Deductive and Inductive Reasoning EQ: What clues indicate deductive and inductive reasoning? Sherlock – a study in pink season 1, episode 1, 24:00 minutes- 30:00 min 

What is inductive reasoning and what is deductive reasoning? Come up with an example of each from your own life.

Reasonable Assumptions? Gym class makes students sweat. Randall takes gym class. Therefore, Randall is ________________. Pink is a popular color for girls. Susan is a girl. Therefore, Susan ___________.

Reasonable Assumptions? 2, 4, 6, ________ red, blue, green, red, blue, _______

Conclusion BROAD SPECIFIC Deductive Reasoning Deductive reasoning is a way of making an argument where a general statement, rule, or principle is used to support specific statements All humans are mortal. John Smith is human. Therefore, John Smith is mortal. Premise Conclusion BROAD SPECIFIC Think of Deductive as: All for One!

DEDUCTIVE REASONING To use the deductive reasoning process you will: Identify specific examples to support a broad/general statement, rule, or principle. Deductive reasoning is used: A.) Also when your teacher presents the Theory of Plate Tectonics in Science and you have to prove or “support” the theory through activities. You are using deductive reasoning.

DEDUCTIVE REASONING: STEPS IN THE PROCESS 1. Identify the generalization(s) that apply to the situation. 2. Identify the reasons that have to be in place for that generalization. 3. Then, identify the things that must be true based on the generalization(s). NOTE: If the information in the premise is true and the reasoning is valid, the conclusions must be true.

DEDUCTIVE REASONING: Example Emily said, “That's Newton's Law. Everything that goes up must come down. And so, if you kick the ball up, it must come down.” Emily is using deductive reasoning arguing from the law of gravity. Emily’s argument is clearly from the general (the law of gravity) to the specific (this kick). Emily’s deductive argument is supported by her reference to the law of gravity. Emily could provide additional support by discussing Newton’s law even if Emily herself had never seen a ball kicked.

Assessment Prompt 1: 1. Which of the following arguments would lead to a deductive conclusion? A. There was a mild winter this year, and previously whenever there’s been a mild winter the cherry crop suffers. B. The cherry crop needs at least a week of freezing temperatures for best results, and this winter the temperature stayed several degrees above freezing. C. Marshall noticed that whenever the skiing was good in winter, the cherry crops was profitable, and this year the skiing was good. D. Not since 1972 have I seen a good cherry crop after a mild winter, and this winter has been mild. THE CORRECT ANSWER IS!!! Although the premise about this year is based on observation, the general or “major” premise, “The cherry crop needs at least a week of freezing temperature,” seems to be an assertion of established principle, making this a deductive argument with the conclusion, “The results won’t be best this year.” 9

General Theory/Hypothesis Specific Observations Inductive Reasoning: Inductive reasoning is a way of using general trends and observations to make a broad rule. Observation 1 Observation 2 Observation 3 General Theory/Hypothesis Specific Observations Think of Inductive as: One for All! 10

Inductive Reasoning To use Inductive Reasoning you will: Inferring generalizations from information or observations. Inductive reasoning is used: In elementary schools, when you studied patterns and predicted what the next would be, you were using inductive reasoning. When you make predictions as you read, you are using inductive reasoning. And in Science when you develop a hypothesis based on lab observations, you are using inductive reasoning).

INDUCTIVE REASONING: STEPS IN THE PROCESS Focus on specific pieces of information or observations. Look for patterns or connections in the identified information. Make a general statement that explains the observed patterns. Make additional observations NOTE: Even if the information used to reach a conclusion is true and the reasoning valid, the conclusions may or may not be true.

Example: Jalen said, “I've noticed previously that every time I kick a ball up, it comes back down, so I guess this next time when I kick it up, it will come back down, too.” Jalen is using inductive reasoning - arguing from observation. Jalen’s argument is from the specific (each individual instance he observed the ball being kicked up and coming back down) to the general (the assertion/prediction that a similar even will result in a similar outcome in the future). Jalen’s inductive argument is supported by this previous observations.

Specific Observations The event is a surprise birthday party. A cake with sixteen candles lit up the room. All the guests were wearing party hats. When Shelley opened the door, they all shouted, “Surprise!” The event is a surprise birthday party. 14

Assessment Prompt 2: 2. Which of the following claims would be best expressed by inductive reasoning? A. Your first quiz grade usually indicates how you will do in the course. B. The final exam accounts for 30% of the course grade. C. Late papers will not be accepted. D. Gravity’s Rainbow is required reading in your course. THE CORRECT ANSWER IS!!! A Your first quiz grade usually indicates how you will do in the course. It is much more likely that this claim stems from personal observation than from adherence to some general principle, and so it would be best expressed by an inductive argument. 15

Smith owns only blue pants and brown pants Smith owns only blue pants and brown pants. Smith is wearing a pair of his pants today. So Smith is wearing either blue or brown pants today deductive

Inductive or Deductive? January has almost always been cold here in Siberia. Today is January 14th so it is going to be another cold day in Siberia. inductive 17

Inductive or Deductive? The soccer game is on either Thursday or Friday. I just found out that the game is not on Thursday, so the game must be on Friday. deductive 18

Inductive or Deductive? The local branch of Wachovia Bank was robbed yesterday. Jenny needed money to pay off her gambling debts. She just bought a gun two days ago, and I saw her hanging around the local Wachovia Bank yesterday morning. Today the bookie’s goons stopped looking for Jenny. So Jenny robbed Wachovia Bank yesterday. inductive 19

What are your interpretations? What are your observations about this scene? What are your interpretations? Mock Crime Scene: http://www.masss.gov