10+Philosophy+-+reason,+rationality+&+science


 * Year 10 Philosophy: Reason, Rationality and Science**

Students take 5 question rationality test. (See Appendix A) Remainder of class. The test will be conducted anonymously. The aim is not to score the students or show who won. The aim is simply to collect data to use for the analysis which will take place in later classes.
 * Lesson 1:**

Opening question: ‘What is rationality?’ Sub-questions: ‘Are we rational?’ ‘Why would we be?’ 20-25mins

Go through results of the test. This will take up to 3 lessons.
 * Homework** for Ego: Do you think you are rational and why? (1/2 page – 1 page)
 * Lesson 2:**

Question 1: Half the class will have had the test with the quote attributed to Thomas Jefferson, and the other half will have had the test with it attributed to Adolf Hitler (they both said it).

Results of the question will be shown on the board. E.g. Students who had Jefferson were 70% agree / 30% disagree, while those who had Hitler did 10% agree / 90% disagree or whatever. Though the students may have discussed the test amongst themselves already, they otherwise won’t yet know the point of this question.

One student who circled ‘agree’ to offer their reasoning to the class, and one student who circled ‘disagree’ to offer up theirs. Other students may then contribute to the discussion.

The key point of course is to discuss how we can maintain an insistence that we analysed the statement rationally when our view of the content was clearly skewed by our impression of the speaker. Approx 25mins to this point.

Question 2: Again results will be put up on board in a ’12 (or 7, 15 etc) students picked ‘A’, and 12 students picked ‘B’ form’.

Again, students will be asked to offer up their reasoning. A short debate shall be allowed to see if anyone can get the correct answer with correct reason.

This question has a correct answer which is A. The reason this is so, is that B is a subset of A, so the probability of A occurring must be greater. This will be explained, and questions taken. Rest of class.

Test analysis continued.
 * Lesson 3:**

Question 2 will be finished off in the first 10 mins if it wasn’t finished properly in the last class.

Question 3: As ridiculous as this sounds, many students will get this incorrect. The answer is 22. Many students will be amazed that they answered it incorrectly as they would have assumed that the question was a ridiculous gimmie.

The key question for discussion will be to ask the students “Why?”

The class will be asked for some ideas as to why so many got it wrong. The key question to posit is; “What does this say about how we read?” Some new theories might be proffered when informed that native speakers of English do WORSE on this question than non-native speakers. There is no definite explanation to this problem. Key theories include the fact that we read “f’s” as “v’s”, and also that native speakers read whole words and don’t analyse individual letters. Approx 30mins to here.

Question 4: Like questions 2 & 3, this does have a correct answer. Again, it is 22. Many students will have answered 183 (365/2 rounded up). Before giving the students the answer, again it will be interesting to hear the logic of the students who are willing to defend the reasoning of their particular answers. The specific reasoning for the answer obviously relies on probability theory a long way beyond the students’ capability, so there will be not much more to be said after the answer is given and a general explanation given for the reason. It will give them a very good intro to the concepts behind the topic of combinations and permutations they will study in later mathematics. Rest of class.

Test analysis continued:
 * Lesson 4:**

Question 5: This is the classic Prisoners dilemma, and will introduce them to the important idea of the Cancellation Principle in logic. This does surprisingly have a correct answer (sort of). Whatever the friend does, the subject will be better off by confessing. This will be demonstrated to the class graphically. The point for them to understand is that they should not be trying to guess what the friend will do, because it doesn’t affect what they should do. Some students will remain unconvinced, and may be right to do so, depending on their reasons (they need to assume that the welfare of their friend is a consideration that in itself warrants personal detriment. They are wrong to not confess on the grounds of trust in the friend. They also need to recognize an assumption – that their partner was offered the same deal).

This should lead to a very interesting class discussion. Should the discussion be about morals and ideas about ‘right and wrong’, I will let it go for a while but soon bring it back to the idea of the Cancellation Principle.

If time allows, students will be asked to offer up some examples they can think of in their everyday life where the Cancellation Principle would be of use. Other students will critique the examples, and conclusions can be reached regarding whether it was a sound example of the Cancellation Principle. Whole class

Go back to original questions in Lesson 1: ‘Are we rational?’
 * Lesson 5:**

Who has changed their mind and why. 15mins
 * Homework (to do in class):** ½ page review/reassessment of what you wrote earlier in Ego.

