LEARNERS’ KNOWLEDGE: COMMON FRAMEWORKS AND CONCEPTUAL SITES
Philip Anding
Faculty of Cognitive Sciences & Human Development
Universiti Malaysia Sarawak
94300 Kota Samarahan,
Sarawak, Malaysia
Abstract
This study investigates learners’ knowledge of d.c. circuits and considers
students’
knowledge
in
the
conceptual-procedural
and
qualitativequantitative continua. Knowledge in short-term memory is accessible
indirectly to a researcher because a researcher interprets meaning from
data that represent knowledge in the brain. Verbal data are coded by
interpreting the meaning of ‘action’ concepts used by learners when they
performed cognitive tasks. A specific meaning of an ‘action’ concept
represents a piece or a group of pieces of knowledge in short-term memory
and is referred to as a facet of knowledge. Facets of knowledge that are
about the same concept formed a category. Categories are categorized
further into major categories whereby a major category is about a superordinate concept. A major category reflects different dimensions of
learners’ knowledge of a super-ordinate concept. Common frameworks are
constructed by linking categories along similar dimensions and a core
concept is discovered from the common frameworks. This study suggests a
core concept as a ‘conceptual site’ for constructing teaching-learning
interventions of d.c. circuits.
1. Introduction
Piaget and Vygotsky saw learning as an active process whereby learners
construct their own knowledge. According to constructivist’s views, the
construction of knowledge in the brain occurs in piecemeal involving a
series of steps of limited size and it is a process which takes time
(Taber 2006). ‘Building blocks’ of knowledge are constructed to form a
knowledge construct. A learner’s knowledge is unique because a learner
constructs her own knowledge. Learners not only construct their own
knowledge, but they come to science classrooms with already existing
knowledge of many physical phenomena which has consequences for learning
(Driver & Bell 1986; Driver & Easley 1978; Driver & Erickson 1983;
Gilbert, Osborne & Fensham 1982; Gilbert & Watts 1983; Osborne &
Wittrock 1983; Pope & Gilbert 1983; Taber 2006).
2. Background
Physics is a difficult subject for most students or learners. Learners
often developed alternative conceptions from everyday physical and
linguistic experience (Driver & Erickson 1983). Physics is difficult
because it involves qualitative-quantitative representations, also
referred to as physical and mathematical knowledge representations.
Learners tend to memorize equations, apply purely quantitative treatment
of physical phenomena and often lack deeper understanding of the
equations that are used to produce the numerical answers (Ploetzner et
al. 1990).
2.1 Re-presentations of Knowledge
Knowledge in long-term memory is re-presented as representation
concepts and propositions in short-term memory. The processing
of
of
knowledge in short-term memory may be considered as the ‘tracing’ of
memory (Seung 1982) and is limited to 7±2 chunks (Miller 1956). A
‘memory trace’ could be in the form of a learner’s verbalisations,
written statements, calculations, sketches and so forth. Ericsson and
Simon (1982) are of the view that think-aloud protocols closely
represent a learner’s knowledge because verbalisations and the
processing of knowledge are assumed to involve the same cognitive
process. It is possible to access indirectly a learner’s knowledge by
interpreting the meaning of a learner’s verbalisations, written
statements, calculations, sketches and so forth.
2.2 Physics Knowledge
Concepts in physics and everyday usage may have the same names, but the
concepts often have different meaning. Chi (1992) mentioned three basic
ontological categories of knowledge which are ‘matter or material
substances’, ‘events or processes’ and ‘abstractions’, and acknowledged
that there may be other ontological categories as well. Concepts based
on everyday situations belong to the so called ‘matter-based’ or
‘material-based’ category whereas physics concepts are ‘events-based’ or
‘processes-based’ category (Chi 1992). Knowledge in the ‘matter-based’
or ‘material-based’ category does not operate in the same manner as
knowledge in the ‘processed-based or events-based’ category (Chi 1992).
Solomon (1993) considered knowledge in terms of two distinct ‘domains’,
the ‘symbolic’ and ‘life-world’ domains. The two ‘domains’ represent two
largely distinct, non-interacting ‘regions’ of conceptual structure
characterised by distinct modes of cognition, different genesis or
origin and different mode of operation (Solomon 1993; Taber 2006).
2.3 Knowledge Representations
Scientific models, propositions, definitions and formulae are expressed
as qualitative-quantitative knowledge (Eylon & Ganiel 1990; Heyworth
1999; Licht 1991; Ploetzner & VanLehn 1996). Some researchers prefer to
use the terms physical and mathematical knowledge to imply qualitativequantitative knowledge representations (Carey & Spelke 1994; Greca &
Moreira 2002; Nersessian 1999; Lee & Law 2001; Sabella 2000).
