Teaching concrete or Teaching concrete or formal concepts at an formal concepts at an

early ageearly age

Dušan KrnelDušan Krnel

Faculty of Education Faculty of Education University in LjubljanaUniversity in Ljubljana

What kind of concept are we teaching?What kind of concept are we teaching?

Definition of concept Definition of concept

concept = ideaconcept = idea

In the Blackwell’s dictionary of cognitive In the Blackwell’s dictionary of cognitive psychology is the concept defined as psychology is the concept defined as mental image or idea which includes mental image or idea which includes description of important properties of a class description of important properties of a class of objects or of a word (Eysenck, 1990). of objects or of a word (Eysenck, 1990).

The similar The similar is is definition of concept as a definition of concept as a class of entities that have the same relevant class of entities that have the same relevant or defining characteristics (Gagne 1997)or defining characteristics (Gagne 1997)..

Concept as a class of entities that have the same Concept as a class of entities that have the same relevant or defining characteristics.relevant or defining characteristics.

chair liquidchair liquid

dog mixturedog mixture

Gagan or Lowell definition suits some of them but is not valid Gagan or Lowell definition suits some of them but is not valid for concepts such as love and justice, or light, mass, weight, for concepts such as love and justice, or light, mass, weight,

frequency and others frequency and others

Concepts:Concepts:

- love love densitydensity- justicejustice velocity velocity

- mass mass rate of reaction rate of reaction - weightweight- frequencyfrequency- ↓↓ ↓↓- - pprinciplesrinciples

relational relational conceptsconcepts

??

Concepts:Concepts:

- centimetre- centimetre- electron electron →→ identitiesidentities

It seems there is no uniform definition It seems there is no uniform definition because different authors define the because different authors define the term concept from different term concept from different perspectives and different contextsperspectives and different contexts

In science teaching we are encountered with the number of In science teaching we are encountered with the number of different abstract concepts. Each category caused specific different abstract concepts. Each category caused specific problem for the students when they are faced with them. problem for the students when they are faced with them. For science education purpose Herron (Herron 1971) For science education purpose Herron (Herron 1971) identified few categories:identified few categories:

- concepts with no perceptible instances (atom, molecule, - concepts with no perceptible instances (atom, molecule, nucleus, universe, light year,….),nucleus, universe, light year,….),

- concepts with critical attributes which are not perceptible - concepts with critical attributes which are not perceptible (element, compound,…),(element, compound,…),

- concepts which require knowledge (mole,…), - concepts which require knowledge (mole,…), - concepts involving symbolic representation (chemical - concepts involving symbolic representation (chemical

symbol, formula, equation,…)symbol, formula, equation,…) - concepts that name processes (melting, oxidation, - concepts that name processes (melting, oxidation,

photosynthesis, …)photosynthesis, …) - concepts that named attributes and properties (mass, - concepts that named attributes and properties (mass,

weight, electric charge, flammable,…),weight, electric charge, flammable,…), - concepts that describe attributes or properties (gram, - concepts that describe attributes or properties (gram,

kilo, molarity, pH,…kilo, molarity, pH,…

Many researchers see the act of Many researchers see the act of classification as a key operation in classification as a key operation in the formation of concepts. According the formation of concepts. According to Gagne (1997) discrimination is the to Gagne (1997) discrimination is the first step in the process of first step in the process of classification, followed by the classification, followed by the generalisation of the characteristic generalisation of the characteristic that form the class or sets. This that form the class or sets. This generalisation then leads to the generalisation then leads to the formation of new concept. A similar formation of new concept. A similar process is described by Lovell (1971). process is described by Lovell (1971).

Lovell however, includes an Lovell however, includes an additional step in the development of additional step in the development of concepts: differentiation between the concepts: differentiation between the properties of objects in the set. This properties of objects in the set. This is followed by the discrimination is followed by the discrimination between properties that are specific between properties that are specific to an object and those which are to an object and those which are common to the set. The identification common to the set. The identification of common properties then leads to of common properties then leads to the development of new concepts. the development of new concepts.

A quick and successful way of A quick and successful way of classifying is possible by comparing classifying is possible by comparing an object with a prototype (Langford, an object with a prototype (Langford, 1987; Rosch, 1980). Prototypes are 1987; Rosch, 1980). Prototypes are used as examples of a class. Children used as examples of a class. Children attribute a limited range of attribute a limited range of properties to these prototypes, thus properties to these prototypes, thus enabling them to represent the class. enabling them to represent the class.

