Problem Solving and Reasoning Flashcards

1
Q

_____ is useful because it provides a means of communication which is powerful, concise and unambiguous

A

Mathematics

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2
Q

sophisticated capacity for logical thought and actions, such as analyzing, proving, evaluating, explaining, inferring, justifying, and generalizing.

A

reasoning

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3
Q

is the process of using existing knowledge to draw conclusions, make predictions, or construct explanations.

A

reasoning

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4
Q
  • is a reasoning from specific case or cases to derive a general rule. It is sometimes referred to as bottom-up logic. It draws inferences from observations to make generalizations.
  • types of _____ includes the use of visual patterns, number patterns and conjectures.
A

inductive reasoning

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5
Q

______ is a conclusion or proposition which is considered to be true due to some preliminary evidences

A

conjectures

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6
Q
  • sometimes referred to as top-down logic. It starts with a general case and deduces specific instances.
  • ______ includes hypothesis and conclusion
A

Deductive reasoning

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7
Q

_____ is the statement which is accepted or known at the beginning

A

hypothesis

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8
Q

_______ is a statement usually drawn from the hypothesis

A

conclusion

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9
Q
  • Observation based.
  • Specific -> General
  • Conclusion may not be valid.
  • Used to form hypotheses.
  • Draws general principle from specific instances.
  • always involves uncertainty
A

Inductive reasoning

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10
Q
  • Theory based.
  • General -> Specific
  • Conclusions are correct and valid.
  • Used to prove ideas.
  • Draws specific conclusions from general principles.
  • Certain and true
A

deductive reasoning

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11
Q

the ability to understand something instinctively without the need for conscious reasoning or without having an actual evidence of it.

A

intuition

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12
Q

an argument that convinces other people that something is true

A

mathematical proof

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13
Q

a conclusion or outcome that is beyond doubt.

A

certainty

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14
Q

This refers to mathematical tasks that have the potential to provide intellectual challenges for enhancing mathematical understanding and development.

A

problem-solving

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15
Q

Who formulated the steps for problem-solving?

A

George Polya (1887 - 1985)

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16
Q

3 basic functions of problem-solving

A

1) Seeking information
2) Generating new knowledge
3) Making decisions

17
Q

4 stages of problem-solving according to Polya

A

1) Understanding the problem
2) Devising a plan
3) Carrying out the plan
4) Looking back

18
Q

4 problem-solving strategies?

A
  • guess
  • act it out
  • draw
  • make a list
19
Q
  • one of the simplest strategies.
  • guess the answer to a problem and then check if the answer fits the given scenario.
  • 3-step-approach: Guess –> Check –> Repeat if needed
A

Guess and Check

20
Q
  • slightly more sophisticated than guess and check.
  • The idea is that you use your first incorrect guess to make an improved next guess
A

Guess and improve

21
Q
  • a strategy in which students physically act out what is taking place in a word problem.
  • is an effective strategy for demonstration purposes in front of the whole class.
A

Act it Out

22
Q
  • is a strategy related to Act it Out.
  • any object that can be used in some way to represent the situation the students are trying to solve, is equipment.
A

Use equipment

23
Q
  • is a problem-solving technique in which students make a visual representation of the problem.
  • use the draw a picture strategy to solve problems involving space or organization, but it can be applied to almost all math problems
A

Draw a Picture/Model

24
Q
  • a graphic design that explains rather than represents.
  • a line drawing made for mathematical or scientific purposes.
  • a drawing that shows the different parts of something and how they work together
A

Draw a diagram

25
Q
  • is a way to organize data presented in a problem.
  • problem solving strategy allows students to discover relationships and patterns among data.
  • helps students to bring a logical and systematic development to their mathematics.
A

Make a List/Table

26
Q
  • refers to any game, puzzle, or activity that teaches math skills.
  • range from riddles, puzzles, brain-teasers and games carried out for recreational or leisure rather than as research or application-based professional activity.
A

Recreational Math

27
Q

Examples are: monopoly, number of card games, tangrams, rubik’s cube, magic squares, fractals, logic puzzles and mathematical chess problems, ken-ken puzzle, and etc.

A

Recreational Math