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Asymmetric translation between multiple representations in chemistry


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Experts are more proficient in manipulating and translating between multiple representations (MRs) of a given concept than novices. Studies have shown that instruction using MR can increase student understanding of MR, and one model for MR instruction in chemistry is the chemistry triplet proposed by Johnstone. Concreteness fading theory suggests that presenting concrete representations before abstract representations can increase the effectiveness of MR instruction; however, little work has been conducted on varying the order of different representations during instruction and the role of concreteness in assessment. In this study, we investigated the application of concreteness fading to MR instruction and assessment in teaching chemistry. In two experiments, undergraduate students in either introductory psychology courses or general chemistry courses were given MR instruction on phase changes using different orders of presentation and MR assessment questions based on the representations in the chemistry triplet. Our findings indicate that the order of presentation based on levels of concreteness in MR chemistry instruction is less important than implementation of comprehensive MR assessments. Even after MR instruction, students display an asymmetric understanding of the chemical phenomenon on the MR assessments. Greater emphasis on MR assessments may be an important component in MR instruction that effectively moves novices toward more expert MR understanding.
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Asymmetric translation between multiple representations in
Yulan I. Lin
and James A. Rudd II
Department of Chemistry & Biochemistry, California State University, Los Angeles, CA, USA;
Department of
Psychology, California State University, Los Angeles, CA, USA
Experts are more procient in manipulating and translating between
multiple representations (MRs) of a given concept than novices.
Studies have shown that instruction using MR can increase student
understanding of MR, and one model for MR instruction in
chemistry is the chemistry triplet proposed by Johnstone.
Concreteness fading theory suggests that presenting concrete
representations before abstract representations can increase the
effectiveness of MR instruction; however, little work has been
conducted on varying the order of different representations during
instruction and the role of concreteness in assessment. In this
study, we investigated the application of concreteness fading to MR
instruction and assessment in teaching chemistry. In two
experiments, undergraduate students in either introductory
psychology courses or general chemistry courses were given MR
instruction on phase changes using different orders of presentation
and MR assessment questions based on the representations in the
chemistry triplet. Our ndings indicate that the order of
presentation based on levels of concreteness in MR chemistry
instruction is less important than implementation of comprehensive
MR assessments. Even after MR instruction, students display an
asymmetric understanding of the chemical phenomenon on the
MR assessments. Greater emphasis on MR assessments may be an
important component in MR instruction that effectively moves
novices toward more expert MR understanding.
Received 5 May 2015
Accepted 18 January 2016
Science education; multiple
representations; chemistry
education; concreteness
fading; assessment
Multiple representations
The ability to link information and ideas across multiple representations (MRs) for a given
concept is a more meaningful indicator of understanding than manipulation of symbolic
notation (Ainsworth, 1999; Prain, Tytler, & Peterson, 2009; Prain & Waldrip, 2006; Trea-
gust, Chittleborough, & Mamiala, 2003). For example, many chemistry students can learn
to balance reaction equations, but providing correct coefcients and chemical symbols for
equations is not the same as understanding the molecular behavior or macroscale
phenomena represented by the equations (Gabel, Samuel, & Hunn, 1987; Yarroch,
© 2016 Informa UK Limited, trading as Taylor & Francis Group
CONTACT James A. Rudd II Department of Chemistry & Biochemistry, California State Uni-
versity, 5151 State University Drive, Los Angeles, CA 90032, USA
1985). The importance of MR understanding is also true of other elds, including physics,
math, and biology (Hmelo-Silver, Marathe, & Liu, 2007; Kohl & Finkelstein, 2008; Kohl,
Rosengrant, & Finkelstein, 2007; McNeil & Fyfe, 2012; Schnotz & Kulhavy, 1994; Tsui &
Treagust, 2013). Previous work in MR has investigated expert use of MR (Chi, Feltovich, &
Glaser, 1981; Kozma & Russell, 1997; Larkin, McDermott, Simon, & Simon, 1980), student
understanding of MR, and the use of MR in instruction (Bibby & Payne, 1993; Dienes,
1973; Hennessy et al., 1995; Kaput, 1989; Oliver, 1997; Schwartz, 1995; Tabachneck, Koe-
dinger, & Nathan, 1994; Thompson, 1992).
Experts are better at manipulating and translating between MRs than novices. They
tend to represent underlying function and behavior in their models, while novices base
their models on surface features of appearance and structure (Chi et al., 1981; Hmelo-
Silver et al., 2007; Kozma & Russell, 1997; Larkin et al., 1980). Chemistry experts
connect MR that are conceptually related more efciently and accurately than novices
(Kozma, 2003). Physics graduate students translate between MR during problem-
solving more easily than physics undergraduate students (Kohl & Finkelstein, 2008).
Even in domains outside of the natural sciences (e.g. economics), experts reason by seam-
lessly transitioning between MR (Larkin & Simon, 1987).
Unlike experts, novices generally nd working with MR difcult. Studies assessing MR
understanding have demonstrated that students are worse at problems that require them
to translate between different representations than single-representation problems (Ains-
worth, Wood, & Bibby, 1996,1998; Ramnarain & Joseph, 2012; Tabachneck, Leonardo, &
Simon, 1994; Yerushalmy, 1991). However, there has been little work to address what
types of MR problems may be more difcult than others. It is commonly assumed that
deciencies in MR understanding may be traced back to instructional practices: not all
representations are given the same weight in instruction. For example, there may be an
overpresentation of one particular representation type in instruction or it may be more
common to ask students to translate from one representation to another than vice versa
(e.g. typically students are asked to provide a graph from equation than the other way
around, Dugdale, 1982). There have been many attempts to improve MR translations
through innovative pedagogy (e.g. Hennessy et al., 1995; Kozma, Chin, Russell, & Marx,
2000; Thompson, 1992).
Given the centrality of MR in expert-like thinking, each knowledge domain should con-
sider which MR to include in instruction. One model for MR in chemistry instruction is
the chemistry triplet, rst proposed by Johnstone (1982) and consisting of three represen-
tations: the macroscale, the nanoscale (also referred to as the microor the sub-micro),
and the symbolic (Figure 1) (Johnstone, 2000a,2000b,2009).
The macroscale representation is at the human scale in which natural phenomena can be
observed through the senses (sight, touch, etc.). The nanoscale representation is at the
molecular scale of molecules, atoms, and other particles that cannot be directly observed
by human senses. The symbolic representation is the abstract representation of natural
phenomena through the use of symbols, equations, and so on. The chemistry triplet is
often shown as the corners of an equilateral triangle to symbolize the equal importance of
each type of representation and the links between them in understanding chemistry. The
edges of the triangle represent possible translations among the three representations.
