PROBLEM SOLVING AND REASONING

Question 1

The two (2) fundamental types of mathematical reasoning

Answer 1

Inductive and Deductive reasoning

Question 2

It refers to the process of taking information gathered from general observations and making specific decisions based on that information; In other words, from general to specific ideas

Answer 2

Deductive reasoning

Question 2

It refers to the process of making generalized decisions after observing, and/or witnessing, repeated specific instances of something; In other words, from specific to general ideas

Answer 2

Inductive reasoning

Question 3

is the ability to understand something instinctively, without the need for conscious reasoning

Answer 3

Intuition

Question 4

is an inferential argument for a mathematical statement

Answer 4

Proof

Question 5

is an argument which convinces other people that something is
true

Answer 5

Mathematical proof

Question 6

total continuity and validity; a conclusion or outcome that is beyond doubt

Answer 6

Certainty

Question 7

the Father of Modern Problem Solving

Answer 7

George Polya

Question 8

Polya’s four steps to problem solving

Answer 8

Preparation, Thinking Time, Insight, Verification

Question 9

first step of problem solving where we try to understand the problem.

Answer 9

Preparation

Question 10

a step of problem solving where we devise a plan for the problem

Answer 10

Thinking Time

Question 11

a step of problem solving where we carry out the plan we devised

Answer 11

Insight

Question 12

last step of problem solving where we look back at the problem, plan and answer to verify if it’s correct beyond doubt

Answer 12

Verification

Question 12

Common problem solving strategies

Answer 12

Guess-and-check, Act out the Problem, Draw the problem, List and Tabulate

Question 13

a classic technique; It may not be very efficient or reliable, sometimes it’s all one has to work with.

Answer 13

Guess-and-check technique

Question 14

slightly more sophisticated means developed to a high
degree of complexity

Answer 14

Guess-and-improve

Question 15

is an effective strategy for demonstration purpose and have a grip problem on hand.

Answer 15

Act-It-Out

Question 16

pictures, Venn diagrams, sketches, maps, and other representations help solve mathematical problems, well as problems in mechanics (physics).

Answer 16

Draw

Question 17

helps discover hidden hints towards solutions to some problems.

Answer 17

List and Tables

Question 18

show how things are connected, how things work and how group of objects in same way

Answer 18

Patterns

Question 19

is a previous statement or proposition from which another is inferred or follows as a conclusion

Answer 19

Premise