CHAPTER-5 ELEMENTARY STUDENTS’ CONCEPTIONS ABOUT ENERGY 5.1 Introduction 5.2 Scientific Evolution of the Concept: Energy 5.3 Pedagogical Perspective of the Concept: Energy 5.4 Development of the Concept maps: Energy 5.4.1 The Intended Concept Map: Indian Source 5.4.2 The Intended Concept Map: International Source 5.4.3 The Derived Concept Map: Energy and Energy Resources 5.5 Students’ Conceptions of Energy: Primary Source 5.5.1 General Analysis of Students’ Conceptions about Energy 5.5.2 Comprehensive Analysis of Students’ Conceptions about Energy 5.5.2.1 Students’ Conceptions about Sources of Energy 5.5.2.2 Energy-Meaning, Forms of Energy, Transformation of Energy 5.5.3 Discussion 5.6 Conclusion
Transcript
CHAPTER-5
ELEMENTARY STUDENTS’ CONCEPTIONS ABOUT ENERGY
5.1 Introduction
5.2 Scientific Evolution of the Concept: Energy
5.3 Pedagogical Perspective of the Concept: Energy
5.4 Development of the Concept maps: Energy
5.4.1 The Intended Concept Map: Indian Source
5.4.2 The Intended Concept Map: International Source
5.4.3 The Derived Concept Map: Energy and Energy Resources
5.5 Students’ Conceptions of Energy: Primary Source
5.5.1 General Analysis of Students’ Conceptions about Energy
5.5.2 Comprehensive Analysis of Students’ Conceptions about Energy
5.5.2.1 Students’ Conceptions about Sources of Energy
5.5.2.2 Energy-Meaning, Forms of Energy, Transformation of Energy
5.5.3 Discussion
5.6 Conclusion
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CHAPTER-5
ELEMENTARY STUDENTS’ CONCEPTIONS ABOUT ENERGY
5.1. Introduction
‘Energy’ concept is a cornerstone in science education which explains many
other phenomena such as work, force, motion, photosynthesis, chemical
reactions, chemical bonding etc (Watts, 1983). Energy concept is considered to
be important because it contributes to fundamental process which allows
predicting and interpreting the behaviours of a wide variety of physical systems
and/or other areas of science. Moreover, the understanding of energy supply
and use within a sustainable development approach (socio-cultural character of
energy) is of equal importance now-a-days. Teachers, leaders, industry and the
public agree that school teaching should equip students with the knowledge,
skills and abilities needed to live in a world faced with rising energy demands
and shrinking energy resources.
The concept of energy is widespread in all sciences and is interpreted in
multitude ways. In the context of chemistry, energy is an attribute of a
substance as a consequence of its atomic, molecular or aggregate structure.
Since a chemical transformation is accompanied by a change in one or more of
these kinds of structure, it is invariably accompanied by an increase or
decrease of energy of the substances involved. Some energy is transferred
between the surroundings and the reactants of the reaction in the form of heat
or light; thus the products of a reaction may have more or less energy than the
reactants.
In biology, energy is an attribute of all biological systems from the biosphere to
the smallest living organism. Within an organism it is responsible for growth and
development of a biological cell or organelle of a biological organism. Energy is
thus often said to be stored by cells in the structures of a biological organism,
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such as molecules of substances such as carbohydrates, lipids, and proteins,
which release energy when reacted with oxygen in respiration.
In school science curriculum, energy is a compulsory topic at secondary level,
but is simplified in primary science curriculum. There seems to be lack of clarity
regarding the developmental appropriateness of the concept, as well as
correctness of possible simplifications (Trumper, 1990). In most cases energy
is associated with sources or from the perspective of objects like battery & fuels
rather than light and heat (Duit, 1984). There appears to be a tendency to
strongly link energy as a property of living organisms commonly associated with
motion or physical work (Solomon, 1992).
The concept of energy is not immutable, as the history of physics show that
ideas about energy are still developing and cropping up in new contexts. Hence
many of the earlier ideas are now considered as fallacies by physicists. Some
physicists have pointed out that we do not know what energy is. If there is no
clear idea of what energy is, teaching the concept must be a problem. There
has been much research on the subject energy: either on students’
misunderstandings (Watts 1983, Duit 1986, Nicholls and Ogborn 1993, and
many others) or on teaching methods in order to avoid misconceptions
(Solomon 1983, Trumper 1990, 1997). Explanations of energy in school
textbooks have been criticised (Sexl 1981, Duit 1981, Duit 1987, Cotignola et
al, 2002 and Doménech et al, 2007).