For example water if often used as a For example water if often used as a prototype for liquids, so that liquids are prototype for liquids, so that liquids are viewed as transparent, colorless, runny viewed as transparent, colorless, runny substances that wet surfaces on which they substances that wet surfaces on which they are placed (Krnel, Watson and Glažar, are placed (Krnel, Watson and Glažar, 1998). 1998).

The properties of prototypes can be formed The properties of prototypes can be formed from actions on objects or materials (Bliss from actions on objects or materials (Bliss and Ogborn, 1994). For example the action and Ogborn, 1994). For example the action of pouring leads to the formation of a of pouring leads to the formation of a schema that differentiates liquids from schema that differentiates liquids from other substances. This is one of the limited other substances. This is one of the limited range of properties that is attributed to range of properties that is attributed to water and enables it to act as a prototype water and enables it to act as a prototype for liquids. for liquids.

In describing mercury we found out In describing mercury we found out a good example of the development a good example of the development of the concept of substance of the concept of substance (Krnel, Watson (Krnel, Watson and Glažar, 2005). and Glažar, 2005).

category of answers

3 years 5 years 7 years 9 years 11 years 13 let

water water(4) water (3) water(2) water

colored water different water

white water grey water

Grey water, black watergold water, silver water (2)

silver liquidsilver water (3)

dirty water,magnetic water

water (liquid) and other substance

Water + other

lead + watermetal + water

liquid with other substance (mixture)

liquid- metal sea-ironliquid - bronze

color as a liquid substance

silver color silver color,grey color

grey color

different substance

nail colorpoison

plasticine,pudding

melted metal melted iron liquid silver.melted silver

melted lead (3),melted metal + something

liquid zinc,melted iron,melted lead

other melted substance

melted rock

lava

other metal gold,lead

lead (2),iron

aluminum

mercury mercury (2) mercury mercury (6) mercury (8)

concrete abstractconcrete abstract

formal formal

concrete conceptconcrete concept - concrete reasoning - concrete reasoning patterns patterns

↓↓ (action, observing, (action, observing,

classifying, matching, etc.)classifying, matching, etc.)

formal conceptsformal concepts - formal reasoning - formal reasoning patternspatterns

↓ ↓ (other concepts, functional (other concepts, functional

relationship, ratios, relationship, ratios, inferences, idealisation, inferences, idealisation, models)models)

This distinction between concrete and This distinction between concrete and abstractabstract concept is usually expressed concept is usually expressed as:as:

concrete concepts are formed through concrete concepts are formed through

experience with objects and phenomena experience with objects and phenomena

and abstract concepts are learned by and abstract concepts are learned by

definition.definition.

Are the early years of schooling Are the early years of schooling reserved for concrete concepts?reserved for concrete concepts?

concrete thinking – concrete conceptsconcrete thinking – concrete concepts

Analysis of almost every curricula for science in Analysis of almost every curricula for science in primary school shows that we are in fact teaching primary school shows that we are in fact teaching

very formal conceptsvery formal concepts. . But are we successfulBut are we successful??

SpaceSpace TimeTime ForceForce MatterMatter

EnergyEnergy LivingLiving

Even with the concrete concept of Even with the concrete concept of plant young children have difficulties. plant young children have difficulties. In this and similar cases in spite of In this and similar cases in spite of concrete and perceptible concrete and perceptible representative misunderstanding representative misunderstanding appear because of the difficulties in appear because of the difficulties in finding out the common properties finding out the common properties and generalised them to the whole and generalised them to the whole class. class.

Recent studies confirm that children Recent studies confirm that children are able of correct classification are able of correct classification between living and non living, but between living and non living, but this ability is not indicative of a this ability is not indicative of a biological grasp of the implications of biological grasp of the implications of the life concept. When children are the life concept. When children are thought about biological criteria thought about biological criteria (nutriment, breathing, reproduction,(nutriment, breathing, reproduction,…) they use them pragmatically and …) they use them pragmatically and context depended. context depended.

Many times they use only one (the Many times they use only one (the suitable one) of the critical attributes suitable one) of the critical attributes (movement) and this can lead to (movement) and this can lead to false classification e. g. false classification e. g. ffireire,, clouds, clouds, sun, candle, river, car all of these sun, candle, river, car all of these things can be alive. things can be alive.

All these reasoning about being alive All these reasoning about being alive and not alive is in children’s mind more and not alive is in children’s mind more frequently connected with animals frequently connected with animals rather than plants. This is justified also rather than plants. This is justified also with the development of the analogical with the development of the analogical thinking. The fist prototype for living thinking. The fist prototype for living being is human or even better child being is human or even better child itself, more similar the being is to the itself, more similar the being is to the human more chance has to be classify human more chance has to be classify as alive. From these reasoning we can as alive. From these reasoning we can understand why animals are treated understand why animals are treated different form the plants. different form the plants.

