Year 7 Challenge Demo Feedback

Following the demo of the Game Theory Challenge yesterday, I got some very useful feedback
The games were a little bit to complicated to explain quickly. A little more time will be needed to make the rules absolutely clear
The game took longer than I had thought and there wasn't enough time to wrap up properly. Should just stick to a couple of games
The main thing I think was the use of the sweets. I gave each player a pile of sweets to bet with. This meant that the players already had GAINED something so there was little incentive to play the games! If the prize was less than their pile they just folded early on. This was the case since the games are meant to show that they end up betting more than the pot.
A solution to this is to have the players play against the `banker' i.e. Ambassador so the banker holds all the sweets and then offers them at each turn.

I can't think of a way to auction without the players having their own stash so I've included the traveller's dilemma in its place.

I've also tried to make the Ambassador sheet a lot clearer. It basically a verbatim script now. I've bulleted most of the script and highlighted in a different colour exactly what is script and what is not.

Game theory 15 minutes challenge develpment

Potential games:
2/3 of the averageconsensus gameprisoners dilemmatravelers dilemmacentipede gamemuddy childrendollar auctionnumber battlesecretery/marriage problem
The focus of this should be how people think about risk. How do we weigh the pros and cons of what we've got relative to what we could have. How rational is our appreciation of the uncertainties about some outcome when there is something to be lost and gained.Examples of this thinking are seen in the Weakest Link and Who Wants to be a Millionaire. In the former it is the decision as to when to bank- should the contestant bank earlier to ensure some money banked or later to potentially bank more money but risk banking nothing? WWTBAM the contestant can walk away without playing the next question but may risk answering the question for a potentially significantly more amount of money.I think playing the centipede game with sweets could be a good interative game to start.then discuss the strategies usedwhy did they do what they didwhat did they learnwhat would they do differently next time.We want to develop an appreciation of individual levels of trust, risk aversion and selfishness.
Ground in day to day life: continuously making personal judgements in the present of uncertainty and risk. Whether is is going to rain, should we change job (probably not good for a school child!), should we cross the road, should we spend or money on item X, etc?
In business and politics the same thinking applies: should business X advertise more that business Y? should country X spend more on defence than country Y? should university X charge more fees??The marriage problem could be relevant to teenagers because of the dating element. How can we know whether to stick or continue?
The muddy children game can be played with post-it notes or coloured hats instead. This demonstrated what we learn when NOTHING happens.

Random number bias

Its been suggested to me to ask each pupil to write down a random number between 1 and 10. Then when they reveal these it is expected that most people pick either 3 or 7!

The Manchester Science Fair is focused on Maths this weekend and they've got the group working with Marcu Du Sautoy there, a maths comedian (!) and the maths busking.

Manchester Science Fair

I spent half a day on Saturday making paper airplanes and Sunday doing `science busking' for the Manchester Science Fair.

I got some encouragement for my game theory idea because one of the organisers has been to a similar talk before and really enjoyed it. She said its good to keep grounding it with real world examples like playing chicken.

She suggested a check out something called British Interactive Group(BIG).

I also saw a poster on probability that used the example of shoot at a goal and there are different probabilities of scoring depending on where about you shoot.