Duit (1987), for instance, pointed out some inconveniences of the concept of
energy as something quasi material, defended by some physicists. According
to Beynon (1990), there is so much confusion with energy “because it is not
treated as an abstract physical quantity but something real, just like a piece of
cheese”. Empirical educational research shows alternative ideas such as
‘Energy is fuel’ or ‘Energy is stored within objects’ (Nicholls and Ogborn 1993).
There is, however, a reason for that concept of energy. The most common
presentation of energy in contemporary textbooks states: energy cannot be
destroyed nor created but only transformed. If energy can be transformed, then
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forms of energy must exist. Connected with transformation appears the
indestructibility of energy, which reinforces the idea of its reality. Thus, it is
understandable that some textbooks present energy as something quasi
material, as Duit stressed, and students think of it as something real.
The concept of energy took a long time to historically unfold, and is still being
unravelled with advent of modern research at the level of sub-atom or the
universe. The following section traces the evolution of the concept of energy
historically from the time of Aristotle in the 4th century BC to the present.
5.2. Scientific Evolution of the Concept: Energy
The word energy derives from Greek energeia which appears in the work of
Aristotle in 4th Century BCE. The concept of energy emerged out of the idea of
Vis viva (living force), which Leibniz defined as the product of the mass of an
object and its velocity squared and he believed that total Vis viva was
conserved. Gottfried Wilhelm Leibniz 1646-1716) convinced himself that the
true measure of the efficacy of a force is the product of the mass and the
square of the velocity, which he termed the Vis viva or living force, as
contrasted to the “Vis Mortua” or dead force of statics.
To account for slowing due to friction, Leibniz claimed that heat consisted of the
random motion of constituent parts of matter. Isaac Newton too shared this
view, but this was generally accepted more than a century later.
In 1802 during his lectures to the Royal Society, Thomas Young was the first to
use the term ‘energy’ in its modern sense, instead Vis viva. Thomas Young
(1807) defined energy “the product of the mass of a body into the square of its
velocity may be properly termed its energy”.
Gustave – Gaspard Coriolis described kinetic energy in 1829 in its modern
sense and in 1853; William Renkine coined the term “potential energy”.
It was argued for some years whether energy was a substance (the caloric) or
merely the physical quantity.
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The concept of energy and indeed all science is here investigated from the
roots of the concept which is the notion of invariance or constancy in the midst
of change.
A closer approach to the energy construct as we employ it today is found in the
famous treatise by Lagrange, Mecanique Analytique, (1788) he refers to the
conservation of Vis viva. D’ Alembert 1743) can be considered to settle the
momentum vs. Vis viva controversy. The fact remains that D’ Alembert did set
forth the general argument that modern physics has found satisfactory.
Before 1842, Robert Mayer had been to Java as a doctor on board. During an
operation of the lungs he observed that the venous blood appeared lighter in
colour in the hot climate of Java compared to the cold areas of Europe. He
suggested that to attain this, ‘something’ will have to be spent. He connected
this idea to the idea of force cause. In 1842 Mayer put forward 2 questions,
what forces are and how they are related to each other. Mayer defended that
forces are causes as per prevailing idea in science at that time. For Mayer,
force disappears to make the effect. For example, weight was the cause of
falling in mechanics. According to Mayer, the cause of falling is not only weight,
but also the height of the body. By falling, the height decreases and the velocity
of falling increase. The meaning of force cause as given by Mayer is that the
‘force of falling’ diminishes and in its place another force ‘motion’ arises.
Joule (1843-1850) established the connection with the science of that time
through the concept of heat. There are two main thesis concerning the nature
of heat. According to Rumford (1798) and Davy (1799), heat was motion.
According to Carnot 1824) or William Thomson (1849), heat was a substance.
Some authors had posed the question, ‘what is heat?’ in connection with their
experimental works during the first part of the nineteenth century. Joule’s
research concerns these questions: heat is either a substance or motion. If heat
is a substance, its quantity cannot change. If this is not the case, then heat
cannot be a substance. If it cannot be a substance, it can only be motion,
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according to the science of that time. Joule’s experimental work aimed to show
that heat is not a substance. If it is motion then the question arose of how much
motion of mechanical character there must be in order to obtain a unit of heat.
