# Demand planning

Demand Planning

Although a three-hour slot was put aside for this workshop it absolutely flew by. We were all so absorbed in how we were going to buy next and what was going to make us the most money etc. we finished with over £50,000 profit! Pretty good considering we started with £5000.

The mathematics involved in this task was endless. We worked within the financial quarter and started with April-June. Not only did we have to work out how many products we were going to buy, we had to first look and see what kind of products would make us the most money. Tinned beans (pack of 4) could be bought at the bargain price of 25p but sold for a whopping £2. From there we had to then decide how much of our budget we many tins of beans we would order. This process was repeated for maximum of 5 products in the first instance. When we had chosen 5 or less products, Richard gave us the percentage of products that were sold for that quarter. Cue more maths. We had to multiply the number of products we had bought by the percentage and then multiply that amount by how much they were sold for. And then repeat for maximum of 5. And then move on the next quarter. Now we knew that some of the products did not sell as well as other we could make wiser decisions and also incorporate new products as we still had some old ones left over.

This went on and on and I absolutely loved this task. We were all so engaged. Richard did put in a few trip ups for us – for example all beans had to be recalled -which for one group was a nightmare as they had spent almost all of their money on beans because it was going to make them the most amount of money and then they were left with not very much at all. Also, the wafers had a shorter sell by date so any leftover products had to be disregarded.

Richard also explain at the end of the year if we had any left-over products, the suppliers would buy some of them back. This allowed any products which we had previously anticipated to sell at a higher percentage to then be bought back and not leaving us at a total loss. He explained stores such as Home Bargains and B&M buy products with shorter sell by dates from suppliers who know they may not sell them in time at the profit they would like. Therefore, allowing these discount shops to keep the prices extremely low. The suppliers do not really have an option here as they may lose out of money anyway if they decide not to sell them to the shops at a low cost.

Although the mathematics involved seemed complicated, we used calculators and were really working out basic percentages. What we were doing was relatively simple – to us. To get to this point we had to have sound knowledge of basic arithmetic, ability to use a calculator to work out percentages, budgeting, problem solving, such as time of year to buy products i.e. probably not as wise to buy selection boxes in April etc.

Profound Understanding of Fundamental Mathematics (PUFM)

Multiple perspectives applied here as with working out how much you have made from a quarter there were two options. Calculating how many ordered by the percentage sold, then calculate the cost or calculate how many ordered by the cost then by the percentage sold. We did it the first way as it just seemed easier but both ways would have been fine and perhaps the second way would have been less confusing for some.

Basic ideas – the basic mathematics was not difficult but the thought and problem solving behind this.

Connectedness – there were so many topics pulled together in order to complete this task we had to combine a lot of previous knowledge. To be able to get to this point to carry out this task, if doing this with an upper stages level, it would be beneficial of the teacher to have revised some of these previous topics in the run up to this.

Cross curricular opportunities and wider world connections

The demand planning task allowed for opportunities of awareness of “financial awareness, assessing risk and making informed decisions”, all of which are stated in the Experiences and Outcomes of Curriculum for Excellence (Scottish Government, undated, pg. 1). Taking beyond basics and connections within mathematics, by predicting increase and decreasing in prices drawing on other knowledge out with mathematics demonstrates the Experience and Outcome mentioned above. Although the basics and fundamentals within this task were mathematical, due to the context, it did not seem this way, showing how this gives many more opportunities to link to other curricular areas.

References

Ma, L. (2010) Knowing and Teaching Elementary Mathematics. London: Routledge.

Scottish Government (undated) Principles and Practice: mathematics. Edinburgh: Scottish Government. Available at: http://www.educationscotland.gov.uk/learningandteaching/curriculumareas/mathematics/principlesandpractice/index.asp. (Accessed: 10th November 2016).

# Multiples perspectives

Multiple perspectives

Ma’s Multiple Perspectives of not only having the ability to adopt different strategies but to know the advantages and disadvantages of them to differentiate for the students is something of difficulty to ask for teachers. Although I do see the importance of multiple perspectives, sometimes there is just an easier way of doing this and over complicating things for children obviously has its disadvantages. Some teachers may use that type of attitude as a cop out however the following examples prove to me the importance of a teacher to know and when and where to apply multiple approaches.

During placement there were a small group who did not understand BODMAS. This was a mixture of ability groups also so it was not down to a less able group not grasping this. We were doing brackets and adding really simple numbers in two brackets first then adding those together. I found it really difficult find a different way to explain what we were doing, especially as the majority of the class understood just as I had intended. Ultimately, they did show understanding and proved this to me using mini white boards and making up their own equations. However, I think lack of experience of having a different/multiple approaches to what we were doing contributed to both mine and the student’s frustration. I think especially because with something like BODMAS, as I mentioned in a previous post, there are rules surrounding the process which is as difficult to explain as grammar.

Another example during my school placement was a pupil whose parent, at home, was showing them how to do a mathematical problem differently to the teacher. The way they had been taught was not only resulting in incorrect answers they were also unable to explain their thinking process behind it. I cannot imagine how stressed this student must have been feeling as they perhaps their parent did know a better way. However, due to the incorrect answer and inability of explanation this caused great confusion because the teacher was progressing this topic further it caused more confusion (It would be helpful to myself and others reading this if I could remember the topic to pick it apart but I can’t – sorry!] Looking at this now, I see that perhaps the parent and teacher’s fundamental mathematics did not correspond which could simply have been from the language they were using right down to the understanding of the basics. Now I wasn’t there long enough to see this through and I am not sure how this would have been resolved. However, this does highlight the ability to adopt multiple approaches/perspectives is important but in order to be able to justify you must know the advantages and disadvantages of your own and other approaches.

References

Ma, L. (2010) Knowing and Teaching Elementary Mathematics. London: Routledge.

# Forcing Connections?

Connectedness and basic ideas

Haylock states teachers should move away from the “notion of teaching recipes and more towards development of understanding” (Haylock, 2006, pg. 7). I believe this applies to both, student and teacher.

When learning multiplication for example it could mean that multiplication in its simplest form is repeated addition. Although most teachers would know this, the purpose of explaining these strategies in the first instance may take away any anxieties students may have when they see multiplication for the first time. So then connecting the basic ideas that multiplication is repeated addition, which they can do with ease, then moving to long multiplication will seem less fragmented. This is where teachers need to be careful in how they frame “rules” within mathematics (Devlin, 2008). Basic multiplication e.g. 4×4=16 is like repeated addition – 4+4+4+4=16. Therefore, is useful in the introduction of simple multiplication, however, moving on to multiplication of fractions, the “repeated addition” statement no longer makes sense (Devlin, 2008). This also corresponds with Haylock states about learning recipes. This also evident when introducing multiplication of negative numbers where the “repeated addition” no longer applies. Rote learning although may help with consolidating processes of how to do a particular concept, the meaning of why must also be in the mind of the teacher.

BODMAS

I think it is hard to connect something like BODMAS to the wider world. It’s almost like grammar, where there are rules that help you make sense to read and write something and that is it. This doesn’t agree with Haylock’s statement above, of moving away from teaching recipes because that is what BODMAS really is. There is a way to do something and it has to be in that order for it to be correct. However, when moving looking at concepts within BODMAS and multiplication in brackets which is a topic which I taught during my placement there is opportunity for making connections. Explaining to the children that the mathematics they were doing was not something new but it was the way (order) they were to do it in I think made the children feel at ease. I think it is very important that teachers not how know the connections but show positive attitudes when connecting topics.

Forcing connections

Ma’s view of connectedness is a teacher making and demonstrating connections between topics within mathematics. This is possible in a topic such as BODMAS however, making connections to the wider world is harder to make. I think children do need to see the connections between concepts and topics however certain areas, as proven with BODMAS, there cannot be a connection to the wider world so why force it?

Some teachers may feel under pressure to make connections with everything after reading Ma’s definitions of Profound Understand of Fundamental Mathematics (PUFM). I feel as long as they can see themselves and show the connections where possible and where necessary, without confusion the children. Making connections with every possible topic does not show PUFM. Making the decision when and where to show the connections shows the “profound” in my opinion.

References

Devlin, K. (2008). ‘It ain’t no repeated addition’ Available at: https://www.maa.org/external_archive/devlin/devlin_06_08.html (Accessed: 14th November 2016)

Ma, L. (2010) Knowing and Teaching Elementary Mathematics. London: Routledge.

# Nature of time

Time is something that I hadn’t really thought about as it just something that we have come to learn and know. It is probably one of the most important aspects of mathematics that directs our lives. Everything we do is according to a time and schedule.

It was a bit of a surprise to me that some aspects of time are man-made, such as second, minute, hour and week. However, days, months and years are not. The latter are natural aspects of time are shown from the Earth turning to turn light to dark (day), the moon and its shape (month) and changing of seasons and migration leading to recognition of division of seasons and therefore a year.

All aspects of time coincide with the sun and the moon. To me, I know that it is a new month because another day has passed and my calendar tells me so. But without a calendar of a digital clock telling the day how did people before this invention tell the time. The oldest artefact found and thought to be 35,000 years old, called the “Lebomba bone,” had 29 lines scratched in to which could represent the recording of a lunar cycle (Bellos, 2010).

