Teaching The Logic Of Scientific Discovery With Games – Part 3: Better Analogies

Posted on 2012/03/03

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Feature Image - Teaching The Logic Of Scientific Discovery With Games - Part 3 Better Analogies

Introduction

This is the last article where I explore methods for teaching the logic of scientific discovery. I consider these three remaining games to be the best examples I have found that model our relationship with the world.

RDF’s ‘Which Card Wins?’ Game

The Richard Dawkins Foundation, in collaboration with the British Humanist Association, wrote some lesson plans to accompany the viewing of Dawkins’ Royal Institution Christmas Lectures of 1991.

As part of the teaching pack ‘Growing Up In The Universe’, there is a lesson called ‘What Is Science For?’, which address the value of science, and how it is done. One of the suggestions they present is a unique card game called ‘Which Card Wins?[1]

Meta-Rules

  • The game is for four players and one dealer.
  • One pack of cards is required. The dealer deals out all of the cards from the pack, not including the Jokers.
  • Each player picks up their cards. They can look at their own cards but not those of other people.
  • The dealer then asks the teacher for the game’s rules. Only the dealer should know this, not the players.
  • The player to the dealer’s left plays one of their cards by placing it face up on the table. They can play any card from their hand.
  • The other players in turn then play one of their cards, in the same way.
  • Once all the players have played one card, the dealer will say which player has won that round (according to the game’s rules) but without saying what the rule is.
  • The players play further rounds of the game, with the dealer saying who has won each time.
  • The players should treat each round of the game as an experiment. They can note down the result of each experiment in a table (an example is provided below).
  • Once a player has spotted what they think the rule is (their hypothesis) they can try to predict which card will win a round.
  • If a player predicts the rule correctly, a new game can start with a new rule and a different person acting as the dealer.

Analysis

  • This game is not a ‘Trainee Demiurge’ game as outlined in part 2, since there is no mention of the players ‘breaking a rule’. Yet, the players are still active participants, and can conduct experiments.
  • The rules pertain to a criteria that selects a winner from various candidates. Considering this is from Richard Dakwins (I don’t know if he personally authored the game), the rules seems to be an analogy for environmental evolutionary selection pressures.
  • Thus, rather than try to guess a fundamental law of nature, it seems the players are attempting to guess the nature of this selection pressure.
  • The cards represent organisms that are selected by the nature of this environment. ‘Winning’ the round corresponds to an organism surviving an event, or successfully breeding. [Note, there is nothing in the analogy that corresponds to inheritance and variation; each game is independent.]
  • The aim of the game is not to win the most rounds, but to guess the pattern. Therefore, experimenters might be deploy a card to test a hypothesis with the guess that it will not be a successful candidate. Indeed, they might consider ‘winning the round’ to apply to their cards, and not themselves.
  • Unlike scientific inquiry, the rules are revealed at the end of each game.

Hypothesis Machines

Defined by M Martin in his book ‘Concepts of Science Education’ as ‘mechanical devices with a hidden mechanism that is to be guessed from known instances of input and output’, hypothesis machines are well known tools for teaching.[2] Perhaps better known “black box tests”, I take Martin’s definition so to avoid confusion with flight data recorders (where the name orginated), and to detach the tool from any allusions behavioral psychology.

For a fascinating example of a literal black box test, see Edward De Bono’s ‘Practical Thinking’.[3]

The book describes how he shows 1000 people a black cylinder that, after positioned upright on a table for some time, seems to spontaneously topple over. Although I strongly disagree with his conclusions of the study, the question ‘what made the black cylinder fall over?‘ produces a wealth of fascinating unscientific explanations from the participants. The majority also demonstrate an incredible misunderstanding of the principle of moments!

I once constructed a series of ‘hypothesis machines’ that had the dual purpose of testing students’ ideas about optics, as well as presenting a model for scientific inquiry.

I fixed some components (lenses, mirrors, prisms, glass blocks) inside sealed shoeboxes, and provided students with light sources to shine through the translucent viewfinders. They had to try to guess what was in the box (see an example below).

This method of testing is useful in many other fields of study.

In computer science, it is a valuable for reinforcing a modular approach to coding and debugging. Students can learn to test parts of their program by comparing actual and expected outputs.

When learning electronics, it is useful for students to treat the basic components as ‘black boxes’, especially when they lack sufficient physics to understand the function of, say, a transistor. Complex components, such as a 555 timer, can be thought of initially as black boxes, and then eventually revealed to be comprised of smaller fundamental black boxes.

However, one clear disadvantage is that the success of these activities depends on a student’s understanding of some aspect of physics. It might be argued that all the card games and chess games also carry some assumption of the student’s ability to construct patterns. However, pattern recognition seems to be a far more universal skill than grasping the subtleties of a physical model.

