Monthly Archives: December 2017

Over and Out.

What do I Think?

I chose the Discovering Maths module as an elective in my second year, because I was afraid of maths and always avoided even attempting any mathematical problems. Despite coming through primary and secondary school in the ‘top maths group’ and being very competent and confident in the subject, it all went downhill when i decided to drop the subject after gaining my National 5 A grade. From then on, I began to experience maths anxiety and my confidence in my own mathematical skills, which were previously very good, began to wither. For that reason, I thought it would be a good idea to face my mathematical fears head on and attempt to regain my confidence through this module.

This module has been great for me. I have thoroughly enjoyed looking at different perspectives of maths and even just becoming aware that a huge proportion of adults and children also experience maths anxiety made me feel at ease again.

Through exploring maths I can now see the importance of it for every day life and in wider society, which I had not recognised before. I was not previously aware of how often I actually use maths in real life and this is something I want to demonstrate to my class when I am a teacher.

Including a variety of contexts in the lectures has been an effective way to make mathematics relative to us as students and I feel I have engaged more with it due to this.

My competences in maths have greatly increased from engaging with this module and I feel more prepared to teach this in schools. I have finally regained the maths skills I once had and can apply them to real life rather than just equations in a textbook.

My Thoughts on the Necessary Blogs

Blogging was a big part of this module and i feel it has been a great benefit to me. Blogging about the lectures and mathematical concepts has encouraged me to research more in depth about the topics and in return, has helped my subject knowledge as i know stuff I otherwise wouldn’t have known without researching and questioning it. It has also allowed me to take on more responsibility for my own learning and create blogs which are personal to me.

Through engaging with writing blogs, it has increased my confidence in putting my work out there in public for anyone to see. I am now more relaxed about who views my blogs and i feel i could continue to keep my blog up to date after this module has been completed.

My Future in Maths

In my future profession as a teacher, I want to show children that maths is fun and is all around us every day. I will specifically use Liping Ma’s theory of Profound Understanding of Fundamental Mathematics to aid me in the way I teach maths to pupils.

Overall, this maths module has been very influential for me and i hope to pass on the teaching to another generation of children.

Would you Take a Chance?

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.

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?

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.