There are various theories about how the 24-hour day developed. The fact that the day was divided into 12 hours might be because 12 is a factor of 60. There is also reason to believe finger-counting with base 12 was a possibility – the fingers each have 3 joints, and so counting on the joints gives one ‘full hand’ of 12. Another theory based on Egyptian time was that the 24-hour day was broken down to 10 hours of sunlight, 10 hours of darkness, 2 hours of dusk and 2 hours of dawn. However, how did they account for time at night as one of the oldest ways of telling time was a sundial. We looked at the history of water clock which again seem so simple yet the sophistication of this invention is amazing considering the period of time.

Time is not something I had put much thought in to before and this occurred to me that it is because the foundations of it were taught at elementary stage (Ma, 2007, pg. 124). We are so used to telling the time in 60, but that really is quite a hard concept to understand as a student. During my placement I was teaching hand of clocks and just the language such as “quarter past, half past and quarter to” are quite difficult concepts to understand. Not only do you need knowledge of how to divide something by two and four, it becomes more difficult where using fraction on the number 60, which is easy enough for you and I because we know it so well. However, when breaking this down to teach and trying to reframe my methods was something I found difficult as it is just something that I’ve come to know so well and use every single day.

Profound Understanding of Fundamental Mathematics (PUFM)

I think many of Ma’s principles of PUFM can be applied to the concept of time. However, defining “telling time” is very difficult as there are so many stages and blocks to build on.

Basic ideas – recognising numbers in a sequence that is different to the base 10 system we use for everything else. Children may not be able to tell the time but they can recognise the numbers on a clock.

Connectedness – Following simple routines for break and lunch times e.g. knowing that it is nearly lunchtime due to positioning on the clock. To moving on to connecting language from other topics such as fractions e.g. “quarter past”, “half past”.

Multiple perspectives – time becomes very confusing switching between 12 and 24 hour clocks so knowing when to it is necessary for children to be able to differ between the two is also important. Children are exposed, even more so nowadays in our digital world, to digital clocks telling 24-hour time so it is important the difference is taught as soon as possible without causing confusion.

Longitudinal coherence – I think this principle plays a vital part when learning, understanding and teaching “time”. Being able to tell the time is not the only part children need to understand. The ability to understand a routine or a timetable are difficult concepts to grasp along with “telling the time”. The level of intellect used in problem solving for structuring and deciphering timetables is optimum at elementary level. Teachers who keep in mind why they are laying foundations of basic ideas of time exhibit longitudinal coherence and showing responsibility out with their horizontal teaching.

What have I learned?

As I’ve said, the mathematical concept of “time” does direct the world around us in all that we have ever done. I have taken from granted my own ability to tell the time and use it to direct my own day. My new knowledge of how some aspects of time were developed has given me a deeper understanding and confidence for teaching this topic in schools in the future. Connecting the language between topics e.g. quarter past for time, which I taught on placement would have been greatly beneficial to appreciate and understand at the time. Children often think they are learning isolated topics and I’d have said, before delving in to this module, I would agree slightly. Based on, that a lot of mathematics I think I learned is no longer of any use to me. Deciphering and making up my own timetables in school may have been a boring subject but I did not realise the learning and “time” it would have taken me to get to that stage now helps me organise my own day.

What do I want to find out?

Day lights saving is a fairly new concept that was introduced in the last 100 years or so what that’s all I know of the why. It is something that will affect all of us – in the winter we get an extra hour in bed – win! However, understanding why and what happened before this was introduced would be something further to research.

References

Bellos, A. (2010). Alex’s Adventures in Numberland. London. Bloomsbury Publishing Plc.

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

Rogers, L. (2011). A Brief History of Time Measurement. https://nrich.maths.org/6070 (Accessed: 14th November 2016).

# Number systems and Connectedness

Richard said to us that in order to look at some of what we would look at in Discovering mathematics, we would have to forget everything we know. And he was right. One of our lectures we looked a place value and binary and my mind boggled. So much so that Richard went over binary in greater detail in another lecture – thank you!

I never knew the existence of any other number system until this module. Well, I knew time was not a base 10 however as I said in a previous post, time along with a base 10 system and place value a base 10 system is taught from the very beginning of school. In the use of units, tens, hundredths and so on. One of the first things we learn with numbers, and that I have taught my daughter I to count to ten (even though technically a base 10 system is 0-9, but who learns to count this way?) I do this every day with her, from counting going up stairs and reading books. 1-10 and so on is the way it is, she does not know why, and I did not think about it in depth until this module either.

The idea of different base systems because of how easy I think the one we use is seems bizarre. We looked at “yan, tan, tethera…” a base 20 system Lincolnshire shepherds used to count their sheep. If a shepherd had more than 20 sheep, he would record one cycle of 20 by putting a pebble in his pocket or marking a line in the ground and start again (Bellos, 2010). So five marks or pebbles would represent 100 sheep. This base 20 system works well for what it was used for – counting sheep. If a base 10 system was used for this example, then there would be a lot of notches or pebbles to carry (depending on the size of course) and could possibly become more confusing. However, using this base 20 system for anything other than herding and counting sheep, does not seem the most sensible option.

Bellos suggests the trick of a good base system is that the base number needs to be large enough to be able to express numbers such as 100 with ease. Obviously this why a base 10 system works so well in his option but I also think the base 10 system works so well as it is in tuned with the human body. I still use my fingers occasionally to count. But if we weren’t born with 10 fingers – who knows if we would be using a base 10 system or not.

Binary

So looking at a base 20 system wasn’t too difficult but then we moved on to binary. Cue the utterly puzzled feeling and look on my face! In the first lecture I didn’t really get it and we quickly moved on. I’ve gone through my whole life not knowing what binary is and how it works so I wasn’t too concerned at the time. But, that’s not what this module is about is it! Cue BBC Bitesize website which explained Binary is a base 2 number system that uses 1 and 0 and is processed by computers! WHAT!? Yep, back to not ever knowing or needing it or wanting to look at it again. Thankfully Richard did show us the YouTube video below and showed us a different table to what he had shown in the previous lecture and alas, as I said at the start of this post, in order to understand, we need to unlearn all that we know about numbers. As there is only two digits that can represent values in binary (0 and 1) this what I found hardest, the difference between number and numeral. We are so used to the number 1 meaning 1 and 2 meaning 2. I still don’t feel confident enough to explain how binary works but I can use this table myself and have included an image of my handy work! (I just hope it is correct!)

I don’t suggest going in to great detail of different base number systems with children but perhaps delving in to them to make them aware that we should count ourselves lucky that the one we use is easy compared to “yan, tan tethera”. But, the fact that binary is used our digital world and Code Club was something was popular at my placement school, it is important for at least as a teacher to know one of its existence but to be able to explain it in simple terms. I’m still not entirely keen on Binary, due to it being so different from all I’ve ever known. However, appreciating how difficult it was to get my head around certainly gives me an understanding of how learning something new for a student is and how easily fragmented it could become.

Connectedness

And of course, all of this links to Ma’s “connectedness” of Profound Understanding of Fundamental Mathematics (PUFM). In order to understand different number systems, I had use prior knowledge to link different mathematical concepts together. That is why it is so important for elementary stage to have the simpler “basic ideas” instilled within students so that they can be used instinctively when learning new topics. However, it is the duty of the teacher to show the connections between what they have learned and how that knowledge is implicit to learning new topics and for their future. I feel that by learning about different number systems and binary in particular, I was able to draw on previous knowledge and with that in mind apply it to a new concept which together become the “unified” body of knowledge that Ma describes (Ma, 2010).

References

Bellos, A. (2010). Alex’s Adventures in Numberland. London. Bloomsbury Publishing Plc.

Ma, L. (2010) Knowing and Teaching Elementary Mathematics. London: Routledge.

# Beauty of numbers/art

The golden ratio is also known as Phi (Φ) and goes (a + b)/ b = b/a

Using Fibonacci’s number sequence to calculate the Golden Ratio works for all of the numbers after number 3 in the sequence. 1,1,2,3,5,8,13,21,34,55

Example:

• (2+3)/3=1.6666666
• (8+13)/13=1.612384

To anyone who did not have the opportunity of having this equation explained and demonstrated to them may be sitting there thinking that looks rather complicated. I like to think of it as where by you divide any number by the one before you will always get 1.6…. Much simpler – to me anyway.

What is the point in all this. Well the Ratio 1.6… is known as the optimum ratio of aesthetic beauty. We tried this out on measuring our own bodies – from our hands to our full bodies to work out the ratio and if we are “beautiful”. This was a fun activity, giving us a real life example of the Golden ratio and how it works. Imagine my horror when I found my hands were not the optimum beautiful hands I thought they were and disproportionate to the rest of my body – perhaps my measurements were wrong!!! That or I have massive shovel hands!

The Fibonacci sequence and ratio occurs so frequently in our world and is applied across many areas of human endeavour including architecture and other forms of art.

During the Renaissance period where Leonardo Da Vinci painted The Last Supper and the Mona Lisa, further observation of these show the use of the Golden Ratio making them aesthetically pleasing to the eye. Having never been aware of the existence of the Golden ratio and how it makes up some of most famous paintings in the world I now feel slightly more knowledgeable and sharp of where and when to look out for it. I especially feel if I was teaching an art lesson on for example self-portraits I feel more confident in my ability to explain the ratio’s (perhaps not to use them in practice) but to at least outline and explain the use and aesthetic advantages it holds.

