2 Prof. Knowledge & Understanding

October 29, 2018October 29, 2018

Can we touch the moon?

Education is one of the first places that allow children to build a realistic foundation of knowledge. It wasn’t until my first school placement that I began to understand the importance of putting fact into visual representation that all children understand. Therefore, if this is inaccurate it will result in a generation (or even generations) of flawed understanding. There is no better example of this than Space.

Without most teachers realising, there will be a time that a child in there class stares out of the window imagining what is beyond our drizzly, damp and occasionally blue sky. It is this unknown environment which beacons children to explore and build there experiences and knowledge of Space. I can happily say that I was most definitely one of those children. Primary 5 was the year of Space! Without a shadow of a doubt the experience that I had was incredible, I was well on my way to becoming a fully fledged astronaut. However, despite having amazing experiences, I cannot say that my knowledge of Space is at all realistic. Sadly this will be the case for many others who have or are in education at this time.

Until recently, I did not realise the enormity of Space. There is no word to describe how ginormous Space actually is and this is exactly where Space education must start. For me this is where my own knowledge is false because I was not aware of the scale of space.

To put this into perspective you can look at the distance between The Earth and The Moon. To the majority of people – including myself- believed that the The Moon was only a short distance away when in reality it is actually much greater than that. To scale you can approximately shrink The Earth down to the size of a basket ball and The Moon down to the size of a tennis ball. Using this scale this means that a basketball and The Earth along with a tennis ball and The Moon are at a ratio of 5, 280, 000: 1 (The Science Asylum, 2017).

Using this scale we can put the distance between The Earth and The Moon into a realistic visual perspective. The distance between the core of The Earth and The Moon is 238, 855 miles, when scale down using the ratio of the basket and tennis ball this distance is only 7.2 meters. In terms of what this looks like to scale it would look the picture below.

Encouraging ourselves as Educators to understand scale is extremely important, not only to physically represent Space in our own mind but in the minds of the those within the classroom. As fun as it may sound, taking children to Space is not a class trip that can be offered within my lifetime. This is why it is so important to allow children to experience accurate scale. This can be linked to the ideas of a logarithmic scale present in the minds of those inadequate and unrealistic experiences. Bellos (2010) maintains that children believe that with unresolved understanding will be unable to fully interpret the realistic size of maximal numbers. From experience children believer that space looks simplistic; with planets knitted closely together on a perfectly circular orbit surrounding the sun.

Generic image of Space.

In reality it is believed that space actually looks like this!

This is only a small part of Space. Space is actual made up of millions of solar systems that most of which can be easily understood. In other words the universe is made us of billions of stars, these stars form galaxies and galaxies form the universe. Overall, in order to promote a Profound Understanding of Fundamental Mathematics educators must invite children to build knowledge into compound understanding. This can relate to Ma’s (2010) key concept of connectedness which focuses on connecting mathematical procedures to wider concepts, thus enabling a greater understanding. In terms of Space, knowing the size of an the environment highlights intellectual solidity (Frobisher, 2007). Only when this happens children will be able to be able to explore the immensity of Space purposefully.

References

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

Frobisher, L.J. (2007) Learning to teach shape and space: a handbook for students and teachers in the primary school. Cheltenham: Nelson Thornes.

Ma, L. (2010) Knowing and teaching elementary mathematics: teachers’ understanding of fundamental mathematics in China and the United States. Available at: https://ebookcentral.proquest.com/lib/dundee/detail.action?docID=481154. (Accessed: 25 October 2018).

The Science Asylum (2017) How far is the Moon? Available at: https://www.youtube.com/channel/UCXgNowiGxwwnLeQ7DXTwXPg. (Accessed: 25 October 2018).

September 29, 2018September 29, 2018

the maths and creativity sandwich.

Never would I have imagined that myself or anyone could sandwich together maths and creativity. Yet what a wonderful sandwich it is! Realistically, the majority of people would strongly argue against this opening statement, my self being one of them, however let me tell you that it is more than possible.

Like most sandwiches it all begins with the bread and in this case it begins with MATHS and Art. If you wanted to find these breads on a supermarket shelf you would instinctively look at opposite ends. However, this is not true because they could actually be found right next door to each other. My own experience of maths and art at school was not in anyway this experience. I would have confidently argued during my time at school that art was the elegant French baguette – thick, crunchy and popular- and on the other hand maths was the sourdough of all breads – bland, odd tasting and for the select few. Although reflecting on this now I think differently. This week in discovering maths we were exposed the creative aspects of this once bland subject.

This adventure was sparked by looking in detail at shapes. We discussed the names, number of side and angles of a variety of 2D shapes such as triangles, squares and hexagons.

You are now wondering how does this relate to maths? And it begins by introducing the idea of tessellation. ‘Tessellation (or tiling) is a repeating pattern of shapes that fit perfectly together without any overlaps or gaps.’ Brown (2018). Simple shapes such as triangle and squares can tesselate because their angles can make a full rotation. But how do you do make it personal?….