Although this interpretation of the triplet is common, other valid frameworks and per-
spectives exist and are in use in chemistry education research and instruction (Gilbert &
Treagust, 2009a; Taber, 2013; Talanquer, 2011). Thus, implementation of the triplet model,
whether for research or instruction, requires clear identication of the triplet and the
aspects that are being emphasized. To provide clarity before proceeding further, our
implementation attempts to hold closely to Johnstones views of the macroscale, nanoscale
(submicro), and symbolic. Our view of the macroscale emphasizes the actual physical
phenomena experienced tangibly through human senses, rather than a macroscale property
or conceptual framework such as density or pH. Our view of the nanoscale emphasizes ball-
and-stick and space-lling models as descriptive, explanatory, and predictive represen-
tations of the nanoscale, rather than as mere symbolic icons (Talanquer, 2011). Lastly,
our view of the symbolic emphasizes that the symbols, formulas, equations, and so on,
span the macroscale and nanoscale (Taber, 2013), for example, H
O(s) symbolizes both
the macroscale ice and the nanoscale collection of water molecules vibrating closely
together in xed positions in an ordered structure.
Perhaps due in part to the potential for ambiguity in interpretations of the triplet,
chemistry novices (students) are far less skilled than chemistry experts at translating
between the corners of the triplet and understanding the underlying concepts that tie
the different representations together. Not only do chemistry students correctly balance
equations without understanding the meaning of the equations (Gabel et al., 1987),
they are most comfortable manipulating symbols and symbolic representations using
awed algorithms, rather than considering underlying concepts (Gabel, 1993; Gabel
et al., 1987; Nurrenbern & Pickering, 1987; Nyachwaya, Warfa, Roehrig, & Schneider,
2014; Smith & Metz, 1996). Students also misunderstand the relationship between macro-
scale properties and nanoscale processes (Grifths & Preston, 1992; Lee, Eichinger, Ander-
son, Berkheimer, & Blakeslee, 1993). For example, some students assume that an atom
isolated from a gas will embody the bulk properties the gas exhibits on the macroscale,
just on a smaller scale (Ben-Zvi, Eylon, & Silbemein, 1986). A study of student perform-
ance on a standardized chemistry exam revealed that South African 12th graders per-
formed worse on questions that require translation between MR than on questions that
do not require translation (Ramnarain & Joseph, 2012).
Student prociency in manipulating symbols without understanding the underlying
meaning and their discomfort in translating across MR may be a result of chemistry
instruction that concentrates on symbolic representations. Unsurprisingly, instruction
that explicitly teaches MR has been shown to strengthen student understanding of MR
and increase their ability to translate between the different corners of the chemistry
triplet (Gabel, 1993). In one study, tenth-grade Lebanese students who were explicitly
Figure 1. The chemistry triplet
Source: Adapted from Johnstone (1982).
taught the different corners and the relationships between corners performed signicantly
better on a concept map task than students who did not receive the MR instruction (Jaber
& BouJaoude, 2012). In a study of eighth-grade Greek students who were taught macro-
scale representations rst, then symbolic, and then nanoscale performed better on postas-
sessments and retained more information (Georgiadou & Tsaparlis, 2000). Even in
domains outside of chemistry, explicitly teaching MR has been found to improve
student understanding of MR (Kohl et al., 2007; Tsui & Treagust, 2013).
Although MR instruction in science appears to be more effective than single-represen-
tation instruction, less work has been done identifying what types of MR translations are
most difcult for students and whether MR instruction can alleviate those difculties.
Translations between different corners of the chemistry triplet may vary in difculty
depending on the corners involved and the direction of translation. In other words,
there may be an asymmetry in studentsability to move between different representations.
As a theoretical framework for investigating these issues, we look to the research on the
benets of concrete and abstract representations in the learning sciences.
Concreteness fading: combining learning benets of concrete and abstract
There have been many empirical investigations regarding the role of concrete and abstract
representations in advancing conceptual and generalizable understanding. Concrete rep-
resentations are connected to their referents through perceptual similarity and are often
linked to learnersprior experience. For instance, a concrete representation of melting
could be a video of ice melting in a glass. In contrast, abstract materials are more arbitrarily
associated with referents and are perceptually stripped down in form. A chemical equation
represents melting in an abstract way because symbols such as (s) and (l) reference phys-
ical states only by convention. Studies in cognition have demonstrated two principles: (1)
instruction with MR generally leads to more robust understanding than with a single rep-
resentation (e.g. Brenner et al., 1997; Gentner & Markman, 1997) and (2) presenting the
most concrete instantiation rst then presenting abstract materials, known as concreteness
fading, leads to better generalization (see Fyfe, McNeil, Son, & Goldstone, 2014 for a recent
review). University students in the USA who received instruction about complex systems
with concrete-then-abstract representations performed better on a transfer test than stu-
dents who either received abstract-to-concrete instruction, abstract representations only,
or concrete representations only (Goldstone & Son, 2005). Another study examined con-
creteness fading instruction in the context of learning algebra and found that undergradu-
ates who received concreteness fading instruction outperformed those who either received
abstract-only instruction or concrete-only instruction on delayed tests administered three
weeks after initial learning (McNeil & Fyfe, 2012).
The mechanism behind the success of concreteness fading may have to do with max-
imizing the benets of concrete and abstract materials (Fyfe et al., 2014). Concrete
materials ground a new concept in a familiar or graspable context, while abstract materials
limit unnecessary detail, facilitating generalization. Progressing from concrete to abstract
examples initially anchors new knowledge in already familiar territory then moves the
learner toward a more abstract and transferrable understanding of the concept.
A second benet of progressing monotonically along a concreteness continuum is that
it minimizes the cognitive leaps needed to move from one example to the next (Freu-
denthal, 1983; Kotovsky & Gentner, 1996). For instance, moving from a macroscale rep-
resentation to a nanoscale representation may be more accessible than moving all the way
from a macroscale representation to a symbolic representation.
Concreteness fading and MR assessment
Much of the research on concreteness fading has focused on the presentation of MR to
novice learners (Fyfe et al., 2014). Only a few studies have examined concreteness in
assessment, and these studies contrast assessments utilizing concrete materials with assess-
ments utilizing abstract materials (e.g. Petersen & McNeil, 2013). Very little research has
focused on the design and implementation of assessing studentsability to connect and
translate across concrete and abstract MR. One study on pattern perception in pre-
school-aged children found that the direction of assessment, in this case an abstract cue
with concrete answer choices versus a concrete and perceptually rich cue with abstract
answer choices, can affect generalization (Son, Smith, & Goldstone, 2011). Research on
the direction of assessment is critical because the way in which we query students
denes the scope of understanding that students can demonstrate. A student might
appear quite competent on one type of assessment but not be able to demonstrate their
understanding on a different type of assessment. Thus, in considering how to measure
student understanding of MR, we need assessments that examine connections between
MR. An open question is whether science students can translate from concrete to abstract
representations as well as they can translate from abstract to concrete.