References

Knott, R. (2010) Fibonacci Numbers and Nature. [Online]. Available at: http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibnat.html#petals (accessed 31/10/16)

# Fibonacci

I was a bit dubious before coming to this lecture and naively thought “what does maths have to do with art”. We had previously discussed the Golden ratio in previous lectures and I had not linked the two. My ideas, having only heard what the golden ratio was, was it made buildings look symmetrical – but again I thought that was perhaps to do with the structure etc.

We first looked at the Fibonacci sequence. Did he (Fibonacci) invent this sequence or merely discover its existence?

It goes, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89 and so on.

The rule of this number series is the next term is formed by the sum of the two previous terms.

(There other rule is if you divide each by the number before it you will get 1.6 – sounds complicated and I will talk about this in another post).

This sequence seems simple enough however, we watched a video of how it explains rabbits and it was, to me, rather confusing. However, if you remove the part of where I watched the video I understand. The sequence is what it is and it makes sense to me. The rule is very simple to follow and it makes mathematical sense.

Golden Spiral

The Fibonacci number sequence is found in natural objects and phonema. For this to make sense we drew the golden spiral based on the sequence above following written instructions of drawing squares but the number of squares followed the Fibonacci series. From the example you can from the squares drawn you can create a spiral.

This spiral is found in many natural objects and phenoma including:

So back to my earlier questions of did Fibonacci invent this sequence.

“We don’t invent mathematical structures – we discover them, and invent only the notation for describing them”. (Tegmark, 2014, p259).

It has been proven to us through many different examples such as the curve of a wave, nautilus shells, sunflowers, pineapples, the reproduction of bees and rabbits. The list goes on and on and now that I’ve seen it in so many different places and forms I will be on the look out. However, the sequence is recurrent according to Bello and the cyclical nature of it explains why it comes up in many natural life forms as they grow by a process of recurrence also (Bellos, 2010).

References

Bellos, A. (2014) Alex’s Adventures in Numberland. London. Bloomsbury.

Knott, R. (2010) Fibonacci Numbers and Nature. [Online]. Available at: http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibnat.html#petals (accessed 31/10/16)

Tegmark, M. (2014) Our Mathematical Universe.

# Can animals count?

It does make evolutionary sense as why they would need to do this. Mathematics helps us direct the world around us so why not animals too?

But what really is counting?

“To name or list (the units of a group or collection) one by one in order to determine a total; number”.

So can animals understand numerosity?

This seems a bizarre question and not one I have put much thought in to before. During our lecture with Richard he proposed a few ideas on how some people thought different animals could count.

The first example was Clever Hans – the horse who could apparently count. It seemed bizarre at first. Hans’ owner would point to number and Hans would stamp his hoof however many times. This animal could not only understand the numeral but the number (concept) that represented the numeral – amazing right? This was eventually debunked by psychologists who found that Hans was merely following subtle cues by his owner so knew when to stop “counting”.

During the lecture I thought there were some degree of ability of some animals to count. My logic was thinking about an animal, a lion for example, would know how many cubs it had. If one was missing, the lion would know that two wasn’t enough and off they would go to look for the third.

I then thought about my own daughter, who is two years old. She can you tell you that she is two but not two years. She can recite numbers 1-10 then 11, 12, 13, 14, 17, 19, 20, 20 20 – she loves saying the number 20!

She has a new book which counts down from 10-1 with lady birds. This is something she is struggling with as we have always practiced counting from 1-10. Again, we have recently been practicing jumping in puddles citing 3-2-1 blastoff. However, she always says 1-2-3 blastoff. So yet another confusion for her.

So can she count? Yes, to an extent. She can recite the numbers.

Does she know what the numbers mean? No, not yet. She cannot yet assign numeric value to a group of objects yet.

She understands that if she insists on taking three teddies to Tesco and one goes AWOL (or mum has hidden it) she knows that one is missing. One not being the correct word here – the exact one. She knows that something is not right and what she had is now not there. She doesn’t know that three is suddenly two. Not the concept of number anyway. But, what she does know that she had Peppa, George and Iggle Piggle and recognizes which one is missing. (A similar analogy to the lion example I had thought about).

This brings me back to my own argument about whether animals can count their young. They know that each of their cubs represents a number and if one is gone – I think they would know which it is.

Lions can count to a degree – what I found what slightly more complex than I originally thought above. Below is a video which explains that lions can count based on the number of roars they hear. The results were that if their roars out numbed the roars played to them by two they would go ahead and fight/defend themselves.

So what about Ayumo the chimpanzee who could count.

As a class we tried to the tests that this chimp did and were not very successful. Perhaps with some practice (and a reward like Ayumu received) we would improve on this. When watching this it did seem more like memory of number rather than understanding numerosity.

I did find another clip however, which shows a chimp counting dots thus demonstrating they do understand numbers and numerals.

References

http://www.thefreedictionary.com/counting (accessed on 18th October 2016)

# Maths and play

Maths and Play

In our lecture we discussed some reasons of importance of play when teaching mathematics. Some of which included:

• Enabling children to experiment
• Providing meaningful context
• Promoting social learning
• Encouraging creative and flexible thinking

All of these reasons would be helpful in any area of learning so why are we so focused on making maths fun?

Maths is so deeply embedded in our society that if from an early age if it seems too difficult, boring or irrelevant and a person switches off from it then this may have consequences for their future. Therefore, the early experiences need to be positive ones, as do the latter, however in order to stamp out any anxieties especially, the early experiences must be positive ones.

Are we disguising what CfE wants all learners to do which is “opportunities for communication, discussion and explanation of thinking” (Scottish Government, 2009, p 189) by calling it play or is what is described above is actually play. Reading that quote does not first bring play to mind for me. However, I think sitting at a desk, being didactically taught new concepts is exactly how our curriculum is designed not to be taught. As a former maths textbook enthusiast (as a pupil not as a student teacher) this is the complete opposite of what is described in CfE so play or whatever you think it should be called has its place as was proved to me in some maths lectures we’ve had for this module so far.

In one game we had to describe to our partners a shape that was on a card. This proved to be quite difficult to explain but easier as the person trying to figure out the shape. I first started by describing whether it was a 2D or 3D shape then could move on to how many faces (sides) the shape had. Haylock and Manning suggest the importance of experiencing this type of game (naming, sorting) are components of young children’s play which lay foundation for genuine mathematical thinking through the classification. This type of game could be used with children to consolidating different types of shapes e.g. square and triangles and then used as a building block to understand new concepts such as equilateral and isosceles triangles or being able to distinguish between 2D and 3D shapes.

Another task in a different lecture we were asked to complete was to find a formula for how many snaps of chocolate to break a bar in singular pieces of chocolate. The thought of doing this on my own was a bit daunting especially when the word “formula” comes up. You think it will be complicated.

However, as we got to work together as a group on this task, had props to help us and it was relatable as we could all imagine the blocks we had were actually chocolate this was a relatively easy task.

I think the four areas of Lipping Ma’s profound understanding of maths are promoted in these games or come through at some points.

Interconnectedness (how mathematics topics depend on each other). Simply as, in order to understand and describe 3D shapes we needed to know the properties and characteristics of 2D shapes such as squares, rectangles, circles.

Multiple perspectives: In a group setting we were able to approach mathematical problems in different ways. This was shown in the formula challenge with chocolate. With six in a group it was difficult to for one person’s idea to be the same as everyone’s. The ability to look at this problem with a flexible approach was important but something that we all did. This again links to what is promoted in CfE as mentioned above where emphasis on explanation of thinking is important.

Basic ideas (or principles) e.g. ordering, place value, commutativity, etc. The mathematical language we used to describe the properties of the shape links to basic ideas described as we need to know the basic characteristics in order to describe a shape.

Longitudinal coherence:  that one basic idea or principle builds on another. i.e. the understanding and properties of 2D shapes must be understood before moving on to 3D shapes.

The four ideas of Lipping Ma may seem boring (sorry!) when written out. However, experiencing maths games and linking it to these four ideas, they are more simplistic and obvious than I first initially thought. There were many opportunities for discussion and explanation of our thinking and we did have fun doing these tasks/games. I would not say that just by playing these games you will profound understanding of fundamental mathematics (PUFM). Lipping Ma describes PUFM having breadth, depth and thoroughness which goes much deeper than the four ideas. Although I was able to explain my own thinking and appreciate others perspectives, the ability to not only find a new way but to explain new procedures to a student who wasn’t understanding something is not something I feel I could do confidently at this stage. The thoroughness of my understanding of PUFM is not quite there yet.

References

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

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

Scottish Government. (2009) Curriculum for excellence, experiences and outcomes for all curriculum areas. Available at: http://www.educationscotland.gov.uk/Images/all_experiences_outcomes_tcm4-539562.pdf

# What is mathematics?

What is mathematics?

Though this question is impossible to summarise in a few words, these were my responses to this question from today’s input:

“mathematics is solving problems with numbers”

“mathematics is universal”

“mathematics is everywhere” (This was proven to us by being tasked to highlight in a newspaper wherever we saw maths. The yellow highlight strewn across the front page was evidence enough).