Take an original shape, such as a square, and cut segments out of it.
You then take your segments and add them back onto a different side of the square.
You can then repeatedly join this new shape together by repeating, rotating or mirroring it.
Repeat it all over the page, your final result should be a wonderful tessellated pattern.

When this is practiced you can make magnificent patterns and works of art. Traditionally this commonly used within Islamic art and patterns.

(Please watch this short clip to see many different types of visual tessellations)

Watson, C (2015)

As I discussed this shows that maths can be used in an engaging and exciting way and this is what is extremely important when introducing maths into any classroom. I believe that when you begin a maths lesson you have only a few moments to make it interesting otherwise children will switch off. This what brings me back to the sandwich. Do NOT present maths as the sourdough bread! Within tessellation alone there are hundreds of opportunities for children to put there own creative stamp on their maths sandwich. They can experiment with fillings, experiment with topping, experiment with size and most importantly of all they will understand how the sandwich is made.

This reiterates the concepts of Profound Understanding of Fundamental Mathematics (PUFM). For myself, by investigating this topic of tessellation alone my view of PUFM has evolved because I can see it represented in Maths! The root of tessellation is shape. Children’s basic understanding of shape will be to name the shape they see. However, if pupils have PUFM they can understand that if you alter the shape it will still have the same area. In other words pupils will not only be able to name the types of bread, they will understand how the bread is actually made.

However because of constraints children will not have time to explore this and there for be unable to sandwich maths with creativity. So how do educators step of our this narrow box. Haylock and Thangata (2007) argue that drill like teaching methods which are reused over decades betray creativity. Thus how maths is taught in the classroom can either uplift or damage creative the link between maths and creativity. Similarly Maths needs to be understood by the educator before it can be understood by pupils (Setati, 2011). As a future teacher I will continue to encourage creative thinking and tasks classroom maths topics. If this is done by all it can transform Maths from a bland sourdough into a baguette.

References:

Brown, J. (2018) ‘Maths, creative? No way!’ ED21006: Discovering Maths. Available at: https://my.dundee.ac.uk/webapps/blackboard/execute/displayLearningUnit?course_id=_58988_1&content_id=_5217933_1 (Accessed: 29 September 2018).

Haylock, D. and Thangata, F. (2007) Key concepts in teaching primary mathematics. London: SAGE.

Setati, M. (2011) Mathematics in Multilingual Classrooms in South Africa: From Understanding the Problem to Exploring Possible Solutions. Dordrecht: Springer Netherlands 2012.

Scottish Government (no date) curriculum for excellence: mathematics principles and practice. Available: https://education.gov.scot/Documents/mathematics-pp.pdf (Accessed: 29 September 2018).

Watson, C (2015) What is Tessellation? Available at: https://www.youtube.com/watch?v=7GiKeeWSf4s (Accessed: 29 September 2018).

September 19, 2018September 24, 2018

Do you know what an angle really is?

Most recently I have began the studies of my elective module Discovering Maths at University. Although we are only breaking into the second week of this module, I have immediately found it abundantly clear that this module will serve more than just knowledge of the Primary School mathematics curriculum; it will indefinitely open my eyes to the cracks of this subject.

On our very first input the class was asked how well we believe we know mathematical topics. Quickly I began to think that, like all others in the room, we would at least have a National 5 qualification in mathematics, therefore our knowledge of maths would be quite solid. Yet, is it actually? This was quickly answered when my lecturer was discussing angles he asked ‘What is an angle? It is the measurement of a rotation.’

Image result for boom

In this single moment I realised that my knowledge of angles was molded into a way that I could only answer textbook questions. In my thirteen years of schooling I had never once understood what an angle was. My head was filled with knowledge about seeing right angles in every stair, corner and cupboard at my home, knowing how to measure them with a protractor and being able to name the different types of angles at the drop of a hat. Looking back on my experiences at school now, I know that I do have valuable knowledge about angles but none of it made sense until that moment. This is because I understood what an angle is.

It is moments like this that every child must have within their learning. As a student teacher there is an expectation that we must equip children with the knowledge to meet curriculum requirements. In many lessons this is the case, however knowledge should never be put in front of understanding. We can teach children a million different facts about the world around us, but if they do not understand these facts how will they be of any value to them? As a future teacher I now find that it is crucial that this should be a part of all learning because it will equip children with the ability to see and make links within their learning. This matters seems controversial throughout schools across the world as many have differing opinions about what the purpose of mathematics is.

Understanding mathematics is key aspect of specialist knowledge of fundamental mathematics. My early understanding of this phrase so far is that it is understanding the thing itself and all of its properties. Enthusiasts of maths in education such as Liping Ma highlight that understanding of mathematics in crucial in making sure that students have the greatest success (2010). Therefore, if children can understand the roots of mathematical topics, not just what they look like, this will allow them to have a profound understanding needed to progress learning. Similarly Haylock et. all (2007) found that mathematics promotes profound learning that allows children to understand the world around them. Thus, mathematics in school should not just require children to solve problems; they must create links with how these issues relate to everyday life. Looking forward I am excited to find out how my experience in this module will allow my conception of understand in maths to flourish and develop.

