubella (MMR) vaccine could be linked to causing colitis and autism amongst children. The media were quick to publish the story and vaccination rates fell rapidly putting children at severe risk. The public instantly believed the findings as Wakefield was seen as a figure to trust resulting in his publishing not being questioned. One flaw with his experiment was that he only used 12 children for the experiment and some of these children had previous underlying medical conditions which were not taken into account before the experiment (he also did not disclose this information to the general public). This is a good example of science illiteracy as members of the public did not evaluate the quality of the science. Many people did not question the findings or see the flaws within the experiments and as a result put their own children’s lives at risk. Perhaps if we were a more science literate nation controversies and scandals like the 1998 MMR vaccine be avoided.
It is important that when teaching science, children are taught about fair testing. Without having a sound knowledge of fair testing children would struggle to do anything else in science. Being scientifically literate means having the ability to use scientific knowledge, and so in order to learn how to use and apply your knowledge you must first understand fair testing. A lot of science work within the classroom is practical and involves experiments. Science experiments require fair testing in order for them to provide accurate results, and so if children are not taught the importance of fair testing then they will not be able to develop their knowledge and understanding of science.

References – (Explanation of the concept of scientific literacy)
http://www.literacynet.org/science/scientificliteracy.html
http://www.curriculumsupport.education.nsw.gov.au/investigate/
http://www.nier.go.jp/symposium/sympoH20/john.pdf
http://www.ejmste.com/v3n2/brv3n2_cakmakci.pdf

Behaviour Management TDT

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How do they help maintain the attention of the children?

In this short clip, the teachers use multiple ways to maintain the attention of the children in their class. The most common approach was the use of arm gestures. By gesturing their arms and nodding their heads, the teachers invite the class into the lesson and encourage them to share their ideas. Another common technique is that of pacing up and down the classroom, this allows the teacher to ensure that the distance between themselves and their class never becomes too great and reinforces the idea that they are there to be listened to. By varying the pitch of their voice the teacher can encourage children to stay engaged in their lesson

How do they show respect for the children?

One way the teachers respect the children is by encouraging them to share ideas. When the shared idea may be incorrect the teacher does not embarrass the pupil by immediately saying “no that is wrong”, instead he takes the wrong answer and manipulates it and presents it back to the class. They also tend not to raise their voice when they are annoyed with a situation, respecting the children by not shouting but simply changing the tone of the sentence.

How do the teachers show authority?

They show authority by freely moving around the classroom and mingling amongst the classroom. They do not allow the children to have this freedom as they are there to listen and learn. The teachers also show authority by only allowing children to share ideas when asked and not allowing them to shout out or speak over them.

How does the teacher gain and maintain authority through using and moving in their space?

When first coming into the classroom the children are persuaded to walk in single file by the teacher positioning herself carefully in the doorway. This settles the class down so that upon entering the classroom they are reading to learn. When using the whiteboard the teacher paces back and forth to maintain attention but this also ensures that every child can see the board. They do not stand behind their desk as this can seem like a protective barrier and can suggest the teacher is not confident.

How do the teachers manage the movement of the children?

One teacher encourages the children to enter her class in single file. This instantly calms them down. When tidying up after a lesson, the teacher assigns each pupil with a specific job and monitors this closely to ensure that children are following her instructions. By continually talking the pupils through the process the children remain aware that the teacher is still in command and in control. Upon ending her lesson the teacher asks each table a question and if they answer correctly they are allowed to stand ready to be dismissed. The teacher then conducts them to leave one table at a time, this again reinforces that she is maintaining control.

How do the teachers manage the behaviour of the children?

One teacher adopts a ‘thinking pose’ by touching her chin with her hand. This indicates to the children that she wants them to think about the question she has asked. When a pupil continues to talk over the teacher she signals that he should stop by placing her finger in front of her mouth signalling “shht”. Instead of raising her voice to the pupils the her intonation remains reasonably flat even when she seems angry or irritated. Instead, she maintains control by using signals collectively.

Personally I really like the idea of the teachers constantly grabbing their pupils’ attention through big hand gestures and whole body movements. I tend to have quite closed body language and know this is something I definitely need to work on in order to show my confidence and authority. Before this video I didn’t really understand the importance of gesturing things such as the ‘thinking pose’ to pupils however I feel that this is something I may try if my class are not engaging with my questions as it seemed to work extremely well for these teachers. Another technique I would like to try out when on placement is voice control. These teachers all remained calm and in control no matter how they were really feeling inside. Varying pitch allowed the teacher to maintain the pupils attention but also showed when she was impressed with answers or perhaps displeased with behaviour. I believe that every teacher will have a technique that works extremely well for them and others that do not work at all. I hope to try as many of these techniques as possible whilst out on placement in order to find out which suits me best but more importantly which stimulates pupils learning most successfully.