As with all these analogies, they will be closer to actual scientific inquiry if you resist showing students the ‘correct answer’. This may cause a riot, but maintains philosophical standards.

Fermilab’s ‘Hypothesis’ Card Game

As part of their 1998 ‘ARISE‘ program (American Renaissance In Science Education), Fermilab advocated that ‘the three sciences’ should not be taught separately, as is often supposed.[4] They made a case for teaching physics first, then chemistry, and finally biology; moving from the simply to the complex.

In the teaching materials for biology, they introduced the ‘Hypothesis’ Card Game.[5]

Meta-Rules

  • There are two players: a ‘Scientist‘ and ‘Nature’.
  • The Scientist‘s goal is to discover Nature’s Law. Nature has no goal.
  • Each player has their own deck of playing cards. It is useful if the decks have different coloured backs, so they are easier to separate if mixed up.
  • Remove the Queens, Kings and Jokers, leaving each player with 44 cards.
  • The numbered cards carry their value, Aces are ‘1’, Jacks are ‘0’.
  • Nature must shuffle their deck of cards, and keep it concealed from the Scientist at all times.
  • Nature is provided with a ‘Nature’s Law‘ card (see below) and they must learn how to correctly follow the pattern on the card (else the game becomes very hard for the Scientist!).
  • Nature must never talk to the Scientist, especially to provide any clue about Nature’s Law.
  • The game begins with the Scientist playing a card of their choice from their deck. In response, Nature plays a card from their deck that agrees with the pattern written on the Nature’s Law card.
  • If Nature cannot play a card that fits the Nature’s Law, they should play a card face down to indicate ‘no data‘. For instance, if the rule is ‘add two’, and a 9 is played, there is no card that fits this rule.
  • Nature may replay a card from the table if they runs out of cards that fit the pattern.
  • This repeats, with the Scientist playing first, and Nature second. The player place their cards in two opposing rows (see below).
  • When the Scientist thinks that they have discovered a pattern, they should write an understandable, concise ‘Hypothesis’ on a card provided.
  • The Scientist is then required to test their Hypothesis by laying out three more cards while predicting what Nature will play.
  • If the Hypothesis is falsified by experiment, they classify it as false, and continue to try to find a new pattern that fits the data.
  • If the Hypothesis successfully predicts the new data, the scientist can attempt more tests if they wish. Three or more successful tests in a row is sufficient to end the game.
  • A new game begins with a Nature’s Law card. Nature does not reveal if the Scientist was correct! The players may swap roles if they wish.

Suggestions for ‘Nature’s Laws’

Easy

  • Match the number. Play any colour.
  • Match the number and colour.
  • Always add two to the number; always play red cards.
  • Play black on even numbers, red on odd.
  • Always make the sum of their card and your card equal to eight.

Medium Difficulty

  • If their number is five or larger, subtract one; if less than five, add one.
  • Always make the sum of their card and yours an even number.
  • Play spade on diamonds; club on hearts; heart on clubs; and diamond on spades.
  • If their number is: 0, 1, or 2 – play hearts; 3, 4, or 5 – play diamonds; 6, 7, or 8 – play clubs; 9 or 10 – play spades.

Difficult

  • If they play: black, you play 7 or higher; hearts, play 4, 5, or 6; diamonds, you play 3 or less.
  • Play any card and then tap your foot lightly as many times as his number is (don’t give it away!)
  • Play a card face down on their first card. Then on the next card, play a card that is one lower than their first card. Keep this pattern up, always playing on each new card by reacting to the previous card.

The creator of the game even suggest that you might include the rule: “The pattern is, there is no pattern! Always play the top card in your hand no matter what the Scientist plays.”

Analysis

  • This great game corrects the problem with ‘Trainee Demiurge’ games, while maintaining a focus on fundamental physics.
  • The call and response aspect to the game also allows for a discussion about Hume’s problems of Induction and Causation.
  • The wild suggestion that you occasional play with no pattern offers discussion about our assumption that there are objective Laws of Nature.
  • The more difficult games allows for discussion about our assumptions that the laws of nature are time and space invariant.

References

[1] http://humanistgrid.net/guu/science.htm by the RDF and BHA [Accessed 2012/03/03]

[2] Martin, M. (1972) ‘Concepts of Science Education’ Glenview, IL: Scott, Foresman and Company pp 16-17

[3] De Bono, Edward (1991) ‘Practical Thinking’  Penguin Books, New Edition p 21 onwards

[4] http://ed.fnal.gov/arise/guide.html

[5] http://ed.fnal.gov/arise/guides/bio/1-Scientific%20Method/1d-HypothesisCardGame.pdf Game invented by John Chamberlain at Fermilab’s Education Office

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