This became then the main objective of his experimental work: the
determination of the mechanical equivalent of heat. He devised experimental
set ups.
Colding (1843-1856) aimed to prove his idea ‘forces of nature are
imperishable’. Observation shows that forces disappear. Colding had put
forward the thesis that they are not destroyed but transformed. The elements of
this transformation are observable, such as motion and heat. If what is given at
first, for instance motion is capable of being represented quantitatively by q, the
effect, for instance heat, must be equal to q. His experimental work
corroborates his idea in the following way: the more force that is produced, the
more that appears the force added does not disappear but becomes heat.
Helmholtz (1847) wrote a treatise on conservation of energy written in the
context of his medical studies. He discovered the principle of conservation of
energy while studying muscle metabolism. He tried to demonstrate that no
energy is lost in muscle movement, and there were no vital forces necessary
to move a muscle. Drawing on the earlier work of Carnot and Joule he
postulated a relationship between mechanics heat, light, electricity and
magnetism by treating them all as manifestations of a single force (energy in
modern times).
The term ‘energy’ meant activity and had been used with this meaning in the
18th century and in the first part of the 19th century. In1851, William
Thomson, later on Lord Kelvin, used the word to refer to the mechanical
activity of a body, i.e., its capacity of doing work. The division into two sets –
static and dynamical – of the stores of activity available led to the distinction
between potential and kinetic energy. Attempts made in order to adapt the
concept to phenomena led to the concept of energy as a substance. Energy
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was considered a substance towards the end of 19th century. This was the
reason for criticism and for some of the difficulties with the understanding of
energy. The variety of theses concerning the nature of heat, falling of bodies,
energy and the fact that these theses were used to explain phenomena
highlight an important characteristic of science: scientific theories include an
interpretation of phenomena. Present theses concerning heat, which is a form
of energy or transference of energy, force, which is the cause of acceleration
or a thing of thought and energy, which exists or is an abstracted concept,
help students to understand that such problems are not only from the past
and foster their thinking about science.
James P. Joule (1818-1889) determined energy equivalence of heat, and work
equivalence of electric energy (1 cal=4.184 J).
Max Planck (1858-1947) explained the energy aspect of light.
Albert Einstein developed the special theory of relativity and gave the energy
equivalence of mass, E = m c2 (rest mass of electron = 511 keV).
The recent statement about energy includes the following (Sefton. lan, 2000).
- Energy is an attribute of a system which may consist of one or more objects.
- Whenever the energy of a system increases (or decreases - there is a
corresponding decrease (or increase) outside the system, thus holding the
idea of conservation of energy as weak version.
- There are only 2 basic kinds of energy, K.E and P.E
- KE is associated with motion
- PE is associated with interactions between objects
- Electro-magnetic PE can be described as being stored in and transmitted by
electric and magnetic field.
Energy: The Subject Matter
Energy is in everything – it is often described as the ability to do work. Almost
all food energy comes originally from sunlight. The chemical elements that
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make up the molecules of living things pass through food webs and are
combined and recombined. At each link some energy is stored, but much is lost
along the way in the form of heat into the environment.
Some examples of energy use
- When we eat food, our body uses (chemical) energy embodied in the food
to move around.
- Most of the electricity produced in the world comes from the chemical
energy released in the burning of coal, oil or gas.
Science classifies energy into 2 categories.
Kinetic Energy Potential Energy
Electrical energy- the movement of electrical charges
Gravitational Energy
Radiant energy- electro-magnetic energy that moves in waves. Visible light, X-ray and radio waves
Elastic Energy
Sound energy Chemical energy
Motion/kinetic energy Nuclear energy
By nuclear fission and fusion
In physics, energy is an indirectly observed quantity that is often understood as
the ability of a physical system to do work on other physical systems. Since
work is defined as force acting through distance (a length of space) energy is
always equivalent to the ability to exert pulls or pushes against the basic forces
of nature along a path of a certain length.
The total energy contained in an object is identified with its mass and energy
cannot be created or destroyed. When matter (ordinary material particles) is
changed into energy such as energy of motion or into radiation), the mass of
the system does not change through the transformation process. However,
there may be mechanistic limits as to how much of the mater in an object may
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be changed into other types of energy and thus into work, on other systems.
Energy, like mass, is a scalar physical quantity, in the international system of
units (SI) energy is measured in joules, but in many fields other units, such as
kilowatt hours and kilocalories are customary. All of these units translate to
units of work, which is always defined in terms of forces and the distances that
the forces act through.
