Deductive methods
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[edit] Definition
Much like Sherlock Holmes, deductive methods involve beginning with a general concept or given rule and moving on to a more specific conclusion. Solving a math problem or conducting a science experiment is just like the mysteries presented by Sherlock Holmes. Clues are presented concerning the conclusion and using the information given as well as previous knowledge, you can solve the mystery!
Deductive reasoning is the process of reaching a conclusion that is guaranteed to follow, if the evidence provided is true and the reasoning used to reach the conclusion is correct. The conclusion also must be based only on the evidence previously provided; it cannot contain new information about the subject matter. Deductive reasoning was first described by the ancient Greek philosophers such as Aristotle. (from Wikipedia)
"drawing conclusions by applying rules or principles; logically moving from a general rule or principle to a specific solution" (Woolfolk, 2001, p. 286)
[edit] Comparison of two Reasonings
(Retrieved May 03, 2005, from Deduction and Induction)
Deductive reasoning works from the "general" to the "specific". This is also called a "top-down" approach. The deductive reasoning works as follows: think of a theory about topic and then narrow it down to specific hypothesis (hypothesis that we test or can test). Narrow down further if we would like to collect observations for hypothesis (note that we collect observations to accept or reject hypothesis and the reason we do that is to confirm or refute our original theory). In a conclusion, when we use deduction we reason from general principles to specific cases, as in applying a mathematical theorem to a particular problem or in citing a law or physics to predict the outcome of an experiment.
Inductive reasoning works the other way, it works from observation (or observations) works toward generalizations and theories. This is also called a “bottom-up�? approach. Inductive reason starts from specific observations (or measurement if you are mathematician or more precisely statistician), look for patterns (or no patterns), regularities (or irregularities), formulate hypothesis that we could work with and finally ended up developing general theories or drawing conclusion. In a conclusion, when we use Induction we observe a number of specific instances and from them infer a general principle or law. Inductive reasoning is open-ended and exploratory especially at the beginning. On the other hand, deductive reasoning is narrow in nature and is concerned with testing or confirming hypothesis.
Properties of Deduction
In a valid deductive argument, all of the content of the conclusion is present, at least implicitly, in the premises. Deduction is nonampliative. If the premises are true, the conclusion must be true. Valid deduction is necessarily truth preserving. If new premises are added to a valid deductive argument (and none of its premises are changed or deleted) the argument remains valid. Deductive validity is an all-or-nothing matter; validity does not come in degrees. An argument is totally valid, or it is invalid.
Properties of Induction
Induction is ampliative. The conclusion of an inductive argument has content that goes beyond the content of its premises. A correct inductive argument may have true premises and a false conclusion. Induction is not necessarily truth preserving. New premises may completely undermine a strong inductive argument. Inductive arguments come in different degrees of strength. In some inductions the premises support the conclusions more strongly than in others.
Intuitive Reasoning A third type of reasoning, intuitive reasoning, is what many young children use, as well as older children/adults in highly unfamiliar situations. Intuitive reasoning has to do with the way something appears to be, how something "seems" or "looks", and is based on unverified guesses. While it may seem to be very rudimentary, it is very useful in giving a starting point from which induction or deduction can proceed. It is the chief type of reasoning used by early elementary students, and students must be shown the flaws in it by the use of cognitive conflict in order to learn to move past intuition towards induction and deduction.
[edit] Applications
In most subject areas, both deductive and inductive methods are taught as ways to reach a solution. In mathematic and science related subjects, the method of reasoning is most apparent. However, in all subjects of education, a method of reasoning is in place. The following are some resources to see how specific methods influence a variety of subject areas.
The deductive method in subjects of education
The opposite of deductive methods is: Inductive methods
Cultural Variations in Approaches to Learning
"Teachers may use inquiry methods that emphasize deductive approaches to learning, analytical examinations of details or parts, or the solving or the problems by examining the relationship of one part to another. This linear model, moving sequentially from the specific to the general and examining objects/concepts without a context may not be the preferred approach to learning for some children from groups of color. Students of color often use a more inductive problem solving and reasoning process. They may use observed instances in context to generate an idea or a concept. They move from whole to part from the general to the specific"( Sheets, 2005, p. 160).
[edit] Research
Thesis involving deductive versus inductive methods in English Grammar
[edit] External Links
Wikipedia's Deductive Reasoning
The Inductive(Scientific) Method
Inductive and Deductive Reasoning
[edit] References
Sheets, R. H.. Diversity pedagogy : examining the role of culture in the teaching-learning process. Boston : Pearson/Allyn and Bacon, 2005.
Woolfolk, Anita. 8th ed. Educational Psychology.Boston: Allyn and Bacon, 2001.
[edit] Testimonials
In its most simple state, deductive reasoning is a logical thought process. It is a series of ideas where one thought leads to the next thought. For the more analytic minds in our society, this process seems simple. For the less analytic people, however, this process can be almost traumatic. Take for example writing a proof in a geometry class. We start with a given and chain together a series of theorems or postulates, etc until we reach the desired conclusion. For some of my students this process is harrowing. Certain students see each theorem as an if-then statement. If I know "a," then I know "b". They then look for another theorem that begins with "If I know "b," and use this process until they reach the end. Other students don't see things in this way. Sometimes it is due to not knowing the theorems, etc to the best of their ability. Other times it is due to a lack of interest in doing the problem at all. And in some cases the problem lies in the fact that thinking in this way is not what they're used to in math class. For this reason I believe that these skills must begin before the student reaches high school. State testing requirements almost always require students to be able to express their ideas in writing. As is the case in our state, the students are allowed to use a t-chart to express their thought processes - the steps on one side of the chart and their justifications on the opposite side. Using this method relieves the students of the stress of writing complete sentences, using correct grammar, etc but also teaches the student how to begin using logical though processes in what will eventually become proof-writing. MFoshee