Concreteness and the chemistry triplet
The concreteness and abstractness of the three corners of the chemistry triplet can be
interpreted through different perspectives. Gilbert and Treagust (2009b) raise the issue
of relating typesof representations to levelsof representations that dene the cognitive
relationship between the types of representations (i.e. the separate corners of the triplet)
from the human learner perspective. Level could mean differences in physical scale
from macro to meso to nano (submicro), but level could also indicate differences in the
language that describes phenomena, such as concrete descriptions of macroscale to
abstract chemical symbols. Thus, two psychological dimensions of concreteness may be
operating in the chemistry triplet: scale, where the macroscale that is more perceptible
to humans could seem more concrete and the less perceptible nanoscale could seem
less concrete, and language, where familiar language is more concrete and more special-
ized language that requires training and education is more abstract. Justi, Gilbert, and Fer-
reira (2009) identify concrete as one mode of representation used to communicate a
persons mental model and indicate that the model can be expressed as a mixture of rep-
resentation modes (concrete, verbal, etc.) when providing the external representation to
the learner (p. 286). This dimension of concreteness in modes of communication allows
for representations to be viewed as more or less concrete, for example, a broad qualitative
analogy describing a concept may feel more concrete to a learner than a quantitative,
mathematical expression of the same concept.
In the work presented in this paper, our goal was to map the corners of the triplet to a
single concreteness continuum in order to situate our research within the broader frame-
works developed in the cognitive and learning sciences, and we began with the basis that
all representations (verbal, pictorial, symbolic, video, gesture, etc.) can be placed on a con-
creteness continuum. Specically, we dene the concreteness of a representation as simi-
larity to the referent or the intended meaning of the representation. Thus, the macroscale
is considered the most concrete of the three corners because macroscale representations,
whether they are verbal descriptions or videos of macroscale phenomena, most closely
resemble their referents. For example, a video of ice melting more closely resembles the
actual observable phenomena of ice melting, and is therefore more concrete than the sym-
bolic representation of ice melting: H
Symbolic representations, such as chemical symbols, formulas, and equations, are less
concrete because they are more arbitrarily connected to the referent. Also, symbolic rep-
resentations are very reduced representations of the referent, and the relationship between
the symbolic representation and the meaning of the representation is more obscured.
Specialized training is typically needed in order for a person to succeed in connecting
the representation with its meaning. Using Hto mean hydrogen simply because hydro-
gen starts with the letter His a connection between the symbolic representation and
referent that is arbitrary and reliant on conventions in our culture and language. For
instance, Cuas the symbolic representation of the substance copperis more arbitrary
for English speakers than for French speakers (cuivre). In French, the symbolic represen-
tation at least resembles the word more closely than in English, but in both languages, the
symbols are still more arbitrary than the relationship between a macroscale representation,
such as a picture showing a sample of each metal, of these referents.
We place nanoscale representations in between the more concrete macroscale and more
abstract symbolic representations. Nanoscale representations are somewhat concrete in
that ball-and-stick and space-lling models capture some of the perceptual qualities of
the referent of atoms and bonds than the arbitrariness of symbols. However, ball-and-
stick nanoscale representations are also less concrete than macroscale representations
because nanoscale representations also have elements of arbitrariness, for example,
colors are assigned to different elements by convention, such as oxygen atoms are often
colored red and the size of the balls distort the actual and relative size of atoms.
Essentially, the more concrete end of our concreteness continuum captures more of the
qualities of the referent and requires less specialized training to understand the meaning of
the representation, whereas the more abstract end of the continuum has fewer and weaker
connections between the representation and the referent and requires more specialized
training for learners to interpret the representation. Although this approach is not the
only way of describing the concreteness and abstractness of the corners of the chemistry
triplet, it allows us to connect to the learning literature research on manipulating concre-
teness to help students move between concrete and abstract representations.
Concreteness fading and the chemistry triplet
In this study, we investigated the application of concreteness fading to MR instruction and
assessment in teaching chemistry. To do this, the chemistry triplet was mapped to a con-
creteness continuum (Figure 2(a)).
For the purposes of this study, the macroscale representation of objects, phenomena,
and manipulations is on the human scale (i.e. observed or experienced through sight,
hearing, touch, etc.) and is considered the most concrete (Johnstone, 2000a,2000b,
2009). The nanoscale representation of the molecular level is less concrete because the
nanoscale is less perceptually accessible to humans; however, molecules, atoms, and so
on can be represented by graphical icons (e.g. pictures of spheres to represent atoms)
or physical models (e.g. ball-and-stick models) that provide a perceptual anchor. Lastly,
the symbolic representation is the least concrete (most abstract) because chemical
symbols and equations reference substances and processes by convention in a highly ef-
cient and simplied manner (Johnstone, 2000a,2000b; Taber, 2013). Thus, in mapping the
chemistry triplet onto a concreteness continuum, we have placed the macroscale and sym-
bolic at the extremes and the nanoscale as intermediate between them.
Because the chemistry triplet is typically shown as an equilateral triangle, there may be
an underlying assumption that each representation (corner) and each direction of trans-
lation between representations are somehow equal (Figure 2(b)). However, considering a
linear concreteness continuum may help us explore the hypothesis that these represen-
tations and translations may not be cognitively equivalent for chemistry novices. Although
the ideal may be that chemistry students should understand each representation equally
well, some translations may initially be easier than others (Figure 2(b)).
If deep understanding of chemistry includes understanding all three corners, how they
relate, and how to translate between them, then using a concreteness continuum provides
a framework for asking questions about MR instruction and assessment. Should the more
or less concrete representation be presented rst in MR instruction? Are students equally
adept at translating from concrete to more abstract representations or from abstract to
more concrete ones? That is, does the direction of translation matter in assessment?
Here, we report new ndings on MR instruction and assessment, and our ndings shed
light on studentsability to translate between representations. Specically, our investi-
gation addressed the following research questions to examine the role of concreteness
in learning MR in the domain of phase changes in chemistry:
(1) Type of rst presentation: do students perform better with concrete-rst or abstract-
rst instruction? That is, do students perform better with macroscale instruction rst
or symbolic instruction rst?
Figure 2. (a) The relationship between the chemistry triplet and concreteness fading. (b) Directionality
of transitions between the corners of the chemistry triplet.
(2) Inclusion of a progression: do students perform better with instruction that progresses
monotonically along a concreteness continuum vs. instruction that does not include a
progression? That is, would students benet most from macroscale, then nanoscale,
then symbolic instruction?