A system can transfer energy to another system by simply transferring matter to
it (since matter is equivalent to energy, in accordance with its mass). However,
when energy is transferred by means other than matter-transfer, the transfer
produces changes in the second system, as a result of work done on it. This
work manifests itself as the effect of forces applied through distances within the
target system. For example, a system can emit energy to another by
transferring (radiating) electromagnetic energy, but this creates forces upon the
particles that absorb the radiation. Similarly, a system may transfer energy to
another by physically impacting it, but in that case the energy of motion in an
object called kinetic energy, results in forces acting over distances (new
energy) to appear in another object that is stuck. Transfer of thermal energy by
heat occurs by both of these mechanisms; heat can be transferred by
electromagnetic radiation or by physical contact in which direct particle-particle
impacts transfer kinetic energy.
Any form of energy may be transformed into another form. For example all
types of potential energy are converted into kinetic energy when the objects are
given freedom to move to different position (as for example, when an object
falls off a support). When energy is in a form other than thermal energy, it is
theoretically possible to transform it with very high efficiency to any other type
of energy, including electricity or production of new particles of matter. (Exactly
100% efficiency is impossible only because of friction and similar loses). By
contrast, there are strict limits to how efficiently thermal energy can be
converted into other forms of energy, as described by Carnot’s theorem and the
second law of thermodynamics.
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Fig. 5.1: Timeline – Energy
From the timeline of energy (Figure 5.1), it is evident that individual scientists
had understood and coined kinetic energy in the year 1829 and potential
energy in 1853. There was confusion as to whether energy was a substance or
merely the physical quantity.
Energy Concepts
1829 French Physicist Gustavo Coriolis
introduce the term ‘kinetic energy’
1843 James Joule’s experiments show
how heat, work and power are related
1847 Joule and German physicist Hermann von
Helmholez and Julius Meyer independently state the
law of conservation of energy
1853 Scottish scientist William
Rankine devises the concept of
potential energy
1881 The World’s first
electricity generating power
station opens in Surrey, UK.
1884 Irish Engineer Charles
Parsons invents the Steam
Turbine
1905 German physicist Albert
Einstein suggests that matter is a
form of energy, and vice versa
1980s Declining fossil fuel
reserves and pollution
bring calls for machines and
industries to be more
energy efficient
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The experiments of Joule, Helmholtz and Mayer independently put all the
confusion regarding the physical nature of energy to rest. If energy was not a
substance then it could only be motion according to the science of that time.
Joule’s experimental work proved that a certain amount of motion is required to
obtain a unit of heat 1Cal = 4.184 Joules.
Scientific theories attempt to interpret phenomena. It is also evident that
theoretical aspect of energy was in scientific discussions for some time and
then experimentation proved the theoretical premise followed by mathematical
formula such as the formula propounded by Einstein. The relation between
heat, work, and energy, power and motion got established one by one.
Historically energy was thought as force till the time of Mayer and as a
substance till the end of 19th century. The simultaneous but independent work
of Joule, Mayer and Helmholtz established the law of conservation of energy.
Hence other forms of energy light, electricity, sound etc. were discovered.
Einstein suggested then that matter is energy and vice versa. Discovery of
many theories (aspects) of energy opened up other the technological
contributions like power stations, turbines and even nuclear energy.
From the study of the evolution of energy, the implications for school science is
that it is difficult to understand energy as a physical quantity till they understand
the effect of energy. They would probably understand phenomena related to
energy first, then understand the meaning of energy as the ability to do work
and then forms of energy. Conceptualizing conservation of energy and
transformation would be possible once students are ready to go beyond
observation of phenomena to explanation of phenomena (possibly by
theoretical aspects). The attention of students needs to be drawn to conceptual
explanation behind physical phenomena like water wheel, wind mill etc. The
discoverers of energy did not find anything that is indestructible, transformable,
but rather that the concept of energy underwent a change of meaning from
substance to a quantity.