Probability Session: Lessons Learnt

Timetable
5 mins intro
10 mins Head/Tails game
10 mins card game
20 mins probability scale
5 plenary, wrap-up and summary
Rushed too fast through the first part of the session and then had to pad during the probability scale section. Suggest taking more time on the introduction in particular  but generally slowing down and adding an extra task. Could talk about what they think a statistician/mathematician does as a job and what subjects its necessary to know maths for. Maybe make some more links with probabilty in their daily lives, TV programmes.
Introduction
Welcome. Introduce who I am & what I do.
Garbled explanation of what my job is which needs preparing better. Need to make it clear to the kids what the role is and why its imporant.
Going to talk about probability. This is like a ruler for random things.
Maybe ask about how different things are measured: height, length, time, weight...
Lottery video of the ball jumping around. Why can’t we predict what the winning numbers will be? Why do they do this mixing? What is the pattern of winning numbers?
Ask them to multiply all the lottery numbers together!
Tell them that at the end I will tell them what the best strategy for playing the lottery is.
The lottery video was a little bit too long. remove some of the chat before hand.
ipod shuffle picture: How does ipod shuffle decide what song to play next? What is the chance of getting your favourite song?
They didn't come up with the fact that it was a shuffle.
Head/Tails Game
Don’t explain the motivation to the game at first. “Let’s see how much they know about randomness”
Everyone stands-up and chooses either ‘head’ or ‘tails’ from a toss of a coin by either touching their head or bum. When someone is incorrect they sit down. Repeat the process until everyone is sat down. If there is a play-off at the end then bring the pupils to the front.
Prize for last person standing.
What was their strategy? Why?
Explanation: each toss of the coin is independent. The history of the tosses is irrelevant for a fair coin. E.g. lottery numbers are independent of past results.
Needed to keep the kids who had sat down engaged a bit better. It might be worth recording how many are sat down in each go and discuss what we see. Could mark these on the board. We should expect to see about half each time but they are not independent selections!
Could use a video on the computer to show the coin toss better.
Card Game
‘Play you cards right’ format. Several large ‘cards’ are turned over in sequence at the front. The pupils are told that the cards are between 1 and 10. Between each turn the pupils choose higher (H) or lower (L) than the previous card by holding up a card with the appropriate letter on it. Consensus determines the group decision.
This demonstrates a type of probability scale (between 1 and 10). If the number is high then there is more chance of the next number being lower because there are more possible cards.
Again, a slightly uncelar explanation of the outcome of the game. This needs improving. The kids did not use the `H', `L' cards very well, e.g. waving the `H' when they thought it was lower. Seemed to be more engaged when they were asked to shout out what they thought.
Could go back and get them to work out the number of possible card higher and lower. Think that should consider with replacement to make the probabilities more straightforward.
Could then give them something related to work on individually/in groups. ??
Probability Scale
Introduce the modification of the card game scale to the probability scale.
a) Individually have a worksheet. Put the listed events on the scale in the right place. Aim is to think about other locations to 1, 0.5 and 0.
b) Each pupil is given a probability event card, e.g. lottery win, rain tomorrow, eat tea today. They come up one-at-a-time and put these on a line of probability. Can do the selection is steps so first decide which half of the line, then which part of that half and so on.
Quick discussion amongst themselves about the relative probabilities.
Reassess whether their classmates have put the cards in the right place.
They really didn't get the idea of 1,0 probabilities never happening. They thought that everything was either 0,0.5 or 1. I think when the first kids puts their paper at 0.5 then all of the others follow. I think that is important to stress the relative probability of events.I think that the paper should have an arrow on it or something to mark exactly where on the line they mean to put it. I think it would have helped to have fraction markers on the line.IDEA: to get the pupils to think about what 0 and 1 probability events actually mean could get them to come up with reasons why things are not 0 or 1 i.e. something really unlikely but with a non-zero probability e.g. martians landing or the laws of physics change.
An idea is to not use a line at all but rather subdivide something else, like for example a cake. Pupils can then imagine slicing the cake into two pieces.
Plenary
Learnt about:
Independent events (H/T game)
Relative probability (card game)
Probability scale between 0 and 1.
What is my job? How do I use probability in my job?
I think that I need a hard example which connects more directly with what they've been doing. Something to do with the probability line?
What other probability course and jobs are there?
I think that it needs to be a lot clearer why probability, stats and maths is important and useful. Maybe go back to the examples from the beginning.
Could list lots of jobs that need maths and stats including law, physics, ...
Benefit of university? Benefit of doing mathematics?
Consider in their lives where probability occurs. What is random from day-to-day? What is unlikely and likely?
Best strategy for playing the lottery is DON’T PLAY!