Qualitative knowledge representation expresses semantic meanings and
relationships of terms and entities (Greca & Moreira 2002), and does not
facilitate the determination of exact results. Quantitative knowledge
representation relies on mathematical formalisms and allows the
determination of exact results (Greca & Moreira 2002; Ploetzner &
VanLehn 1996). It is not possible to separate learners’ knowledge in a
clear-cut manner into qualitative and quantitative knowledge (Ploetzner
& VanLehn 1996; Ploetzner et al. 1990). Qualitative and quantitative
knowledge refers to the ends of the qualitative-quantitative continuum
(Ploetzner et al. 1990; Ploetzner & VanLehn 1996; White & Frederiksen
1990). Learners operate at different levels along the qualitativequantitative continuum.
2.4 Descriptors of Knowledge
Driver and Easley’s (1978) described young learners’ knowledge of
physical phenomenon in terms of alternative conceptual ‘frameworks’ that
exist in the private domain of the mind. Other researchers such as
Gilbert and Watts’ (1983) considered young learners’ alternative
conceptual ‘frameworks’ to be in the public domain. Gilbert, Osborne and
Fensham (1982), Driver and Erickson (1983), Gilbert and Watts (1983),
Osborne and Wittrock (1983) appear to consider that knowledge forms
conceptual structures in the brain and that it is possible to a certain
extend to model learners’ conceptual structures.
There is often little consistency on the descriptors of knowledge that
are used to represent learners’ knowledge. Gilbert and Watts (1983)
suggest conceptions, categories and frameworks as three levels of
descriptions. However, it may be necessary to consider not just
conceptions but also the range of ideas, reasoning, explanation,
calculations, sketches and so forth, that learners used when they
consider physical phenomena. Gilbert and Watts (1983) and Watts, Gilbert
and Pope (1982) described an alternative ‘framework’ as ‘a composite
picture based upon ideas shared by a number of pupils’, ‘generalised
non-individual descriptions’ and ‘thematic interpretations of data,
stylised, mild caricatures of the responses made by students’. Central
to a ‘framework’ is a concept and there maybe different concepts
associated with learners’ manifold ‘frameworks’ (Harrison & Treagust
2000; Osborne & Wittrock 1983; Redfors & Niedderer 2002; Taber 2000).
The ‘framework’ which is use first is likely to represent the knowledge
which is stronger in a learner’s cognitive domain (Redfors & Niedderer
2002). However, some researchers questioned the findings about manifold
or multiple ‘frameworks’ especially with regard to the adequacy of the
researchers’ descriptions of learners’ conceptions because manifold or
multiple ‘frameworks’ suggest that learners’ ideas are not theory-like
or structured (Claxton 1993; Kuiper 1994; Pope & Denicolo 1996).
2.5 Structured or ‘In-Pieces’
Rather than a tightly connected, logically organised structure, people
have ‘knowledge-in-pieces’ which are loosely connected ideas about the
world; ideas that are diverse, often incoherent and relatively
independent of each other (di Sessa 1996; di Sessa, Gillespie & Esterly
2004).
diSessa
(1996)
calls
these
ideas
‘p-prims’.
They
are
phenomenological because ‘p-prims’ are responses to experienced and
observed phenomena. They are primitive in the sense that they generally
are self-evident and need no explanation; they simply happen (Karlgren &
Ramberg 1995). The ‘knowledge-in-pieces’ and ‘knowledge constructs’
views appear to be contradictory views regarding the coordination of
learners’ knowledge in the brain. It is again more beneficial to
consider a learner’s knowledge along a ‘knowledge-in-pieces’ and
‘knowledge constructs’ continuum because it may well be that learners’
knowledge is ‘structured’ or partly in ‘pieces’ depending on a learner’s
level of expertise.
3.0 Concept Area: D.C. Circuits
Learners often have difficulties learning about d.c. circuits (Eylon &
Ganiel 1990; Saxena 1992; Shipstone, von Rhöneck, Jung, Kärrqvist, Dupin,
Johsua & Licht 1988; Tsai 2003). Children’s ideas and conceptions of
battery-bulb circuits are often represented as conceptual models of
current (Borges & Gilbert 1999; Osborne, Black, Smith & Meadows 1991;
Shipstone 1984). Conceptual models are often too simple, limited and do
not represent in a holistic manner learners’ knowledge of physical
phenomena. Conceptual models of ‘battery-and-bulb’ circuits do not
reflect the type of d.c. circuits that older learners study in their
course.
According to Osborne (1981) and Shipstone (1984), learners’ general
understanding of current flow in d.c. circuits improves with age and
with physics teaching in classrooms, but other studies such as Härtel
(1982) argued that even after extensive teaching learners still fail to
grasp some of the basic characteristics of electrical circuits. This
shows that some ideas learners have of d.c. circuits are easily
challenged through teaching while others persist and resist change ().
