Uncategorized – Discovering Mathematics LAG

Mathematics is all around us- Medicine

Medical personnel including doctors and nurses require a very solid understanding of mathematics in order to obtain exact figures.

Drug doses must be extremely accurate in order to avoid severe damage to patients. In Children the doses are measured in kg so the measurements must be correct. Doctors that have miss-calculated doses have been shamed by reporters and the outraged general public. The ability to identify how strong medication or aesthetics is requires an in depth understanding of the mathematics involved.

Another aspect of mathematics in medicine is the number of charts and graphs that are used and completed on a daily basis. Sews charts allows patients vital signs to be monitored to ensure their health is steady or improving.

Charts and graphs medical personnel to monitor statistics, patients progress and condition, notice patterns in diseases, and predicting results.
Charts and graphs provide a visual representation of the facts that allow doctors to make quick educated decisions about the patients treatment and care.

The Crutch

A wise secondary school maths teacher would often have us bring out our crutches. We were only allowed to use them however when the problem infringed upon us was to intricate to decipher at our own merits.

This crutch as Mr G would call it is in fact a calculator.

pink-calc

I’ve always appreciated this metaphor as I feel it is completely appropriate. Even when completing simple additions and subtractions we reach for the calculator app on our phones. “Nowadays… people plug numbers into a calculator without any intuitive sense of whether the answer is correct.” (Bellos, 2010).

The standard electronic calculators we have today were by no means the first calculating devices. Abacus’ are thought to have been used from as early as 2700BC, they are often constructed as a bamboo frame with beads sliding on wires, but originally they were beans or stones moved in grooves in sand or on tablets of wood, stone or metal. (‘Abacus’,2016)

Then came the Slide Rule “The Reverend William Oughtred and others developed the slide rule in the 17th century based on the emerging work on logarithms by John Napier. Before the advent of the electronic calculator, it was the most commonly used calculation tool in science and engineering. The use of slide rules continued to grow through the 1950s and 1960s even as digital computing devices were being gradually introduced; but around 1974 the handheld electronic scientific calculator made it largely obsolete and most suppliers left the business.” (‘Slide Rule’, 2016)

sliderule

There were a variety of other calculating creations through time but many came to a standstill after the creation of the HP-35. Hewlett-Packard launched his creation in 1972, at the time these devices of 35 buttons and a red LED display would cost £365. By 1978 the electronic calculator was growing and was eventually priced under £5 making it accessible to the general public (Bellos, 2010).

hp-35

References:

‘Abacus’ (2016) Wikipedia. Available at: https://en.wikipedia.org/wiki/Abacus (Accessed: 22 November 2016)

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

‘Slide Rule’ (2016) Wikipedia. Available at: https://en.wikipedia.org/wiki/Slide_rule (Accessed: 22 November 2016)

Mathematics is all around us- Art

The most common examples of maths in art are symmetry, tessellation, size and proportion. All of which are taught at primary school level mainly as an art subject than maths.

Symmetry is almost like a reflection, commonly used to draw an exact image only flipped adjacent to the original.

symmetry

Image: (https://binged.it/2fxVXar)

Tessellation is a pattern of shapes that fits together perfectly.

Image: (https://binged.it/2eOCIPv)

Size and Proportion are simply how large or small, and how many times they need to be increased or decreased in size appropriate.

proportion

Image: (https://binged.it/2f9Zlvf)

Mathematics has been used in art for thousands of year, Ancient Greek architects and sculptors used the Golden Ratio to ensure buildings like the Parthenon in Athens was pleasing to the eye and the sculpture of David adheres to strict proportions.

Renaissance portrait painters ensured that proportions of their subjects’ facial features and the size of their subjects’ heads in proportion to the rest of their body followed mathematical ratios, e.g. the Mona Lisa.

Islamic art is heavily reliant on tessellating geometric shapes and is not purely decorative but represents a spiritual vision of the world.

Earlier I mentioned the Golden Ratio, this is a famous number sequence that appears frequently in our day to day lives. It is known by some other names, such as the Golden Spiral or The Fibonacci Sequence. The Fibonacci Sequence is characterized by the fact that every number after the first two is the sum of the two preceding ones. The Rule is x_n = x_n-1 + x_n-2.

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, … the list is infinite.

In art the Fibonacci Sequence can create the golden spiral.

spiral

Image: (https://binged.it/2eRQZoM)

An example of the golden ratio can be seen in a variety of famous paintings such as:

The girl with the Pear Earing

The Mona Lisa

and

The Last Supper.

goldan-spiral

Maths, myself and I

Growing up in my household it was expected that you would either be a maths whizz or absolutely hopeless. My brother, father, gran, grandpa and great aunt all have the incredible ability to tackle most equations with ease. However half my family have never needed a calculator with more than 19 buttons.

Regardless of my background of secondary school maths teachers, a doctor and a lawyer I was not considered a maths whizz. BUT I wasn’t hopeless either. My relationship with maths is a fond one.

In primary school I was a square. This means I was in the middle group and as desperate I was to become a pentagon I never made it, but this didn’t dent my relationship with maths at all it merely pushed me to try harder. In secondary school my first maths teacher explained to my parents on a parents night that there was more than one way to cook an egg, me being the egg.

Beginning to understand more complex mathematics moving through high school I only gained confidence and regardless of small blips along the way I completed, Standard Grade, Intermediate 2, and Higher eventually. Although now I could probably not even hope to understand a higher maths paper I still consider myself highly confident in maths as a subject and how I use it in the real world.

That was until it came to teaching in my first placement. I struggled with creating maths lessons because I could not simplify in my head the topics so that I could convey it to the class in manageable chunks. With the help of my class teacher I was able to conjure up a few appropriate lessons for the kids but I was still so confused. How could I know exactly how to approach the maths and still not be able to simple it down and teach it? Why were all my ideas so complex? So now I’m stuck- I’m confident whilst being clueless. With this barrier I saw the “Discovering Mathematics” module as a perfect opportunity to understand why I struggled to teach my class, whilst cementing my own knowledge as well. I hope to use this module to get myself back to the fundamentals of mathematics and take it from there.

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