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

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

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

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

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

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

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

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

Time = A basic concept we take for granted everyday

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

Maths is all around us, there is no escape!

Maths… There is no escape.

The Base Twelve-System

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

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

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

12 equals 10?!

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

Binary

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

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

When it finally clicked

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

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

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

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