Problem Solving and Reasoning Flashcards
_____ is useful because it provides a means of communication which is powerful, concise and unambiguous
Mathematics
sophisticated capacity for logical thought and actions, such as analyzing, proving, evaluating, explaining, inferring, justifying, and generalizing.
reasoning
is the process of using existing knowledge to draw conclusions, make predictions, or construct explanations.
reasoning
- 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.
inductive reasoning
______ is a conclusion or proposition which is considered to be true due to some preliminary evidences
conjectures
- sometimes referred to as top-down logic. It starts with a general case and deduces specific instances.
- ______ includes hypothesis and conclusion
Deductive reasoning
_____ is the statement which is accepted or known at the beginning
hypothesis
_______ is a statement usually drawn from the hypothesis
conclusion
- Observation based.
- Specific -> General
- Conclusion may not be valid.
- Used to form hypotheses.
- Draws general principle from specific instances.
- always involves uncertainty
Inductive reasoning
- Theory based.
- General -> Specific
- Conclusions are correct and valid.
- Used to prove ideas.
- Draws specific conclusions from general principles.
- Certain and true
deductive reasoning
the ability to understand something instinctively without the need for conscious reasoning or without having an actual evidence of it.
intuition
an argument that convinces other people that something is true
mathematical proof
a conclusion or outcome that is beyond doubt.
certainty
This refers to mathematical tasks that have the potential to provide intellectual challenges for enhancing mathematical understanding and development.
problem-solving
Who formulated the steps for problem-solving?
George Polya (1887 - 1985)
3 basic functions of problem-solving
1) Seeking information
2) Generating new knowledge
3) Making decisions
4 stages of problem-solving according to Polya
1) Understanding the problem
2) Devising a plan
3) Carrying out the plan
4) Looking back
4 problem-solving strategies?
- guess
- act it out
- draw
- make a list
- 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
Guess and Check
- slightly more sophisticated than guess and check.
- The idea is that you use your first incorrect guess to make an improved next guess
Guess and improve
- 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.
Act it Out
- 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.
Use equipment
- 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
Draw a Picture/Model
- 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
Draw a diagram
