Inductive VS Deductive approaches Deductive and Inductive Logic

Inductive VS Deductive approaches

Deductive and Inductive Logic (distinction #1) • The conclusion of a deductive argument is already contained implicitly in its premises • The conclusion of an inductive argument goes beyond the information in its premises

Deductive and Inductive Logic (distinction #2) • Given the truth of all of its premises, the truth of an inductive argument’s conclusion follows with at most high probability • Deduction argues from a given model’s general principles to specific cases of expected data

Deductive and Inductive Logic (distinction #3) • Deduction argues from a given model’s general principles to specific cases of expected data • Induction argues in the opposite direction, from actual data to an inferred model

Deductive and Inductive Logic • One is based on statistics (inductive) • The other is based on probability

Deductive and Inductive Logic (telling the difference) Given: A “fair coin” is one that gives tails with probability 0. 5 and head 0. 5. • Problem 1: Given that a coin is a fair coin. What is the probability that the coin will produce 45 heads and 55 tails? • Problem 2: Given that 100 tosses of a coin produce 45 heads and 55 tails. What is the probability that the coin is a fair coin?

Why is induction so pervasive and critical in science? Science is almost entirely about unobservables -about things and times outside the database of actual observations. Iron melts at 1, 535°C (but everywhere? ) Water boils at 100°C (but everywhere? )

The basis of induction: Aristotle • Aristotle (384 -322 BC) offered 3 methods of induction • Unifying concept: in deductive arguments, which are composed of premises, inductive arguments are the scaffolds that raise the status of the deductive argument to a law-like status

The basis of induction: Aristotle • Dialectical induction (Topics). Not entirely relevant to scientific research, but useful: – mentor to pupil discourse – “If a skilled pilot is the best pilot and the skilled charioteer is the best charioteer, then, in general, the skilled [person] is the best [person] in any particular sphere” (Perez-Ramos 1988)

The basis of induction: Aristotle • Enumerative induction (Prior Analytics). Statements about individual objects provide the basis or premises for a general conclusion: – from observing numerous adult humans, an inductive argument could conclude that all humans have 32 teeth

The basis of induction: Aristotle • Intuitive induction (Posterior Analytics). Direct intuition of the general principles exemplified in the data: – bright side of the mood always faces the sun, so the moon shines because of reflected sunlight

Empiricism

Concept Empiricism • All concepts from experience; none innate • Hume: “. . . all our ideas are nothing but copies of our impressions, or, in other words, that it is impossible for us to think of anything, which we have not antecedently felt, either by our external or internal senses. ”

Judgment Empiricism • All knowledge of the world comes from experience • There are no synthetic a priori truths

Concept —> Judgment • Locke: “Had those who would persuade us that there are innate principles not taken them together in gross, but considered separately the parts out of which those propositions are made, they would not, perhaps, have been so forward to believe they were innate. Since, if the ideas which made up those truths were not, it was impossible that the propositions made up of them should be innate, or our knowledge of them be born with us. For, if the ideas be not innate, there was a time when the mind was without those principles; and then they will not be innate, but be derived from some other original. For, where the ideas themselves are not, there can be no knowledge, no assent, no mental or verbal propositions about them. ”

Two Kinds of Experience • Sensation – – – Vision Hearing Smell Taste Touch • Reflection

Kinds of experience 10 • Locke: “All ideas come from sensation or reflection. Let us then suppose the mind to be, as we say, white paper, void of all characters, without any ideas: - How comes it to be furnished? Whence comes it by that vast store which the busy and boundless fancy of man has painted on it with an almost endless variety? Whence has it all the materials of reason and knowledge? To this I answer, in one word, from EXPERIENCE. In that all our knowledge is founded; and from that it ultimately derives itself. Our observation employed either, about external sensible objects, or about the internal operations of our minds perceived and reflected on by ourselves, is that which supplies our understandings with all the materials of thinking. These two are the fountains of knowledge, from whence all the ideas we have, or can naturally have, do spring. ”

Distinctions • Impressions —> Ideas – Impressions: received by external or internal senses – Ideas are copies of impressions • Simple & Complex Impressions and Ideas – Complex ideas are compounds of other ideas – Simple ideas aren’t

Simple Ideas • Simple ideas – come from simple impressions – Represent them exactly • Hume: "all our simple ideas in their first appearance are deriv'd from simple impressions, which are correspondent to them, and which they exactly represent. "

Empiricists’ Method • Analyze complex ideas into simple ideas • Find origins of simple ideas in experience • Content of the idea lies in simple impression(s) from which it comes

CONSTRUCTIVISM �Constructivism suggests that the learner is much more actively involved in a joint enterprise with the teacher of creating (“constructivism”) new meanings. �The theory of constructivism suggests that the learners construct knowledge out of their experiences.

CONSTRUCTIVISM - A Learning Theory �Learning is an active process in which a learner uses sensory input and constructs meaning out of it. �People learn to learn as they learn. �The crucial action of constructing meaning is mental. �Learning involves language. �Learning is a social activity. �Learning is contextual. �One needs knowledge to learn. �It takes time to learn. �Motivation is a key component in learning.

TYPES OF CONSTRUCTIVISM • • Cognitive Constructivism. • or • Individual Constructivism. • • Social Constructivism

COGNITIVE CONSTRUCTIVISM • Cognitive constructivism also called as individual constructivism emphasizes on individual, internal construction of knowledge. • Largely based on Piaget’s theory. • Learners should be allowed to discover principles through their own exploration rather than direct instruction by the teacher.

SOCIAL CONSTRUCTIVISM • Knowledge exits in a social context and is initially shared with others instead of being represented solely in the mind of an individual. • Based on Vygotsky’s theory.

PRINCIPLES OF CONSTRUCTIVISM • Learners construct their own meaning. • New learning builds on prior knowledge. • Learning enhanced by social interaction. • Meaningful learning develops through authentic task.

LEARNING IMPACTS OF CONSTRUCTIVISM • Curriculum : Constructivism calls for the elimination of a standardized curriculum. • Instruction : Teacher rely heavily on open ended questions and promote extensive dialogue among students. • Assessment : Constructivism calls for the elimination of grades and standardized testing.

CONSTRUCTIVISM LEARNING DESIGN • • • » SITUATION » GROUPING » BRIDGE » QUESTION » EXHIBIT » REFLECTION