Category Archives: 1 Prof. Values & Personal Commitment

Time travel is real?

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In our recent maths lecture we discussed the topic of time and had a discussion concerning the concept of whether time is linear. At the beginning I was not entirely sure what was meant by this statement. What exactly is linear time? I was intrigued to find out more about this topic and decided to follow it up with some research.

Linear time is when “time flows like a conveyer belt that moves horizontally from past to present to future at the same unchangeable speed for all of us” which is produced by Hall (1983, cited in Randall, 1996). Getting back to the question at hand of whether time is linear, the influence of the media needs to be considered.  Movies and TV Shows like to think that time is not liner! Back to the Future, Bill and Ted’s Excellent Adventure and Doctor Who have machines that travel through time and defy this rule of linear time. I will never give up the hope of time travel becoming a reality, Never!

Anyway, time is quite an important aspect of everyday life. How would the world cope without time? What about timetables that control school days and university lectures? Maths is clearly involved with timetables, such as the number of classes being held in DalhousiSundialse, the number of courses per day and how many people can fit in one room/lecture theatre. Personally, I never considered the fact that time was heavily involved with the creation of timetables.

 

How did the world cope without time before clocks were created? Before mechanical clocks there were sundials. This was the earliest form of timekeeping (The Editors of Encyclopaedia Britannica, No Date) and time was shown by the movement of the sun. There are different types of sundials: “equatorial, a horizontal, and a vertical sundial” (Ling and Yee, 2000/2001). The picture above is a horizontal sundial. The ‘gnomon’ is the central part of the sundial. The ‘style’ is the slopped part of the gnomon, this part of the dial casts the shadow and indicates what time of day it is. This particular sundial has Roman Numerals which is a number system that was used and is still used to this day.

I would consider the fundamental mathematics of the sundial to be position, movements and angles. The position of the sun moves on the sundial throughout the day as the Earth orbits the Moon. Also the way in which the shadow is cast by the gnomon and style is determined using angles. There is also mathematics used when creating a sundial. The North American Sundial Society (2011) have a webpage that explains how to calculate dial lines on a sundial.

“The formula for calculating the hours on a horizontal sundial is: tan(theta) = tan(HA) x sin(lat)

Theta = the resulting dial hour angle measured from the noon line (- is left of the noon line, + is right of the noon line)

HA = the hour angle of the sun from the noon meridian, expressed in (+/-) degrees. The hours are minus in the morning and positive in the afternoon.

lat = sundial site latitude, in degrees.” North American Sundial Society (2011).

This has shown me that mathematics is crucial to the working of time. Looking at everyday time keeping such as 1 minute = 60 seconds and 1 hour = 60 minutes contains the simplest mathematics. I have never thought about looking into the way time was originally found until now. It has been a very interesting topic to research and I think I will be able to use this information within my practice. In the early years it would be useful for the children to speak about the basics of time and even making comparisons about how time was recorded and how it is recorded now. This would be making use of not only mathematics but history too. Activities such as making sundials with the upper school includes mathematics and technology. I believe that during this elective I have explored mathematics further and I am now feeling a little bit more confident with teaching it in the primary classroom. Introducing strategies that I have learned from maths lectures and also from my own research I will provide exciting and motivating maths lessons.

References

Lambert, T. (2012) A Brief History of Clocks and Calendars. Available at: http://www.localhistories.org/clocks.html (Accessed: 17 November 2015).

Ling, L.H. and Yee, L.S. (2000/2001) The Mathematics of Sundials. Available at: http://www.math.nus.edu.sg/aslaksen/projects/sundials/ (Accessed: 17 November 2015).

North American Sundial Society (2011) Calculating Dial Lines – 1. Available at: http://sundials.org/index.php/teachers-corner/sundial-mathematics (Accessed: 27 November 2015).

Randall, S. (1996)Linear Time – Cultural ‘Norm’. Available at:  http://www.manage-time.com/linear.html (Accessed: 17 November 2015).

The Editors of Encyclopaedia Britannica (No Date) Sundial: Timekeeping Device. Available at: http://www.britannica.com/technology/sundial (Accessed: 17 November 2015).

Our universe and it’s incredibly large numbers

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Last week we had a very interesting lecture from Simon Reynolds who is the Science Learning Manager at the Dundee Science Centre. I have very fond memories of going to the Science Centre when I was younger. I loved (and still do) learning new and interesting scientific facts. I only realised in this lecture how crucial maths is to Science and in particular Astronomy.

At the beginning of the lecture we started speaking about how maths is relate to Astronomy. When Astronomers explain how many stars there are in our universe it is usually written as 1022 stars (Reynolds, 2015). This number would be written out like, 10, 000,000,000,000,000,000,000. It takes a lot more effort to write out that number and also it is more logical to write the number out as an exponent.

