# Have I discovered maths?

Today was our last input for discovering mathematics. Throughout this module I have discovered a few things including mathematics. This journey of discovery hasn’t been easy but I can officially say I understand fully the fundamental ideas of mathematics.

Essentially, I have discovered: what the fundamental ideas of mathematics is, different aspects of mathematics within the classroom and how a teacher can accomdate this in the classroom.

At the beginning of this module I believed maths to be counting, equations, sums and dread. The idea of maths always brought fear and anexity to me, however this module has changed the way I think about maths and consequentially the way I will teach in the future.

Essentially, Liping Ma (2010) devised an idea to teach children mathematics through the idea of profound understanding of fundamentals mathematics. This is essentially through four main ideas: basic ideas and principles, interconnectedness, longitudinal coherence and multiple perspectives. To achieve success in primary and secondary mathematics these four ideas must be applied. The idea of basic ideas and principles suggests that all stages of maths should be broken down and applied in a simpler way and then built up into a more complicated way, without this children may get confused and begin to disengage resulting in poor mathematical skills. With this scaffolding children can link ideas and find easier ways to complete a question/sum. Furthermore, children should appreciate interconnectedness throughout their learning. Linking ideas together can make problems easier and can allow children to break things down. By showing children interconnectedness in their learning this will allow them to begin to appreciate the links between real life and maths, for example my previous blog on statistics. Showing children this link can help promote engagement and motivation within the classroom. The idea of longitudinal coherence refers more to the teacher to track progression throughout learning to show children improvements and things to work on, by doing so children can work on their progress points and track improvements. As well as know where they are within the class – doing well or not. Finally, children must have the ability to have multiple perspectives. This relates to the way the teacher teach the class, providing them with different ways to reach the same result, by doing so children can opt for the way they find easiest and guide their learning on their own preferences. By applying all four ideas children have the ability to progress within their learning journey and find their own personal success, however none of this will be done without the scaffolding of the classroom teacher this is something I have learnt throughout my discovery of mathematics.

Within the classroom children have all different ways to learn mathematics which the teacher must accomodate for this is to optimise the attainment within the classroom, throughout this discovery I have learnt that learning can be fun and active a few ways that I have learnt is;

• art to teach thirds
• outside work to optimise distance
• science to incorporate maths

Without this module I would be more hesitant to deliver a maths lesson and this has made me so much more confident in my maths skills. I believe that I have fully discovered maths and I will be taking my knowledge into my future teaching, applying these fundamental mathematics and showing children an easy way to approach a difficult problem. This module has opened my eyes and enlightened me with ways to teach maths.

References:

Ma, L., (2010) Knowing and teaching elementary mathematics New York: Routledge.

# Maths that help

Everyone knows that mathematics can help children in the classroom and academically however, how can they help in real life?

In a recent input we discussed how mathematics is involved in medicine specifically, how statistics can help. This is something that has really interested me in the sense that the NHS can be reliant in this mathematics at times.

According to NHS England (undated) ‘statistics are used to create debate, inform decision making and research both within government and by the wider community.’ This suggests that without statistics research within the medical world would not be able to take place.

This is supported by Annekld (2016) where they believe that statistics are vital to medicine and in specfic nursing and they way they interpret and understand the data they have been presented with. Medical statistics allow nurses to make quick decisions and act on outcomes they have been presented.

Essentially, statistics is an integral part of nursing and the medical profession, this is due to the direct impact it has on the wider community and society. This can effect individuals on a wider scale being without statistics people could be prescribed wrong dosage, or not be prescribed the essential medicine.

According to Caplan (2012)  statistics are used in medicine for a number of reasons most importantly for blood pressure accuracy, this is devolved around statistics – what is healthy and what needs attention. This suggests that statistics are needed to test the healthiness of the patient and allow everyone to achieve the ‘norm’.

SO… what does this mean for us as teachers?

Well, this has certainly opened my eyes to the power of mathematics, without this people have the ability to deteriorate in health and in worst case scenario have a fatal outcome. This statistical values allows people to keep on top of health as well as correctly preform a medical procedure.

As teachers we should always emphasise the importance of mathematics within the real world and consequently this is a big one. This can allow children to further engage with their academic studies as well as show them there is a life of maths outside of the classroom. This links to Ma (2010, pp.22) where she states children should have interconnectedness within their learning in maths, how does this impact on them in the long run and how can they grow up to change the world from maths. This gives them a goal to achieve and a dream to set, to change the medical world through the impact of maths.

Us as teachers need to encourage these goals and plant the right seeds for children to fall in love with maths and see it as so much more than just counting and sums.

