September 2018 – Hannah Robertson

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).

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.’

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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.

the maths and creativity sandwich.

Do you know what an angle really is?