We also discussed how big we think particular planets are by comparing them to particular object such as marbles, beach balls, footballs etc. We also used our hands to judge how small or large we thought each planet was. This was a very physical activity and I would use this in my practice to get the pupils talking about the size, mass and weight, diameter and also the distances between planets which are fundamental components of mathematics involved within Astronomy.

Furthermore, we discussed a picture that was on the PowerPoint which is similar to the image below. Is this a realistic picture to show children? Our Solar System is huge and is filled with big empty spaces between each planet (Reynolds, 2015). Having discussions wiblog post- universeth children about the distances between the planets and the scale size of each planet will not only allow children to extend their knowledge of the solar system but also encourage their mathematical thinking skills.

During this lecture I realised that maths is involved with everything in life in some way. I read an article by Tegmark (2013) that discussed how maths is involved in nature and we cannot escape it. It is apparent that within nature maths is also nearly always involved, such as the shape of a pebble and when it is thrown how it naturally glides through the air or “its trajectory” Tegmark (2013). This could apply to the Earth being round, “…millions, and even trillions of tonnes of mass, the effect of the gravity really builds up.” (Cain, 2009). This is why the Earth has the shape of a sphere as nature creates this shape. This happens when size and mass are increased then the strength of gravity can create the shape of a sphere (Cain, 2009). While Cain (2009) describes the earth to be round, there is in fact research to suggest that the earth is an oval. Choi (2007) states that Isaac Newton suggested that the Earth was in fact not exactly round. It has been found that because mass is not evenly distributed and this is why the Earth has not got an exact spherical shape.

There are also other aspects such as equations that astronomers have to solve daily with extremely large numbers. The equations that are involved should not be looked at as just numbers but what do these represent in the real world (Tiede, 2007, P21). Using equations can turn “a puzzle into a routine exercise” (Mason, Burton and Stacy, 1982, P.196). This suggests that equations can become easier over time as it becomes more like a daily activity.

I found this lecture very enjoyable and I am now aware that maths is used in Astronomy regularly through using equations, calculating mass, distances between planets etc. It is clear that maths is fundamental to Astronomers and without it they would not be able to experiment and find out crucial data needed to explore our universe. I will continue to develop my knowledge of the Solar System as I think this will be beneficial to me when I go on placement. I also intend to show the relevance of maths and Astronomy to my pupils as I now believe it is important to highlight this.

References

Cain, F. (2009) Why is the Earth Round?. Available at: http://www.universetoday.com/26782/why-is-the-earth-round/ (Accessed: 21 November 2015).

Choi, C, G. (2007) Strange but True: The Earth is not Round. Available at: http://www.scientificamerican.com/article/earth-is-not-round/ (Accessed: 28 November 2015).

Tegmark, M. (2013) Everything in the Universe Is Made of math – including you. Available at: http://discovermagazine.com/2013/dec/13-math-made-flesh (Accessed: 21 November 2015).

Reynolds, S. (2015) ‘Maths in Astronomy’ [PowerPoint presentation]ED21006:Discovering Mathematics. Available at: https://my.dundee.ac.uk/bbcswebdav/pid-4535880-dt-content-rid-2953578_2/courses/ED21006_SEM0000_1516/Simon%20Reynolds%20Maths%20and%20astronomy%20presentaion.pdf (Accessed: 19 November 2015).

Tiede, G. (2007) Basic Mathematics for Astronomy. Available at: http://physics.bgsu.edu/~tiede/class/bmastronomy1.2.pdf (Accessed: 21 November 2015).

 

Banishing those maths demons

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I should start at the beginning…

My feelings of maths have changed drastically over the years. Maths has never been my strongest subject and I felt that in primary school it was very teacher led. This has allowed me to perform simple maths equations but when I am faced with a very wordy problem solving calculation, I develop what is called Maths Anxiety (yes, this is actually a real thing). I recently had a lecture about maths anxiety. Maths Anxiety is “a general fear of contact with mathematics, including classes, homework and tests.” (Hembree 1990, p.45).

I feel that through my 19 years of life this has come and gone. I developed this anxiety in primary school, then I began to enjoy maths at high school. I thought that I was beginning to slowly lose my maths anxiety. Until I left high school and I began to realise that I was not performing the maths that I had been taught, such as Pythagoras Theorem, in everyday life. Now when someone begins to talk about maths I feel like my mind goes blank and my head begins to hurt from over thinking the problem.

 

I have taken the maths elective this year as I want to make my maths anxiety vanish. My aim is to not become a teacher who passes their anxiety of maths onto their pupils…I would never forgive myself. I want to show that maths is fun and that it is more than just numerical information that you need in everyday life. During the maths lectures I have been finding out new ways to view maths and finding out ways that I can make my lessons more enjoyable. This has given me hope and I feel like this is the beginning of saying goodbye to my Maths Anxiety. I strive to become a teacher who pushes themselves and I believe once I get over my maths anxiety I will be invincible.