Category Archives: 3.1 Teaching & Learning

Would you Take a Chance?

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Probability & Randomness

As we are all aware, when we can’t decide what to do, we flip a coin. It is well known that by flipping a coin you have a 50/50 chance of either getting heads or tails.

Uncertainty

However, that’s not true.

It is a common misconception that the toss of a coin offers a 1 in 2 chance of landing on either side but we must also take into consideration that the coin will actually land on its edge. Despite the chances of this happening being so slim, it still nonetheless alters the probabilities.

However, on top of that, if we were to remove the chance of it landing on its side, there is still a 51% chance of the coin landing on the same face as it started off on. This is due to the fact that sometimes the coin doesn’t actually fully rotate therefore ends up just falling back down still facing the same way. Seems complicated for just a simple toss of a coin.

Tossing a coin gives a random result, whether it be heads, heads, tails, heads or tails, tails, tails, tails. The chance of the next flip is random yet as humans, we would expect the next turn in the second example to produce a heads as it has not appeared for a while. But if it were to be a tails people would struggle to believe there was no ‘magic’ going on. This demonstrates humans inabilities to truly grasp the concept of randomness.

References

Eastaway, R. (2010) How Many Socks Make a Pair? –Surprisingly Interesting Everyday Maths. London: JR Books

Do I Need to be a Mathematician to Play Games?

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Everyone loves a little bit of Sudoku!

As much as I hate to admit it, I have always been a lover of Sudoku. Despite never thinking highly of my math skills, I always managed to complete puzzle after puzzle – I have even been gifted a 365 puzzle book, one Sudoku puzzle for every day of the year! (Needless to say I still have the majority of them to work through). When I was introduced to the idea that maths is involved in these puzzles I struggled to identify the principles behind it, except the obvious of being able to count from one to nine. Nonetheless, after a bit of conferring and questioning, I realised that there were math skills involved in this particular puzzle. Without being aware of it, I had been problem solving, using the process of elimination, differentiating between the numbers, using sequences and strategies while attempting these puzzles. Newspapers say there is no maths involved in Sudoku, however what they really mean is there is no arithmetic because evidently there is many mathematical concepts involved. To clarify, there is no arithmetic involved in this particular puzzle because the numbers in the puzzle can be removed and replaced by symbols, ultimately removing the arithmetic.

According to Maki Kaji, over 100 million people now regularly indulge in Sudoku puzzles, meaning these people all use these mathematical skills, usually without even realizing it.

“Mathematical riddles, rhymes and games are now collectively known as recreational maths. It s a wide-ranging and vibrant field, an essential feature of which is that the topics are accessible to the dedicated layperson” (Bellos, A. 2010). There are underlying mathematical concepts in nearly every game and puzzle available. For example, the game ‘Battleships’ which I’m sure most are familiar with, involves strategic reasoning and estimations. To play this game you must be confident with locating coordinates on a grid and working out the next point to hit. Also, ‘Connect 4’ is a childhood classic that supports mathematical concepts including geometric thinking, planning and pattern recognition without even realising your doing these things.

 

Recreational mathematics remains in very good shape today. It is an exciting and diverse field that continues to give pleasure to people of all ages around the world, as well as inspiring serious research. Next time you find yourself playing a game or attempting a puzzle, try work out the underlying mathematical principles involved in playing the game and being successful.

In my future career as a teacher, I know for certain I will be reaching for a board game or puzzle to reinforce mathematical skills in my class. Games are so much fun for everyone and you don’t even realise you are practicing maths!

 

References

Bellos, A. (2010) Alex’s Adventures in Wonderland. London: Bloomsbury Publishing Plc.

Conquering Maths Anxiety

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Many of us will be familiar with the shear panic, the sweaty palms, the headaches and the confusion that comes alongside attempting mathematical problems but not many will be aware that this is a diagnosable condition and is extremely prevalent among the population. Maths anxiety has been defined as “a feeling of tension, apprehension, or fear that interferes with math performance” (Ashcraft, M.H 2002, p. 1) and is believed to affect around a quarter of the population including thousands of school teachers.

Why do we have maths anxiety?

For me, the anxiety I have for maths came as a surprise as i was always very competent and able in the subject all through primary and up to secondary school. This anxiety first began when i stopped studying it at high school and saw others around me become more competent in the subject. This created a fear that i wasn’t as good as them and couldn’t understand the concepts they were learning. I felt i was being left behind in my learning and was not as smart as them. Therefore, I opted to avoid any mathematical problems that i perceived as too difficult or simply used my calculator to prevent making mistakes and looking bad.

For others, maths anxiety can often be caused by influential adults such as parents who have negative attitudes towards mathematics because they project their fears onto their children. This leads to the children adopting the same negative feelings, such as “maths is a waste of time” and taking them into school. It can also come from the teachers themselves. If a teacher is negative or afraid of maths then their teaching will influence how the children in the class feel towards it. Maths anxiety can often come from the fear of embarrassment or failure which puts the children off from even attempting the subject. If a child has been embarrassed or made to feel wrong in front of the class, it can destroy their confidence and discourage them to explore mathematical concepts in the future.

Maths is a difficult subject and needs strong support from teachers, not more pressure of succeeding in tests or appearing to be always right.

How does maths anxiety impact us?

