Monthly Archives: October 2018

Would You Chance it All?

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How often do you take a chance? The answer would be every day. Every day we take a chance, whether it be crossing the road, going to the gym or simply choosing to watch the TV. We cannot predict the potential outcome of doing something, yet, without even thinking, we create the factors that are influenced by our decisions. Something of which has lead us to be where we are to this day.

Before this module began, I remembered learning about probability in high school. I was never intrigued by the prospect of learning about probability. However, after the lecture about this I have felt that I can relate chance and probability to my personal experiences and highlight to pupils the basic maths behind this, whilst making it enjoyable to learn about. Inter-connectedness is a concept of Liping MA’s that can be used between maths and our everyday lives (Ma 2010). By interconnecting our experiences with the subject of probability, basic mathematical skills can be integrated into our everyday experiences, something which I believe is important when obtain fundamental maths skills.

Probability is “the likelihood or chance that something may happen” (Turner, n.d. p5) and can be worked out by:

Probability of something happening = The number of  ways it can happen – over – the total number of outcomes

For example, when rolling a dice there are 6 possible outcomes. However, if I were to only try and role a 5, the possibility of this would be 1 in 6. In many cases people try to predict the possible outcome, however as we have discovered in maths, it is not as simple as this.

Gambling has a profound and direct link to probability and chance. By taking this chance it can be the profit or the lost to some people’s bank balances. Those who are serious gamblers are costing the government £1.2 billion a year (IPPR, 2016). This is not only impacting the economy but can also cause extreme debt for some people, and a break down in relationships and mental health. This is why some people try to predict casino games and influence the outcome, in the hope they can solve the problem (Aasved, 2004).

There are aspects of gambling which are linked to multiple perspectives. This is about having a variety of different ways to reach an answer. For example, there are variety of meals you can have in a restaurant. Say for example there were 2 choices for a starter, 3 for main meal and 3 for dessert, you have to list of different meals that you can possibly have. Therefore, there are many different combinations and to figure this out multiple perspective is important.

Gambling is something which relies on randomness and probability (Turner, n.d). When discussing this in our lecture, we all thought that surely humans can create randomness effectively? Wrong! We wrote our predictions of either heads or tails, if we were to flip our coin 30 times. I thought I would try and mix it up a bit, put heads 4 times in a row, a couple tails etc, but the answers truly baffled me. It ended up being completely 50/50. Even when I was trying to be as random as possible. The results were similar on a larger scale of our class, with the majority of people being one or two off the other. When actually flipping a coin, my results were 21 heads and 9 tails, and this varied around the lecture room. Therefore, as humans, we THINK we are being random, however nothing is quite that simple and we actually try to create logic results rather than random. I remember when conducting my answers, I thought I had to put a head and not another tails because 4 tails in a row was being silly, yet the physical experiment proved this to happen with heads.

Using a coin is a simple way of introducing probability and chance to children, as there are only two outcomes. If they have the basic skills and understanding of what a half or 50% means then probability can quickly follow behind. This aids their longitudinal development, as they have the basic skills prior to probability and therefore they can build on this to have a deepened understanding of problem solving and the possibilities of finding the answer. It also helps them in more complex scenarios, for in class work and future work, if they were working in a restaurant for example. Therefore, multiple perspective, basic skills and longitudinal coherence, all key skills in profound fundamental maths (Ma, 2010) can be shadowed through everyday maths.

It is important that we recognise that gambling can possibly be predicted. However, slot machines and casinos profit more from us than we would ever earn back (unless you’re the 1 in 45057474 to win big on the lottery! (Lottoland, 2016)). Slot machines are to us, a quick and easy way to win money back. Charles Fey, developed the Liberty Bell machine in 1895, which has 3 reels and 5 symbols. This machine in particular pays out 50% of the time with an average of 75% pay-back. Therefore, although you seem to ‘win’ more, you are in fact, losing more!

Stefan Mandel, 1964, applied to buy every combination to the Romanian lottery. He followed this up by doing this with the Virginia state lottery. The video below highlights the result of this.

In conclusion, probability and chance is something that we use every day. Some people take this for granted and some take it to extremes. However, we have the ability to use multiple perspectives to figure out possible outcomes, which can be used in our daily lives and in maths in primary school. Yet, probability on a gambling scale, as seen in the video, can be on a completely different scale to our everyday probability. I believe that Liping MA’s principles are important here and they are concepts that I will look at deleloping in future placements and my teaching career.

References:

 

Aasved, M. (2004) The Biology of Gambling. Springfiled: Charles C Thomas.

