Nature and Principles of Teaching and Learning in the Subject Areas
PRINCIPLE OF TEACHING: THE LEARNER
The Nature of the Learner- The learner is an embodied spirit. He is the union of sentient body and a rational soul. His body experiences sensations and feels pleasure and pain. His soul is the principle of spiritual acts, the source of intellectual abstraction, self-reflection, and free rational volition. Body and soul exist in mutual dependence. (Kelly, 1965)
The Fundamental Equipment of the Learner. The learner has the power to see, hear, touch, smell, taste, perceive, imagine, retain, recall, recognize past mental acts, conceive ideas, make judgment, reason out, feel and choose.
Five Elements of the Learner
1.
Ability The students’ native ability dictates
the prospects of success in purposeful activity. It determine their capacity to
understand and assimilate information for their own use and application.
2.
Aptitude. Aptitude refers to the students’
innate talent or gift. It indicates a natural capacity to learn certain skills.
3.
Interest Learners vary in activities that are
undertaken due to a strong appeal or attraction.
4.
Family & Cultural Background Students who
come from different socioeconomic background manifest a wide range behaviour
due
5. Attitudes Students have unique way of thinking and reacting. Confronted with the same situation in the learning environment each one would react differently depending on their personal characteristics.
The Nature of the learner-comparison of the Views on
Intelligence
|
Old View |
New View |
|
Intelligence was fixed Intelligence was measured by a number Intelligence was used to sort students and predict
success |
Intelligence can be
developed Intelligence is not
numerically quantifiable and is exhibited during a performance or problem
solving process Intelligence can be
exhibited in many ways. Intelligence is
measured in context/real life situations |
Intelligence is used to
understand human capacities and the many and varied ways students can achieve.
MULITIPLE INTELLIGENCES
AS DISPOSITIONS
Howard Gardner of Harvard has identified seven distinct intelligences.
This theory has emerged from recent cognitive research and "documents the
extent to which students possess different kinds of minds and therefore learn,
remember, perform, and understand in different ways," according to Gardner
(1991).
According to this theory, "we are all able to know
the world through language, logical-mathematical analysis, spatial representation,
musical thinking, the use of the body to solve problems or to make things, an
understanding of other individuals, and an understanding of ourselves. Where
individuals differ is in the strength of these
intelligences - the so-called profile of intelligences -and in the ways in which such intelligences are invoked and combined to carry out different tasks, solve diverse problems, and progress in various domains."
Visual-Spatial - think in terms of physical space, as do architects and sailors. Very aware of their environments. They like to draw, do jigsaw puzzles, read maps, daydream. They can be taught through drawings, verbal and physical imagery. Tools include models, graphics, charts, photographs, drawings, 3-D modeling, video, videoconferencing, television, multimedia, texts with pictures/charts/graphs.
Bodily-kinesthetic - use the body effectively, like a dancer or a surgeon. Keen sense of body awareness. They like movement, making things, touching. They communicate well through body language and be taught through physical activity, hands-on learning, acting out, role playing. Tools include equipment and real objects.
Musical - show sensitivity to rhythm and sound. They love music, but they are also sensitive to sounds in their environments. They may study better with music in the background. They can be taught by turning lessons into lyrics, speaking rhythmically, tapping out time. Tools include musical instruments, music, radio, stereo, CD-ROM, multimedia.
Interpersonal - understanding, interacting with others. These students learn through interaction. They have many friends, empathy for others, street smarts. They can be taught through group activities, seminars, dialogues. Tools include the telephone, audio conferencing, time and attention from the instructor, video conferencing, writing, computer conferencing, E-mail.
Intrapersonal -
understanding one's own interests, goals. These learners tend to shy away from
others. They're in tune with their inner feelings; they have wisdom, intuition
and motivation, as well as a strong will, confidence and opinions. They can be
taught through independent study and introspection. Tools include books,
creative materials, diaries, privacy and time. They are the most independent of
the learners.
Logical -Mathematical - reasoning, calculating. Think conceptually, abstractly and are able to see and explore patterns and relationships. They like to experiment, solve puzzles, ask cosmic questions. They can be taught through logic games, investigations, mysteries. They need to learn and form concepts before they can deal with details.
