Category Archives: 3.1 Teaching & Learning

Stick or Twist

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

Doctor Who?

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Time Travel – a Doctor Who-esque phenomenon that has been a fantasy to many for thousands of years. But it turns out that we have been doing it all along. How? You might ask. The answer is simply light, the five-letter word that we all take for granted. Light has been enabling us to see way back in time for ages and ages, literally.

Take the big bang for example. We have learned that we can see right back until a few million years before the Big Bang and it occurred 13.8 BILLION years ago. So how is this possible?

Let us put the universe into perspective: if you were to drive on one straight road around the Earth at its largest circumference, 24,900 miles, at an average on 60 mph it would take 415 hours – 17 and a half days (Quora.com). We are just one planet in our solar system made up of 8 planets in which we are the fifth smallest – Jupiter being the largest at 1120% of our size (universe today.com). Feel small yet? Well our solar system orbits around just one start in our Galaxy – the Milky Way. There are approximately 100,000,000,000 stars in our galaxy. That means we are 1 in 100,000,000,000… feel small now? But that is just a galaxy, galaxies make up our universe – in fact, 100,000,000,000 galaxies make up our universe. This colossal number of stars has intrigues people to put this into perspective, people like Carl Sagan who came to the conclusion that there are in fact more stars in the universe than grains of sand on all the beaches and deserts on Earth COMBINED (outerplaces.com)

So now we know roughly just how big our universe is we can now begin to understand why we can see back in time. Because our universe is so exponentially massive, the time it takes for light to be emitted from a source and then to reach a telescope on Earth is astronomical. This distance is measure in light years – the equivalent distance that light travels in one year. So, if a star is millions of miles away that is emitting light we will not see that light until the amount of light years it takes for that light to reach us, therefore we are seeing the light that has been emitted in the past. Between the time it takes for the light to be given off and then to meet our telescope, that star could cease to exist and we would not know until the light no longer reached us, light years later. Hence, we are seeing back in time.

If you wanted to see back in time you don’t need a Tardis, your answer is all in light.

https://www.quora.com/If-you-were-to-drive-around-the-world-how-long-would-it-take

https://www.universetoday.com/36649/planets-in-order-of-size/

https://www.outerplaces.com/science/item/2631-are-there-more-stars-in-the-universe-than-grains-of-sand-on-earth

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/

Scientific Literacy

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Scientific literacy is the knowledge and understanding of scientific concepts and processes required for everyday experiences, for example decision making. Scientific literacy allows a person to read or hear an article or newspaper online and decide on its validity. A literate person should be able to evaluate the worth of certain scientific information based on the sources and methods used to produce the conclusion or argument appropriately. It is important for educators to give students the opportunity to develop their understanding of scientific concepts and processes and show how they relate to our society. Without scientific literacy children are more likely to buy into false scientific facts and findings.

According to the Organisation for Economic Co-operation and Development, scientific literacy is, “the capacity to use scientific knowledge, to identify questions and to draw evidence-based conclusions.” (OECD, 2003) Without this there would be no evidential backing to many scientific theories and scientific knowledge. The reason that science, for many people makes sense, is because everything is backed up with evidence and research. However, there are many times in the media where scientific literature is used incorrectly, or even not at all. An article written by Ben Goldacre (2016) explains how many new drug trials and testing do not give an accurate idea of how good the drug is. This is due to a lack of testing and a small amount of people in the trials. Without this explicit scientific data, there is no way a correct conclusion can be made about the new drugs. If proper testing was carried out, there would be a higher chance new drugs would either be more effective or pulled before being released to the public to save people having undue side effects. This also gives people the wrong impression of drug trials, as the lack of concrete scientific evidence means there is no proof, however if this is missed out completely in media then nobody will think bad of it.

How teaching Fair testing in schools links to scientific literacy:

A fair test is an experiment where you change one factor (variable) at a time whilst keeping all other factors and conditions the same. For example, if you are measuring what object travels fastest down a ramp you would only change the object and not the angle of the ramp or the force the object is pushed with.

Fair testing is taught throughout primary school with the help of other science topics. Through this, children develop skills and independence in planning and performing fair tests.

Fair testing is taught throughout the curriculum and not as a separate topic a it involves a variety of skills. Children will use fair testing as a way to investigate questions within every science topic from plants to forces.

Fair testing links to scientific literacy as it shows “knowledge and understanding of scientific concepts and processes required for personal decision making” (discover magazine). Children require specific skills to carry out fair testing that shows they have adequate scientific literacy for that stage they are working at.

Science Buddies (Undated) Available at: https://www.sciencebuddies.org/science-fair-projects/science-fair/doing-a-fair-test-variables-for-beginners (Accessed on: 9th February) What is a fair test? (Undated) Available at: (https://www.theschoolrun.com/what-is-a-fair-test, (Accessed: 9th February)

Kirshenbaum, S (2009) ‘ What is Scientific Literacy?’, Discover (March), Available at: http://blogs.discovermagazine.com/intersection/2009/03/17/what-is-scientific-literacy/#.WoA1qFJ0egQ (Accessed: 9th February)

OECD [Organisation for Economic Co-operation and Development] (2003) The PISA 2003 Assessment Framework – Mathematics, Reading, Science and Problem-Solving Knowledge and Skills. Paris: OECD.

Goldacre, B. (2016) The Cancer Drugs Fund is producing dangerous, bad data: randomise everyone, everywhere! Available at: http://www.badscience.net/2016/09/the-cancer-drugs-fund-is-producing-dangerous-bad-data-randomise-everyone-everywhere/ (Accessed 11 February 2018).