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| ==Reasoning and Education== | ==Reasoning and Education== | ||
| Deductive reasoning is generally thought of as a skill that develops without any formal teaching or training. As a result of this belief, deductive skills are not taught in secondary schools, where students are expected to use reasoning more often and at a higher level.<ref>{{cite journal|last=Stylianides|first=G. J.|coauthors=Stylianides|title=A. J.|journal=Mathematical Thinking and Learning|year=2008|volume=10|issue=2|pages=103-133|doi=10.1080/10986060701854425|accessdate=04/23/2012}}</ref> For example, students have an abrupt introduction to ] – which heavily relies on deductive reasoning – in high school. |
Deductive reasoning is generally thought of as a skill that develops without any formal teaching or training. As a result of this belief, deductive skills are not taught in secondary schools, where students are expected to use reasoning more often and at a higher level.<ref>{{cite journal|last=Stylianides|first=G. J.|coauthors=Stylianides|title=A. J.|journal=Mathematical Thinking and Learning|year=2008|volume=10|issue=2|pages=103-133|doi=10.1080/10986060701854425|accessdate=04/23/2012}}</ref> For example, students have an abrupt introduction to ] – which heavily relies on deductive reasoning – in high school. | ||
| In addition, an increase in deduction skills will benefit those students who plan on continuing into higher education. Deductive reasoning is a central component to many scholarly disciplines and is often fundamental to success in many professional activities.<ref>{{cite journal|last=Leighton|first=J. P.|title=Teaching and assessing deductive reasoning skills|journal=Journal of Experimental Education|year=2006|volume=74|issue=2|pages=109-136|doi=10.3200/JEXE.74.2.107-136|accessdate=4/23/2012}}</ref> | |||
| One efficient and guaranteed to succeed method that is being used to apply Piaget’s theory is utilizing the power of vision, and understanding the role it plays in reasoning. Educational software is being built to interact with the students visually, and take them on a step by step explanation to the answer of the problem, so that the students can deduce how they can get from one step to the next. Through the use of such resources, like a three dimensional drawing and analyzing software, a student can create something so intricate and so revolutionary with just a few permutations and combinations of the tools provided in it. The field of computer programming is another great example that illustrates the use of deductive reasoning. It is often so hard to learn because humans usually use inductive reasoning but computers always use deductive reasoning. They follow a set of rules and always abide by them. | |||
| Thus, by observing the evolution of deductive reasoning through historical events, the fact that this gift will continue to play a major role in our future is hardly a difficult deduction. One area which exemplifies this method as an excellent tool is forensic science, in which it aids profilers and investigators in solving crimes. To reap its benefits as time goes on, in a project managed by Intel, students will delve into the world of criminal investigation. “They will engage in deductive reasoning activities and practice math and science forensics labs. Then, using the scientific inquiry process, they will collect clues, test and analyze evidence, and draw conclusions to solve the crime.”<ref>{{cite web|title=Designing Effective Projects : Project-Based Units to Engage Students|url=http://www97.intel.com/en/ProjectDesign/UnitPlanIndex/Forensics/|publisher=Intel|accessdate=04 May 2012}}</ref> | |||
| ==See also== | ==See also== | ||
Revision as of 03:36, 6 May 2012
Deductive reasoning, also called deductive logic, is the process of reasoning from one or more general statements regarding what is known to reach a logically certain conclusion. Deductive reasoning involves using given true premises to reach a conclusion that is also true. Deductive reasoning contrasts with inductive reasoning in that a specific conclusion is arrived at from a general principle. If the rules and logic of deduction are followed, this procedure ensures an accurate conclusion.
An example of a deductive argument:
- All men are mortal.
- Socrates is a man.
- Therefore, Socrates is mortal.
The first premise states that all objects classified as "men" have the attribute "mortal". The second premise states that "Socrates" is classified as a "man" – a member of the set "men". The conclusion then states that "Socrates" must be "mortal" because he inherits this attribute from his classification as a "man".
Deductive reasoning moves from theory to observations or findings. So, in the above example, the theory is that "all men are mortal" and the observation is that "Socrates is a man". So, the conclusion can be made that "Socrates is mortal".