(3) Directionality of assessment: do students perform better on concrete-to-abstract or
abstract-to-concrete questions? That is, are students more adept at translating from
more concrete to less concrete corners of the chemistry triplet (black arrows in
Figure 2(b)) or vice versa (white arrows in Figure 2(b))?
Experiment 1
Students were shown chemistry instructional videos on phase changes in small groups that
were randomly assigned to one of four instructional conditions. Each participant com-
pleted pen-and-paper pre- and postassessments that contained two types of questions
(concrete-to-abstract, abstract-to-concrete).
One hundred forty-seven undergraduate students (100 female, 44 male, 3 declined to
state) from the Psychology department subject pool (most of whom were enrolled in intro-
ductory Psychology courses) at a mid-sized comprehensive public university on the west
coast of the USA participated in Experiment 1. Participants were given course credit for
being in the study. Twenty additional participants were excluded from analysis because
they did not complete the study.
Instructional videos
Participants viewed three videos during the instruction, and each video presented phase
changes from the perspective of one corner of the chemistry triplet.
The macroscale instructional video introduced the macroscale, showed videos of water
freezing and ice melting (obtained from by permission of the owners), and had
added voiceover narration that described the melting and freezing of water being shown.
The nanoscale instructional video rst introduced the nanoscale, including a brief
nanoscale drawing tutorial. Then, the video showed a screencast recording of one of the
researchers interacting with the States of Matter: Basicssimulation (PhET States of
Matter: Basic Simulation, n.d.), which again had added voiceover narration.
The symbolic instructional video introduced symbolic notation, and presented sym-
bolic representations for phase changes and three properties associated with phase
changes (velocity, kinetic energy, and temperature). Because velocity, kinetic energy,
and temperature were presented to the participants as symbols (i.e. V, KE, T), we con-
sidered these to be symbolic representations (although the actual underlying concepts
could be interpreted through other perspectives of the triplet, e.g. temperature as a macro-
scale construct and kinetic energy as a nanoscale concept).
All videos discussed kinetic molecular theory; the relationship between velocity, kinetic
energy, and temperature; and the relationship between the energy of the atoms or mol-
ecules and the phase or state of matter.
Participants completed two-part assessments before and after instruction, which were
designed to assess studentsability to translate between the different representations of
the chemistry triplet. Each question required students to connect different representations
by giving one representation of a concept and asking students to provide a different
In Experiment 1, questions were written to assess two directions of translation: con-
crete-to-abstract and abstract-to-concrete. Figure 3 shows the relationship between ques-
tion directionality and the chemistry triplet.
The questions were also designed to assess transfer beyond memorization of presented
materials. Though the instruction focused on melting and freezing of water, participants
were asked about other substances and states of matter. Two parallel versions of the assess-
ments were created with nearly identical questions. For example, if Assessment A Ques-
tion 1 asked about a substance melting, then Assessment B Question 1 asked about the
same substance freezing. Participants randomly received either Version A of the pretest
and posttest or Version B. Sample questions are shown in Table 1.
The pretest and posttest had concrete-to-abstract and abstract-to-concrete translation
questions. At the end of the posttest, participants ranked their condence in their answers,
estimated their ability to learn science, and reported how much they liked science.
Experimental design and procedure
The experiment used a pretest, intervention, and posttest procedure and a 2 × 2 × 2 mixed
repeated-measures design corresponding to the three research questions. The two
between-subjects factors were rst presentation (concrete-rst, abstract-rst) and pro-
gression (progression, no progression) (Table 2). The within-subjects factor was question
directionality (concrete-to-abstract, abstract-to-concrete).
For the concrete-rst, progression condition, the videos were presented in the order
macroscalenanoscalesymbolic (MNS). The MNS condition is a progression
Figure 3. Assessment questions classied by directionality. (a) Concrete-to-abstract; (b) abstract-to-
concrete; and (c) abstract-to-abstract.
because the examples progress monotonically along the concreteness continuum from
most concrete to most abstract. For the abstract-rst, progression condition, the videos
were presented in the order symbolicnanoscalemacroscale (SNM). The SNM con-
dition is a progression because the examples progress monotonically along the concrete-
ness continuum from most abstract to most concrete. For the concrete-rst, no
progression condition, the videos were presented in the order macroscalesymbolic
nanoscale (MSN). For the abstract-rst, no progression condition, the videos were pre-
sented in the order symbolicmacroscalenanoscale (SMN). Both MSN and SMN
conditions did not progress monotonically on the concreteness continuum.
Participants signed up for experimental sessions in groups of 1016 students. Each
session was randomly assigned to one of the four presentation conditions. Participants
were allotted 11 minutes to complete the pretest and were then shown the instructional
videos for 23 minutes. Participants were then given 11 minutes to complete the postassess-
ment. At the end of the posttest, participants completed a brief demographic survey.
Data analysis
The responses were scored using a rubric for each question and yielded for each partici-
pant an overall score, a concrete-to-abstract score, and an abstract-to-concrete score for
the pre- and postassessments. For each participant, a gain score was calculated as posttest
score minus pretest score.
Responses involving drawn nanoscale images were independently scored by another
rater using the same scoring rubric, and discrepancies were resolved by an experienced
chemistry professor. This coding was blind to presentation condition.
Statistical analysis
The gain scores were analyzed using a 2 × 2 × 2 mixed repeated-measures ANOVA (question
direction × rst presentation × progression) with participantspretest scores as a covariate.
Table 1. Sample questions classied by direction.
Sample concrete-to-abstract question Sample abstract-to-concrete question
(Given macro provide symbolic)
Given a chunk of solid aluminum, represent it in symbols.
(Given macro provide nano)
Draw a nanoscale picture to represent solid aluminum.
(Given nano provide symbolic)
Given a set of nanoscale pictures below, pick out the
corresponding chemical equation.
(Given symbolic provide nano)
Select the nanoscale picture that most accurately represents a
sample with the symbol H
(Given symbolic provide macro)
Name the physical process represented by the chemical
equation N
(Given nano provide macro)
Name the physical process represented by the nanoscale
image below.
Table 2. Four instructional conditions based on rst presentation and progression.
Progression No progression
Concrete-rst MNSMSN
Abstract-rst SNMSMN
10 Y. I. LIN ET AL.
Results and discussion
The ANOVA results revealed that rst presentation and progression had no statistically
discernable effect (F< 0.20, p> .700) and no signicant interactions (F< 1.5, p> .23).
However, there was a main effect of question directionality (F(1, 147) = 233.67, p< .001,
= 0.62). Students improved signicantly more on concrete-to-abstract questions than
on abstract-to-concrete questions (Figure 4) for all presentation conditions.