References:

NHS England (undated) Statistics[online] Available at: https://www.england.nhs.uk/statistics/category/statistics. (Accessed on: 11 November 2018)

annekld. “What are the uses of statistics in nursing?”, 29 Jan. 2016, https://www.enotes.com/homework-help/what-uses-statistics-nursing-361410. (Accessed 11 Nov. 2018.)

Lorraine Caplan. “What are the uses of statistics in nursing?”, 22 Sep. 2012, https://www.enotes.com/homework-help/what-uses-statistics-nursing-361410. (Accessed 11 Nov. 2018.)

Ma, L., (2010) Knowing and teaching elementary mathematics New York: Routledge.

# Is maths beautiful?

Maths makes our portraits beautiful.

Recently, we had an input surrounding maths and art. This is something I really enjoyed, after this input I began to think about how much mathematics is actually involved in life, even art.

So, how does maths make us beautiful?

To explain, I think I should firstly show you some art I have done in a recent input. The left side of the picture is free hand drawing, of a person put up on the board. The right side of the picture is using maths, the difference that using maths made was amazing.

it is hard to believe that those two faces has been drawn from the same picture.

So how did I turn that awful drawing into that better drawing?

# MATHS!

I followed some mathematical steps from this link.

To break it down:

Step 1: Similarly draw a circle in the middle of the page. From the middle/top of that circle draw a vertical line to below the circle. From this join up the line and the circle with straight lines to make a jawline.

Step 2: Draw guidelines to the right of the circle. This is the mathematical part. Take a ruler and line it up to the right side and make a vertical line slightly longer then the entire face outline. Calculate the length of this line, e.g. 14 cm make 7 equal horizontal lines coming from the vertical one, e.g. every 2 cm make a horizontal line.  Label them beginning from line 4.

Line 4 – Centre Line

Line 5 – 1

Line 6 – 2

Line 7 – 3

Line 1 – A

Line 2 – B

Line 3 – C ( As seen in the picture above)

Step 3 -Draw the eyes on the centre line, this is half way down the face. Half of the eye above the line half under giving the ideal eye shape. Centre the eyes half way between the vertical line and the edge of the circle.

Step 4 – Draw the nose. From the middle of the eyes made a vertical line down to horizontal line 3. Add nose features between lines 1 and 2.

Step 5 – Add the eyebrows on line C. Use short lines to create the hair effect.

Step 6 – Draw the mouth. Draw a triangle from line 2 – 3 just below the nose. Draw a vertical line from below the eyes to line 3 and shape the mouth between the triangle and the vertical lines.

Step 7 – Add the ear of the centre line, on the same line as the eyes. And then add other personal feature e.g. hair, freckles or glasses.

So using mathematics, I was able to present a better proportioned face and a more life like drawing. So why does this matter? Maths is involved in every aspect of daily lives. Arts use maths in most of their drawings, above is just an example of how maths can be applied and how I used it personally but artists use mathematics to create perceptions, and dimensions.

A piece of art which is centralised around mathematics which many people don’t know is  the Mona Lisa. This painting is drawn according to the “golden ratio.”  This is 1:0.618 and it is named this as it is satisfying to the eye.  This pleasing proportion is simply a rectangle with dimensions that show the golden ratio, this painting has lots of rectangles to make the painting  The Mona Lisa has many golden rectangles throughout the painting to make it look better.   If the  rectangle is divided on her forehead with a line drawn across her eyes, we get another golden rectangle, this shows that the  proportion of her head length to her eyes is ‘golden’ .

(Natasha Glydon, undated)

Okay, so how can we apply math to modern life art? Instagram.

By using something called the rule of third you can make Instagram pictures more appealing. I tried it out. This is an original picture that I took. Its not very attractive right now:

By applying the rule of third I have made a third chairs and 2 thirds grass with the central person off centre. This can make the image much more interesting to the eye. This makes the picture a lot more creative and beautiful.

So what is the point of all of this?

Mathematics has the ability to make art beautiful, so does that mean maths is beautiful? By opening your mind to the application of mathematics it can show you much beauty and relevance it has in the real world. If you accept that maths is beauty then why not begin to see why you need it? This links back to Ma (2010, p.22) theory of profound understanding of fundamental mathematics that by applying the main principles including interconnectedness, by showing children the connections between maths and other aspects of live it has the abilty to find mathematics more relevant and applicable to their own individual lives. Some children might not believe they are good at maths but they might believe they are good at art, show them the connection.

Therefore, maths is beautiful.

References:

Ma, L., (2010) Knowing and teaching elementary mathematics New York: Routledge.

Natasha Glydon (undated) The Mathematics of Art Regina: Pacific Institute for Mathematical Sciences

Darlene Nguyen (undated) Learn to draw a face in 8 easy steps: Beginners Available at: https://rapidfireart.com/2015/12/07/how-to-draw-a-face-in-8-steps/#