Naturalist intelligence
This area has to do with nurturing and relating
information to one’s natural surroundings.[7] Examples include classifying
natural forms such as animal and plant species and rocks and mountain types.
This ability was clearly of value in our evolutionary past as hunters,
gatherers, and farmers; it continues to be central in such roles as botanist or
chef.[6] This sort of ecological receptiveness is deeply rooted in a
"sensitive, ethical, and holistic understanding" of the world and its
complexities–including the role of humanity within the greater ecosphere.[13]
Existential
Further information: Spirituality
Some proponents of multiple intelligence theory proposed
spiritual or religious intelligence as a possible additional type. Gardner did
not want to commit to a spiritual intelligence, but suggested that an
"existential" intelligence may be a useful construct EAt first, it
may seem impossible to teach to all learning styles. However, as we move into
using a mix of media or multimedia, it becomes easier. As we understand
learning styles, it becomes apparent why multimedia appeals to learners and why
a mix of media is more effective. It satisfies the many types of learning
preferences that one person may embody or that a class embodies. A review of
the literature shows that a variety of decisions must be made when choosing
media that is appropriate to learning style.TAKE YOUR TEST AT:
Learning styles-an individual’s preferred mode of gaining knowledge
|
Individuals differ in how they learn. If a teacher aims to’ provide for individual’s needs, they need to consider learning styles as one
important factor in learning. Proponents of the use of learning styles in
education recommend that teachers assess the learning styles of their
students and adapt their classroom methods to best fit each student's
learning style. Although there is ample evidence for differences in
individual thinking and ways of processing various types of information, few
studies have reliably tested the validity of using learning styles in
education. |
Critics say there is no evidence that identifying an
individual student's learning style produces better outcomes. There is
evidence of empirical and pedagogical problems related to the use of learning
tasks to "correspond to differences in a one- to-one fashion".[3]
Well-designed studies contradict the widespread "meshing
hypothesis", that a student will learn best if taught in a method deemed
appropriate for the student's learning style.[2] |
The Nature of Mathematics
|
Since Math relies on both logic and creativity, its
real essence lies in its beauty and intellectual challenge. Mathematics is the science of patterns and
relationship. It explores the possible relationship among abstract numerical formulas which
can be anything from numbers to geometric figures to equations. |
Mathematical Inquiry Phase 1-abstraction and symbolic representation abstraction—that is, noticing a similarity between two
or more objects or events. Aspects that they have in common, whether concrete
or hypothetical, can be represented by symbols such as numbers, letters,
other marks, diagrams, or even words. Whole numbers are abstractions that
represent the size of sets of things and events or the order of things within
a set. The circle as a concept is an abstraction derived from human faces,
flowers, wheels, or spreading ripples; the letter A may be an abstraction for
the surface area of objects of any shape, for the acceleration of all moving
objects, or for all objects having some specified property; the symbol represents
a process of addition, whether one is adding apples or oranges, hours, or
miles per hour. |
Phase 2-Manipulating Mathematical
Statements
After abstractions have been made and symbolic
representations of them have been selected, those symbols can be combined and recombined
in various ways according to precisely defined rules. Sometimes that is done
with a fixed goal in mind; at other times it is done in the context of
experiment or play to see what happens. Typically, strings of symbols are
combined into statements that express ideas or propositions. For example, the
symbol A for the area of any square may be used with the symbol s for the
length of the square's side to form the proposition A = s2 . This equation
specifies how the area is related to the side—and also implies that it depends
on nothing else. The rules of ordinary algebra can then be used to discover
that if the length of the sides of a square is doubled, the square's area
becomes four times as great. More generally, this knowledge makes it possible to
find out what happens to the area of a square no matter how the length of its
sides is changed, and conversely, how any change in the area affects the sides
Phase 3- Application
Mathematical processes can lead to a kind of model of a
thing, from which insights can be gained about the thing itself.
Example: 3 cups of water + 2 cups of water = 5 cups of water right? Or wrong?
But: 2 cups of sugar + 3 cups of hot tea= 5 cups of sugar and hot tea?