Because participant credit was based only on attendance, rather than performance on
the postassessment, participants had little incentive to learn the material and perform well
on the assessment. To address this limitation, Experiment 2 was designed to include
general chemistry students who were motivated to learn the material.
Experiment 2
Two types of students were randomly assigned to one of four instructional conditions
(Table 2). Each participant completed an online assignment composed of instructional
videos and a postinstructional assessment with three types of questions (concrete-to-
abstract, abstract-to-concrete, abstract-only).
Two hundred forty-nine undergraduate students enrolled at a mid-sized comprehensive
public university on the west coast of the USA participated in the study for course
credit. Students from the Psychology department subject pool (n= 168; 124 females, 36
males, 8 declined to state) received credit for attendance. Students enrolled in a general
chemistry course (n= 81; 43 females, 38 males) received credit scaled to their assessment
performance. The inclusion of chemistry students enhances the validity of the study
results because these students had incentive to learn the material and perform well on
the assessment.
Figure 4. Mean gain scores for the two different types of questions (n= 146).
Datasets were excluded from analysis if participants did not complete the study, includ-
ing those who spent less than 20 minutes on the study because the instructional videos
were over 17 minutes in length and the assessment required a minimum of three
minutes for one of the researchers to complete.
The instructional videos and assessment questions were the same as for Experiment 1,
except the questions were slightly modied for online delivery. Also, a third type of assess-
ment question (abstract-to-abstract) was added because most general chemistry tests focus
on symbolic understanding and manipulations.
Experimental design and procedure
The experiment used an intervention and posttest procedure and a 2 × 2 × 2 × 3 mixed
repeated-measures design. The pre-assessment was removed to reduce participant time
and pretest effects. The between-subjects factors were rst presentation (concrete-rst,
abstract-rst), progression (progression, no progression), and student population (psy-
chology students, chemistry students). The within-subjects factor was question direction-
ality (concrete-to-abstract, abstract-to-concrete, abstract-to-abstract).
Participants were randomly assigned to one of the four presentation conditions using
Qualtrics software (Provo, UT). The postassessment and demographic survey were also
presented on Qualtrics immediately after the instructional videos.
Students from the Psychology department subject pool signed up in groups of 120 to
participate in a computer lab. Each participant had an individual workstation with head-
phones and was given 45 minutes to complete the study.
Students enrolled in the general chemistry course received the link to the Qualtrics
experiment from their course instructor after the rst midterm exam. Students completed
the study independently as a homework assignment and were asked to provide their name
and instructor name to award them appropriate class credit. Before data analysis, all iden-
tifying information was decoupled from the performance data.
Data analysis
The responses were scored using a rubric for each question and yielded for each partici-
pant an overall score, a concrete-to-abstract score, an abstract-to-concrete score, and an
abstract-to-abstract score. These raw scores were converted to proportion correct postas-
sessment scores. All coding was blind to presentation condition.
Statistical analysis
The postassessment scores were analyzed using a 2 × 2 × 2 × 3 mixed repeated-measures
ANOVA (rst presentation × progression × student population × question direction).
Results and discussion
The ANOVA results showed that rst presentation and progression did not have a stat-
istically signicant effect (Fs < 0.1, p> .2); however, there was a statistically signicant
12 Y. I. LIN ET AL.
effect of student population, F(1, 241) = 53.01, p< .001, η
= 0.24, and question direction, F
(1, 241) = 74.56, p< .001, η
= 0.34. There were no reliable interactions.
Unsurprisingly, students enrolled in the chemistry course (M= 0.71, SD= 0.20) per-
formed signicantly better than students enrolled in the psychology course (M= 0.54,
SD = 0.22). Post-hoc-corrected simple comparisons revealed that participants performed
the best on abstract-to-abstract questions, then concrete-to-abstract questions, and
worst on abstract-to-concrete questions (ps < .001). Mean scores on these three question
types are shown in Figure 5. The asymmetry in student performance based on question
direction that was found in Experiment 1 was conrmed here with a sample of students
that had more motivation to learn chemistry and do well on the assessment, and presum-
ably, more initial chemistry knowledge.
Taken together, the experiments reveal unexpected ndings regarding concreteness and
MR chemistry instruction and assessment. First, neither experiment yielded differences
in student performance between different instructional conditions. The order of MR
instruction, whether starting with most concrete vs. most abstract or including a pro-
gression, did not observably impact student performance, meaning that concreteness
fading did not appear to have an effect, at least for learning how to translate between
MR in chemistry. Although our experimental design did not yield any signicant inuence
of instructional order, it may be that the brief instructional period limited studentsability
to gain sufcient understanding of the triplet, and additional research may detect an effect
of MR instructional order over longer time periods (e.g. an entire class period or course)
and/or with a wider variety of chemistry topics.
Differences in the learning goal between this study and most concreteness fading
studies may also explain the absence of any effect. In most concreteness fading studies,
the goal is for students to learn to generalize to a new and completely different concrete
example of the abstract concept being examined (Goldstone & Son, 2005; McNeil &
Figure 5. Mean postassessment scores for the two different types of questions (n= 249).
Fyfe, 2012). For example, in a typical study, US undergraduates were taught the commu-
tative rule using generic symbols, cups, and pies and were assessed by being asked to gen-
eralize to examples with ladybugs, vases, and rings (McNeil & Fyfe, 2012). In this study,
however, the goal was for students to understand and translate between MR of the
concept, and students were assessed by being asked to translate across MR for new
examples of the concept, rather than simply by identifying new instances of the
concept. Similarly, another study assessing MR use in chemistry evaluated participants
on their ability to translate between videos, graphs, animations, and equations of the
same concept (Kozma & Russell, 1997).
When translation is the goal, rather than just identifying examples in new contexts,
presentation order may matter less. In addition, the MRs in the chemistry triplet may
be less like a continuum of concrete to abstract examples of a given concept and more
like three very different aspects of the concept. For example, a realistic video of ice
melting and a cartoon depiction of ice melting can represent more and less concrete
examples of melting, respectively. In contrast, a realistic video of melting, a cartoon
depiction of molecular movement during melting, and the chemical symbols for
melting are less like different examples of melting, but instead, are more like three differ-
ent dimensions or perspectives on the same phenomena that highlight very different
Second, the experiments reveal unbalanced or asymmetric student understanding of
chemistry. Students were better at translating from concrete to abstract representations
vs. abstract to concrete representations, regardless of instructional condition for both
experiments. In other words, students apparently possessed an asymmetric understanding
of phase changes because they exhibited a greater ability to translate from representation A
to representation B (i.e. concrete-to-abstract) as compared to translating from represen-
tation B to representation A (i.e. abstract-to-concrete).