LottoLand. (2018). The Probability of Winning the Lottery. Available: https://www.lottoland.co.uk/magazine/the-probability-of-winning-the-lottery-.html. (Accessed on: 17th October 2018)

Ma, L. (2010) Knowing and Teaching Elementary Mathematics (Anniversary Ed.) New York: Routledge.

Slot Machine History (2010). Who is Charles Fey? Available: http://slotmachineshistory.com/charles-fey.htm. (Assessed on: 15th October 2018)

The Progressive Policy Think Tank. (2016). Cards on the table: The Cost to Government Associated with People Who Are Problem Gamblers in Britain. Available: https://www.ippr.org/publications/cards-on-the-table. (Accessed on: 16th October 2018)

Tuner, N. (no date) Probability, Random Events, and the Mathematics of Gambling

 Wherbert, P. (2010). Stefan Mandel (online video) Available: https://www.youtube.com/watch?v=4TqFp0efLK0 (Accessed on: 16th October 2018)

 

 

 

 

 

 

 

 

 

Teaching New Phrases – French

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French was never my strong point at school. I felt that I didn’t have the underlining and basic skills to forward my development and therefore the subject broke down for me. In Scotland, we are now introducing a second language in Primary 1. This is a positive means of having the underlining basis of a language such as French or German and therefore moving forward and learning another, for example Spanish, will become easier in accessing the grammar and speech.

Children learn a modern language through receptive skills and productive skills. Receptive is similar to our language – learning through listening and reading. It is important that children have the opportunity to listen to a language before attempting to read it. This is because in many European languages they use accents. These can change the way the words are pronounced. Therefore, if a child were to read a new word first, they would have an interpreted pronunciation and continue to say the word wrong. It is important that productive skills are brought forward also. These are talking and writing. Talking is important feature that can run alongside listening. Teachers can get involved with this also, as demonstrated by Carrie on Tuesday. Carrie used a lesson with us where the teacher used associated actions with a word, such as a left-hand wave with “bonjour” and right-hand wave with “au revoir”. This repeated back and forward from the teachers and pupils can reinforce specific phrases and therefore they have a sound understanding of new vocabulary. This makes it easier in future to receive the words through recognition of sounds and phrases.

These new phrases can then be brought forward through the introduction of the words being written and read. As a teacher, it can be difficult to bring forward a second language when a child’s first language is continuing to develop. Therefore, as mentioned previously, it is important that they are not bombarded with phrases and lessons are focussed on a maximum of 8 new words in a lesson. This provides opportunity for new vocabulary to become embedded in a child and talking and listening activities can progress through writing and reading lessons.

When Carrie was carrying out the lesson she solely focussed on some individuals. This was a reflection task for us all as we were required to think like a class of primary school pupils would. As a teacher, we have to understand that not everyone will be confident in accessing a different language or confident enough to say phrases in front of their peers (Jones, J and Coffey, S 2006). It is therefore important to make activities group tasks to get everyone involved and if feedback is required this is done on a collective basis. We must also keep the work engaging for pupils, whilst progressing at the same time. Keeping activities relevant to the language by having lessons based around a song, a game or an art lesson, provides pupils with fun activities whereby the language is not their sole focus. However, we must develop progression. In Primary 1-3 talking and listening is emphasised, so the pupils have a key understanding of basic language. But older pupils will engage more with reading and writing lesson so therefore they are expanding their skills (Jones and McLachlan 2009). This however may require for teachers to recap pre-taught language to gage the level of the pupils’ understanding and reinforce the words. Therefore, by checking for understanding, use of progression and the use of the four main language skills, children CAN have a sound understanding of a foreign language and maintain this language throughout primary school, with progression in upper stages.

References:

Jones, J. and Coffey, S. (2006) Modern Foreign Languages 5-11: Issues for Teachers. David Fulton. London

Jones, J. and McLachlan, A. (2009) Primary Languages in Practice: A Guide to Teaching and Learning. McGraw-Hill Education

 

 

 

What is a Number?

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We come into contact with numbers every day. Time, working out how many portions of dinner we’ll need to make or simply “hey what’s your number?”. But have we ever taken the time to think, what is a number and why do we even use them?

My first question is, why does the number three collectively represent other items in threes? Surely three dinosaurs would be more than three peas, even though they represent the same amount collectively. But it’s not due to weight, height or mass, its due to the value of the number three. Numbers are a language. For value, comparison and equivalence. They help us understand how many there is of something (value), help us compare that five dinosaurs are two more than three peas and that three peas and three dinosaurs are equal.