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5.3. Pedagogical Perspective of the Concept: Energy
Energy is chosen as a focus of interest of most science curricula since it
provides key to our understanding of the ways things happen in physical,
biological and technological world. Moreover energy issues have personal,
social and environmental implications for students creating their interest in
learning. Understanding these implications is necessary for students to make
informed decisions concerning current situation. Sources of energy and energy
transformations are inter-related concepts and curriculum places emphasis on
the development of knowledge and attitudes in these areas. Energy as a
concept is problematic, not easily understood. Nobel laureate physicist Richard
Feynman during a 1961 lecture for undergraduate students at the California
Institute of Technology said this about the concept of energy: “There is a fact,
or if you wish, a law, governing all natural phenomena that are known to date.
There is no known exception to this law—it is exact so far as we know. The law
is called the conservation of energy. It states that there is a certain quantity,
which we call energy that does not change in manifold changes which nature
undergoes. That is a most abstract idea, because it is a mathematical principle;
it says that there is a numerical quantity which does not change when
something happens. It is not a description of a mechanism, or anything
concrete; it is just a strange fact that we can calculate some number and when
we finish watching nature go through her tricks and calculate the number again,
it is the same.”(Feynman Lectures) Earlier, researchers like Stead (1980),
Solomon (1980), Duit (1981), and Watts (1983) have been interested to
investigate into the frameworks of students’ and adults’ conceptions about
energy. The seven frameworks that were found useful as means of analysing
and describing the complex responses students provide as they discuss the
concept of energy are:
Human-centred models: Energy is associated with human beings;
Depository model: Some objects have energy and expend it;
Ingredient model: Energy is a dormant ingredient within objects, released by
trigger;
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Activity model: Energy as an obvious activity model;
Product model: Energy is a by-product of a situation;
Functional model: Energy as a general kind of fuel with making life comfortable;
Flow transfer model: Energy as type of fluid transferred in certain processes.
Later researchers using quantitative data also fell back on these frameworks.
Later researchers like Coehlo (2009), Lijnse(1990), María I. Cotignola (2002), et
al have attempted to find whether difficulties in learning energy concepts are
linked to the historical development of this field and also whether using
historical ideas in pedagogy helped in removing these difficulties.
Research shows that concepts based on singular ideas such as identifying an
energy source is easily understood by primary students. When students have
ideas about energy sources and transformation processes, they can learn
energy conservation by recognizing a system with various components. This
means that the learning progression/evolution of energy can be facilitated when
students can generate and connect ideas of sources of energy forms of energy
and transformation of energy. A highly integrated concept like energy
conservation may be difficult at the elementary level.
Researchers have investigated into students’ conceptions of energy using
techniques and tools according to various perspectives. From all the available
research in the area of elementary students’ understanding of energy concepts,
one can conclude that researchers have investigated on the sub-concepts of
fuels, renewable sources of energy, energy in living systems, forms of energy,
transformation and conservation of energy. Concepts about fuels of younger
students’ of class 3rd have been researched (Urevbu, 1984).Forms of energy
may be conceptualised in specific contexts by students of class 6th (Tsangliotis,
2005). Duit (1984) has studied the understanding of students of class 7th to 10th
about transformation of energy as well as conservation of energy. None of the
researchers have attempted to find the conceptualisation about conservation of
energy in elementary students except Duit (1984). The table below summarises
the sub-concepts chosen by investigators in research literature.
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Table 5.1: Investigators Studying Conceptions of Elementary Students about various Energy Concepts
Sub-concepts of Energy
Investigators
Class
III IV V VI VII VIII
Sources of Energy-Fuels
Urevbu (1984) � � � � � �
Sources of Energy-Pollution
Boylan (2008) � � � � � �
Sources of Energy-Renewable
Boylan (2008) � � � � �
Sources of Energy-Non-renewable
Boylan (2008) � � � � �
Energy in Living Systems
Nicholls & Ogborn (1993) Trumper (1993)
� � �
Sun as Ultimate Source of Energy
Tsangliotis (2005): transformation in specific contexts of toys and science fair, solar energy and mechanical energy only
�
Energy and Work Duit (1984) � �
Forms of Energy Tsangliotis (2005) � � �
Duit (1984) � �
Transformation of Energy
Tsangliotis (2005) �
�
Duit (1984) � �
Different investigators have different opinion about inclusion of energy concepts
in primary or elementary curriculum.
According to Watt (1983) if youngsters are to be encouraged to undergo
conceptual change towards the scientific view of energy, then both the content
and practice of science education must change. Pupils' ideas must be valued
and built on. He recommends that both student and teacher need to find out
and to know both their own - and each others’ - meanings for energy.
