Unit-VI

Fennema and Franke (1992) determined the components of mathematics teachers’ knowledge as;

1) Knowledge of mathematics, Content knowledge, The nature of mathematics, & The mental organization of teacher knowledge

2) Knowledge of mathematical representations

3) Knowledge of students & Knowledge of students’ cognitions

4) Knowledge of teaching and decision-making.

Knowledge of mathematics and knowledge of mathematical representations are related to content knowledge, while knowledge of students and knowledge of teaching are related to pedagogical content knowledge.

According to An, Kulm, and Wu (2004) pedagogical content knowledge has three components:

• Knowledge of content

• Knowledge of the curriculum

• Knowledge of teaching

However, they also outlined that the content of pedagogical content knowledge is ‘content-specific and at the same time goes beyond simple knowledge of mathematics therefore a mathematician may not posses it (Kahan, Cooper and Bethea, 2003: 223)’.

Instructional objectives (also known as behavioral objectives or learning objectives) are basically statements that clearly describe an anticipated learning outcome. When objectives were first coming into their own in education, they almost always began with the phrase: "Upon completion of this lesson, the student should be able to…." This phrase focused on the outcome of learning rather than on the learning process. In fact, one of the criteria for a well-written objective is that it describes the outcome of learning, that is, what the learners can do after learning has occurred that they might not have been able to do before the teaching and learning process began.

Characteristics of a Well-Written Objective

A well-written objective should meet the following criteria:

(1) describe a learning outcome,

(2) be student oriented,

(3) be observable (or describe an observable product).

A well-written objective should describe a learning outcome (e.g., to correctly spell the spelling of the words on page-17 of English text book). It should not describe a learning activity (e.g., to practice the words on page-17 by writing each one ten times). Learning activities are important in planning and guiding instruction but they are not to be confused with instructional objectives.

Characteristics of Instructional Objective

To be useful for instruction, an objective must not only be well written but it also must meet the following criteria:

(1) be sequentially appropriate;

(2) be attainable within a reasonable amount of time;

(3) be developmentally appropriate.

Kinds of Instructional Objectives

Instructional objectives are often classified according to the kind or level of learning that is required in order to reach them. There are numerous taxonomies of instructional objectives; the most common taxonomy was developed by Benjamin Bloom and his colleagues. The first level of the taxonomy divides objectives into three categories: cognitive, affective, and psychomotor. Simply put, cognitive objectives focus on the mind; affective objectives focus on emotions or affect; and psychomotor objectives focus on the body.

Cognitive objectives call for outcomes of mental activity such as memorizing, reading, problem solving, analyzing, synthesizing, and drawing conclusions. Bloom and others further categorize cognitive objectives into various levels from the simplest cognitive tasks to the most complex cognitive task. These categories can be helpful when trying to order objectives so they are sequentially appropriate. This helps to insure that prerequisite outcomes are accomplished first.

Affective objectives focus on emotions. Whenever a person seeks to learn to react in an appropriate way emotionally, there is some thinking going on. What distinguishes affective objectives from cognitive objectives is the fact that the goal of affective objectives is some kind of affective behavior or the product of an affect (e.g., an attitude). The goal of cognitive objectives, on the other hand, is some kind of cognitive response or the product of a cognitive response (e.g., a problem solved).

Psychomotor objectives focus on the body and the goal of these objectives is the control or manipulation of the muscular skeletal system or some part of it (e.g., dancing, writing, tumbling, passing a ball, and drawing). All skills requiring fine or gross motor coordination fall into the psychomotor category. To learn a motor skill requires some cognition. However, the ultimate goal is not the cognitive aspects of the skill such as memorizing the steps to take. The ultimate goal is the control of muscles or muscle groups.

General Instructional Objective: An intended outcome of instruction that has been stated in general enough terms to encompass a domain of student performance 

Specific Learning Objectives: A goal or aim serves as a guide for a teaching unit, directed toward the eventual achievement of a general objective. It is stated in terms of specific and observable pupil performance. It describes the specific behaviour, a learner will exhibit after learn­ing a particular unit. Let us discuss separately different criteria for stating, general instructional objectives and specific learning objectives.

Examples:

General Objective: Understand graphs and charts.

Specific Learning Objective: Distinguish between graph and chart.

Teaching aids provide a stimulus for exploration end thinking. With the added input of verbal, personal communication with an adult, interaction and discussion arise...and these are crucial to reel, activity-based learning. Adults (and older children) help younger ones to interpret sensory and language experiences, to clarify them and relate them to their previous understandings. Children then learn by blending language with experiences. They learn to think.

For maximum mental growth and personality development, a child’s life needs to be filled with stimulating, encouraging experiences. Appropriate learning materials (teaching aids) help children to develop their innate abilities.

Concept of Teaching Aids:

Teaching aids are known as audio-visual aids, and sensory aids. Helps to make teaching concrete, effective, and interesting. Cannot replace a teacher. Communication of ideas between persons & groups.

Sources of Learning:     Direct sensory contact, Pictures or similar other representation of facts, Oral or printed words

Types of Teaching Aids: Following are some of the classifications 

Classification – 1:

a) Audio Aids: Audio aids mean learning through listening. Audio tape, Radio, Tape Recorder etc.    

b) Visual Aids: Visual aids mean Learning through seeing. LCD projector, Chart, Model, Picture, Chalk Black Board,  etc.

c) Audio–visual aids are devices that can be heard or as well as seen. This aids to impart knowledge through senses to ensure quick and effective learning. Video with Audio, TV etc.

    Classification – 2:

1. Projected Aids: Aids which help in their projection on the screen are called projective aids. When a projected aid is used and enlarged image of the material (slide, filmstrips etc) is projected on a screen kept at a distance from the projector. 
2. Non Projected Aids : Visual instructional devices which are simply presented without any projection equipment are non projected aids. Examples: blackboard, chart, etc. Projected Aids: visual instructional devices which are shown with a projector are called projected aids.