//Introduction to logic://
 * Lesson 6:**

A is heavier than B. B is heavier than C. Is A heavier than C? [Yes] 5mins Hopefully most/all of the class say ‘Yes’. One student to explain.

A is faster than B 100% of the time. B is faster than C 100% of the time. Is A faster than C 100% of the time. [Yes]

Same as first question. Answer is yes. Same reason. Student to explain. 5mins.

A is faster than B 60% of the time. B is faster than C 60% of the time. Is A faster than C at least 60% of the time?

Students will be asked to explain. Most will say yes. Answer is No. Can anyone get it? If no-one gets it in 10 mins, I’ll explain. Some still won’t believe it. Can they explain why not? Rest of class. Problem distributed to class: Blue/green taxi problem In Univille, 80% of the taxis are blue, and 20% are green. One night Mark witnesses a crime, and sees what he believes to be a green cab speeding from the scene. He is the only witness. Mark’s eyes are tested and it’s found out his identification is correct 80% of the time with respect to both blue and green taxis. What are the odds that the taxi was green?
 * Lesson 7:**

Students take 5-10 minutes to answer the problem by themselves. 10mins

Students get into groups of 3 or 4 to discuss answers and come up with a solution and reason in about 10 mins. Approx 20mins to here.

Each group representative to give explanation of their answer. Approx 30mins to here.

Teacher to give answer [50%] and explain reason – Bayes theorem. Rest of class.

Students to give problem to one other family member and bring back their answer and reasons.
 * Homework**: (results in Ego)

Continuation of Blue/green taxi problem:
 * Lesson 8:**

What were some of the answers that the family members came up with? 10mins

What do you now really believe the ‘true’ answer is? I.e. Have you been convinced? If not, why not? Approx 25mins to here.

Introduction into some areas of everyday life that this problem is evident in (AIDS testing etc). Approx 40mins to here.

Final thought (and if time, discussion): Juries. If we all (or at least everyone else) believe the answer is 80%, how can we present this information accurately, and in a way that people believe it?

New topic: //Motivation & Rewards//
 * Lesson 9:**

Question: How can we encourage kids to read more?

Class to discuss possible answers and their merits. I want to get onto the topic of rewards and the role they play in education. Some students will probably suggest setting up some reward scheme. Here, I want to analyze why they think this will help students read more. Approx 15mins to here.

Question: Do rewards work? Sub questions – How? What do they work at doing? Approx 30mins to here.

//Tale of the old man and the mean kids//: - One student to read An old man is continually being teased by a group of school kids who pass his house on the way to school everyday. The old man grew tired of the jeers and ridicule about his age, hunched back and baldness, and hit upon a brilliant scheme to stop the students: “Tomorrow I will give one dollar to anyone who comes back and teases me.” The students couldn’t believe their luck and were back earlier than ever the next morning with a fresh round of ridicule more hurtful than ever. True to his word, the old man ambled out and gave each boy a dollar. “Come back tomorrow, and I’ll give you 50 cents for your troubles.” The kids thought this was still pretty good and were back the next morning. After the usual heckling, the old man walked out and dutifully paid the students 50cents. “From now on,” he announced, “I can only give you 10 cents for doing this.” The kids looked at each other in disbelief. “10 cents!” one said, “you’re kidding?” mocked another, “forget it!” cried another. And they never came back again.

What had the old man done, and why did it work? Approx 40mins to here.

Back to question at start of lesson: How can we encourage kids to read more? Rest of class

Study at university of Illinois: 3 groups of 10y.o.’s asked to taste new fruit-flavoured yogurt drink. Group 1 were simply handed a full glass. Group 2 were praised for drinking (“Well done, you drank the whole thing” etc.) Group 3 were offered a free movie ticket for drinking the whole thing.
 * Lesson 10:**

Which group drank the most drink? [Groups 2&3 did drink more – the incentive had worked]

Which group liked the drink the most a week later? [Group 1 liked the drink just as much, and probably slightly more, a week later. Group 3, and even group 2, found it much less appealing]. Approx 10mins to here.

Pizza Hut in America had a popular food-for-reading program. What do you think happened? Do you think students read more? [Analysis finds that, yes, they did read more, but much shorter and simpler books, and they performed MUCH worse at answering questions about the books. The program would probably have encouraged reading much more effectively if they offered a free book for every pizza they ate! (and maybe helped them lose weight?!)]

Now class discussion on analogies in the students own education. Rest of class.

- grades, tests etc.
 * Possible Homework?:** reflection on the misuse of rewards in their own education.