Maths anxiety is not something I believe I have, however, being informed in our lecture that in order to be numerate, you must not only understand the mathematics you are doing, you must be able to explain your thinking. If I was confident in my own ability to do a maths problem and was put on the spot to show how I did it, I think I would feel immense pressure and embarrassment in case I was wrong. Showing me there can always be doubt and fear.

Before my first year school placement I felt confident about teaching mathematics and felt I had an understanding of the basics at least. Maths is a subject I enjoyed and was good at, at school until Higher level – but that’s a different story and I won’t go there now. However, during my placement, I taught an extensive amount of mathematics. During one lesson I won’t forget, I had a really tough time helping a small group understand the lesson objective. Repeatedly breaking down the success criteria for the children but this group just weren’t getting it. I thought the way I was explaining it was simple enough however saying it over and over again did not work. I realised the problem lay with me and my inability to explain it in a different way. Therefore, my confidence in my own ability plummeted.

The example above is why I am glad I chose this elective module as I need to better understand mathematical concepts, to improve not only my competence but re-build my confidence in a subject that I enjoy.

Our lecture on “what is maths? Why teach it?” was really interesting and dare I say fun! The task to work out how many snaps to break up a bar chocolate with 64 squares brought about many things which are so important to exploring maths: discussion, conversation, sharing language and most importantly, play. We were able to visualise and draw connections from this task to help us and we had help with props too.

I think we have got off to a great start in not only understanding but actually doing what mathematicians do. In the lecture we did all of the following without even realising it:

• solve problems
• investigate
• explore
• discover
• use symbols, tables and diagrams
• collaborate

Another task was to discuss which way we would calculate this problem:

“In a warehouse you can obtain 15% discount but you must pay 20% VAT. Which way would you prefer your final bill to be calculated: with discount first or with VAT first?”

I first dove in with working out the answer doing 15% off first then 20% VAT and vice versa and was not surprised to find that both answers were the same. It was interesting to hear other people’s ideas that the reasoning behind perhaps adding the VAT first was that so there was a greater number therefore when it came to the 15% discount there would be more money off. This was a great task to see how other people’s mind worked as, as I said I just dove straight in, however, others had more logical thinking, albeit the answers were the same, it shows that no two minds think alike.

# Scientific Literacy

Scientific Literacy TDT completed by myself, Katie-Rebecca and Kim.

AC1 – Maienschein, J. et al. (1998) states that there are two main definitions for science literacy. The first emphasizes a huge focus on gaining units of scientific or technical knowledge. Second emphasizes scientific ways of knowing and the process of thinking critically and creatively about the natural world. Knowing about science means that you can make informed decisions about the world around us from an economic, social and personal point of view. Science literacy links in with some of the principles with the Curriculum for Excellence which are depth, coherence and relevance (Education Scotland, 2016). It is important for children to look at science in depth because if you don’t the children may not have the chance to understand at any other point. Coherence comes in because if the children link up their previous knowledge to their current learning then they may have a better overall understanding. Lastly, relevance is important because if you cannot justify why the children are learning what they are, then why are they learning it? If their work isn’t relevant to the Curriculum and the children’s interests then they won’t be interested in science.

AC2 – A shortage of scientific literacy could result in the development of false scientific conclusions. In 1998 one false accusation reported by the media was the investigation into the MMR vaccine. Andrew Wakefield, who no longer practices medicine, came to the conclusion that a child who is given this three in one vaccine for measles had an increase chance of developing autism. Of course, when these findings were released by the media many parents were hesitant and refused to get this vaccine for their children meaning the chances of the child catching measles increased.

In 2004 it was finally realised that these findings were false. Wakefield only research on twelve children and these twelve medical reports did not match what Wakefield claimed in this findings. His findings were therefore false making the paper he published inaccurate and this paper was taken down. This illustrates how important science literacy is, the outcome of this false information resulted in children suffering for unnecessary reason. In new, recent research it has been found that there is no link between the MMR vaccine and autism. However, there are some parents who may still be hesitant or refuse this vaccine for their child as they still believe Wakefield’s findings.

AC3 – Fair testing is one of many ways of learning through science enquiry. Testing is kept fair by experimenting in a controlled environment and changing one variable at a time. Teaching children how to test one variable at a time along with a control group shows them that by only one variable can affecting the outcome with a comparison (the control) reliably. An example of a fair test in a school to improve scientific literacy could be to dissolve sugar in water. In each cup the same volume of water and sugar would be placed, one cup would have warm water and the other cold. The cold water (the control) gives them the comparison and proof that it is in fact the temperature that speeds up the sugar dissolving and not any of variables such as time left in water. Being scientifically literate is the ability to think critically about the world knowing that what they have in front of them may not always be reliable. So science literacy, the example of how false scientific conclusions and teaching fair testing iterates to children that not everything they say or hear is on based on evidence and they should challenge it if necessary.

Education Scotland (2016) – See here http://www.educationscotland.gov.uk/learningandteaching/thecurriculum/howisthecurriculumorganised/principles/index.asp

Greenslade, R (2013). The story behind the MMR scare. Available at: http://www.theguardian.com/society/2013/apr/25/mmr-scare-analysis

Jane Maienschein et al. (1998) “Scientific Literacy” in Science:Vol. 281, Issue 5379. page 917 NHS Choices, Ruling on doctor in MMR scare, 2010. Available at: http://www.nhs.uk/news/2010/01January/Pages/MMR-vaccine-autism-scare-doctor.aspx

Science Kidz (2016) – http://www.sciencekids.co.nz/experiments/dissolvingsugar.html (Accessed: 14th February 2016).

UTMB Health, Wakefield Autism Scandal, David Niesel and Norbert Herzog, 2012. Available at: http://www.medicaldiscoverynews.com/shows/237_wakefieldAutism.html

# Upstart Campaign- Introducing Kindergarten to Scotland

During last semester a few different lecturers mentioned that of the Nordic school model where children start school later (around 7) and catch up very quickly and even overtake those who started school earlier by the time they reach eleven or so. This was something I wanted to look into further but never got round to doing.

Last night I attended the Upstart Scotland Campaign debate organised by Brenda Keatch in the Dalhousie Building at the University of Dundee. There was fantastic turn out with a host of different people from different professions there including student teachers, lecturers, health visitors, child minders and parents. Brenda said that she had originally anticipated around 40 people attending yet there were over three hundred tickets requested so the event location had to be changed three times! This did just show how interested people are in hearing more and supporting this campaign.

So what is Upstart Scotland?

“Upstart Scotland is campaigning to have the principles of our Curriculum for Excellence transformed into practice by introducing a kindergarten stage for three-to-seven year-olds based on the Nordic model. This is influenced by research that indicates there is no educational advantage to an early start to formal education and that this may in fact causes social, emotional and mental health problems for many children. The emphasis of a kindergarten stage is to provide children with opportunities to play (with a strong emphasis on outdoor play)”.

I really value the power and significance of play as it stimulates qualities such as social, cognitive and personal qualities including communication, problem solving and self-regulation. All of these especially self-regulation make the difference for teachers dealing with behaviour issues. It makes sense to think that a 4 or 5 year old who does not have the ability to “learn” how to read or write will be unable to self-regulate their emotions which will have a knock on effect to confidence, self-esteem etc.

However, a friend and I had the discussion that what everyone else who has started school at the age of 4 or 5 who are all successful curious adults? … Technology. Technology has transformed everyone’s lives enormously and especially in play. This was a huge talking point in last night’s debate and unfortunately, play for some children mostly includes sedentary TV screens and tablets. Children are not getting the chance to experience play in the way that once was. The rate at which technology is developing is not going to slow or change but the fact is that humans are not developing at the same unprecedented rate is a problem.

The evidence is so clear and I agree that the Nordic model is better than ours. Finland is the near highest achieving country in both education and childhood well-being. The statistics (which unfortunately I don’t have where they are from as I just noted them down) are of school starting ages around the world:

• 4/5 year olds – 12%
• 6 year old – 66%
• 7 year olds – 22%

Delaying children starting to school would cause outrage for some people. Key speaker from last night, Dr Suzanne Zeedyk said that people are suspicious of play and think children are not learning from playing – that they are having fun. They could not be more wrong. They are building on the foundations for the future such as friendships, being inquisitive, imaginative and finding a sense of self.

There was also an emphasis of trying to slow down children’s childhoods. Life expectancy is getting longer and yet childhood is getting shorter. The word “tween” has been added to the dictionary to describe a child aged between 9-12 who is “no longer a little child, but not quite a teenager”. This has already been done and it won’t change so therefore I feel attitudes need to change to play.

I don’t believe the school age is something that will be raised any time soon in Scotland but creating awareness of the importance of play and outdoor play and the qualities that children learn through this is completely necessary for them to be able to learn effectively in school. Effective learning is what is most important and is what will ultimately bridge the attainment gap.

I realise I do sound like a walking, talking (blogging) advert for Upstart but I really feel quite passionate about it. There will be plenty scepticism about Upstart but as was discussed last night, once upon a time not all children went to school, females didn’t go to university, there were physical punishments as a norm in school so hopefully one day starting school at a later age will be a norm too. Upstart is a vision and a national movement and its purpose is to change the ethos of education.