Learners with maths anxiety will repeatedly go above and beyond to avoid doing maths in class and outside class, which in turn results in even poorer competences in the subject and applications of maths to real life. Children are unfortunately led to believe maths is about having right answers and are therefore too afraid of making mistakes to even try. This means as children grow up avoiding maths and not trying they are likely to have the same poor abilities in their adulthood.

As adults, a lifetime of maths anxiety can have devastating consequences. Some avoid applying for jobs which may involve some mathematical reasoning, therefore limiting their career opportunities. They may have a lack of confidence dealing with their own personal finances, their mortgage, buying/running a car etc. From these examples we can see just how important maths skills are in the real world outside of the classroom. This is why, as future teachers, we need to promote the positivity and relevance of maths to children.

Conquering Maths Anxiety!

As teachers, it is vital that we help children understand maths and not be afraid of it. Allowing children to experiment and discover maths in their own time is so important for their futures and the quality of life they will receive from doing so. We need to show them the relevance of maths and ensure that mathematical problems are set in meaningful contexts to the children. This will make the questions worth solving!

Making maths fun in the classroom will encourage children to enjoy discovering concepts in maths and be curious in their discoveries.

Make children feel comfortable to ask questions and explore as children should not be afraid of getting it wrong – focus more on the discovery and on the excitement!

This Ted Talk by Robert Ahdoot is a great place to start on learning how to conquer maths anxiety in the classroom!

References

Ashcraft, M.H. (2002), Math anxiety: Personal, educational, and cognitive consequence, Current Directions in Psychological Science, 11: 181–185

Atkinson, E (1992) Mathematics with Reason, Oxon: Bookpoint Ltd.

Brian, K (2012) Maths Anxiety: the numbers are mounting The Guardian [Online] Available at: http://www.theguardian.com/education/2012/apr/30/maths-anxiety-school-support [Accessed: 7 October 2017]

“Maths is hard”

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Why is Maths Hard?

What is it that makes maths appear to be a hard subject? Is it all the rules you must follow or all the formulas you need to remember? Is it the focus on accuracy or all the strange unfamiliar symbols?

Most people you ask will tell you they found maths difficult at school and they were never very good at it. In the UK, it has now become culturally acceptable to be ‘bad’ at mathematics and we more than often overhear the words “I can’t do maths” (Kowsun,2008). Negativity towards the subject is, unfortunately, something that people take pride in and boast about. This may be due to the stereotype that maths has been given, thus leading people to believe that only the rare and gifted people are capable of doing maths. It is seen as male dominated and ‘nerdy’, all of which are untrue stereotypes.

A research study by BAE Systems found that approximately one in six adults admitted to being embarrassed by how difficult they find mathematics and one in five adults required the use of a calculator to work out simple sums. The proportion of adults struggling with mathematics has greatly increased as today, 49% of adults have the maths skills expected of an 11 year old child still at primary school (Garner, R. 2012). Low adult numeracy skills lead to many disadvantages in life such as difficulty getting a job, struggling to do their job as it may entail some form of mathematics or even just simply difficulty dealing with home finances and everyday shopping. Low skills in mathematics costs the nation around £20.2 billion (National Numeracy).

Importance of Maths

Little do these people know how important mathematics is to them and their everyday lives and perhaps, even how much they really use maths on a day- to-day basis. For example, a routine task of crossing the road requires many mathematical processes including estimating the speed of oncoming vehicles, the speed you can walk across, the time it will take you to cross and the distance to the other side. These are all common calculations our brain carries out each day however not many would include this as being ‘maths’ .The preconception is that mathematics is all about finding a ‘right answer’ whereas in reality, “mathematical discovery relies on the same guesswork that informs our everyday maths” ( Pound, L 2008). This meaning that maths is all around us and is vitally important to our lives.

Maths is for Everyone!

Despite all these factors insinuating that maths is hard, we as human beings are born mathematical which makes learning maths significantly easier than it would be otherwise.

Everyone can do maths and we all carry out calculations in our head every single day without our realisation. The only boundary we have stopping us succeeding in maths is our own attitude towards it. “Doing mathematics does not require any special ability not possessed by every one of us” (Devlin, 2000 p253).

 

References

Devlin, K. (2000) The Maths Gene London: Weidenfeld & Nicolson.

Garner, R. Independent. 2012. Almost 50 per cent of adults can’t do basic maths. [ONLINE] Available at: http://www.independent.co.uk/news/education/education-news/almost-50-per-cent-of-adults-cant-do-basic-maths-that-means-half-7469119.html. [Accessed 6 October 2017].

Hall, J (2013). Adults Struggling with Basic Maths. [ONLINE] Available at:http://www.independent.co.uk/news/uk/home-news/adults-struggling-with-basic-maths-with-one-in-five-requiring-a-calculator-for-even-the-most-simple-8532488.html. [Accessed 6 October 2017].

Kowsun, J. (2008). This innumerate isle – Article – TES [Online] Available at: http://www.tes.co.uk/article.aspx?storycode=2033102 (Accessed 6 October 2017)

National Numeracy. Attitudes Towards Maths. [ONLINE] Available at:https://www.nationalnumeracy.org.uk/sites/default/files/attitudes_towards_maths_-_updated_branding.pdf. [Accessed 6 October 2017].

Pound, L (2008) Thinking and Learning about Mathematics in the Early Years. New York: Routledge