The simple addition of volumes is appropriate to the first situation but not to the second—something that could have been predicted only by knowing something of the physical differences in the two situations. To be able to use and interpret mathematics well, therefore, it is necessary to be concerned with more than the mathematical validity of abstract operations and to also take into account how well they correspond to the properties of the things represented. Sometimes common sense is enough to enable one to decide whether the results of the mathematics are appropriate. For example, to estimate the height 20 years from now of a girl who is 5' 5" tall and growing at the rate of an inch per year, common sense suggests rejecting the simple "rate times time" answer of 7' 1" as highly unlikely, and turning instead to some other mathematical model, such as curves that approach limiting values. Sometimes, however, it may be difficult to know just how appropriate mathematical results are—for example, when trying to predict stock-market prices or earthquakes.
Often a single round of mathematical reasoning does not
produce satisfactory conclusions, and changes are tried in how the
representation is made or in the operations themselves. Indeed, jumps are
commonly made back and forth between steps, and there are no rules that
determine how to proceed. The process typically proceeds in fits and starts,
with many wrong turns and dead ends. This process continues until the results
are good enough.
Principles of Teaching Mathematics
1.
Teachers should allow children and young people
to experience success in mathematics and develop the confidence to take risks,
ask questions and explore alternative solutions without fear of being wrong.
2.
They should be given opportunity to enjoy
exploring and applying mathematical concepts to understand and solve problems,
explaining their thinking and presenting their solutions to others in a variety
of ways.
3.
At all stages, an emphasis on collaborative
learning will encourage children to reason logically and creatively through discussion
of mathematical ideas and concepts.
4.
Through their use of effective questioning and
discussion, teachers will use misconceptions and wrong answers as opportunities
to improve and deepen children’s understanding of mathematical concepts.
5.
Teachers should utilize experiences and outcomes
that encourage learning and use teaching approaches that challenge and
stimulate children and young people and promote their enjoyment of mathematics.
To achieve this, teachers will use a skilful mix of approaches, including:
• planned active learning which provides opportunities to observe, explore, investigate, experiment, play, discuss and reflect
• modelling and scaffolding the development of mathematical thinking skills learning collaboratively and independently
• opportunities for discussion, communication and explanation of thinking • developing mental agility
• using relevant contexts and experiences, familiar to young people
• making links across the curriculum to show how mathematical concepts are applied in a wide range of contexts, such as those provided by science and social studies
• using technology in appropriate and effective ways
• building on the principles of Assessment for Learning, ensuring that young people understand the purpose and relevance of what they are learning
•
developing problem-solving capabilities and
critical thinking skills.
Sometimes common sense is enough to enable one to decide whether the results of the mathematics are appropriate. For example, to estimate the height 20 years from now of a girl who is 5' 5" tall and growing at the rate of an inch per year, common sense suggests rejecting the simple "rate times time" answer of 7' 1" as highly unlikely, and turning instead to some other mathematical model, such as curves that approach limiting values. Sometimes, however, it may be difficult to know just how appropriate mathematical results are—for example, when trying to predict stock-market prices or earthquakes.
Often a single round of mathematical reasoning does not
produce satisfactory conclusions, and changes are tried in how the
representation is made or in the operations themselves. Indeed, jumps are
commonly made back and forth between steps, and there are no rules that
determine how to proceed. The process typically proceeds in fits and starts, with
many wrong turns and dead ends. This process continues until the results are
good enough.
Answer the following
questions:
1-3. what are the phases or stages in Mathematical inquiry?
4. What should a teacher do with students misconception and
erroneous ideas?
a. probe them further with questions until they arrive at
the correct answer
b. tell them the right concept right away
c. reprimand them for their ideas
d. tell them their answer is wrong
5. A teacher makes a review on fractions before he moves on
to decimal numbers. what specific approach is she using?
a. modelling
b. scaffolding
c. using technology
d. discussing and reflecting.
Nature and Principles of Teaching and Learning Natural Science
Over the course of human history, people have developed
many interconnected and validated ideas about the physical, biological, psychological,
and social worlds. Those ideas have enabled successive generations to achieve
an increasingly comprehensive nand reliable understanding of the human species
and its environment. The means used to develop these ideas are particular ways
of observing, thinking, experimenting, and validating. These ways represent a
fundamental aspect of the nature of science and reflect how science tends to
differ from other modes of knowing. It is the union of science, mathematics,
and technology that forms the scientific endeavour and that makes it so
successful. Although each of these human enterprises has a character and history
of its own, each is dependent on and reinforces the others. Accordingly, the
first three chapters of recommendations draw portraits of science, mathematics,
and technology that emphasize their roles in the scientific endeavour and
reveal some of the similarities and connections among them.
