TEACHING CONCRETE OR FORMAL CONCEPTS AT AN EARLY AGE
Du{an KRNEL
Faculty of Education, University in Ljubljana, Slovenia
What is a concept?
What kind of concepts are we teaching? The answer to this question depends on the
definition of the concept of ‘concept’ we use. In its common use, the term concept is synonymous
with idea. In Blackwell’s dictionary of cognitive psychology, concept is defined as a mental image
or idea which includes a, description of important properties of a class of objects or of a word
(Eysenck, 1990). The similar definition of concept as a class of entities that have the same relevant
or defining characteristics (Gagne 1997) suits some but not all concepts such as love and justice,
or light, mass, weight, frequency and others. This narrow definition is also problematic for
concepts such as density, velocity or the rate of reactions. These ideas are more similar to
principles. Gagne refers to such ideas as ‘relational concepts’. The third category comprises
concepts like centimetre or electron, so-called ‘identities’ (Herron et al., 1977). It seems there is no
uniform definition because different authors define the term concept from different perspectives
and different contexts.
Many researchers see the act of classification as a key operation in the formation of
concepts. According to Gagne (1997), discrimination is the first step in the process of
classification, followed by the generalisation of the characteristics that form a class or set. This
generalisation then leads to the formation of a new concept. A similar process is described by
Lovell (1971). Lovell, however, included an additional step in the development of concepts:
differentiation between the properties of objects in the set. This is followed by discrimination
between properties that are specific to an object and those which are common to the set. The
identification of common properties then leads to the development of new concepts.
Imposing patterns on the world in this way helps children make sense of the world. In
new encounters with an object or substance, the child classifies the object in a class that has
already been generated. In this way new objects can be assimilated into existing mental structures.
Alternatively, an encounter with a new object may not exactly fit with existing classes and may
require a process of accommodation in which the characteristics of an existing class are modified,
thus bringing about conceptual change (Labinowicz. 1989). A quick and successful way of
classifying is enabled by comparing an object with a prototype (Langford, 1987; Rosch, 1980).
Prototypes are used as examples of a class. Children attribute a limited range of properties to these
prototypes, thereby enabling them to represent the class.
For example, water is often used as a prototype for liquids so that liquids are viewed as
transparent, colourless, runny substances that wet the surfaces on which they are placed (Krnel,
Watson and Glažar, 1998). The properties of prototypes can be formed from actions on objects or
materials (Bliss and Ogborn, 1994). For instance, the action of pouring a liquid leads to the
formation of a schema that differentiates liquids from other substances. This is one of the limited
range of properties that is attributed to water and enables it to act as a prototype for liquids.
When describing mercury we found a good example of the development of the concept
of substance (Krnel, Watson and Glažar, 2005). The pattern of development with age can be seen
in Table 1. It started with a description of mercury using a prototype for liquids (i.e. water),
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children then began recognising differences between mercury and water, and described mercury as
water with something added to it. Next children identified metal in the mercury when they
recognised the properties of metals (e.g. lustre). They therefore described mercury as a metal plus
water. The recognition of mercury as a particular kind of metal is apparent in their descriptions of
mercury as a melted metal or a metal in a liquid state.
Table 1 Words used for describing mercury
Category of
answers
3 years
5 years
7 years
water
Coloured water
different water
water(4)
white water
grey water
water (3)
grey water,
black water
gold water,
silver water (2)
water+other
water(2)
silver liquid
silver water (3)
liquid- metal
sea-iron
liquid - bronze
silver colour
silver colour,
grey colour
Plasticine,
pudding
water (liquid)
and other
substance
liquid with
other substance
(mixture)
colour as a
liquid substance
different
substance
melted metal
nail colour
poison
11 years
13 let
water
dirty water,
magnetic
water
lead + water
metal + water
other melted
substance
other metal
mercury
9 years
mercury (2)
grey colour
melted iron
liquid silver.
melted silver
melted lead
(3),
melted metal
+ something
melted rock
lava
gold,
lead
mercury
lead (2),
iron
mercury (6)
liquid
zinc,
melted
iron,
melted
lead
aluminiu
m
mercury
(8)
In the context of the school classroom, we often talk about concrete and abstract
concepts. But can a concept be concrete? According to the theories of concept development all
concepts are abstract, abstracted from many specific instances and concrete examples. It is
therefore not a concept but a representative of some class or its defining attributes that are
observable and thus concrete.
Lawson’s (1977) differentiation between concrete and formal concepts is based on
Piaget’s operational levels. ‘Those concepts which can be derived from direct experience (action,
observation, examples) by using concrete reasoning patterns ( e. g. classification) are called
concrete concepts. The formal concepts must be understood in terms of other concepts, functional
relationships (e.g. laws), inferences, idealisation, models,…. Require formal reasoning patterns’.
This distinction between a concrete and abstract concept is usually expressed as: concrete concepts
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are formed through experience with objects and phenomena and abstract concepts are learned by
definition.
