1.1 Some Terms Used in the Course

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  Facts, Skills and Concepts

Facts are information which are unconnected or arbitrary such that they cannot be directly supported by conceptual structure. These are names, symbols, objects, and locations.

General Objective
To know notational conventions and correct terms for concepts.
Behavioral Objective

To know that the name given to the point (0, 0) is origin. To know that 2.54 cm. is equal to 1 inch. To know that g (gravitational accelaration) is 9.84 meter/square of second.

Skills is the knowledge and ability that enables you do something well. They include not only the use of the number, facts and the standard computational procedures of arithmetic and algebra, but also of any well established procedures which it is possible to carry out by the use of a routine.

General Objective
To know how to carry out standard procedures.
Behavioral Objective

To be able to multiply long operations quickly and accurately. To be able to follow rules for manipulating and solving equations.

Concepts define classes of objects or events. Concepts can be conjunctive (all defining attributes must be present), disjunctive (one subset or another subset of attributes must be present) or relational (the attributes must exist in some specific relationship to each other).

General Objective
To understand the meaning of concepts and how they relate to each other.

Behavioral Objective

To be able to interpret a graph. To be able to translate a graph into an alternative representation.

  Strategies, Reasoning, Critical Thinking

Strategies are procedures which guide the choice of which skills to use or what knowledge to draw upon at each stage in the course of solving a problem or carrying out an investigation.

General Objective
To know when particular method may or may not be appropriate.

Behavioral Objective

To be able to use strategies such as, classifying, trying simple cases, symbolising, finding helpful representations, looking for pattern, making predictions.

Reasoning is the act of process of adducing a reason or reasons; manner of presenting one’s reason. In other words, reasoning is that which is offered in argument; proofs or reasons when arranged or developed.

Reasoning is technically different from the argumentation. Reasoning is a broader term which includes both deduction and induction. Argumentation denotes simply former, descend from the whole to some included part; while reasoning embraces also the latter, and ascends from a part to a whole.

Reasoning is occupied with ideas and their relation. Argumentation has to do with the forms of logic. It supposes that there are two sides and that both agree to the same rules. Reasoning, on the other hand, is often a natural process from the general analogy of the nature, or presumption in the case,conclusions which have greater or less degrees of force, and which may be strenghtened or weakened by subsequent experience.  

Critical thinking is the intellectually disciplined process of actively and skillfully conceptualizing, applying, analyzing, synthesizing, and/or evaluating information gathered from, or generated by, observation, experience, reflection, reasoning, or communication, as a guide to belief and action.

Critical thinking -in being responsive to variable subject matter, issues, and purposes- is incorporated in a family of interwoven modes of thinking, among them:

Scientific thinking, mathematical thinking, historical thinking, anthropological thinking, economic thinking, moral thinking, and philosophical thinking.

Critical thinking can be seen as having two components:

a set of skills to process and generate information and beliefs, and the habit, based on intellectual commitment, of using those skills to guide behavior.

It is thus to be contrasted with:
1. the mere acquisition and retention of information alone,
2. the mere possession of a set of skills, and
3. the mere use of those skills ("as an exercise") without acceptance of their results.

Critical thinking of any kind is never universal in any individual; everyone is subject to episodes of undisciplined or irrational thought. Its quality is therefore usually a matter of degree and dependent on, among other things, the quality and depth of experience in a given domain of thinking or with respect to a particular class of questions.

For this reason, the development of critical thinking skills and dispositions is a life-long endeavor.

  1.2 Definition of the Effective Teacher

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Teaching is a complex and difficult task demands extraordinary abilites. What is an effective teacher? How do I become one? How long does it take?...

A century ago, teachers were judged primarily on their goodness as people and only secondarily on their behavior in the classroom. They were expected to be honest, hardworking, generous, friendly, and considerate, and to demonstrate these qualities in their classrooms by being organized, disciplined, insightful, and committed. But it soon became evident that this definition of an ideal teacher lacked clear, objective standards of performance that could be consistently applied to all teachers and that could be used to train future teachers.

There is no simple definitions of an effective teacher. In addition to be good person, psychological characteristics, level of subject matter knowledge and teaching strategies should be taken into account to be effective teacher. So, being effective teacher is related to the effective practices in classroom and positive outcomes in learners. Some of these are clear lesson, variety in instruction, high task orientation, high engagement and high success rate. These effective teaching practices do not tell the whole story of what an effective teacher is, but they do form an important foundation.