Little published work has examined the idea of symmetric and asymmetric under-
standing of and translation between MR. In mathematics, symmetric understanding
has been suggested as a necessary requirement for a complete understanding (Rider,
2007), and one study found asymmetric understanding in math students who were
more procient at translating from equations to graphs versus translating from graphs
to equations (Yerushalmy, 1991). The same study found that students were instructed
to generate graphs from equations more often than the reverse (Yerushalmy, 1991),
so asymmetric understanding may be a result of asymmetric instruction and/or
Depending on the specic concept and even the scientic domain, different trans-
lations may be more or less challenging for students. The nature of the subject itself
could foster asymmetric understanding, which may be further compounded by or
result in asymmetric instruction. For example, in chemistry, the macroscale represen-
tation is usually more familiar and more concrete to students (e.g. melting of an ice
cube), but in astronomy, the macroscale may be so expansive (e.g. stars light years
away and appearing as points of light) as to be unfamiliar and less concrete to students.
Students who exhibit stronger ability to translate from concrete-to-abstract vs. abstract-
to-concrete in chemistry may exhibit the opposite asymmetry in astronomy. Even
within one domain, such as chemistry, different asymmetries may exist when translating
between MRs for different concepts.
14 Y. I. LIN ET AL.
This study shows that the order of MR chemistry instruction by levels of concreteness does
not impact student understanding and that comprehensive MR assessments reveal asym-
metric understanding of chemistry. First, the order of presenting macroscale, nanoscale,
and symbolic representations of chemistry in very brief instructional periods may not
matter as much as providing instruction on all three corners of the chemistry triplet in
any order to develop more expert understanding. Alternatively, the pedagogical approach
may be related to the ideal order of presentation. For more passive pedagogy, such as the
viewing of video lectures in this study, the order may not have an effect, but for more
active learning methods, such as problem-based and inquiry-based learning, the presen-
tation order may have a greater role (e.g. the problem or question being investigated
may benet from initially being presented at the concrete macroscale). For any approach,
MR instruction should explicitly teach translation between representations in multiple
directions to develop more symmetric understanding and translation ability. Such an
approach may help students move beyond one mode of thinking to develop stronger con-
ceptual understanding of a subject.
Second, we nd asymmetric understanding even after MR instruction on all three
corners of the chemistry triplet. Typical chemistry instruction does not cover all three
corners to the same extent but rather focuses on symbolic representations, and our
ongoing research conrms that additional asymmetries can exist when instruction is
limited to fewer corners. Further research may also ascertain whether asymmetries
occur across scientic domains as well as elucidate the role of asymmetries in pedagogy.
Importantly, the use of MR assessments may play a critical role in framing MR instruc-
tion and research on MR instruction. Assessments not only reveal the limits of student
understanding, but they also circumscribe the range of understanding that students can
demonstrate. Because the types of assessments signal to students what concepts and
skills they should learn, asymmetric assessments focus students on developing asymmetric
understanding and translation skills. Designing and implementing comprehensive MR
assessments that translate in multiple directions would be more likely to promote
student ability to translate in all directions. In other words, a greater focus on MR assess-
ment (i.e. MR testing as part of teaching) would enhance MR instruction for all students
(primary, secondary, tertiary). Such assessments would also be useful for informing the
instructional design cycle by indicating the types of translations that are most challenging
for students.
Similarly, the design of symmetric assessments is an area where further research is
needed for all levels (primary, secondary, and tertiary) of MR instruction. As found in
this study, assessment design revealed more about student performance than pedagogy
design. There is a tendency in the research to compare different types of instruction
more than different types of assessments, but for investigations of MR instruction, an
increased focus on the assessment design may yield useful insights about highly effective
MR instructional approaches. It is likely that different pedagogies bias student learning
toward asymmetries in MR translation but need symmetric assessments to identify the
asymmetric performance.
Finally, MR and concreteness fading are broad concepts encompassing multiple modes
of thinking. Although the approach in this study may not apply to all types of MR, it may
be relevant to disciplines that utilize models potentially analogous to the chemistry triplet
(Table 3).
The ability to translate between MR goes beyond understanding and learning science
and math in academic contexts. Phenomena such as trafc jams, global trade, poverty,
and the preservation of ecosystems all function at multiple levels, with different infor-
mation and concepts relevant at each level (Holland, 2006). Information about these
real-world problems are presented using MRs, and being able to translate effectively
between these representations is critical for decision-makers and stakeholders. Developing
effective MR pedagogy and assessments is a modest but crucial contribution that educators
and educational researcher can make.
The authors would like to acknowledge Donna Chen for assisting in coding and Angela Guererro
for assisting with literature review. Krzystof Dwornik, Jonathan Shrader, and youtube user 33342
shooting channel provided permission to use their videos.
Disclosure statement
No potential conict of interest was reported by the authors.
Notes on contributors
Yulan Lin graduated with honors with the Bachelor of Science degree in chemistry from California
State University, Los Angeles in 2014.
Ji Son is an assistant professor of psychology at California State University, Los Angeles.
James A. Rudd II is a professor of chemistry and biochemistry at California State University, Los
Ainsworth, S. (1999). The functions of multiple representations. Computers & Education,33(23),
Ainsworth, S., Wood, D., & Bibby, P. (1996). Coordinating multiple representations in computer
based learning environments. In P. Brna, A. Paiva, & J. A. Self (Eds.), Proceedings of the
European conference on Articial Intelligence in Education (pp. 336342). Lisbon: Edicoes
Ainsworth, S., Wood, D., & Bibby, P. (1998). Analysing the costs and benets of multi-represen-
tational learning environments. In S. Vosniadou, K. Matsagouras, K. Mardaki-Kassotaki, & S.
Kotsanis (Eds.), 7th European conference for research on learning and instruction (pp. 500
501). Athens: Gutenberg University.
Table 3. Multiple levels of concreteness in representations from different disciplines.
Math Physics Chemistry Biology
Concrete example Macroscale Macroscale Macroscale
Faded example Invisible (forces) Nanoscale Microscale
Symbolic notation Symbolic Symbolic Biochemical
Source: Adapted from Johnstone (2000a) and McNeil and Fyfe (2012).
16 Y. I. LIN ET AL.
Ben-Zvi, R., Eylon, B., & Silbemein, J. (1986). Is an atom of copper malleable? Journal of Chemical
Education,63(1), 6466.
Bibby, P. A., & Payne, S. J. (1993). Internalizing and the use specicity of device knowledge.
Human-Computer Interaction,8(1), 2556.
Brenner, M. E., Mayer, R. E., Moseley, B., Brar, T., Duran, R., Reed, B. S., & Webb, D. (1997).
Learning by understanding: The role of multiple representations in learning algebra. American
Educational Research Journal,34(4), 663689.
Chi, M., Feltovich, P., & Glaser, R. (1981). Categorization and representation of physics problems
by experts and novices. Cognitive Science,5, 121152.
