# Time travel is real?

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 Dalhousie, 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

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 with 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).

# Mathematics and Music

It is stated by Galileo Galilei (1623, quoted in Rosenthal, 2005) that the world “is written in the language of mathematics”. There are so many aspects of music that are maths based but nobody really ever stops to think about the mathematical elements within music. The rhythm, tempo, note values, beats in a bar, scales etc.

At high school I studied Music and I really enjoyed it. It had never occurred to me that mathematics was heavily involved within music until now. We had a lecture last week about how mathematics is involved in making music. Something so simple as the rhythmic pattern within a musical composition shows the mathematical links. We actually tried some clapping sequences ourselves to prove this. Our lecturer, Anna, gave us the opportunity to clap out some rhythms so that we could see that counting and speed were involved in this activity. The picture shown below is what we used, the yellow boxes told the class when to clap and the white boxes were to indicate a rest. Anna split us into groups and allowed each group to perform a particular clapping sequence. We then added them all together so that the rhythm over lapped one another.

After the lecture I reflected on what activities I can use in my professional practice. This activity is simple but effective and most importantly fun. Using the colours to indicate who claps when encourages children to get involved without getting confused. Beginning a maths lesson with a clapping pattern does not only encourage music but maths, as there is counting, speed and rhythm involved. This also enables the children to be engaged and encourages cross- curricular teaching.

In the lecture we also discussed the Fibonacci Sequence and how it  relates to music. I discovered that “there are 13 notes in an octave and a scale is composed of 8 notes” (Robb, 2015). We discussed the Fibonacci sequence in another lecture, earlier that week, and I was not very confident in my knowledge so I decided to use my initiative. I decided to read some online resources which explored how it effects music. It is stated that The Fibonacci sequence consists of particular numbers, some of them are 1,1,2,3,5,8,13…, these numbers continue and there is no end to them (Iyer, 2009). Iyer (2009) states that the sequence is also linked with the Golden Ratio, “…the ratios of two successive Fibonacci numbers…this ratio gets closer and closer to…the “golden ratio” :1.6180339887.” This number gets used within many different activities such as art, architecture and also used by composers to create music. The Fibonacci Sequence is used “when composing music to make patterns of notes that are pleasing to the ear.” (Passy, 2011).

Having time to digest the information I received in the maths lecture and also researching more information has allowed me to have a better understanding of the Fibonacci Sequence. I am glad I have taken this maths elective as I feel that I am extending my knowledge of how maths is not just ‘a subject’ within the primary classroom but it exists within everything that we do.

References

Iyer, V. (2009) Strength in numbers: How Fibonacci taught us how to swing. Available at: http://www.theguardian.com/music/2009/oct/15/fibonacci-golden-ratio (Accessed on: 10 November 2015).

Passy. (2011) ‘Fibonacci Sequence in Music’, Passy’s World of Mathematics, 26 July. Available at: http://passyworldofmathematics.com/fibonacci-sequence-in-music/ (Accessed: 10 November 2015).

Robb, A. (2015) ‘Discovering Maths: Music’. [PowerPoint presentation] ED21006: Discovery mathematics (University Elective). Available at: https://my.dundee.ac.uk/webapps/portal/frameset.jsp?tab_tab_group_id=_2_1&url=%2Fwebapps%2Fblackboard%2Fexecute%2Flauncher%3Ftype%3DCourse%26id%3D_54593_1%26url%3D (Accessed on: 10 November 2015).

Rosenthal, J. (2005) Plus Maths. Available at: https://plus.maths.org/content/magical-mathematics-music (Accessed on: 10 November 2015).

# Is rote learning the way to learn?

I have recently read an article called What is the secret to being good at maths? (Lo and Andrews, 2015). This has really got me thinking about the way maths is taught in schools and the techniques that can be used.

I noticed that there was a reoccurring theme throughout the article about if rote learning should be used within schools. I agree to a certain extent that rote learning needs to be used in order to learn certain aspects of maths, such as times tables. I am unsure if this is the way to consistently teach maths in a primary classroom. I found this article interesting as it is a very controversial subject in education and I thought I would explore this further.

In the article by Lo and Andrews(2015) they focus on the difference between children who are taught in Japan and the children who are taught in Australia. Their research shows that children in ‘Asian countries like Singapore and Japan lead the ranks in first and second position on maths performances in the Program for International Student Assessment Tables.’ (Lo and Andrews, 2015). In these countries rote learning is the most common way of teaching and children use their love of ‘competition to fuel their passion for maths.’

It is found that Australia is entirely against the idea of pupils being taught in this ‘drilling’ manner. They have found that pupils do not benefit from rote learning and will lack understanding to perform mathematical problems. Lo and Andrews(2015) did state that ‘research suggests that memorisation and rote learning remain important classroom techniques.’ Learning should be made enjoyable for students and teachers should aim to focus on keeping their class engaged with the lesson.

I also found another article which was written by Stephen Adams called Understanding maths ‘more important than learning by rote’. I thought I would include this as Adams(2012) encourages teachers to promote other ways of learning compared to just rote learning. It is stated in the article that students should be focusing more about the mathematical thinking and problem solving rather than memorising tools e.g. times tables. This article is written about the English education system and the new curriculum that they have implemented is to ‘raise the requirement of what children are expected to know at each age.’ (Adams, 2012).

I understand both articles view points and I have consider the arguments that have been made. I am still to make up my mind about if rote learning is necessary in the primary school. I can say that reading these articles has allowed me to become a little more open minded about other peoples perspectives on the subject of rote learning.

I do have one question.

What do you think. Should rote learning be used in primary schools?

References

Adams, S.(2012) Understanding maths ‘more important than learning by rote’. Available at: http://www.telegraph.co.uk/education/educationnews/9415280/Understanding-maths-more-important-than-learning-by-rote.html (Accessed: 3 November 2015).

Lo, S. and Andrews, S. (2015) What is the secret to being good at maths? Available at: http://theconversation.com/what-is-the-secret-to-being-good-at-maths-49222 (Accessed: 30 October 2015).

# Banishing those maths demons

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.

# Maths Elective

Last week I began the maths elective which shows how teaching maths in the primary classroom can be fun, engaging and not just about numbers. We watched a film called Stand and Deliver which showed how the teacher was passionate, encouraging and dedicated to helping his pupils succeed in their calculus exam. Jaime Escalante, the calculus teacher, creates a new and exciting way to teach mathematics. This will affect my personal teaching practice as I will take into consideration that my lessons will need to be engaging, attention grabbing and most importantly enjoyable!