4.0 Approach to investigate Learners’ Knowledge
The research paradigm of this study is post-structural and employs the
approach of grounded theory. ‘Slices of data’ include think-aloud data,
interviews, verbal data generated from a d.c. circuit-cards task and
small group discussions. Data analysis involves interpretation of
meaning of ‘action concepts’ and interpretation at a thematic level.
The various meanings of ‘action’ concepts are referred to as facets of
knowledge because they represent little ‘faces’ of the various sides of
learners’ knowledge. A little ‘face’ or ‘facet’ of knowledge refers to a
specific meaning that is associated to an ‘action’ concept. Pope and
Denicolo (1986) considered facets of knowledge as the range of ideas,
‘theories’, reasoning and operations of learners. A ‘facet’ is a little
‘face’ or ‘side’ of a many-sided thing. In this study, conceptions,
ideas, reasoning, explanations and mental operations are collectively
termed as ‘facets’ of knowledge. Facets of knowledge that are about the
same concept are categorised as a category of facets of knowledge. The
categories are categorised further into major categories whereby a major
category is about a super-ordinate concept of d.c. circuits. The members
of a major category may differ dimensionally. Categories that relate
along the same dimension are connected to form a common framework based
on ‘thematic interpretations of data’ (Gilbert & Watts, 1983). A major
category that exhibits dimensional differences between its members links
the common frameworks and may be considered a core category or concept
which is central to all the common frameworks (Glaser & Strauss 1999;
Strauss & Corbin 1998; Strauss 1987). A core concept is common to all
the common frameworks, but is associated with different meaning in each
framework and represents the different ways students consider a concept.
A core category is a ‘conceptual site’ that forms the basis of a
theoretical scheme or model of learners’ knowledge of d.c. circuits
because a core category may serve as a conceptual site where ‘bridges’
may be built across different common frameworks.
5.0 Research Objectives
The research objectives of this study are to:
(i)
Uncover facets of knowledge;
(ii) Generate categories of facets of knowledge;
(iii) Generate major categories of facets of knowledge;
(iv) Construct common frameworks; and
(v)
Discover a core concept that is central to learners’ knowledge
of d.c. circuits.
6.0 Results
Open coding through microanalysis of data uncovered 125 facets of
knowledge of d.c. circuits. The 125 facets are categorised and 24
categories of facets of knowledge are generated. The categories are
categorised further into nine major categories. The categories are
connected along dimensions and resulted in the construction of three
common frameworks. These common frameworks are referred to as (a)
‘Connection-Consumption’ Framework, (b) ‘V=IR Dominant’ Framework and (c)
‘Relationship-Ratio-V=IR’ Framework. In the ‘Connection-Consumption’
Framework, learners determine ammeter and voltmeter readings based on
the physical connections of the components of d.c. circuits and a
resistor is a component which consumes current and voltage. In the ‘V=IR
Dominant’ Framework, learners determine ammeter and voltmeter readings
based on purely the manipulation and calculation of the V=IR equation or
representation. Resistance is a number that fits into the V=IR equation
and a resistor may or may not consume current or voltage. In the
‘Relationship-Ratio-V=IR’ Framework, students determine current and
voltage based on the relationship between variables, ratio of the
resistances and application of the V=IR equation. The ‘resistorresistance’ concept is identified as the core concept of d.c. circuits.
7.0 Discussion
The common frameworks and core concept informed teachers of learners’
knowledge of d.c. circuits. Learners’ ideas and way of thinking can be
identified from the common frameworks. Modelling learners’ knowledge
helps create awareness amongst teachers of the nature of learners’
knowledge such as awareness of the difficulties in communicating
scientific ideas and reasoning with learners (Watts 1983). It is
possible to teach science more effectively if learners’ existing ideas
are taken into account (Driver & Easley 1978; Gilbert, Osborne & Fensham
1982; Driver & Erickson 1983; Gilbert & Watts 1983; Osborne & Wittrock
1983). The most important factor that influenced learning is what
learners already know (Ausubel 2000, 1963; Taber 2006). Teaching needs
to be constructed and negotiated by considering learners’ knowledge
(Larochelle and Bednarz 1998; Osborne, Bell and Gilbert (1983).
Informing
teaching
requires
developing
theory
and
presenting
generalisations that could guide science teachers (Taber 2006). This
study constructed three common frameworks that could be used to inform
teachers on learners’ knowledge of d.c. circuits. The common frameworks
constructed in this study are consistent with Chi’s ideas on ontological
categories. The discovery of a core concept is important to teaching
because a core concept represents the various ways learners understand
d.c. circuits and it is useful as an ‘organiser’ for designing lessons
and teaching in the classroom.
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