In science teaching we encounter a number of different abstract concepts. Each category
causes a specific problem for students when they are faced with them. For science education
purposes Herron (Herron 1971) identified few categories:
− concepts with no perceptible instances (atom, molecule, nucleus, universe, light
year...);
− concepts with critical attributes which are not perceptible (element, compound…);
– concepts which require knowledge of principles (mole…);
– concepts involving symbolic representation (chemical symbol, formula, equation…);
– concepts that name processes (melting, oxidation, photosynthesis…);
– concepts that name attributes and properties (mass, weight, electric charge,
flammable…); and
– concepts that describe attributes or properties (gram, kilo, molarity, pH…).
Are the early years of schooling reserved for concrete concepts?
Are the early years of schooling reserved for concrete concepts because children are then
operating on these concrete levels and are we then following the analogy – concrete thinking:
concrete concepts?
An analysis of almost every curriculum for science in primary school shows we are in
fact teaching very formal concepts such as time, space, matter, living, force and others using the
concrete aspects of these concepts. But are we successful? Even with the concrete concept of plant
young children have difficulties. In this and similar cases, in spite of a concrete and perceptible
representative, misunderstandings emerge due to difficulties finding out the common properties
and generalising them to a whole class.
Further, Piaget found himself facing contradictions about children’s classification of
animate and inanimate objects. In some of his works he claims that toddlers already distinguish
between these options when they feel in their hands a real cat and a toy cat even if it is made very
realistically. So the problem lies in reasoning, defining criteria and definitions and not in an
intuitive feeling for living things. Regarding these is children’s animism often treated too generally
and sometimes unsuitably. Some post-Piagetian studies suggest that young children use animism
metaphorically in order to explain phenomena rather than believing that inanimate objects reason
like human beings. Recent studies also confirm that children are capable of a correct classification
between the living and non-living, but this ability is not indicative of a biological grasp of the
implications of the life concept. When children think about biological criteria (nutriment,
breathing, reproduction…) they use them pragmatically and context-dependently. They frequently
only use one (the suitable one) of the critical attributes (movement) and this can lead to a false
classification e.g. fire clouds, sun, candle, river, car – all of these things can be alive.
Often a misunderstanding between children and a researcher is caused by using different
terms for the same question e.g. ‘Is an object living’ or ‘Has it a life’. For a representative share of
children these words hold different meanings. Researchers have found that a similar weak
distinction is also characteristic for the following pairs of words: destruction and dying, seeing and
knowing, contact and feeling, ears and hearing, making noise and talking, expanding and
growing…
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In children’s minds all of this reasoning about being alive and not alive are more
frequently connected with animals rather than plants. This is also justified by the development of
analogical thinking. The first prototype for a living being is a human or even better a child itself,
the more similar the being is to a human the greater chance it has to be classified as alive. From
this reasoning we can understand why animals are treated differently from plants. And even
between animals some are more alive or more animals than others (e.g. a monkey and a worm).
This developing pattern is confirmed by several research papers. All of them confirm the
wide gap between understanding animals or plants as being alive. The distinction between animals
and plants is so firm that it can also resist the influence of teaching. Researchers also report this
misunderstanding between middle and high school students. These students use different attributes
for animals and different ones for plants. For plants one of the leading attributes is growth, while
for animals it is movement. Consequently, trees and mushrooms are considered alive less
frequently than herbaceous plants. The different treatment and understanding of animals and plants
is also caused by language. In Hebrew the word for ‘life’ is similar to that for ‘animal’, in
Slovenian the word ‘plant’ is derived from the word ‘growth’. In everyday language we describe
humans in a special condition as a ‘plant’! In many languages the words for ‘growth’ and ‘death’
in animals are different from those applied to plants.
The concept of ‘plant’ in children’s minds is even narrower. Researchers reports that in
classification tasks only a minority of children used generalised criteria such as ‘grows in the soil’,
‘has leaves, ‘has roots’ to describe the general properties of a plant. Similarly to the alive – nonalive classification, where trees were less frequently classified as alive, is the exclusion of trees
from the narrow concept of ‘plant’. This is well illustrated by the explanation that the ‘tree was a
plant when it was little’. From other studies it appears that many children view weeds, vegetables
and seeds not as sub-sets of the set plant but rather as comparable sets. The classification depends
on the items and their numbers so the parallel and not subordinate sets could also be ‘plant’, ‘tree’
and ‘flower’.
It should be noted that several researchers view the idea that children classify objects as
living or non-living through the systematic use of criteria as a simplistic notion. They suggest that
children are more likely to appeal to expert adult knowledge than to particular biological criteria in
reaching their decision. One of the results of this behaviour is mutually exclusive rather than
hierarchically ordered groups. An interesting finding connected to the formation of the concept
‘plant’ is that students encountered more difficulties classifying organism in taxonomic categories
as regards plants than animals.
How to help a student construct new concepts
(precursors and anchoring concepts)
In the Piagetian sense, for every formal concept there are intuitive precursors. This
phenomenon appears very much akin to the experience we have all had when we ‘know’
something is true but just cannot seem to find the words to explain this (Lawson 1975). From the
definition of the formal concept above we can infer that precursors can also be concrete concepts.