References:

Haylock, D. and Thangata, F. (2007) Key concepts i teaching primary mathematics. London: SAGE.

Ma, L. (2010) Knowing and teaching mathematics: teachers’ understanding of fundamental mathematics in China and the United States. New York: Routledge.

October 12, 2017

Hartsford Uniform Conflict

Last year at the beginning of the first school term it became nationwide news when Hartsford High School in Kent had refused to let pupils enter school grounds because of their ‘inappropriate’ uniform which did not follow the school code of conduct.

While the head teacher of Hartsford had received positive feedback from local parents commenting that the code had set ‘high standards’ for school to be a highlight in the local community a small group of parents were out radged. Due to the teenagers being sent home from school parents brought it to the attention of the media that this had a catastrophic effect on their child’s education. The main issues came from a number of people who had ‘skin tight clothes on’, ‘inappropriate’ shoe wear and those who came without their blazers on. Many complained that those caught up in the situation were being prevented from missing the utmost vital education which could damage their studies, especially for those sitting exams. Since becoming local new this has become a conflicting topic of discussion.

Who is in the right?

In my perspective this could be argued from two points of view.

Firstly it is known that the way we dress allows us to express our different personalities. For some people wearing different shoes, clothes, hairstyles and accessories this can be a structure, which adds to their confidence, while they are at school. If this is true then why would it be acceptable to take this away from these young adults? On the other hand one of the main concerns coming from this story is money. In some cases the children’s parents were told to buy new uniform that was more appropriate but just because these things can be easily sourced in shops does that mean that everyone can afford them? Reading about child poverty this week has opened my eyes to the fact that a large majority of families struggle to make ends meet, if so then I don’t think it would be right to dismiss the fact that pupils might not have appropriate uniform because this is what is affordable for their family.

However on the other side of the fence I feel that having a set uniform for everyone in schools provides equality among pupils and their peers. If this code was not implemented it would isolate those from less fortunate backgrounds. All of a sudden school would become a competition of who has the best and most expensive outfit rather than what the real concern is. LEARNING.

As an aspiring professional I believe that the consistent attitude of the Head teacher and his staff has been positive in ensuring that standards will be kept in the school. By maintaining these standards will provide an education to pupils on what to expect in their future careers as the majority of professions have a set standard of how they expect their colleagues to dress. I see it from the perspective that, if you see a nurse on ward wearing a tracksuit or a police officer wearing jeans and a t-shirt while arresting someone, how would you react? How would that be different than wearing the correct uniform to school?

Sometimes building the small pieces of the puzzle first will help create a better idea of the picture. In this case I believe that this was the schools intentions and in the long term it will be worthwhile.

October 12, 2017

Resource Allocation Input

When we first arrived in the seminar we were told to disperse ourselves among the tables so that we would be equally divided into 5 groups. The task to complete in our groups was to create an item which students like us would be able to use on welcome week to help guide us throughout our first few weeks at university. As we all began to discuss the ideas of what we could make, our lecturer had passed out envelopes to each table which inside contained different materials. These materials were what we would eventually use in order to create our product. Looking around I had no idea why we would be doing this task in particular.

While we opened our envelopes we found a wide range of materials inside such as paperclips, sticky notes, coloured paper and pens. However looking around the room I found that each group had different amounts of resources most particularly one group who had 1 piece of paper, blue tack and a pen. When observing oneanothers envelopes we found it extremely strange that we hadn’t been given equal materials. All I could think at the time was “what is going on?”

As each group separately began to explain their ideas in front of the class I noticed that the first two groups had been given so much praise for their ‘astonishing’ and ‘absolutely brilliant’ ideas. This put pressure on our group because we had fewer materials than them and our student help box was being held together by some paper clips. As we began to present our design we received no praise. Not a ‘Well done that’s great’ or even an ‘I like the idea’. Derek did not seem impressed with our design at all. The feedback got worse until it came to the last group and finally it clicked what was going on when Derek made it obvious he wasn’t listen in and stood on his phone through the entire presentation.

This was a lesson on teaching attitudes and resource allocations throughout schools and it is a valuable one.

By praising some groups for their efforts and leaving others to ask what they had done wrong it highlighted what is probably happening in schools RIGHT NOW. As a whole class we agreed that by changing our attitudes towards different children is can diminish their confidence in the class. It showed that those who come from wealthier, nurtured and sheltered communities are much more likely to receive the praise for their progression than others. Those who have the support of their families can sometimes progress faster than others, for some children this can make the difference in there future careers and ambitions. As teachers we have the ability to create a class atmosphere were children understand; everyone can help each other to improve, we aren’t good at everything and no one should ever be put down by their social background.

Moving on to resource allocation I find it extremely important to highlight that every school has better or worse resources than each other but it is how we use those resources to enhance the same level of learning that matters. Just because you go to a school in a deprived area doesn’t mean that you should be treated any differently in what you can accomplish academically. After completing our Resource Allocation seminar I found myself thinking about how when we as teachers take on a class we are working with children who have completely different cognitions.