I would urge you to have a look at the website and associated articles and please give me your thoughts.  I look forward to hearing more about just how Upstart hope to bring about this change.

http://www.upstart.scot/

# Not so scary Maths

When asked to rate ourselves on a scale of 1-10 for enjoyment and confidence of maths I rated 8 and 4 respectively. Maths is a subject that I enjoyed at school but the thought of teaching maths is frightening. It’s been while – almost 2 years since I’ve studied maths and prior to that 5 years since school – so I am nervous children may know more than I do!

In Tara’s input we discussed maths myths and anxieties:

• It’s not needed for everyday life
• You are better at maths or language and not both
• My mum wasn’t good at maths so I won’t be either
• Some people just can’t do maths

Genuinely, I’d never heard of maths anxiety until I started University but it is something I need to understand. Maths is not something I was ever frightened of. That’s not to say I’m an expert but I did and still do enjoy using numbers. I feel I do have a positive attitude to maths and but must admit I did/do agree one of the myths that you are stronger in either maths or language as I felt exactly that, that maths was my stronger subject compared to language. (Something I need to get out of the habit of thinking).

It is paramount that teachers show a positive attitude and confidence to maths. As soon as you show weakness with any subject but particularly in maths you give reason for children to doubt their own abilities. Mistakes can be made but not being embarrassed and using them as learning opportunities is important as a teacher to show children it’s ok. Equally saying something like “I wasn’t very good at maths” or “I was better at language” sets doubt and leads to a self-fulfilling prophecy.

My thoughts were that I may have confidence in my own ability but not teaching maths and as long as I show enthusiasm then I’ll be ok. However, Tara then showed us a quote:

“Teaching enthusiasm cannot be maintained where a teacher is unsure of the material… consequences of unsound subject knowledge is hesitancy in teaching, lack of direction to the lesson and lack of clarity in explanation”. Banks and Mayes, 2001, p25.

This then scared me.  I have only engaged with the Online Literacy Assessment a few times (okay only once) and my score was embarrassingly low.  I really need to get my knowledge up to scratch and there is little time left until placement.  We are not required to teach hard mathematics but unless there is understanding (apparently) then doubt will be cast over my teaching of the subject. Better get to it…

# Not just a warm up…

I was really excited for our P.E. input as anyone who knows me knows I enjoy exercising and playing sports. I think we were all a bit nervous as we weren’t sure what was going to be involved in terms of efforts of exertion however I think we knew Will wouldn’t have us running laps for the whole hour. I was surprised the find out the aims of a warm up that I had not considered before in a P.E class. For our warm up Will gave us a series of simple instructions to follow. He asked us what the intention of this and most of our answers were as you would expect such as increase heart rate and preparing the body. Will then explained his intentions were not only of that mentioned but to also identify areas such as:

• Physical ability
• Ability following instructions
• Potential bullying
• Competitiveness
• Motivation

The simple instruction that were given for us to follow were also allowing Will to assess who is or isn’t physically able to do some movement. If a child cannot bend down to touch their toes or they aren’t co-ordinated they may need further help in certain areas. Another of the instructions was to stop jogging and sprint in the opposite direction – this was so assess spacial awareness.

The next part of our warm up was to jog round the hall and when will shouted “freeze”, he would show the number of fingers of how many people to get in to groups. What he was doing here was to see if we could follow non-verbal instruction but also identifying possibilities of bullying e.g. do the same people always go in a group and are some people always left out. By doing this when it comes to grouping for further drills or activities the teacher can work out ways to put people in different groups. I am guilty of saying in school we did try to outsmart our teachers by not all lining up in a row to try to be grouped together.

Next in partners we took turns to dribble a ball, however there were only one or two full sized basketballs. What Will was showing us here is that the resources available to us may not match up with our lesson plans so we should checking to see what is available before planning.

I did come across some interesting information while researching for this blog post and came across this report. sportscotland and Education Scotland invested £5.8m to support local authorities in providing two hours for primary and two period for secondary school of quality physical education per week. This report details how some local authorities spent this money including buying resources, sports equipment and inclusion training for teachers to fully include children with additional support needs. From this hopefully the schools we work in will have benefited from this investment and resources won’t be an issue.

Most importantly from this input I learned that P.E isn’t about doing a gym class for two hours per week and that’s it. It provides learners with the opportunity to build and improve physical fitness but also build upon interpersonal skills from working in groups. It allows for children to take on leadership roles and demonstrate fair play.

# Encouraging the collegiate environment of EduShare

Reading the blog posts assigned for today’s TDTs has inspired me to get my own blog up to date. At the start of Semester 1 I was really into GLOW and posting my TDTs. During this first semester there was such a huge focus on becoming an enquiring practitioner and a professional who challenges their self for their own benefit and of that of their practice. However, life did get in the way and there were other things that required more attention such as assignments and VIVA’s. All results are in so there really are no more excuses for me to not be re-engaging in the ePortfolio. I have understood from the beginning of this course that the intention of the ePortfolio is for me to show evidence of my understanding and working towards the SPR. However, the lack of engagement from my peers and lecturers on my blog posts is something that put me off before the Christmas break and I never got back in to the swing of things.

Personally, it takes me a lot of time to prepare, preview, draft, redraft and finally publish a blog post. I have a tendency (like now) to start writing and go off on different tangents. I then have to go back to my original thought and edit, edit, edit. I hope that with practice this becomes more straightforward and isn’t so consuming so I can utilise my time more effectively to perhaps research what I would like to write before jumping straight in.

I really enjoy reading my peers posts and I feel I benefit from them as I see different thought processes and opinions. There are a lot of people in our cohort so our ePortfolio’s do give everyone the opportunity to get to know each other better.

There was one post we were assigned to read today that really caught my attention – Problematic Problems. This is a very well thought out post and I can see Michelle’s train of thought and I really like how personalised it is e.g. including family members ideas of maths etc. Although she discussed her previous anxieties with maths I especially liked how you have included the next steps to prepare you for teaching maths. It is so informative and the further reading is especially helpful for your peers.

By evaluating the blog posts I will definitely be taking some tips to make my own posts more interesting such as including more links, pictures, references and further reading. I’ve also realised considering how many of my peer’s posts I have read but I have never fully engaged in commenting on them. Without comments on the ePortfolio I feel we will remain anonymous which is counter intuitive to the intention of collegiate environment of EduShare. Without engaging in my own ePortfolio along with commenting on my peer’s work I would really be letting our hard work go unappreciated.

# Truth, lies and the internet

The internet is undoubtedly the greatest origin of information today. The vast amount of information that is readily available is overwhelming. “I’ll Google it” is a phrase I think and use most days. It could be for absolutely anything from symptoms of a mystery illness, to finding out what movie an actor was in. Ultimately, I use the internet for absolutely anything and everything. The authenticity of the information that I come across is now a concern due to the number of spoof websites. Sharon suggested we search for Martin Luther King and the 5th website on the first page is a complete spoof. Who knew!!? I am also guilty of looking at only source and believing that information. Sometimes, we come across inaccurate information and reiterate it. But because there is so much out there on the World Wide Web who is it say that it’s right or wrong, the internet says it so surely it must be right?  If I am naïve to what I find on the internet, I can’t imagine how this impacts young impressionable children.

In Sharon’s input we found out using Boolean terms such as “and”, “or”, and “not” and using quotation marks can reduce the number of hits from that search quite drastically. By narrowing this search down, it is likely children will come across less accurate information. According to a survey in Truth, Lies and the Internet, 47% of teachers surveyed report having encountered arguments in lessons or homework containing inaccurate information that has been found on the internet containing misleading information i.e. denial of the holocaust!! This is quite unbelievable that this type of information is even allowed on the internet.

There are other search engines out there and some that are child friendly.  Some examples of there are:

By showing children there are alternatives to Google and teaching them skills of using the Boolean searching they will come across less inaccurate information.  This is not to say that every website they look on will be accurate so they still need to know how to tell the truth from the lies and always being safe in the digital world. There are many tools available on the internet to show demonstrate how to use the internet safely and to show just how easy it is to put anything on the internet.

I have created a Fakebook page using this link and it is so remarkable the likeness to a real Facebook page (obviously that is the point!!).

Using Fakebook, I have created a profile for Albert Einstein.  Fakebook is really useful and a fun resource not only to consolidate learning from lessons and topics but to build on ICT skills such as searching, retrieving and uploading information and images .  Creating this Fakebook involved using Boolean terms to find out information about Einstein, including his birthday, family members, photograph and associated people to add as Fakebook “friends”.  To do this I had to save images to my desktop and upload them to the website.  The experiences and outcomes associated with this task could be linked to – “I can access, retrieve and use information from electronic sources to support, enrich or extend learning in different contexts”  TCH 1-03b.   By doing a task like this, the children enhance and consolidate their learning through developing ICT skills.

# Nurturing their nature

Deciphering different personality types and understanding different theoretical approaches of personality is paramount when it comes teaching. The ability to recognise and accommodate why children of the same, age, and ability react in different ways is fundamental. Being a positive role model is central in teaching as children learn behaviour through observation and not only reinforcement as the behaviourist theorists would suggest. However, as a mother myself, I would tend to agree more with Bandura’s social learning theory that personality is reinforced through interaction between environmental factors. My daughter’s standards and ideas of self-efficacy will reinforce her personality then through the behaviourist approach they will be further strengthened.