Ideas development

• Instigate meetup with other MHS people. Discuss the yr7 challenges, to be doen by the beginning of December
• Think about developing the epidemic/rumour modelling ideas. This what are we trying to show?
• How can we present game theory ideas? what is the focus?
• National Science and Engineering week: get involved in the planning and organisation of the event and develop a session for yr10/11
• draw on experience at the MOD for warning and reporting and hazard management. Think of an equivalent scenario in e.g. the Arndale centre. What are the steps/process taken?
• EPQ: read up on the 'investigation' area and see if there is a need for data presentation and interpretation. Aim to do an online resource. Not priority

 

Early Ideas for sessions

• Voting Schemes: I thought this was my idea but the first Google hit gives this http://www.math.princeton.edu/math_alive/Voting/index.html. Talking to Alan, he says there are voting pads that could be useful for this kind of thing. Could be made relevant with discussion about FPTP http://www.electoral-reform.org.uk/article.php?id=54 or x-factor, say?

• How safe is the internet? This would look at public key encryption http://en.wikipedia.org/wiki/Public-key_cryptography, which is the most common way of keeping something secret on the internet. Pupils could set up their own and send messages. It uses something called RSA http://en.wikipedia.org/wiki/RSA which is basically loads of prime numbers times together.

• What is probability? Classically, it’s the frequency of occurrence of a given even but what if this even only happen once? Or very rarely or if the conditions change between events? How can we predict with probabilities i.e. what should we expect to happen? There are all sort of things with this like buying a lottery ticket, getting on a plane. A good way to think about it is in terms of hosting and placing a £1 prize bet; how much would you pay to play?

•

• Understanding uncertainty. How can we measure it? There are all kinds of uses and abuses of stats in the media, for example. How can we interpret this? Predictions about foot and mouth, swine flu, bird flu, MMR, the election outcome. How are these done and what are the errors/variances?

• This then feeds into making decisions when things are uncertain. The idea of rational decision making when decisions are consistent between events and over time. Should we panic?!

• Epidemiology. Thinking about the spread of something in a population. I like the idea of this as a rumour. So that’s the spread of information. This could be gossip in the playground or on internet chat rooms (http://www.cl.cam.ac.uk/techreports/UCAM-CL-TR-767.pdf). I’m not sure at the moment but we could get the student to spread something amongst themselves and take snap shots(?)

Ideas

Link with "Numbers" TV program
How to present data as an Extended Project Qualification class
Understanding Risk- concept of probability zero events using a dart board
Unlikely probabilities with potentially large utility (gain)-->Expected utility in decision making
subjective probability and personnal beleif
epidemic spread of contageous disease-->rumour modelling
what does a statistician aactually do? why be a statistician?
voting schemes: using coloured cards or electronic pads
     X-factor, weakest link, Big Brother evictions, Come dine with me
Monty Hall game show
Deal or no deal for random selection
ipod shuffle to demonstrate uniform randomness
game theory: prisoners dilema (businessness, waring countries), catepillar game
randomness of the weather
link with every day decision making in the presence of uncertainty
Experimental Design ideas- baking soda and film cases, paper helicopters
understanding uncertainty and misinformation in the media, advertising, politics

Resources:
David speigelhalters web page on explaining uncertainty
Macus Du Sautay
Royal Statistical Society GetStats campaign
Royal Society Christmas lectures by Du Sautay, Ian Stewart
Gelman book on teaching statistics

15 minute challenges: battleships type probabilistic search strategies
Simpsons paradox
voting scheme in two teams
game theory strategies

Accelerated Failure Rates

Accelerated failure time models encompasses a wider range of survival time distributions than the proportional hazards model (Wiki page).

Although in principle any non-negative distribution can be used, the log-logistic distribution is most popular. This is similar in shape to the log normal but has heavier tails.

 The lognormal, gamma and inverse Gaussian are also used.
The  fact that the survivor and hazard functions for the lognormal can only be expressed in terms of integrals limits its usefulness.
The gamma distribution is quite similar to the Weibull. In fact, the generalised gamma distribution includes the Weibull and lognormal as special cases.
The inverse gamma has a rather complicated survivor function.


One limitation of the distributions used in the proportional hazards model is that they are monotonic in time, which may not always hold. A unimodal hazard function may be more appropriate in some cases.

first podcast

First Blog