THE SCIENTIFIC WORLD VIEW
Scientists share certain basic beliefs and attitudes
about what they do and how they view their work. These have to do with the
nature of the world and what can be learned about it.
The World Is
Understandable
Science presumes that the things and events in the universe occur in consistent patterns that are comprehensible through careful, systematic study. Scientists believe that through the use of the intellect, and with the aid of instruments that extend the senses, people can discover patterns in all of nature.
Science also assumes that the universe is, as its name
implies, a vast single system in which the basic rules are everywhere the same.
Knowledge gained from studying one part of the universe is applicable to other
parts
Scientists Try to Identify and Avoid Bias
When faced with a claim that something is true, scientists respond by asking what evidence supports it. But scientific evidence can be biased in how the data are interpreted, in the recording or reporting of the data, or even in the choice of what data to consider in the first place. Scientists' nationality, sex, ethnic origin, age, political convictions, and so on may incline them to look for or emphasize one or another kind of evidence or interpretation. For example, for many years the study of primates—by male scientists—focused on the competitive social behavior of males. Not until female scientists entered the field was the importance of female primates' community-building behavior recognized.
Bias attributable to the investigator, the sample, the
method, or the instrument may not be completely avoidable in every instance,
but scientists want to know the possible sources of bias and how bias is likely
to influence evidence. Scientists want, and are expected, to be as alert to possible
bias in their own work as in that of other scientists, although such
objectivity is not always achieved. One safeguard against undetected bias in an
area of study is to have many different investigators or groups of
investigators working in it.
Scientific Ideas Are Subject To Change
Science is a process for producing knowledge. The process
depends both on making careful observations of phenomena and on inventing
theories for making sense out of those observations. Change in knowledge is
inevitable because new observations may challenge prevailing theories. No
matter how well one theory explains a set of observations, it is possible that
another theory may fit just as well or better, or may fit a still wider range
of observations. In science, the testing and improving and occasional
discarding of theories, whether new or old, go on all the time. Scientists
assume that even if there is no way to secure complete and absolute truth,
increasingly accurate approximations can be made to account for the world and
how it works.
Scientific Knowledge Is Durable
Although scientists reject the notion of attaining
absolute truth and accept some uncertainty as part of nature, most scientific
knowledge is durable. The modification of ideas, rather than their outright
rejection, is the norm in science, as powerful constructs tend to survive and
grow more precise and to become widely accepted. For example, in formulating the
theory of relativity, Albert Einstein did not discard the Newtonian laws of motion
but rather showed them to be only an approximation of limited application
within a more general concept. (The National Aeronautics and Space Administration
uses Newtonian mechanics, for instance, in calculating satellite trajectories.)
Moreover, the growing ability of scientists to make accurate predictions about
natural phenomena provides convincing evidence that we really are gaining in
our understanding of how the world works. Continuity and stability are as
characteristic of science as change is, and confidence is as prevalent as
tentativeness.
Science Cannot Provide Complete Answers to All Questions
There are many matters that cannot usefully be examined
in a scientific way. There are, for instance, beliefs that—by their very nature—cannot
be proved or disproved (such as the existence of supernatural powers and
beings, or the true purposes of life). In other cases, a scientific approach that
may be valid is likely to be rejected as irrelevant by people who hold to
certain beliefs (such as in miracles, fortune-telling, astrology, and
superstition). Nor do scientists have the means to settle issues concerning
good and evil, although they can sometimes contribute to the discussion of such
issues by identifying the likely consequences of particular actions, which may
be helpful in weighing alternatives.
Science Demands Evidence
Sooner or later, the validity of scientific claims is
settled by referring to observations of phenomena. Hence, scientists
concentrate on getting accurate data. Such evidence is obtained by observations
and measurements taken in situations that range from natural settings (such as a
forest) to completely contrived ones (such as the laboratory). To make their
observations, scientists use their own senses, instruments (such as microscopes)
that enhance those senses, and instruments that tap characteristics quite
different from what humans can sense (such as magnetic fields). Scientists
observe passively (earthquakes, bird migrations), make collections (rocks,
shells), and actively probe the world (as by boring into the earth's crust or
administering experimental medicines).