Numerals play a significant part in this. A numeral is the symbol or collection of symbols used to represent a number. A child’s first experience of a number is most likely going to be an adjective that would collectively describe a set of something e.g. five cats or two arms, this is more commonly known as the ‘cardinal aspect of a number’ (Haylock, 2014). This highlights that children can recognise an equivalence between two sets of objects and is why we understand that three dinosaurs are equal to three peas. At this stage numerals are the link to numbers. Therefore, children can look at numerals such as pictures of shapes or objects and count how many are there of one thing. This will therefore help them connect to real life situations and when shown beside numbers, they can begin to connect numerals and numbers together. By beginning to connect the two, children will have a deepened understanding of numbers and therefore their longitudinal coherence will develop. Starting their journey with numbers and maths simply and positively to prevent future maths anxiety (MA, 2010).

Numerals have been shown throughout our history and teach us a lot about the development of mathematics. One of the oldest is hieroglyphics, used by the Egyptians, dated as far back as 3000 BC. Their numerals were shown through drawings and symbols such as a bird and an Egyptian man (O’Connor and Robertson, 2000). Maths was commonly used by Egyptians if they were dividing food, solving problems for trade and market and most importantly for the pyramids (Mastin, 2010). This highlights the first use of maths for economy and trade. Wealth played a significant part in Egyptian life and social class was divided by money but more than anything, maths. Through looking at our history, we can see the similarities in the importance of economy then and now. We live in a world that’s economy changes daily and has the power to change and impact upon people’s lives. If we looked more in depth at historical economy such as Egyptian trade and social classes, we could learn and reflect on our economy nowadays and therefore maths is a historical aspect of economy that involves counting and numbers.

All factors of numbers have a place in fundamental maths, but most importantly teach us a lesson for now. We can apply what we have seen previously in history and the importance of numerals and numbers to aid our development with maths and see that it is essential for our wider society and not just basic classroom use. Relevance is a fundamental principle of Curriculum for Excellence (Scottish Government, 2010) and therefore it is important that teachers bring this forward from historical findings into our everyday maths lessons and make children think about their future with maths in society.

Number Patterns and Sequences

Another way of teaching maths can be through number patterns and sequences. This can be another way of making maths interesting for children whilst developing their relationship with numbers. Vale and Barbose (2009, p9), stated that the use of patterns in maths can challenge students to use “higher order thinking skills and emphasise exploration, investigation, conjecture and generalisation.” Therefore, basic skills in maths are used within problem solving to develop not only longitudinal coherence but also multiple perspectives as they can use different methods to find the solution to a problem.

An interesting number pattern is Pascal’s Triangle, named after Blaise Pascal, a French mathematician. This is a triangle that starts with the number ‘1’ and then below are the sum of the addition from the numbers above. For example, if 1 is beside 2 in the triangle the sum (number written below) would be 3. An example of this can be seen below.

Pascal’s Triangle makes maths fun for children whilst learning about addition and number patterns. Addition is a fundamental aspect of maths that it taught as early as ages 4-5 and can be continued to be taught throughout primary school through ways such as Pascal’s Triangle. The introduction of colours can also produce other findings within the triangle. For example, pupils can colour odd and even numbers or work out the horizontal sums of the triangle (Maths is Fun, 2017). This therefore keeps maths relevant and allows for differentiation in a classroom, as some can complete the main body of the triangle (addition) and some can move forward looking at other aspects of the triangle. Therefore old maths techniques and problem solving continue to find a relevance in our everyday maths and classroom.

References:

Haylock, D. (2014) Mathematics Explained for Primary Teachers. 5th edition: SAGE.

L, Mastin. (2010) Egyptian Mathematics https://www.storyofmathematics.com/egyptian.html (Accessed: 5th October)

J, O’Connor and E, Robertson. (2000) Egyptian Numerals. http://www-history.mcs.st-andrews.ac.uk/HistTopics/Egyptian_numerals.html (Accessed: 5th October)

Ma, L. (2010) Knowing and Teaching Elementary Mathematics. (Anniversary Ed.) New York: Routledge.

N/A (2017) Pascal’s Triangle.  https://www.mathsisfun.com/pascals-triangle.html (Accessed: 6th October 2018).

Scottish Government. (2010) Curriculum for Excellence Building the Curriculum 3 A Framework for Learning and Teaching: Key ideas and Priorities. Available at: http://dera.ioe.ac.uk/1240/7/0099598_Redacted.pdf  (Accessed: 5th October 2018).

Vale, I. and Barbosa, A. (2009) Multiple Perspectives and Contexts in Mathematics Education. Available at: https://www.academia.edu/1485703/Patterns_multiple_perspectives_and_contexts_in_mathematics_education  (Accessed: 5th October 2018).