Dienes, Z. P. (1973). The six stages in the process of learning mathematics. Windsor, Ontario: NFER
Dugdale, S. (1982). Green globs: A micro-computer application for graphing of equations.
Mathematics Teacher,75, 208214.
Freudenthal, H. (1983). Didactical phenomenology of mathematical structure. Dordrecht: Kluwer
Fyfe, E. R., McNeil, N. M., Son, J. Y., & Goldstone, R. L. (2014). Concreteness fading in mathematics
and science instruction: A systematic review. Educational Psychology Review,26(1), 925. doi:10.
Gabel, D. L. (1993). Use of the particle nature of matter in developing conceptual understanding.
Journal of Chemical Education,70(3), 193194.
Gabel, D. L., Samuel, K. V., & Hunn, D. (1987). Understanding the particulate nature of matter.
Journal of Chemical Education,64(8), 695. doi:10.1021/ed064p695
Gentner, D., & Markman, A. B. (1997). Structure mapping in analogy and similarity. American
Psychologist,52(1), 4556.
Georgiadou, A., & Tsaparlis, G. (2000). Chemistry teaching in lower secondary school with
methods based on: a) psychological theories; b) the macro, representational, and submicro
levels of chemistry. Chemistry Education Research and Practice,1(2), 217226.
Gilbert, J. K., & Treagust, D. F. (Eds.). (2009a). Multiple representations in chemical education.
Dordrecht: Springer.
Gilbert, J. K., & Treagust, D. F. (2009b). Towards a coherent model for macro, submicro, and sym-
bolic representations in chemical education. In J. K. Gilbert & D. F. Treagust (Eds.), Multiple rep-
resentations in chemical education (pp. 333350). Dordrecht: Springer.
Goldstone, R. L., & Son, J. Y. (2005). The transfer of scientic principles using concrete and ideal-
ized simulations. The Journal of the Learning Sciences,14(1), 69110.
Grifths, A. K., & Preston, K. R. (1992). Grade-12 studentsmisconceptions relating to fundamental
characteristics of atoms and molecules. Journal of Research in Science Teaching,29(6), 611628.
Hennessy, S., Twigger, D., Driver, R., OShea, T., OMalley, C. E., Byard, M., Scanlon, E. (1995).
Design of a computer-augmented curriculum for mechanics. International Journal of Science
Education,17(1), 7592.
Hmelo-Silver, C. E., Marathe, S., & Liu, L. (2007). Fish swim, rocks sit, and lungs breathe: Expert-
novice understanding of complex systems. Journal of the Learning Sciences,16(3), 307331.
Holland, J. J. H. (2006). Studying complex adaptive systems. Journal of Systems Science and
Complexity,19(1), 18.
Jaber, L. Z., & BouJaoude, S. (2012). A macromicrosymbolic teaching to promote relational
understanding of chemical reactions. International Journal of Science Education,34(7), 973
998. doi:10.1080/09500693.2011.569959
Johnstone, A. H. (1982). Macro and microchemistry. School Science Review,64, 377379.
Johnstone, A. H. (2000a). Chemical education research: Where from here. University Chemistry
Johnstone, A. H. (2000b). Teaching of chemistry Logical or psychological? Chemistry Education
Research and Practice Europe,1(1), 915.
Johnstone, A. H. (2009). Multiple representations in chemical education. International Journal of
Science Education,31(16), 22712273. doi:10.1080/09500690903211393
Justi, R., Gilbert, J. K., & Ferreira, P. F. M. (2009). The application of a model of modelingto illus-
trate the importance of metavisualisation in respect of the three types of representation. In J. K.
Gilbert & D. F. Treagust (Eds.), Multiple representations in chemical education (pp. 285307).
Dordrecht: Springer.
Kaput, J. J. (1989). Linking representations in the symbol systems of algebra. In S. Wagner & C.
Kieran (Eds.), Research issues in the learning and teaching of algebra (pp. 167194). Reston,
Kohl, P., & Finkelstein, N. (2008). Patterns of multiple representation use by experts and novices
during physics problem solving. Physical Review Special Topics Physics Education Research,
4(1), 010111. doi:10.1103/PhysRevSTPER.4.010111
Kohl, P. B., Rosengrant, D., & Finkelstein, N. D. (2007). Strongly and weakly directed approaches to
teaching multiple representation use in physics. Physical Review Special Topics Physics
Education Research,3(1), 010108. doi:10.1103/PhysRevSTPER.3.010108
Kotovsky, L., & Gentner, D. (1996). Comparison and categorization in the development of rela-
tional similarity. Child Development,67, 27972822.
Kozma, R. (2003). The material features of multiple representations and their cognitive and social
affordances for science understanding. Learning and Instruction,13(2), 205226.
Kozma, R., Chin, E., Russell, J., & Marx, N. (2000). The roles of representations and tools in the
chemistry laboratory and their implications for chemistry learning. The Journal of the
Learning Sciences,9(2), 105143.
Kozma, R. B., & Russell, J. (1997). Multimedia and understanding: Expert and novice responses to
different representations of chemical phenomena. Journal of Research in Science Teaching,34,
Larkin, J., & Simon, H. (1987). Why a diagram is (sometimes) worth ten thousand words. Cognitive
Larkin, J. H., McDermott, J., Simon, D. P., & Simon, H. A. (1980). Models of competence in solving
physics problems. Cognitive Science,4(4), 317345.
Lee, O., Eichinger, D. C., Anderson, C. W., Berkheimer, G. D., & Blakeslee, T. D. (1993). Changing
middle school studentsconceptions of matter and molecules. Journal of Research in Science
Teaching,30(3), 249270.
McNeil, N. M., & Fyfe, E. R. (2012). Concreteness fadingpromotes transfer of mathematical
knowledge. Learning and Instruction,22(6), 440448. doi:10.1016/j.learninstruc.2012.05.001
Nurrenbern, S. C., & Pickering, M. (1987). Concept learning versus problem solving: Is there a
difference? Journal of Chemical Education,64, 508.
Nyachwaya, J. M., Warfa, A. R. M., Roehrig, G. H., & Schneider, J. L. (2014). College chemistry stu-
dentsuse of memorized algorithms in chemical reactions. Chemistry Education Research and
Practice,15(1), 81. doi:10.1039/C3RP00114H
Oliver, M. J. (1997). Visualisation and manipulation tools for modal logic (Unpublished doctoral
dissertation). Open University, UK.
Petersen, L. a, & McNeil, N. M. (2013). Effects of perceptually rich manipulatives on preschoolers
counting performance: Established knowledge counts. Child Development,84(3), 10201033.
PhET States of Matter: Basic Simulation. (n.d.). University of Colorado, Boulder.
