CURRICULUM MODELS/ORIENTATIONS AND ITS RELATION TO MATHEMATICS CURRICULUM - AN OVERVIEW

There are few popular curriculum models or orientations adopted by various education systems

throughout the world such as :

1. Competency-based curriculum (focus on performance/competency or skills - mathematical skills
    and competency)

2. Standards-based curriculum (focus on pre-determined criterias/standards eg KSSR and KSSM,
    NCTM)

3. Outcome-based curriculum (OBE) (focus on outcomes - outcomes drive teaching and learning)

4. Problem - based curriculum (focus on solving real life problems - problems drive teaching and
    learning eg problem-based learning (PBL))

5. Content (Subject/discipline) - based curriculum (focus on content and mathematical structures
    -  epistemological issues eg how knowledge begins, grows, its potentials and limitations )

6. Humanistic curriculum (focus on developing human potential in a broader sense- self-growth,
    talents or potentials, generic skills eg leadership, communication, team- work, creativity etc)

7. Thinking curriculum (focus on developing thinking skills - the process of mathematical thinking,
    HOTs/KBAT, problem posing, creativity, advanced mathematical thinking etc)

8. Integrated curriculum (focus on integration, holistic, unified or thematic approach
    - integrated mathematics (vs compartmentalized) eg KBSM

Different models/orientations(specific or mixed) based on certain philosophy/ideology/theory/belief system will have different influences on the aims, objectives, selection and organization of contents, skills and values/attitudes (KSA), as well as on teaching, learning and assessment methods.

BASIC STEPS IN CURRICULUM DESIGN

There are at least 8 important steps ( based on Taba 1962) in curriculum design : (discuss example of maths curriculum - KBSM/KSSM)

1. Diagnosing needs (situational analysis - educational philosophy/ ideology, world-view etc)

2. Formulating aims, goals and specific objectives (learning outcomes)

3. Selecting content (areas -arithmetic, algebra, geometry etc)

4. Organizing content (depth, breadth, scope, etc)

5. Selecting learning experiences (teaching and learning activities based on learning theories such as
    behaviourism, cognitivism and humanism etc)

6. Organizing learning experiences (activities)

7. Evaluating (formative and summative)

8. Checking for balance and sequence

EPISTEMOLOGY OF KNOWLEDGE

How knowledge begins ?

Examples:

1. Biology : The study of biology begins as a study of living things/ organisms (plants, human, animals, micro-organisms etc), their life processes as well their interactions with the environment.

Biology can divided into few main areas such as botany, zoology, anatomy, genetics and ecology .

2. Chemistry : the study of chemistry begins as a study of the changes in matter (related to properties, structure, composition and reactions between atoms, ions, elements and substances) which are followed by changes in energy.

Chemistry can be divided into few main areas such as bio chemistry, physical chemistry, organic and inorganic chemistry.

3. Physics : the study of physics begins as a study of natural phenomena and an attempts to explain it scientifically.

Physics can be divided into two main areas ie classical physics (deals with matter, motion and energy ) and modern physics ( deals with atomic, nuclear, particle physics).

4. Mathematics : the study of mathematics begins as a study of numbers, shape and relations.

Mathematics can be divided into two main areas ie pure mathematics and applied mathematics.

Mathematics developed as a body of knowledge and it can be seen from 4 perspectives : language, science, a way of thinking and as a tool for problem solving.

5. Technology : the study of technology begins with the application of science to practical human needs ( ie increase productivity, improve quality of life etc) in agriculture, engineering, manufacturing, transportation, communication, medicine etc.

Discuss the importance of epistemology of knowledge in teaching and learning of science and mathematics.

DESIGN AND IMPLEMENTATION OF MATHEMATICS CURRICULUM

Synopsis : This course addresses issues and problems in designing and implementation of mathematics curriculum. The topics that will covered include : factors influencing curriculum design,various models used in curriculum design, several examples of mathematics curricula viewed in terms of contents, pedagogical and psychological aspects. Problems related to the implementation of a particular curriculum model. Current issues and trends of  mathematics curriculum in several developed countries will be discussed.

Main text :

Robert S. Zais (1976); Curriculum - Principles and foundations, Thomas Y. Crowell Co, Inc


Assessment :

1.   Individual assignment and presentation  ( 30 marks )
2.   Group assignment and presentation       ( 30 marks)
3.   Final examination (comprehensive)        ( 40 marks)

Introduction :

The word curriculum comes from a latin root, meaning "racecource"- ie racecourse covered by students in their race toward the finish line (eg getting a diploma, degree, etc)

Concepts of the curriculum - what is the curriculum? many definitions : As an examples

1. Curriculum as the program of studies and course content

2. Curriculum as a (written) plan for action ie plan which guides teaching/instruction

3. Curriculum as planned learning experiences

4. Curriculum as a structured series of intended learning outcomes

Curriculum design most commonly refers to the arrangement of the main components or elements of a curriculum :

1. aims, goals, and objectives - curriculum policy
    ( how does philosophy and ideology/world view influence the curriculum design ? )

2. subject matter or content - curriculum organization (scope, sequence, continuity, and integration;
    models  or orientations -   integrated, thematic, outcome-based curriculum  etc)
    (how does philosophy of mathematics (invented or discovered) influence the curriculum design ?)

3. teaching and learning processes ( activities or experiences) - pedagogical issues/how does the curriculum
    being implemeted? ie curriculum implementation.
    (how does psychological theories (behaviorism, cognitivism, humanistic etc) influence the curriculum
    design?)

4. assessment and evaluation - assessment of learning, assessment for learning and assessment as learning)

    (how does assessment influence the curriculum design?)

Due to the complexity of the curriculum design, it draws from theories in various fields such as from  philosophy, psychology, sociology etc as a guide for the curriculum design.

EPISTEMOLOGICAL, SOCIAL AND ETHICAL ISSUES IN SCIENCE AND TECHNOLOGY

Synopsis : This course is intended to enhance students' understanding of epistemological, social and ethical issues in science and technology and its relation to education.

Brief history (including various definition of science) and philosophy of science and technology will be discussed .

Students will be required to discuss critically the social and ethical implications of the advancement of science and technology to the society and their effects on the environment.

The relationships between science, technology and society (STS) and the role of education will be highlighted.

Introduction:

Philosophy can be generally defined as a study of the nature of being and thinking, and more specifically of the human experience in four main areas:

1. Logic - the study of formal structure of arguments and reasoning

2. Metaphysics - the study of nature of being and reality - the theory of reality

3. Epistemology - the theory of knowledge (TOK) - study the origin,validity and limitation of knowledge

4. Ethics (axiology) - the study of moral/ethical issues (good, right, beauty, values, etc) and

Epistemology ( from Greek word episteme means knowledge, logos - the study) is a branch of philosophy (love of wisdom)

that inquires about the sources/origin of human knowledge (eg science - physics, chemistry,biology, mathematics; arts- geography, history, economics, politics, psychology, etc), the role of experience and reasoning in generating knowledge (rationalistic and empiricistic), the changing forms of knowledge that arise from new conceptualizations, its potential and possible limits, and to what extent it can be certain ( exact) or only probable, the question meaning and truth, the question of validity, objectivity, subjectivity, and scepticism/confident doubter/the theory of doubt etc.