Purpose:

This lesson plan is designed for use early in the FRINQ year in order to establish a mindset of looking for examples of deductive reasoning in the literature the students read and looking for fallacies in deductive reasoning. The anticipatory set could be conducted in a mentor session, but the body should be conducted in a whole class session.

Suggested follow-up: At least once per quarter, choose one of the readings assigned as part of your theme and insert some deductive reasoning questions (similar to the "Assignment for next class" below) into an existing writing assignment.

Goals:

1. To interpret one's own thinking in terms of deductive reasoning
2. To demonstrate the analysis of arguments in articles through basic principles of deductive reasoning

Photocopy the two attachments "Game instructions" and "Deductive reasoning" for distribution to each student in the class. To save paper, you may photocopy these back-to-back. Also bring materials for students to create posters.

Anticipatory Set:

Divide the class into groups of 4 or 5, hand out instructions to the game "Pico, Fermi, Bagels," and tell them to read and discuss the instructions and then play the game 3 or 4 times, choosing a new leader for each round (game instructions attached).

Body:

Instruct students to play the game again, but this time each player (other than the leader) is to write down what she/he is thinking at each step of the game. They are to repeat this process once or twice, choosing a new leader each time.

Ask each group to prepare a poster of one of the games they played, outlining the line of reasoning they followed and describing the point at which they knew the answer and describing why that had to be the answer. Hang the posters around the room and have each group explain its poster.

Ask students to read the Deductive Reasoning handout. Ask them to use the vocabulary of deductive reasoning to discuss in their group the reasoning they used in the game. In particular, they should write two or more syllogisms arising in the course of the game and add those to their poster.
 
 
 
 

Closing:

Discuss the assignment (which appears at the bottom of the Game Instructions handout), including the smoking and SIDS example. Point out that whether a premise is "hidden" may depend on context. For example, if the original quote came from an article about the dangers of smoking, then the "rewrite" is the implied hidden premise. If the original quote appeared in an article about SIDS which discussed other "risk factors" for SIDS, then the implied (valid) conclusion would be: "If you are trying to avoid a SIDS death, don't smoke near your baby."

Students may think that the two SIDS statements listed in the example are equivalent. Note the differences (depicted in the diagram below):

See bottom of Game Instruction page.

Post-assignment suggestions:

After students have completed this homework assignment, it will be helpful for them to share their results. Ask each group of 4 or 5 students to choose the most interesting example (valid or not valid) within their group and present it to the class.

Student assessment:

The posters demonstrate student success in the interpretation of their own thinking in terms of deductive reasoning if the posters include:

1. valid arguments supporting the game conclusion
2. a syllogism which is valid

1. reasonable possibilities for hidden premises are presented ("reasonable" may depend on context)
2. two syllogisms are presented, one valid and one invalid
3. sound reasons support the validity and invalidity of the two syllogisms

Success of this lesson will be demonstrated by student responses to the assignment which reasonably identify examples of correct deductive reasoning and examples of fallacious deductive reasoning.

Goal of the game: Guess the leader's secret 3-digit number.

1. Choose a leader; the leader picks a secret 3-digit number, whose digits are all different (for example 121, 442, 666 are not allowed). The leader writes the secret number on a slip of paper to refer to as the game progresses.
2. Players take turns making guesses; for each guess, the leader responds with the following clues:


BAGELS means none of the digits is correct

PICO means one of the digits is correct, but it is in the wrong place

FERMI means one of the digits is correct and in the correct place

Note that two or more correct digits requires several words:

"PICO PICO" means 2 digits are correct but neither is in the correct place.

"FERMI FERMI FERMI" means you have guessed the secret number.

3. Choose a new leader and play again.

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Assignment for next class: (We'll discuss this after completing today's activities.)

Find one or more articles in a newspaper or magazine that contain both valid and invalid deductive arguments. The premises will often be implicit rather than explicit. For example, the sentence

"Many SIDS cases occur in households where people smoke."

is written to make you think:

"Parents who smoke are likely to have their babies die of SIDS."

Write a description of at least one valid argument and at least one invalid argument, including the following:

1. Identify hidden premises.
2. Write a syllogism of the valid argument, and explain why it is valid.
3. Write a syllogism of the invalid argument, and explain why it is not valid.

Vocabulary

Argument series of statements that support claims within a logical structure

visible for study and review

argument (Note that an argument can be valid even when the premises are not true.

For example, what will occur if the game leader gives an incorrect

argument the argument is valid and the premises are true

Applications

A line of reasoning can be analyzed by rewriting it as a syllogism. For example:

Of course Tran is studying hard! He's taking a FRINQ class!

Written as a syllogism:

Premise: All FRINQ students study hard.

Premise: Tran is taking a FRINQ class.

Conclusion: Tran studies hard.

Note that the original statement contains a hidden premise:

The following syllogism has true premises but is not valid. (Why?)

Premise: If a student is in FRINQ, then he/she is required to write a lot.

Premise: Maria writes a lot.

Conclusion: Maria is in FRINQ.