SCIENTIFIC RESEARCH

Scientific research is a systematic, empirical, controlled, and critical investigation/inquiry of hypothetical propositions/relationships about the presumed relations among phenomena. The research begins with gathering information about a phenomena by careful observations on a situation (mainly by using our five senses, i.e sight, hearing, smell, taste and touch).

Based on the observations, an inference/good guess/tentative explanation of a given situation is made which may not be true. A hypothesis which identify the relationship between variables is formulated and then tested through a carefully planned and controlled experiment.

By collecting, analyzing and interpreting data, then the conclusion is made whether the hypothesis is accepted or rejected.

Scientists should adopt scientific attitudes and noble values in all their research and investigations. Observations should be done objectively,carefully and patiently. Scientists have to be rational, critical and analytical when collecting, analyzing, interpreting data and making conclusions of the research. Each of those values not only increases the validity of the research or investigations, but will also enhance one's scientific thinking and abilities to solve problems in science as well as in other fields.

TRENDS AND ISSUES OF MATHEMATICS EDUCATION IN MALAYSIA

 Background : Moving from traditional curriculum( before 1970) towards new maths curriculum                                (1970s-1990s, KBSM) to smart schools curriculum/21 st century curriculum, KSSM )

1. Introduction of Smart Schools (Sekolah Bestari)   - one of the seven flagship applications in the

    Multimedia Super Corridor (MSC) ;1995.

-  democratization of education/ education for all policy

   offering equal access or opportunities to quality education.

- it is not about technology/ICT alone but rather about "smart learning".

- full implementation in about 10, 000 schools by 2010 

2. Approach of curriculum delivery : self directed, self -paced and self- accessed.

3. Major focus - to develop 5 main smart skills:
                    learning skills (ie how to learn);
                    thinking skills ( ie critical and creative thinking skills/KBKK, HOTs).
                    facilitating skill for teachers;
                    smart assessment(criterion-based, SBA/PBS, PT3)
                    ICT competent .

4. Reduce current exam-oriented approach in teaching and learning instead moving towards on schools based assessment ,on-line assessment, holistic,criterion-referenced, multiple approaches and on-going/formative/developmental.

5. T&L should cater or accommodate different learning abilities (slow. average and fast learners),

learning and cognitive styles ( eg sensory/concrete/practical or intuitive/abstract/theories; visual or verbal; inductive or deductive;active or reflective; sequential or global/holistic learners) and the uniqueness of every individual (student-centered learning  and humanistic approach).

THE GROWTH AND POTENTIAL OF SCIENTIFIC KNOWLEDGE

SCIENTIFIC KNOWLEDGE

Through science process skills and manipulating skills, scientific knowledge grows (with its potential, possible limits and a question of validity) and form the basic or the building blocks of science.

There are six main types of scientific knowledge :

1. Fact- event, phenomena, statement or information accepted to be true based on empirical evidence( eg speed of light, nucleus of an atom consists of protons and neutrons, g=9.8ms-2

etc)

2. Concept- idea or group of ideas (construct), object or process(eg density, force, momentum etc)

3. Hypothesis - general/conjectural statement of the relationship between two or more variables anticipated to be true but has to be proven empirically(eg the longer the length of the pendulum, the longer its period of oscillation)

4. Principle- generalized concept which links together a number of other concepts(eg Archimedes principle)

5. Theory- a connected/interrelated statements, concepts or principles which are generalized (have to be verified by experiment) to describe, explain and predict a phenomena.

6. Law- principle which are repeatedly and empirically proven to be true but its truthfulness may not be absolute( eg Boyle's law, Charles' law, Newton's law etc)- it is a relative truth !

Science process skills and manipulating skills should be developed through scientific method

SCIENTIFIC METHOD

The basic steps of scientific method includes:

1. Identify the problem

2. Formulating a hypothesis

3. Designing an experiment

4. Making observations

5. Recording data from the experiment

6. Analyze the data and confirming hypothesis

7. Forming conclusions

Main characteristics of the scientific method:

1. The method is systematic - this implies a procedure that is marked by thoroughness and has a certain regularity.

2. The method is empirical- grounded in reality ie based on actual data.

3. The method is objective- the results can be replicated by other scientists.

4. The method is logical- the results rationally follow from evidence.

5. The method is critical and analytical in nature

6. The method is an inquiry and investigative in nature.

There are two main types of scientific approaches which contribute to the development of scientific knowledge.

1. Inductive approach is characterized by a strictly empirical approach through repeated experiment/observation of reality in order to make a conclusion.

eg experiment : heating one end of metal rod

observation : the other end gets hot

conclusion : metal conducts heat

2. Deductive approach is a form of inference or a process of reasoning by which conclusion is drawn by logical inference from given premises.

premise: all metals conduct heat

premise : object A(new object found) is a metal

conclusion (or deduction): object A conducts heat

The wheel of science is circular, depending on where one starts the wheel ie from inductive or deductive approach. Both attempt to establish a valid and verifiable knowledge through the correct use of a scientific method. It is a process of continuous inquiry, investigation and discovery.

Pedagogical question - How best can we develop methods of teaching scientific knowledge to our
students in secondary schools?

SECONDARY SCHOOL INTEGRATED CURRICULUM (KBSM - MATHEMATICS)

Integrated curriculum model : Why integrate?

1. The main goal of KBSM (1989) is to develop potentials of the students in a holistic and integrated manner (ie intellectually, spiritually, emotionally and physically balanced)

within the context of National Philosophy of Education.