For plants is one of the leading For plants is one of the leading attribute growth, for animals is it attribute growth, for animals is it movement. movement.

The concept of “plant” is in children’s The concept of “plant” is in children’s mind even narrowermind even narrower. .

““TrTree was a plant when it was littleee was a plant when it was little”.”.

The concept of timeThe concept of time

the concept of the concept of mattermatter

How to help student in constructing new concept How to help student in constructing new concept (precursors and anchoring concepts)(precursors and anchoring concepts)??

In the Piagetian sense, for every formal In the Piagetian sense, for every formal concept there exist intuitive precursors. This concept there exist intuitive precursors. This phenomena appears very much akin to the phenomena appears very much akin to the experience we have all had when we “know” experience we have all had when we “know” something is true but just cannot seem to find something is true but just cannot seem to find the words to explain (Lawson 1975). the words to explain (Lawson 1975).

From the definition of the formal concept From the definition of the formal concept above we can infer that precursors can be above we can infer that precursors can be also concrete concepts. Similar to the idea of also concrete concepts. Similar to the idea of precursors are so-called “anchoring precursors are so-called “anchoring concepts”concepts”..

Anchoring concepts are defined as Anchoring concepts are defined as an intuitive knowledge structure that an intuitive knowledge structure that is in rough agreement with accepted is in rough agreement with accepted theory; intuitive here meaning that theory; intuitive here meaning that which is more concrete than abstract which is more concrete than abstract and more self-evaluated. and more self-evaluated.

Children’s failure to think scientifically Children’s failure to think scientifically comes not from logical disabilities, but comes not from logical disabilities, but from not having acquired key organizing from not having acquired key organizing principles for some domain in principles for some domain in knowledge. knowledge. (Chi, 1991)(Chi, 1991)

Knowledge basis rather than a logic basis Knowledge basis rather than a logic basis for change in conceptionsfor change in conceptions..

It remains the task of the teacher who It remains the task of the teacher who wishes to teach formal concepts to wishes to teach formal concepts to identify these intuitive precursors as identify these intuitive precursors as well as the natural sequence in which well as the natural sequence in which they manifest themselves in formal they manifest themselves in formal conceptualizationconceptualization..

For the concept of photosynthesis For the concept of photosynthesis precursors are:precursors are:

The concept of mass extinction The concept of mass extinction (extinction of dinosaurs)(extinction of dinosaurs): :

““One of the conclusion is that lessons One of the conclusion is that lessons which introduce a topic by providing which introduce a topic by providing a conceptual structure can be more a conceptual structure can be more effective than those without: this is effective than those without: this is likely to be particularly so for topics likely to be particularly so for topics where the child’s level of conceptual where the child’s level of conceptual knowledge and understanding is knowledge and understanding is low.low.””

How we determine the correct and How we determine the correct and necessary precursors for a given necessary precursors for a given formal concept?formal concept?

Concepts map based on epistemology of Concepts map based on epistemology of scientific discipline as “experts map”scientific discipline as “experts map”

(Novak, 1998)(Novak, 1998)

One suggestion for teachers is to build a One suggestion for teachers is to build a concepts map based on the epistemology of concepts map based on the epistemology of scientific discipline. On such a map the scientific discipline. On such a map the concepts are hierarchical and organised in a concepts are hierarchical and organised in a structure. Each subordinated concept could structure. Each subordinated concept could be a precursor for a superordinated concept be a precursor for a superordinated concept in the same branch.in the same branch.

Ontological treeOntological tree

Idealised Ontology (Chi, 1991)Idealised Ontology (Chi, 1991)

The precursors defined by Lawson are tiny branches in the The precursors defined by Lawson are tiny branches in the ontological tree, for example, precursors for the concept of ontological tree, for example, precursors for the concept of matter would be solids, liquids, gases. matter would be solids, liquids, gases.

Other concepts can be used as precursors for testing the Other concepts can be used as precursors for testing the validity of the structure (position of the concept) in different validity of the structure (position of the concept) in different branches. For the branch ‘matter’ the precursors could be branches. For the branch ‘matter’ the precursors could be weight, colour, volume and others. weight, colour, volume and others.

MisconceptionMisconceptions s about:about:

GravityGravity MagnetismMagnetism →→ airair Light ?? Light ?? needs needs

Contact forces, Contact forces, ↓ ↓ implyimply

objcts - matterobjcts - matter

Concept of Concept of fieldfield as precursor for as precursor for

lightlight gravitygravity magnetism magnetism electric fieldelectric field

Slika polja Slika polja

Teaching concrete, Teaching concrete,

thinking formal. thinking formal.