The Big 5 personality test I carried out consisted of 50 questions of which were rated from 1-5; disagree to agree. I agree with the specifications of my results however I was not confident when answering some of the questions with the correct context. The results I received, as no surprise to me, was that I am 96% extrovert. However, I know that depending on the social environment can have an adverse effect on this part of my personality and I can become a complete introvert. Carl G Jung said “there is no such thing as a pure introvert or extrovert. Such a person would be in a lunatic asylum”. It would not be socially acceptable to behave only in the approach these results suggest.

 Openness to Experience/Intellect – 0% High scorers tend to be original, creative, curious, complex; Low scorers tend to be conventional, down to earth, narrow interests, uncreative. You prefer traditional and familiar experiences. Conscientiousness – 83% High scorers tend to be reliable, well-organized, self-disciplined, careful; Low scorers tend to be disorganized, undependable, negligent. You are very well-organized, and can be relied upon. Extraversion – 96% High scorers tend to be sociable, friendly, fun loving, talkative; Low scorers tend to be introverted, reserved, inhibited, quiet. You are extremely outgoing, social, and energetic. Agreeableness – 32% High scorers tend to be good natured, sympathetic, forgiving, courteous; Low scorers tend to be critical, rude, harsh, callous. You find it easy to express irritation with others. Neuroticism – 22% High scorers tend to be nervous, high-strung, insecure, worrying; Low scorers tend to be calm, relaxed, secure, hardy. You are generally relaxed.

# Constructive or destructive

I’ll be honest to say it will take some accustoming to give and receive feedback. Emotions play a huge part in reactions to feedback and we are on a journey now on how to understand and use feedback constructively.  A few weeks ago the whole year were instructed to engage with three peer’s eportfolio’s and I feel this task has highlighted the fact that I commented on two blogs, only one time…. Naughty me!

The feedback I received was mostly positive and framed in a way that didn’t make me feel uncomfortable.  Previously, upon receiving feedback that has firstly been construed negatively had an adverse effect on my confidence and willingness to share future blogs. Confidence is something that can take a long time to build and can be shattered in second and with a few short sentences.  Learning how to frame feedback positively will help immensely deter any conflict in the future with colleagues.  You could list ten positive points about a persons writing but if there is one critique then that can outweigh the positives. To combat this, Nicki mentioned framing feedback in a positive way such as “have you thought about trying this” instead of something like “I didn’t like that”.

The process of giving peer feedback is a daunting.  You might have a thick skin but that doesn’t mean to say the person on the receiving end does.  I found that considering criticising someone’s work before I’ve read it is difficult.  The success criteria of this task was to make suggestions however if you feel the person has met all the criteria do you then pick at their punctuation or grammar?

Certainly from this exercise and in the past I have come to realise the importance of taking time and reading over feedback a few times, as tone is impossible to interpret over text.  In a professional environment, most, if not all feedback will be constructive so I need to learn first time to take my feedback positively to improve my practice.

# What, why, how – the power of enquiry

An enquiring practitioner is responsible for maintaining and enhancing professional competency for pedagogical development. It means going beyond the role of reflecting and conducting practice based research for a deeper insight to improve practice.

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

Teaching in Scotland has been reconceptualised vastly within policy, legislation and what it means to be a teacher; the benefits of which are tangible in practitioner enquiry.  This quote places huge emphasis on the fact that practitioner enquiry should always be carried out in mind of improving practice for the benefit of the children being taught.  An enquiring practitioner creates space to review and engage in reflective practice to help gain an enhanced understanding of not only their own teaching but when working collaboratively.  Now, there is more emphasis about understanding incentives to drive teachers, colleagues and children forward to make a difference.

It’s easy to be critical of others however to challenge yourself takes confidence.  You wouldn’t do the things the way you do if you didn’t feel it was suitable.  What we, as students, need to understand that the fundamental principles of practitioner enquiry is not to root out weaknesses but to refine existing ideas on what it means to be a good teacher.

As first year students there is already huge importance on the Standard for Provisional and Full Registration in preparation for autonomous life-long learning.  Practitioner enquiry impacts on us all as students as we need to always have higher expectations of ourselves, become critically adaptive in how to improve our own learning and utilise this is practice.  Ultimately, the result of practitioner enquiry is to better meet the needs of children and improve achievement.

# Behaviour – Operant Conditioning

Discipline is important for effective learning to place and after today’s lecture I felt I’d like to know more of what it can mean to me as a practitioner. Operant conditioning is a learning process in which behavioural responses are based on consequences.  There are two types of operant conditioning that can be used to modify behaviour: reinforcements are used positively and negatively to increase behaviour and punishments are used positively and negatively to decrease behaviour.

From early in a child’s life they recognise their behaviour is instrumental to an outcome. Positive reinforcement comes in many forms and I believe is the most effective is verbal praise: “Well done Hannah, you are sitting beautifully”.  Undoubtedly children strive to please and will take great pleasure in being positively rewarded, which is likely to continue and other children are likely to emulate this exemplary behaviour.

In today’s lecture, I was slightly confused with the terms negative reinforcement and punishment. I understood that negative reinforcement was to increase desired behaviour however explaining this with terms such as aversive stimulus was confusing. After doing some reading, my understanding of negative reinforcement is that in order to increase desired behaviour aversive (unpleasant event) stimulus must be discouraged or eliminated e.g. removing a negative distraction to improve concentration. Positive punishment is when you present an aversive stimulus to decrease behaviour e.g. a child is reprimanded for behaving in an adverse way. Negative punishment is taking away a desired item after behaviour occurs in order to decrease future responses. As a result, in theory, children will omit behaviour that has an effect on the environment around them.  Carrie mentioned punishment for undesirable behaviour can lead to other aversive behaviours so I feel consistently using, but not overusing positive reinforcements, should reduce the need to use punishments.

It is evident this theory is built on limited range of phenomena as it doesn’t take account of complexities such as meaning, understanding or memory. It doesn’t explain why behaviour doesn’t decrease and that some children are wise to operant conditioning, in the sense that they will behave in a certain way to get what they want then revert back to their original behaviour.

# Physical and Motor Development TDT

A teacher’s aptitude for identifying additional support needs to ensure healthy development in children is to understand the sequence of development, milestones and when they are expected to be reached and recognise disabilities.

Motor skills evolve sequentially but do vary greatly from child to child.  Motor development proceeds in a cephalocaudal direction meaning the nerves and muscles mature in a downward direction.  This is evident in all infants who first learn use their head and neck then move on to developing more complicated movements such as rolling, crawling then walking. The other pattern of development and maturation is proximodistal direction meaning skills develop in the middle of the body then radiate outwards. For example infants first learn to use their hands then acquire fine motor skills such as the pincer grip.

Basic trends in locomotive skill development include a maturation viewpoint.  This is a genetic programme sequence of events, where nerves and muscles mature in a downward and outward direction. Advocates of the experiential or practice hypothesis believe that opportunities to practice motor skills are also important.  Theorist, Kolb (1984) is someone I have been researching for another module and his four stage cycle adequately fits with this hypothesis: experience, reflection, conceptualisation, experimentation.  Dynamical systems theorists view motor skills as active improvements of previously mastered abilities that are undertaken to find more efficient ways of exploring the surroundings or other objectives.

There are factors that affect growth and development that educators will need to be aware of. Poverty, environment, family structure and disability can hinder or affect a child’s development. Fine motor skills are evident in some form at every age and usually by age 6 or 7 children have confidence to use fine motor skills such as hopping, skipping and balancing.  If this is not the case, we as educations, need to look at how to develop the child holistically as progress in one area affects progress in another.

# Improvement without reflection?

Reflection, in its simplest form, is recalling what you have done and is an essential part of learning. There are different levels of reflection that can take many forms. A reflective model I am encouraged to use in my social work module is Stephen Brookfield’s Four Lenses: autobiographical, peer (student), that of or fellow professionals and theoretical. The lens titles have been adapted slightly to suit the module but ultimately have the same meaning. By looking at ourselves through an autobiographical lens we identify our own assumptions in order to reveal pedagogy that may need reinforced. A peer (student) lens focuses on observations, evaluations and group work. Fellow professionals can provide support and feedback to enhance learning and teaching. A theoretical lens offers a view to support, understand and consider teaching or learning.

Reflection correlates with one of the most important professional values of being a teacher in my opinion: integrity. The SPR description of integrity is “critically examining the connections between personal and professional attitudes and beliefs, values and practices to effect improvement and, when appropriate, bring about transformative change in practice”. We must reflect on what we do in order to improve ourselves; it is imperative to recognise strengths and weaknesses. Without reflection there can be no improvement or change and without reflection, we are doing, not only ourselves, but our students a disservice.

Reflective writing is an opportunity to critically analysis what you have or haven’t done and include suggestions of your intentions to improve and develop yourself. I am really enjoying using the ePortfolio to reflect on my university life so far. Previously my writing may only have been conveying information but my ePortfolio is helping not only identify where I am, but what I need to, to help shape me to be the best practitioner that I can.

# Development in Psychology

After yesterday’s input we were asked for our TDT, to look at the timeline of brain development in the 20th century.  I am really fascinated to learn about psychology not only as a practitioner but as a mother with a young child.  Imprinting, attachment theory, cognitive development are all quite sensitive subjects to me because, without this course, I already have the constant worry of “Am I doing a good job?”, “Is she received enough stimulation?”, “Is she developing properly?”  Research into brain development is important as we know that a child develops most in the first seven years of their lives.   As practitioners, we will play no part on the child’s first four or five years of life, however, as I have my own young child I feel immense pressure to give her the best possible childhood with emphasis to the psychology we are learning about.  Understanding the brain development is paramount when it comes to teaching as we have to understand what is playing a part in a child’s learning and how to help them as individuals.

