Category Archives: 2 Prof. Knowledge & Understanding

Stick or Twist

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Gambling – the activity or practice of playing at a game of chance for money (Dictionary.com). But are we really playing by chance? Let’s find out.

First let’s discover what chance is;

Chance is the possibility of something happening (oxford dictionary). It can also be described more mathematically as probability.Say you have a coin. It has two sides; heads and tales. If you flip the coin your chance of getting one of the sides is 1/2.Take a dice, it has six sides. Therefore, by rolling it you have a 1/6 chance of it landing on any of the sides.

probability of an event happening = number of ways it can happen / total number of outcomes (mathsisfun.com)

The first ‘chance’ game we are going to look at is the “Monty hall problem”. This is a situation where you are faced with three doors; two of which conceal goats and behind the other is the star prize, a car. The game show host will ask you to choose a door. After doing so he or she will then reveal one of the doors that you have not picked and reveal a goat. You will then get the choice to stick or switch from the door you have originally chosen. This leaves you with a 50/50 chance, right? Wrong.

So how does this work? By switching doors, you actually change to probability of picking the car. There is a 1/3 chance that the prize is behind the first door that you picked. Therefore, there is a 2/3 chance that the prize is behind one of the remaining doors. Since we know that the prize cannot be behind the door that the game show host has revealed, the probability affectively concentrates to the remaining door – leaving its probability as 2/3 (gizmodo.com). So, you are twice as likely to win the prize by switching doors.

Try it for yourself: https://betterexplained.com/examples/montyhall/montyhall.html

“New research shows that almost half of people in Britain gamble” (Gambling Commission). Is that not shocking? And we are all losing money. “Each game you play at a casino has a statistical probability against you winning. Every single time. This house advantage varies for each game, and helps ensure that over time the casino won’t lose money against gamblers. For people who are really good at Blackjack, the advantage for the casino might only be 0.5%, but certain types of slot machines might have a 35% edge over a player, and other games fall somewhere in between” (Investopedia.com). Of course, people can win, and they do, but the amount of people who do not drastically out-weighs the amount that do. As a nation, we are throwing out money into a pot where the probability is stacked against us.

We are not playing by chance. We are participating in games and gambling where it is designed and planned that we will lose. Just like the Monty hall problem we have to consider the probability of our actions whilst we are playing games to win. The games are designed to make us believe that our chance of winning is no what we think it is. The only way around this is maths. By calculating our probability of winning we can participate in games that give us a better chance of leaving it better off than we started.
References:

Dictionary.com: https://www.dictionary.com/browse/gambling

Oxford Dictionary: https://en.oxforddictionaries.com/definition/chance

Gizmodo: https://gizmodo.com/heres-the-best-explanation-of-the-monty-hall-yet-1580031464

Better Explained: https://betterexplained.com/examples/montyhall/montyhall.html

Maths Is Fun: https://www.mathsisfun.com/data/probability.html

Investopedia: https://www.investopedia.com/financial-edge/0910/casino-stats-why-gamblers-rarely-win.aspx

Gambling commission: https://www.gamblingcommission.gov.uk/news-action-and-statistics/news/2017/New-research-shows-almost-half-of-people-in-Britain-gamble.aspx

All visited 27/10/18

A Different Way to Learn

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I love maths. I find the subject to be so challenging yet so satisfying that I was able to enjoy my experiences of maths throughout my education. My love of maths began in my Primary 5 class when my teacher provided myself and my classmates an opportunity to learn maths in a different way, through play.

Maths through play is an unconventional method of teaching maths skills according to the old traditions of teaching. Maths has always been perceived and a ‘textbooks open, sum after sum’ subject. This old-fashioned way of teaching leaves children bred and disengaged from one of the most valuable curricular areas. By teaching maths trough play we are opening up the possibilities for all children to be able to work problems out in a way that suits them.

According to the Curricular Guidance for pre-school Education “Play is an effective vehicle for fostering Mathematical concepts and developing positive attitudes to mathematics…” This shows that children will be able to successfully deal with more complex problems through play rather than by traditional methods as they are given the opportunity to discover their own way to solve problems. By teaching maths through play, we are allowing children to enjoy the maths that they are learning. Maths will be less daunting as they are learning in a fun and engaging way.

So why can children learn better through play? “Young children engage in significant mathematical thinking and reasoning in their play – especially if they have sufficient knowledge about the materials they are using – if the task is understandable and motivating if the context is familiar and comfortable” (Scholastic) If a child is more engaged in their learning they are more likely to gain a higher level of understanding. If a child is disinterested in their learning they will not be able to take anything from it, therefore the teacher’s precious time will be wasted.

Rather than delivering content rich lessons we should be delivering valuable, engaging and worthwhile lessons. In order to engage more children, we should be delivering lessons that provide them with opportunities to learn in the best way for them. So, learning maths through play can spark new ideas and enthusiasm for the subject and therefore leave children feeling more engaged and confident.

 

Curricular Guidance for pre-school Education cited in http://www.early-years.org/parents/docs/maths-through-play.pdf

https://www.scholastic.com/teachers/articles/teaching-content/math-play-how-young-children-approach-math/