Warren (1986) indicate that energy concepts should be taught only to students
of higher classes, who have developed a high level of abstract reasoning while
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Solomon (1986) claimed that teaching energy, should be started as early as
possible (as early as 3rd or 4th grade) to be encouraged to follow paths of
abstract conceptualization.
Duit, (1989) admits that the abstract nature of the energy concept makes it
difficult to understand. Furthermore, in the primary school education, some
aspects of teaching of ‘energy’ concept are controversial. For example, there
are such questions as “in which class?” and “at which level?” On the other
hand, in view of Driver and Warrington (1985) instruction of energy and related
concepts is difficult for primary school students, but yet those concepts should
be taught. Trumper (1993) argues for early teaching of the concept ‘energy’ to
lead eventually to necessary abstractions.
The typical teaching sequence for the energy concept has been determined
primarily through expert consensus by Liu and McKeough, (2005) based on the
data on TIMSS. This sequence is: (1) energy source, (2) work, (3) energy
transfer, and (4) energy conservation. It is expected that students will acquire
the concept of energy conservation during the high school years (American
Association for the Advancement of Science, 2001), and by the 8th or 9th
grade, students are expected to understand the concept of energy transfer and
the notion of energy as the ability to do work.
Dawson-Tunik (2005) is of the opinion that many ninth graders achieve neither
an understanding of energy as the ability to do work nor an understanding of
energy transfer at the conceptual level.
Hirca N. et al. (2008) found that many eighth graders cannot apply their
theoretical knowledge of types of energy to their daily life experiences, about
the same percentage of them is able to link type of energy plant absorbed with
photosynthesis. They concluded that the students had some difficulty not only
in understanding and correctly using of the concept of energy and the related
concepts, but also making a relationship between theoretical knowledge and
practical one.
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Summarising, the development of understanding energy involves understanding
many aspects of energy such as energy source, transfer, transformation, and
conservation. To be scientifically complete and sophisticated, understanding
should be based on energy as a conserved quantity. Students' overall
understanding can progress toward energy conservation by identifying energy
sources in a system and connecting various forms of energy and energy transfer
processes to changes occurring in the system. In addition, students should be
able to recognize and use energy concepts across mechanical, biological,
chemical, thermodynamic, and technological applications.
5.4. Development of the Concept Maps: Energy
Concept maps were developed to fulfil the following objectives: a) To
understand what the intended curriculum includes in the area of energy in
Indian context and b) To identify what constitutes ‘standard’/expected
knowledge in the area from available curricular resources and c) to derive a
concept map from the maps mentioned above to form a basis for developing
questionnaire.
Concept maps can be defined as visual representations that are added to
instructional material to communicate the logical structure of the instructional
material. The concept map serves as a device to illustrate the hierarchical
conceptual and propositional nature of knowledge. The concepts are arranged
in a hierarchy with a super ordinate concept at the top. The concepts are linked
by lines labelled with connecting words that form the proposition uniting the
concepts. Concept mapping requires the mapper to prioritise and make
judicious use of selected concepts when mapping. It involves identification
concepts in study materials and their organisation from the most to least
general, more specific concepts.
Concept maps are flexible tools that can be used in a variety of educational
settings (Stewart, Van-Kirk and Rowell, 1979).They have been used as a tool
for assessing meaningful learning(Novak,1979) as well as in curriculum
planning, instruction and evaluation( Stewart et al,1979).Concept maps are
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useful in science curriculum planning for separating significant from trivial
content (Starr and Krajcik, 1990) and focussing the attention of curriculum
designers on teaching concepts and distinguishing intended curriculum from
instructional techniques (Stewart et al,1979). Science education reforms have
developed concept maps to decide which concepts are the most important to
learn and use what are important concepts that contribute the big picture or
pervasive principles at the core of scientific disciplines. Science educators
extract, select and prioritize concepts from information-dense materials
(Jonassen, Biessner and Yacci, 1993). Science curriculum reforms in USA and
Australia are such cases and are being presented in the following paragraphs.
AAAS Project 2061 and the National Science Teachers Association published
two volumes of Atlas of Science Literacy. The two volumes include nearly 100
maps which chart all the learning goals specified in Bench marks essential for
every student to learn. The maps given in the Atlas of Scientific Literacy
illustrates the relationships between individual learning goals and shows the
growth of understanding of ideas. Connecting arrows indicate the connections
between ideas which are based on the logic of the subject matter (or on
cognitive research about how students learn).The maps are available at