Looking through the time line, Sigmund Freud is featured heavily during the early part of the 20th century.  He developed some controversial theories including a structured model of the mind and psychosexual stages to explain personality development.  Psychoanalytical theories give us a better understanding of the complexities of personality development and focus on the importance of the emotional quality given by caregivers to the children.  Freud is still regarded as one of the most influential minds of the 20th century.

1929 John Watson and Rosalie Rayner’s classic conditioning of “Little Albert” was an example of stimulus generalisation.  They conditioned Albert to be fearful of white rabbits by exposing him to loud noises and rabbits together.

1963 Stanley Milgram published his study on obedience to authority which showed high obedience rates of someone to hurt another after being given instruction by someone they perceived to be an authority figure.

1971 Philip Zimbardo’s Stanford Prison Experience studied human response to captivity which quickly got out hand and had to be ended early.

The three studies mentioned above were highly unethical due to the distress participants experienced.  Other researchers which I’ve chosen not include, due to its disturbing nature, carried out atrocious research but if I can take anything from this, it is that we wouldn’t know what we do today without this research.  I find it interesting that on the timeline, where I gathered the above information, the number of research listed reduces over time to present day.  There are over thirty studies from 1950’s, over twenty from the 1990’s and only six from 2000’s.  Is this due to ethical approaches changing, research not yet being concluded or is it something else?

# Honey and Mumford learning style questionnaire

For my Social Justice module I was asked to complete the Honey and Mumford learning style questionnaire to identify and build on areas of development as a professional for collaborative working.  The questionnaire was developed based on the work of Kolb, corresponding with the experiential learning cycle he suggests – experiencing, reflecting, generalising and application – and involved answering eighty questions to result in a particular learning style.  There is a maximum score of twenty indicating learning styles and my results are the following:

Activist                 16

Reflector             10

Theorist               9

Pragmatist          15

Activists like to act quickly, get involved and get things done.  Reflectors look at situations from various perspectives and are more concerned with processes than outcomes.  Theorists are known for their thoroughness, solving problems and working alone. Pragmatist’s strengths are getting things done, preferring a more hands on experience with practical application of what they learn.

I can relate to these results based on the types of questions asked however I know that I adopt all four of the learning styles in a different environment or circumstance on a regular basis without conscious thought.  In a previous blog post I discussed the VARK learning styles which gave very different results and Richard Holme pointed me in the direction of this article suggesting that there is no empirical evidence to suggest instruction based on learning styles are effective. The results from the two said learning style surveys actually contradict themselves.  The VARK suggests I am predominantly a read/write learner however Honey and Mumford learning style questionnaire suggests I am more of an activist.  Theorists are described in the Honey and Mumford questionnaire as enjoying being taught in a didactic way which would agree with the read/write method of VARK however this was my lowest score in this questionnaire.

So are learning style questionnaires reliable? I do understand that the point of doing the Honey and Mumford questionnaire in relation to my module was to apply a method to explain and reflect my thinking. I believe that I know what my strengths and weaknesses without doing such learning style surveys. Tasks assigned for us to do such as the Online Unit and thorough reading and reflection of The Study Skills book will help identify how to strengthen my underdeveloped skills to become a more rounded and effective learner.  I appreciate in my profession as an educator, understanding learning styles is important however as previously mentioned there is no absolute way to learn and basing teaching on style-based instruction for a whole class in not practical and some subjects are best taught in a collective way.  Learning is an individual processes however knowing how you process it can help maximise skills that fit your strengths.

# Co-operative Working

The benefits of working co-operatively are endless especially in the teaching profession. Working in a supportive, team environment is much preferred than on my own. Working, studying and discussing ideas with others helps consolidate and enhance your knowledge and learning. Working co-operatively helps develop skills such as effective communication, time management and meeting deadlines, compromising to ensure harmony and commitment. If everyone puts in the same effort and work, the outcome will be significantly more successful. Co-operative working, if successful, will help in future endeavours as you can use your past experiences and put them into practice.

Challenges of working co-operatively

It’s not fair to others to only contribute a marginal amount and doing so completely questions your integrity if you take credit for others hard work. On the other hand it is equally unfair if one person takes charge and makes it difficult for others to contribute their thoughts and ideas. In the first week of my social justice module, we set reasonable rules for everyone to adhere to. One included all taking a turn to scribe for the blog. This allows everyone at some point to take a leadership role and organise our group. If we do not contribute and communicate our ideas then the scribe will be doing all the work their selves for the blog and this is not fair when it comes to your turn.

# Professional Attributes

Integrity and conscience I think are the most important and have shared meaning. Professional integrity means having strong moral principles in the job you do and you want to do the best you can for yourself and for your students. Not only do we need to meet the standards within the GTCS, we need to maintain them through continued professional development in our careers.

Compassion, empathy, kindness, justice, fairness, patience, self-control and moral courage I feel all come under the same category as they all have similar meaning. All of the terms are subjective and can be hard to define by different people e.g. pupils, parents and colleagues. For example, teachers need to be open-minded and patient to allow equal opportunities for students to speak. We need to be concerned about all of our students and be empathetic to their emotions or feelings and also morally courageous to act on something if we feel that child is at risk. A just attitude, a fairness in rewards and punishments are just as important; we have all been through school before and know how unfair things can be. A “that’s just life” approach is not acceptable in the classroom.

All qualities are essential because we as educators need to adapt to the ever changing daily environment. I believe integrity is the most important as it comes in to question if we are not passionate and proactively striving to improve ourselves professionally – we can’t rely on experience alone.

# Balancing personal and professional presence on social media

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

The main challenge is finding a balance on social media presence between my personal and professional life. I have been debating whether I should use separate accounts for social media. The platforms that I use frequently, I rarely post comments or information and use it more as a photo sharing tool. I confess that I am more of a social media ‘ghost’ who floats around observing what people are doing but not acknowledging what they are doing! I actually think that is called Facebook stalking! All of my settings are private so that only my friends can see what I post and I will not be tagged in something until I accept it. This allows me to monitor what I do and don’t want the outside world to see. The more you share the more vulnerable you are. Someone, no matter what you say, what you do, what picture you post, will scrutinise you. We need to be careful how we present ourselves to the outside world. So based on this I don’t see fit to separate my personal and professional social media accounts.

The GTCS has specific guidelines regarding appropriate use of social media. Social media is a valuable tool but as perspective teachers, we should never use it to put ourselves at a disadvantage. Timing on social media is everything. Posting something without considerable thought can lead to massive implications that are very easily preventable. As prospective teachers, not only are we representing ourselves but all teachers. How many times have you stereotyped a profession based on one person? Once a teacher has compromised their professional integrity, their reputation, as well as the school they work in, may forever be remembered.

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

I will frame social media in a positive way in my classroom. The story Derek shared with us about his daughter was a real eye opener. The innocence of children unfortunately is getting shorter and shorter and I am troubled that children are exposed to things at such a young age. However, the sites and resources that are available for teachers are brilliant and I think we need to utilise and embrace them. The GTCS website encourages social media as a way to deliver the curriculum in innovative and exciting ways. In order to do with we first need to use websites such as NCPCC and Share Aware to demonstrate safety in the online world; proactively teaching children how to use it positively and safely.

# Skills and abilities audit

Activity 1

1. Below are a list of skills and abilities. Complete an audit of where you are now. Record this in your learning journal/portfolio.

Rate yourself (1=Not very well developed; 3=very well developed)

 Skills and Abilities 1 2 3 Time management ☺ Setting personal goals ☺ Working under pressure ☺ Conversing confidently ☺ Listing to others ☺ Flexibility ☺ Self confidence ☺ Linguistic skills ☺ Using technology ☺ Take risks ☺

Although it is important to identify where we are now, it is not enough to stop there. We need to reflect upon how we can develop the skills where we are less confident and how we can transfer the skills in which we are confident and competent.
Activity 2

Complete the audit below, using the information from the table above.

 Recognition Reflection Action Skills already developed How will I use these How do I know (evidence)** Personal skills:· Time management Setting personal goals Prioritising my work load and setting goals within a realistic time frame Using a diary, study timetable, listing and priorities the tasks I need to complete.Setting aside time to complete tasks in a distraction free zone.  most of my studying will be carried out at home.  I know it will take a lot of will power to focus on the tasks I have set myself an not become distracted by house work.  I feel the library is not the optimum environment for me now as I have my books, laptop, IPad and notes in one place to refer to.  I may have to re-valuate this in the future if my study environment is not proving to be effective. Interpersonal skills:· Working under pressure (Linking to time management). Using my time effectively will help when it comes to deadlines for assignments and placement. I work well under pressure academically and in a work setting. When I studied at college I was put to the test when I was studying many different subjects with assignment and assessments all in a small time frame. This has helped prepare me with the level of expectation at university. Communication skills: Converse confidently Listening to others Transferring and learning knowledge. These skills have contributed enormously to intellectual discussion that I have already participated in with students on my course

** This section should be completed as you identify when/where/how you have used/developed these skills.

 Recognition Reflection Action Skills to be developed How will I develop these How do I know (evidence)** Intellectual skills:· Critical thinking This will be a gradual process of regular practice. Communication skills:· Taking notes Linguistic skills These can only be developed through practice. More reading and practice. Recording my thoughts and work on my ePortfolio will improve my writing skills Technical skills:· Using technology Be creative Using videos or animations in my ePortfolio. Personal skills:· Take risks Self-awareness I tend to stay within my comfort zone and my preferred learning style. I need to learn identify where needs improvement. I need to learn how my peers learn and how I can effectively use their styles and apply it to my own learning. I need to believe in my abilities own abilities.