Similar to the idea of precursors are the so-called ‘anchoring concepts’ proposed by Clement
(1989). Anchoring concepts are defined as an intuitive knowledge structure that is in rough
agreement with accepted theory; intuitive here meaning that which is more concrete than abstract
and more self-evaluated. It remains the task of the teacher who wishes to teach formal concepts to
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identify these intuitive precursors as well as the natural sequence in which they manifest
themselves in formal conceptualisation.
Similar ideas are ‘critical barriers’, concepts which are associated with restricted
learning. The failure to grasp these concepts gives rise to an insecure cognitive structure that in
turn destabilises or constrains the subsequent learning of related concepts.
How then do we determine the correct and necessary precursors for a given formal
concept?
For the concept of photosynthesis precursors are: gas, oxygen, carbon dioxide, light,
water, food, sugar...
The concept glaciation era requires the learner to engage with a large number of
concepts: ice, temperature, glaciation, climate, geological time and so forth.
The concept of mass extinction (extinction of dinosaurs) requires the conceptualisation
of a host of lower order concepts: organism, death, proportion, fossilisation, evolutionary change
and others.
Herein lies the problem of understanding many scientific concepts: at which point can
intervention be most effective? One conclusion is that lessons which introduce a topic by
providing a conceptual structure can be more effective than those that withhold a conceptual
structure and provide a practical investigation: this is likely to be particularly so for topics about
which the child’s level of conceptual knowledge and understanding is low.
Some precursors (anchoring concept or barriers) are simple and concrete, but others are
more abstract and related to a series of new precursors. In order to grasp them the student should
build the whole network of connected concepts.
One suggestion for teachers is to build a concepts map based on the epistemology of
scientific discipline. On such a map the concepts are hierarchical and organised in a structure.
Each subordinated concept could be a precursor for a superordinated concept in the same branch.
Figure 1. Concept map
To avoid linking concepts which result in misunderstanding and the construction of
misconceptions, Chi (1991) suggested the construction of ‘ontological trees’.
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Figure 2 Ontological tree
The precursors defined by Lawson are tiny branches in the ontological tree, for example,
precursors for the concept of matter would be solids, liquids, gases.
Other concepts can be used as precursors for testing the validity of the structure (position
of the concept) in different branches. For the branch ‘matter’ the precursors could be weight,
colour, volume and others.
With this approach in both the teacher’s and curriculum developer’s minds, the benefits
are many, ranging from better organised and more meaningful teaching to smoother constructions
of formal concepts in the student’s mind. Formal concepts should then represent the final teaching
target for the teacher, albeit thought through concrete concepts.
Literature
[1] Bliss, J. and Ogborn, J. 1994; Force and motion from the beginning: learning and instruction
4, 7-25.
[2] Chi. M.T.H. 1991; An idealized ontology in Chi M.T.H. and Giere, R., (editors) Cognitive
models in Science: Minnesota studies in philosophy of science. Minnesota: University of
Minnesota Press.
[3] Clement, J., Brown, D.E., Zeitsman A., 1989; Not all preconceptions are misconceptions:
finding ‘anchoring conceptions’ for grounding instruction on students intuitions. Int. J. Sci.
Ed., 11, 554-565.
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[4] Driver R. et al. 1994: Making sense of secondary science, research into children's ideas.
London: Routledge.
[5] Eysenck, W. M. 1990; The Blackwell dictionary of cognitive psychology. Oxford: Basic
Blackwell.
[6] Gagne, R.H. 1997; The condition of learning (2nd edition). New York: Holt, Rinehart &
Winston.
[7] Goswami U. 1992; Analogical reasoning in children. Hove (UK): Lawrence Erlbaum
Associates.
[8] Herron J.D., Cantu, L. L., Ward R. 1977; Problems Associated with Concept Analysis.
Science Education, 61(2), 185-199.
[9] Krnel, D., Watson, R. and Glažar, S.A. 1998: Survey of research related to the development of
the concept of ‘matter, I.J.S.E., 20(3), 257-289.
[10] Krnel, D., Watson, R. and Glažar, S.A. 2005: The development of the concept of ‘matter’: A
cross age study of how children describe materials. I.J.S.E. 27(3), 367-383.
[11] Labinowicz, E. 1989; The Piaget Primer. Ljubljana: DZS
[12] Langford, P. 1987; Concept development in the primary school. London: Cromm Helm.
[13] Lawson, A.E. 1977; Concrete and formal concepts in Karplus, R., et al. (editors), Science
teaching and the development of reasoning. Berkeley: Lawrence Hall of Science, University
of California.
[14] Lawson, A.E. 1975; Developing formal thought through biology teaching. The American
Biology Teacher, 37(7), 411- 420.
[15] Leach J. et al. 1996: Children' ideas about ecology 2. Ideas found in children aged 5-16 about
cycling of matter, International Journal of Science Education, 18(1), 19-34.
[16] Lovell, K. 1971, The growth of basics mathematical and scientific concepts in children (5th
ed.). London: Unibooks, University of London Press.
[17] Rosch, E. 1980; Classification of real world objects. In P. N. Johnson-laird, and P.C. Wason
(Eds.), Thinking, reading in cognitive science. Cambridge, MA: Cambridge University Press.
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