Problem Solving And Reasoning Flashcards
it is the process of reaching a general conclusion by examining specific examples.
Inductive reasoning
Inductive reasoning is the process of reaching a general conlusion by examining specific _________
Examples
It is the process of reaching a conclusion by applying general assumptions, procedures, or principles.
Deductive reasoning
Deductive reasoning is the process of reaching a conclusion by applying general __________, ________, or ________.
assumptions, procedures, or principles.
Logic is not the study of ________and __________ rhetorical devices
persuasion
Manipulative
‘______________’ does not mean persuasive argument
Successful Arguement
Human fallibility and manipulative rhetoric lead people to:
- accept poor reasoning
- reject good reasoning
Remember, in a successful argument if the premises are true, then the conclusion is either guaranteed to be _____or likely to be _____
true
The science of correct reasoning.
Logic
The drawing of inferences or conclusions from known or assumed facts.
Reasoning
It can either be inductive or deductive.
Reasoning
It uses facts, rules, definitions or properties to arrive at a conclusion.
deductive reasoning
it uses patterns to arrive at a conclusion (conjecture)
inductive reasoning
In Deductive Reasoning,
TRUE PREMISE + TRUE PREMISE =
TRUE CONCLUSION
In Inductive Reasoning,
TRUE PREMISE + TRUE PREMISE =
PROBABLY TRUE CONCLUSION
Inductive or Deductive Reasoning?
You are a good student.
You get 90+.
Therefore your friends must get all 90+ too.
INDUCTIVE
Inductive or Deductive Reasoning?
Ninety percent of humans are right handed.
Edryshe is human, therefore Edryshe is right handed.
DEDUCTIVE
Inductive or Deductive Reasoning?
What is the measure of angle x?
DEDUCTIVE
Inductive or Deductive Reasoning?
Geometry example…
What is the next figure in the sequence?
INDUCTIVE
Inductive or Deductive Reasoning?
All oranges are fruits.
All fruits grow on trees.
Therefore, all oranges grow on trees.
DEDUCTIVE
Inductive or Deductive Reasoning?
Diding hails from Visayas and Visayans are accented in their mother tongue when they speak English.
Therefore, Diding is accented.
INDUCTIVE
Inductive or Deductive Reasoning?
Argument 1: The sum of two odd integers is an even number.
m and n are odd integers
Thus, m + n is even.
DEDUCTIVE
Argument 1 uses the deductive form of reasoning in drawing a specific
statement from a general principle.
Inductive or Deductive Reasoning?
Argument 2: 3 + 5 = 8, 7 + 11 = 18, and 9 + 21 = 30
Therefore, the sum of two odd integers is even.
INDUCTIVE
As can be observed, the premise consists of specific cases while the
conclusion is just a generalization of what is claimed in the premise.
POLYA’S PROBLEM - SOLVING STRATEGY
One of the recent mathematicians who outlined a strategy for solving
problems from virtually any discipline is ___________(1887 – 1985).
George Polya
George Polya Year
(1887 – 1985).
In his book, “_____________”
“How to Solve It”
A great _____ solves a great _________ but there is a grain of _______ in the __________ of any problem.
Your problem may be __________ ; but it challenges your ________ and brings into play your inventive _______ , and if you solve it by your own means, you may experience the __________ and triumph of ______.”
discovery
problem
discovery
solution
modest
curiosity
faculties
tension
discovery
Father of problem-solving.
George Polya
POLYA’S FOUR - STEP PROBLEM - SOLVING STRATEGY
- Understand the problem
- Devise a plan
- Carry out the plan
- Review the solution
POLYA’S FOUR - STEP PROBLEM - SOLVING STRATEGY
This part of the problem-solving is sometimes (if not always) neglected.
In order to solve a problem, one must first know what is being asked, and what information or data can be extracted from what is given.
You can state the problem in your own words.
Understand the problem
POLYA’S FOUR - STEP PROBLEM - SOLVING STRATEGY
Think of strategies to solve the problem.
- listing, tabulating
- drawing a diagram
- guessing then proving if your answers (guesses) are correct
Devise a plan
POLYA’S FOUR - STEP PROBLEM - SOLVING STRATEGY
Implementing the strategy chosen (in the second step) until the problem is solved.
Carry out the plan
POLYA’S FOUR - STEP PROBLEM - SOLVING STRATEGY
Counter checking if your answers are correct.
Review the solution