# Gender Roles – interview with kids

This video shows how gender roles and stereotypes are engrained in all of us from a young age. These children identify what they believe to be male and female roles such as men go to work and women cleaning and take care of babies and characteristics such as hair, clothing and masculinity.
Functionalist George Murdoch said that functional pre-requisites for the family such as sexual reproduction, economic and socialisation were necessary to reiterate and reproduce individuals in society. I am a mum that has played out the role of looking after the baby, cleaning the house while my partner worked. In my family, my expressive and his instrumental roles, in this instance maintained stability in my family.

There are some matriarchal communities in the world, where women are the head of the family. This shows the traditional stereotypes that the children have in this video are not innate but learned from their parents who learned from their parents and so on.

# Social Mobility

Polly Toynbee’s Guardian article discussing social mobility brings a lot of debate. We are meant to live in an open and meritocratic society so in theory anyone should be able to change their social standing. We have an education system that is fair to all but there are hidden barriers to stop people becoming part of some classes.

Polly suggests an upward surge, post war change of social class from working class to middle class jobs. However, previous to this and over the last 100 years, mass deindustrialisation has changed class structure greatly. During deindustrialisation, popularised money lending allowed working and middle classes a means to owning their own homes where as previously only the upper classes were wealthy enough to own properties etc.

Class has changed so much and modernised objective measurements of class, defined through occupation and income are measured through NS-SEC and the Great British Class Survey. Resulting from the lateral test, I am from the ’emergent service workers’. Reasoning given for this is that I am young, enjoy a cultured social life and rent my home. I don’t believe that social class is or isn’t fading as Polly suggests but that for some, social class is too subjective and people’s perceptions are ever changing. I know (and hope) that in 5 years time if I take the Great British Class survey again I would be categorised to a different class due to changes in my life.

This animation, narrated from a speech by Sir Ken Robinson, a world-renowned education expert looks at how the current education system we use today was designed for a different age. We live in a society that is ever changing with an economy, that even he mentions, cannot be anticipated on a weekly basis.

I found the debate of the ‘plague’ of ADHD in America most interesting.  From my experience, what I’ve read and from the video, children with have ADHD think differently and his speech highlights their stimulus is being dulled and muted by medication in order for them to conform. These children need to learn at their own pace and preferred method and are unfortunately being herded through school.

This video evokes thought and what he is saying makes so much sense. An education reform is in order to embrace and encourage divergent thinking.  We need to teach children how to think and learn for themselves in a society that is changing every day.

# On the technology bus!

As I’ve said in my previous posts I was not on the technology bus. I felt that social media was taking over people’s lives (including my own) for a few reasons. There’s been so many hours of my life lost on social media sites such as Facebook and Instagram. When I’m out for a meal with friends every single person uses their mobile at one point and has it sitting on the table!! When I walk down the street almost everyone is engrossed in their mobile phone! For me I think that people’s over use of social media is an unhealthy addiction.

After the social media input I feel so excited to use different platforms to enhance student engagement. I’ll be honest and say I didn’t know there were so many resources available for teachers to use in the classroom. In our first week, we were assigned the QR code hunt task which was so fantastic. Our group to work collaboratively, people were taking on leading ship roles, we were problem solving to work out ‘who dunnit’. I didn’t know such a thing existing but I have thoughts of how I can use this when I have my own class.

As mentioned Facebook and Instagram are the only social media sights that I use regularly. I have been reluctant to using Twitter mainly because I didn’t want to become addicted to another social media website. Even my mum has been telling me for a long time to get involved with Twitter. She uses this to keep informed of current events in the local community and with my siblings school announcements. With Derek’s recommendation I have now signed up to to Twitter but don’t think I’ll be tweeting just yet.

Having thought more and more about social media I can see the potential and central role in children’s education and certainly in my university education. Glow for example I believe will invaluable for sharing ideas and developing my writing skills. I do still think we need to find the right balance in using social media as an education tool to enhancing learning and using it safely.

# Good Morning boys and girls

It was just a norm that girls and boys did different tasks. Our teachers always say ‘good morning/afternoon boys and girls’ so straight away we are identified by sex but I was not conscious of gender affecting me at the time.

Gender differences manifested themselves in the playground and and classroom and certainly became more apparent as we got older. The boys wouldn’t allow the girls to play football or red rover. It was too rough and the girls would end up crying whereas the boys would shrug injuries off. In the classroom it was always myself or someone from my friendship group who would take the notes other teachers or be asked to do administrative tasks. The boys in my class would be asked to help move chairs and tables and I remember thinking I could do that too, I was strong enough but we weren’t routinely asked to carry out those types of tasks.

My class stayed almost the same through my seven years at primary. The majority of us were exceptionally well behaved but there were a few problem students in my class and they were all boys, they used to sit at the naughty boy table. I always remember thinking none of the girls would end up sitting at that table and we didn’t! Most of the girls in my class were so eager to please our teachers and loved being the teachers pet.

This carried on in to my secondary school where the boys were more disruptive than girls. Gender specific subjects became more apparent too. Most of the girls chose to do subjects such as art and home economic whereas the boys chose techy and woodwork.

As a child at home I was a girlie girl and played with toys such as Barbies and dollhouses. I loved Disney princess films watched them over and over again. I played netball – a predominantly female sport. I also played cello in the school orchestra, (not a very delicate instrument I know) and there was not one boy in our orchestra. My cousin (a boy) used to play with cars and wrestling and was generally quite boisterous and I would shy from that type of play.

# Study skills and time management

Reading the first chapter of the Study Skills book assigned for us I found some parts interesting but I do think some parts are not relevant to me e.g. Student accommodation, freshers week, financial issues, fitting in part time jobs. However having a browse through the book it will be definitely be a useful tool throughout my university career.

Some conclusions from the goal setting exercise were that I want be a positive influence in my daughters life and be a good mum. My career path is of course to be a primary teacher but I would aim to one day be a PT, DHT or HT. MA Education is a specific professional course and I would frankly be terrified going to university to do a a generalised degree. The certainty of knowing I am working toward a vocational degree personally gives me security as a mature student. Having met all of the lecturers over the last few weeks and find out most have a background in teaching is interesting because I know there are other opportunities for me in the future.

The general expectations are realistic and I know that I and I alone have the responsibility to get my work completed. Time management is one thing that will be a major factor in my university experience. I have to manage my time so well due to child commitments and I know nothing can be left last minute in case of unexpected illness or emergencies. Throughout my academic career I have always said ‘Right this it. This is the time I will be organised’ and end up writing essay into the wee hours of the morning. Or writing to do lists and losing them!! Now though in the past two weeks I am the most organised I have ever been. This smug satisfaction of knowing I’m getting my tasks done is such a nice (and new) feeling and I know I will continue.

One main area I’ve identified that I have always lacked confidence is writing, as in essay writing, putting thoughts on paper etc. This is something I know I can develop but it will come with practice and perhaps blogging might help!?

# Recognising change through Wii

Having a lot of experience with my siblings definitely influenced by decision in choosing a career in teaching however when I was a teenager my career was not something that I was focused on.  I’ve always whole heartedly put everything in my previous jobs but these were not jobs that I aspired for a career in. Teaching has always been in on my radar and a few years ago I volunteered with a friend in an orphanage in Sri Lanka for a month.  The experience was absolutely amazing and the children were so clever and eager to learn but did not have the schools or resources that are available to us which really saddened me.  On this trip I realised not only did I definitely want to work with children but I really enjoyed being in a faraway country.  So, I put my saving hat on and decided to travel in South East Asia and Australia for a year. On my return there was no question that I wanted to be a teacher so off to Dundee College I went to gain some more qualifications to meet the entry requirements to start this course.

I barely recognise the person I was a few years ago when I decided I wanted to be a primary teacher.  I have three younger siblings and I was nicknamed ‘Hilter’ because I was strict and regimented and expected all rules to be followed.  I was that uptight they even had my Wii character named Hitler. Fast forward a few years, well I have done a complete 180 turn and I realise I didn’t actually like that uptight person.  Since the birth of my lovely, cheeky daughter Annabel last June I have adopted a more carefree attitude.  She started walking last week at almost 15 months which is well within normal range however for so long I thought she was behind so I’m really starting to understand that every child is different and develops and learns at their own pace.  She has definitely been a positive influence in my life and I hope that the impact she has made on my different attitude will follow through into the type of teacher I will be.

Lastly until last week I was not on the technology bus largely due to my experience in schools and the teachers I know not being tech savvy. Yet I have transformed my view of using technology (from Derek’s lecture) in classrooms using YouTube etc. and that’s just from one lecture.  Again this is showing me that I am more open minded than I previously was and university is already having a positive influence on me.