Science Is a Blend of Logic and Imagination
Although all sorts of imagination and thought may be used
in coming up with hypotheses and theories, sooner or later scientific arguments
must conform to the principles of logical reasoning—that is, to testing the
validity of arguments by applying certain criteria of inference, demonstration,
and common sense. Scientists may often disagree about the value of a particular
piece of evidence, or about the appropriateness of particular assumptions that
are made—and therefore disagree about what conclusions are justified. But they tend
to agree about the principles of logical reasoning that connect evidence and
assumptions with conclusions.
Science Explains and Predicts
Scientists strive to make sense of observations of phenomena by constructing explanations for them that use, or are consistent with, currently accepted scientific principles. Such explanations—theories—may be either sweeping or restricted, but they must be logically sound and incorporate a significant body of scientifically valid observations. The credibility of scientific theories often comes from their ability to show relationships among phenomena that previously seemed unrelated. The theory of moving continents, for example, has grown in credibility as it has shown relationships among such diverse phenomena as earthquakes, volcanoes, the match between types of fossils on different continents, the shapes of continents, and the contours of the ocean floors.
The essence of science is validation by observation. But
it is not enough for scientific theories to fit only the observations that are
already known. Theories should also fit additional observations that were not
used in formulating the theories in the first place; that is, theories should
have predictive power.
Science Is Not Authoritarian
It is appropriate in science, as elsewhere, to turn to
knowledgeable sources of information and opinion, usually people who specialize
in relevant disciplines. But esteemed authorities have been wrong many times in
the history of science. In the long run, no scientist, however famous or highly
placed, is empowered to decide for other scientists what is true, for none are
believed by other scientists to have special
access to the truth. There are no pre-established conclusions that scientists must reach on the basis of their investigations.
In the short run, new ideas that do not mesh well with
mainstream ideas may encounter vigorous criticism, and scientists investigating
such ideas may have difficulty obtaining support for their research.
The Principles of
Teaching Natural Science
1. Start
with questions about nature.
2. Engage
students actively
3. Concentrate
on the collection and use of evidence
4. Provide
historical perspectives
5. Insist
on clear expression
6. Use
team approach
7. Do
not separate knowing from finding out.
Principles of learning Natural Science
•
1.What students learn is influenced by their
existing ideas
•
Progression in learning is usually from concrete
to abstract
•
People do well only what they practice doing
•
Effective learning by students require feedback
•
Expectations affect performance.
•
Reflect on the
following: ?
1.
Recall your feelings and behaviour when you were
young each time the science period came. Picture yourself before and after a
learning activity.
2.
Recall how your science teacher guided the group
in investigating things in order to achieve the lesson objectives. Was her
methodology effective? Discuss in detail
3. How will you make your students interested in the learning activities you plan in each day
The Nature of Language
Of all the creatures that God created, only man can learn a language. This is the trait that differentiates man from animals. In certain cultures, a baby is not considered human because it has not yet learned the language of its people.
When a person knows a language it means he can speak and be understood by others who know the same language. He must know what sounds or signs there are in the language and what sounds are not. This knowledge includes which sounds may start a word, end a word and follow each other. For example, a Filipino may know that the consonant cluster ng may start a word in Filipino as in (ngano, nguni’t, ngiti or ngitngit,) but an American may have difficulty pronouncing these words for the reason that in his language this combination never occurs in the beginning of the word.
Furthermore, knowing a language is knowing that certain sound sequences signify concepts or meaning, and that there is an arbitrary relation between form and meaning. For example “bahay” means house in Tagalog, but the same concept of a house may have a different form or word equivalent in French or in Chinese. The words of language can be listed in a dictionary, but not all the sentences can be, and language consists of these sentences as well as words. This lends very well to the creative quality of language. From out of a finite or countable number of words numerous sentences can be formed. Speakers use a finite set of rules called grammar, to produce and understand an infinite set of possible sentences. To sum it up, a speaker of a language knows the grammar of that language, the phonology or the sound system of the language, the structure of words (morphology) and the ways in which sounds and meanings are related (semantics). Similarly, these features of language need to be known to a learner of English as a foreign language if he needs to learn the language well.