Deductive and Inductive Reasoning in Problem-Solving
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INDUCTION VS.
DEDUCTION
Solution
•
We know one (A, B or C) is defective by .1…so….
•
Weigh TWO ball-bearings from A and ONE from B.
•
If the combined weight is three ounces, then you know
that C is defective.
•
If the combined weight is 3.2 ounces, you know that A is
defective.
•
If the combined weight is 3.1 ounces, you know that B is
defective.
Induction
Inductive reasoning
•
Moves from specifics to a generalization (claim comes
last)
•
Conclusion is probable, but not certain
•
Flexible, but can be misapplied
Every Valentine’s Day in Cleveland’s recorded weather
data has been snowy. Therefore, it will snow this Valentine’s
Day in Cleveland. (probable)
All of the swans we have seen are white. Therefore, all
swans are white. (experiential, but nonetheless unreliable)
Inductive or Deductive reasoning?
Mrs. G. has worn jeans every Friday this school year. A student
concludes she will wear jeans this Friday to work.
The school has a policy that teachers must wear spirit shirts on
Friday. A student concludes that because Mrs. G. is employed by
the school, she will wear a spirit shirt on Friday.
I am eating at a vegetarian restaurant. I conclude all the dishes on
the menu are meatless.
After reading the entire menu I conclude all of the dishes on the
menu are meatless, it must be a vegetarian restaurant.
Deductive vs. Inductive development
DEDUCTIVE
•
Topic sentence/claim
•
Transition to contextualize
•
Subclaims and elaborations
•
Advantage: straightforward; conveys certainty and objectivity
INDUCTIVE
•
Statement of fact (not a claim)
•
Transition to contextualize
•
Subclaims and elaborations
•
Topic sentence/claim
•
Advantages: flexible; offers a likely way to interpret patterns
How is this deductive?
The district has announced a series of acceleration reforms, but
educational reform having a profound impact should be dodged as far as
possible for the sake of continuity and continuum of service
. Such reforms
impact not only teachers, but students, and parents. Teachers, in particular,
will be under great stress to reform curriculum and complete a large-scale
syllabus revision to convert a 4-year program into 3 years, as the district
proposes. Such a radical departure would also disrupt students. Studies
show that adopting new, compressed exam schedules con affect student
learning adversely. Finally, current data indicates that the economic burden
on parents would be heightened by shortening secondary education and
lengthening undergraduate programs, as college tuition is significantly
higher than secondary tuition.
How is this inductive?
The district has announced a series of acceleration reforms. That such
reforms will impact not only teachers, but students, and parents, is
inevitable. Teachers, in particular, will be under great stress to reform
curriculum and complete a large-scale syllabus revision to convert a 4-year
program into 3 years, as the district proposes. Such a radical departure
would also disrupt students. Studies show that adopting new, compressed
exam schedules con affect student learning adversely. Finally, current data
indicates that the economic burden on parents would be heightened by
shortening secondary education and lengthening undergraduate
programs, as college tuition is significantly higher than secondary tuition.
Therefore, without an irrefutable reason, such a drastic scheme must be
avoided
.
Induction example
•
From the ppt, choose a topic of interest to you.
•
Write an
inductive paragraph
that takes a stance/makes a claim
on whichever topic is the most interesting to you. You may have
to do some research to make this work.
Explore the differences between deduction and induction in problem-solving approaches. Deductive reasoning starts with a general statement and moves to specifics, offering certainty and objectivity, while inductive reasoning begins with specifics and arrives at a generalization, providing flexibility and likely interpretations of patterns. Examples and comparisons between the two reasoning styles are illustrated for better understanding.
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Presentation Transcript
INDUCTION VS. DEDUCTION C
Solution We know one (A, B or C) is defective by .1 so . Weigh TWO ball-bearings from A and ONE from B. If the combined weight is three ounces, then you know that C is defective. If the combined weight is 3.2 ounces, you know that A is defective. If the combined weight is 3.1 ounces, you know that B is defective.
Inductive reasoning Moves from specifics to a generalization (claim comes last) Conclusion is probable, but not certain Flexible, but can be misapplied Every Valentine s Day in Cleveland s recorded weather data has been snowy. Therefore, it will snow this Valentine s Day in Cleveland. (probable) All of the swans we have seen are white. Therefore, all swans are white. (experiential, but nonetheless unreliable)
Inductive or Deductive reasoning? Mrs. G. has worn jeans every Friday this school year. A student concludes she will wear jeans this Friday to work. The school has a policy that teachers must wear spirit shirts on Friday. A student concludes that because Mrs. G. is employed by the school, she will wear a spirit shirt on Friday. I am eating at a vegetarian restaurant. I conclude all the dishes on the menu are meatless. After reading the entire menu I conclude all of the dishes on the menu are meatless, it must be a vegetarian restaurant.
Deductive vs. Inductive development DEDUCTIVE Topic sentence/claim Transition to contextualize Subclaims and elaborations Advantage: straightforward; conveys certainty and objectivity INDUCTIVE Statement of fact (not a claim) Transition to contextualize Subclaims and elaborations Topic sentence/claim Advantages: flexible; offers a likely way to interpret patterns
How is this deductive? The district has announced a series of acceleration reforms, but educational reform having a profound impact should be dodged as far as possible for the sake of continuity and continuum of service. Such reforms impact not only teachers, but students, and parents. Teachers, in particular, will be under great stress to reform curriculum and complete a large-scale syllabus revision to convert a 4-year program into 3 years, as the district proposes. Such a radical departure would also disrupt students. Studies show that adopting new, compressed exam schedules con affect student learning adversely. Finally, current data indicates that the economic burden on parents would be heightened by shortening secondary education and lengthening undergraduate programs, as college tuition is significantly higher than secondary tuition.
How is this inductive? The district has announced a series of acceleration reforms. That such reforms will impact not only teachers, but students, and parents, is inevitable. Teachers, in particular, will be under great stress to reform curriculum and complete a large-scale syllabus revision to convert a 4-year program into 3 years, as the district proposes. Such a radical departure would also disrupt students. Studies show that adopting new, compressed exam schedules con affect student learning adversely. Finally, current data indicates that the economic burden on parents would be heightened by shortening secondary education and lengthening undergraduate programs, as college tuition is significantly higher than secondary tuition. Therefore, without an irrefutable reason, such a drastic scheme must be avoided.
Induction example From the ppt, choose a topic of interest to you. Write an inductive paragraph that takes a stance/makes a claim on whichever topic is the most interesting to you. You may have to do some research to make this work.