Law of Detachment
The law of detachment is the first form of deductive reasoning. A single conditional statement is made, and a hypothesis (P) is stated. The conclusion (Q) is then deduced from the statement and the hypothesis. The most basic form is listed below:
- P→Q (conditional statement)
- P (hypothesis stated)
- Q (conclusion deduced)
In deductive reasoning, we can conclude Q from P by using the law of detachment. However, if the conclusion (Q) is given instead of the hypothesis (P) then there is no valid conclusion.
The following is an example of an argument using the law of detachment in the form of an if-then statement:
- If an angle A>90°, then A is an obtuse angle.
- A=120°
- A is an obtuse angle.
Since the measurement of angle A is greater than 90°, we can deduce that A is an obtuse angle.
Law of Syllogism
The law of syllogism takes two conditional statements and forms a conclusion by combining the hypothesis of one statement with the conclusion of another. Here is the general form, with the true premise P:
- P→Q
- Q→R
- Therefore, P→R.
The following is an example:
- If Larry is sick, then he will be absent from school.
- If Larry is absent, then he will miss his classwork.
- If Larry is sick, then he will miss his classwork.
We deduced the final statement by combining the hypothesis of the first statement with the conclusion of the second statement. We also conclude that this could be a false statement.
Deductive Logic: Validity and Soundness
Deductive arguments are evaluated in terms of their validity and soundness. It is possible to have a deductive argument that is logically valid but is not sound.
An argument is valid if it is impossible for its premises to be true while its conclusion is false. In other words, the conclusion must be true if the premises, whatever they may be, are true. An argument can be valid even though the premises are false.
An argument is sound if it is valid and the premises are true.
The following is an example of an argument that is valid, but not sound:
- Everyone who eats steak is a quarterback.
- John eats steak.
- Therefore, John is a quarterback.
The example's first premise is false – there are people who eat steak and are not quarterbacks – but the conclusion must be true, so long as the premises are true (i.e. it is impossible for the premises to be true and the conclusion false). Therefore the argument is valid, but not sound.
In this example, the first statement uses categorical reasoning, saying that all steak-eaters are definitely quarterbacks. This theory of deductive reasoning – also known as term logic – was developed by Aristotle, but was superseded by propositional (sentential) logic and predicate logic.
Deductive reasoning can be contrasted with inductive reasoning, in regards to validity and soundness. In cases of inductive reasoning, even though the premises are true and the argument is "valid", it is possible for the conclusion to be false (determined to be false with a counterexample or other means).
Hume's Skepticism
See also: Problem of inductionPhilosopher David Hume presented grounds to doubt deduction by questioning induction. Hume's problem of induction starts by suggesting that the use of even the simplest forms of induction simply cannot be justified by inductive reasoning itself. Moreover, induction cannot be justified by deduction either. Therefore, induction cannot be justified rationally. Consequently, if induction is not yet justified, then deduction seems to be left to rationally justify itself – an objectionable conclusion to Hume.
Hume did not provide a strictly rational solution per se. He simply explained that we do induce, and that it is useful that we do so, but not necessarily justified. Certainly we must appeal to first principles of some kind, including laws of thought.
Reasoning and Education
Deductive reasoning is generally thought of as a skill that develops without any formal teaching or training. As a result of this belief, deductive skills are not taught in secondary schools, where students are expected to use reasoning more often and at a higher level. For example, students have an abrupt introduction to mathematical proofs – which heavily relies on deductive reasoning – in high school.
See also
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References
- Sternberg, R. J. (2009). Cognitive Psychology. Belmont, CA: Wadsworth. p. 578. ISBN 978-0-495-50629-4.
- Guide to Logic
- Stylianides, G. J. (2008). "A. J.". Mathematical Thinking and Learning. 10 (2): 103–133. doi:10.1080/10986060701854425.
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Further reading
- Vincent F. Hendricks, Thought 2 Talk: A Crash Course in Reflection and Expression, New York: Automatic Press / VIP, 2005, ISBN 87-991013-7-8
- Philip Johnson-Laird, Ruth M. J. Byrne, Deduction, Psychology Press 1991, ISBN 978-0-86377-149-1jiii
- Zarefsky, David, Argumentation: The Study of Effective Reasoning Parts I and II, The Teaching Company 2002
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