2. Mathematics should be seen as an integrated whole (ie connections or relationships of mathematical topics) not as a discrete or fragmented topics. (eg relationships between fraction, ratio, proportion and percentage)

3. Mathematics as an integral part of human experiences, activities and problem solving, emerging from everyday life, interaction with other disciplines especially with science and technology.

How to integrate?

Integration of mathematical contents through three main components ( ie thematic approach):

1. Numbers such as counting and calculating ( ie whole numbers, fractions, decimals, percentages multiples and factors etc

2. Shapes - familiarizing with topics such as angles ,lines, polygons, circle,solid , trigonometry, earth etc.

3. Relations- understanding rules, laws and relationships in the topics such as set, functions and graphs, matrix, statistics, probability etc.

How to implement in teaching and learning?

1. Teaching and learning as an integrated approach ie integration of mathematics as problem solving, mathematics as communication, mathematics as reasoning and mathematical connections.

2. Balance between understanding of concepts and mastering of skills.

3. Apply mathematical skills in real problem solving situations.

4. Inculcate historical elements into mathematics teaching and learning.

5. Emphasize on mathematical thinking strategies.

6. Using inquiry- discovery method

Discuss the factors that may lead to the problems in the implementation of the current KBSM mathematics curriculum in schools.

METACOGNITION AND MATHS EDUCATION

Metacogniton means thinking about thinking ie thinking about one's own thinking process or

knowledge about our own cognitive processes.

It is the ability to monitor one's current level of understanding (self-monitoring) and determine when it is not adequate, be aware of the improvements needed(self-awareness) or correct/modify the faulty thinking involved(self-corrective actions).

Metacognition involves self reflection is an important part of an active learning especially in solving mathematical problems which supports the development of critical and creative thinking skills.

Main operations of metacognition (for example in solving mathematical problem by using Polya Model - understand the problem, device/select a plan/strategy, carry out the plan and looking back ) are planning, executing/implementing, monitoring and evaluating.

Ideally, students should be able to assess their thinking before(do I know what to do?- given data, what to find? , during (am I on the correct track? - using right formula/method?- should I consider alternatives?) and after a problem solving process ( Is the answer correct/reasonable?- check the solution).

In other words it is a self-regulated/controlled or self-directed of learning which promotes independent learners among the students. Metacognition is just as any skill, it improves with practice.

Metacognitive skills can be develop through cooperative learning/group work where students can think aloud( describe precisely their thinking), sharing their thought via description and/or visual representation with other students in the group.

Examine a mathematics textbook (choose one problem in form 4 mathematics), design teaching and learning activities which incorporate metacognitive skills in that lesson.

HOW KNOWLEDGE GROWS ( eg. SCIENCE)

Scientific knowledge is the product of continuous process of inquiry which begins and grows through the acquisition of scientific skills by the scientists:

Scientific skills can be divided into 2 types: Science process skills (SPS) and manipulative skills (MS). SPS involve cognitive processes that are related to thinking skills(critical and creative thinking). MS involve psychomotor skills related to handling of instruments in carrying out experiments.

Some of the main science process skills are as follows: observing, classifying, measuring and using numbers, making inference, predicting, communicating, using space-time, interpreting, defining operationally, manipulating variables, making hypotheses and experimenting.

In each SPS there may be one or more thinking skills involved.

Making observation (eg movement of an object)

- characterizing (eg force, mass, velocity)

- relating (eg F=ma)

Careful observations of nature are main sources of scientific knowledge

Classifying

- looking at similarities and differences (eg animals and plants)

- compare and contrast (eg types of animals)

Measuring and using numbers

- looking for pattern

- sequencing

Making Inference (draws early conclusion)

- relating (one variable with another variable)

- looking at similarities and differences

- analyzing

Predicting ( eg weather, and wave)

- relating

- visualizing (mental representation)

- searching for patterns

Communicating (verbal, mathematical, symbolic etc)

- involve all thinking skills

Using space - time (eg study of shape, motion and change; relativity theory)

- sequencing

- arranging

- relating

Interpreting (eg function and graph )

- summarizing

- generalizing

- meaning

Defining operationally (eg force, momentum, heat etc)

- making analogy

- visualizing

- analyzing

Controlling variables (eg pressure and volume)

- characterizing

- looking at similarities and differences

- relating

- analyzing

Making hypothesis

- relating

- predicting

Experimenting - involve all thinking skills

Some of the main manipulative process skills are as follows: using equipment/ apparatus, handling apparatus safely, keeping safely all scientific equipments and apparatus, careful handling of live specimens (in biology), mixing solutions, pouring solutions etc (in chemistry) etc.

Discuss in what ways the understanding on how knowledge of grows will effect the role of science teachers in the classroom?

COGNITIVE PSYCHOLOGY AND MATHS EDUCATION

• Learning processess are complex, behaviorist psychology cannot explain all learning.

• Theoretical inadequacy/limitations to explain all that our students learn and do.

• Learning is not only limited to observable behaviour that always simple and straightforward but it is more of thought processes (or cognition).

• Learning as internal process (cognitive procesess) that cannot be observed directly; changes in behaviour is a reflection of internal change (the cognitive structure) in the student’s mind.

• Major focus is on knowing (understanding,memory, thinking, perception,meaning,decision making, sense making,problem solving, concepts or ideas etc)

Main representative theorists:

• Piaget ( cognitive development theory)
•   Bruner (discovery learning)
•   Ausubel (meaningful learning)
• Gagne’ (classification of human learning)

With cognitive approach, the emphasis in teaching and learning has shifted from product to process (ie process of mathematical thinking , process of problem solving etc)