Prain, V., Tytler, R., & Peterson, S. (2009). Multiple representation in learning about evaporation.
International Journal of Science Education,31(6), 787808.
Prain, V., & Waldrip, B. (2006). An exploratory study of teachersand studentsuse of multi-modal
representations of concepts in primary science. International Journal of Science Education,28
(15), 18431866. doi:10.1080/09500690600718294
Ramnarain, U., & Joseph, A. (2012). Learning difculties experienced by grade 12 South African
students in the chemical representation of phenomena. Chemistry Education Research and
Practice,13(4), 462470.
18 Y. I. LIN ET AL.
Rider, R. (2007). Shifting from traditional to nontraditional teaching practices using multiple rep-
resentations. Mathematics Teacher,100(7), 494500.
Schnotz, W., & Kulhavy, R. W. (Eds.). (1994). Comprehension of graphics (Vol. 108). North
Holland: Elsevier.
Schwartz, D. L. (1995). The emergence of abstract representations in dyad problem solving. The
Journal of the Learning Sciences,4(3), 321354. doi:10.1207/s15327809jls0403_3
Smith, K., & Metz, P. (1996). Evaluating student understanding of solution chemistry through
microscopic representations. Journal of Chemical Education,73(3), 233235. doi:10.1021/
Son, J. Y., Smith, L. B., & Goldstone, R. L. (2011). Connecting instances to promote childrens rela-
tional reasoning. Journal of Experimental Child Psychology,108(2), 260277. doi:10.1016/j.jecp.
Tabachneck, H., Koedinger, K., & Nathan, M. (1994). Toward a theoretical account of strategy use
and sense-making in mathematics problem solving. In A. Ram & K. Eiselt (Eds.), Proceedings of
the 16th annual conference of the cognitive science society (pp. 836841). Hillsdale, NJ: LEA.
Tabachneck, H. J. M., Leonardo, A. M., & Simon, H. A. (1994). How does an expert use a graph? A
model of visual and verbal inferencing in economics. In A. Ram & K. Eiselt (Eds.), Proceedings of
the 16th annual conference of the cognitive science society (pp. 842847). Hillsdale, NJ: LEA.
Taber, K. S. (2013). Revisiting the chemistry triplet: Drawing upon the nature of chemical knowl-
edge and the psychology of learning to inform chemistry education. Chemistry Education
Research and Practice,14(2), 156168. doi:10.1039/C3RP00012E
Talanquer, V. (2011). Macro, submicro, and symbolic: The many faces of the chemistry triplet.
International Journal of Science Education,33(2), 179195. doi:10.1080/09500690903386435
Thompson, P. W. (1992). Notations, conventions, and constraints: Contributions to effective uses
of concrete materials in elementary mathematics. Journal for Research in Mathematics
Education,23, 123. doi:10.2307/749497
Treagust, D., Chittleborough, G., & Mamiala, T. (2003). The role of submicroscopic and symbolic
representations in chemical explanations. International Journal of Science Education,25(11),
13531368. doi:10.1080/0950069032000070306
Tsui, C., & Treagust, D. F. (2013). Multiple representations in biological education (Vol. 7). Springer
Science & Business Media. doi:10.1007/978-94-007-4192-8
Yarroch, W. L. (1985). Student understanding of chemical equation balancing. Journal of Research
in Science Teaching,22(5), 449459. doi:10.1002/tea.3660220507
Yerushalmy, M. (1991). Student perceptions of aspects of algebraic function using multiple rep-
resentation software. Journal of Computer Assisted Learning,7,4257.
... In this sequence, educators present concrete representations before increasingly abstract representations are introduced in a stepwise manner. Various researchers have suggested that the concreteness fading sequence is applicable widely across mathematics and natural science education (for overviews, see, Fyfe and Nathan 2019; Lin et al. 2016). While several studies have investigated the learning of basic primary school mathematics, only a few have investigated the learning of the more advanced concepts in mathematics, engineering, or the natural sciences. ...
... On the basis of this assumption, the approach further specifies how external representations differing in concreteness should be sequenced, and how many should be sequenced. To be sure, there exist alternative descriptions of concreteness fading sequences that differ from this definition; for example, with regard to whether two vs. three steps are necessary (Goldstone and Son 2005;Jaakkola and Veermans 2018;Johnson et al. 2014;Lin et al. 2016). Nevertheless, the different definitions converge on a common idea. ...
... Not only are there many different ways of representing concepts or principles, but also, as already mentioned, different disciplines may also rely on or prefer different representations. Lin et al. (2016) notice these differences and develop a taxonomy for extending the concreteness fading sequence from mathematics to different natural science disciplines. Table 1 provides this taxonomy, capturing the four disciplines of mathematics, physics, chemistry, and biology. ...
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... Just exposure to multiple representations, however, will not be enough to ensure that students develop flexible and transferable knowledge in a domain (Ainsworth, 2006). It is critical that students develop facility with interpreting, coordinating, and translating across multiple representations (Even, 1998;Lin et al., 2016;Waisman et al., 2014). Only then are they likely to realize the benefits in terms of deeper understanding and more transferable knowledge (Chang et al., 2016). ...
... Only then are they likely to realize the benefits in terms of deeper understanding and more transferable knowledge (Chang et al., 2016). Yet, getting students to engage in this work is something not easily done (Even, 1998;Lin et al., 2016;Waisman et al., 2014). ...
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For students to acquire flexible knowledge in STEM domains, it is important to find ways to help them attend to underlying structures of the domain and practice making connections between these structures. Traditional analogy studies focus on connecting a single type of representation to examples drawn from different contexts. Complex STEM domains, however, often require students to map relations within a context but across different types of representations. The current study developed and tested a representation mapping intervention designed to help students interpret, coordinate, and eventually translate across multiple representations. The study was conducted in the context of a college-level online interactive statistics textbook. The findings of this study support the efficacy of the representation mapping intervention for facilitating students’ learning and transfer and shed light on how to implement analogical learning strategies into authentic learning contexts. Keywords: analogy, multiple representations, analogical mapping, STEM education, online learning
... Одатле произилази специфичност учења хемије, а то је да се садржаји хемије разматрају на три нивоа: на макроскопском, који се односи на чулно опажљива својства и промене супстанци, на субмикроскопском нивоу, који обухвата структуру супстанци, атоме, молекуле и јоне, и симболичком нивоу, који се служи симболима (словима, бројевима, ознакама) да би се представили атоми, молекули, јони, супстанце и промене којима супстанце подлежу (Johnstone, 1993). Повезивање и интеграција информација које пружају различити нивои представљања садржаја хемије потребни су за разумевање хемије (Gkitzia et al., 2011;Jaber & BouJaoude, 2012;Lin et al., 2016;Milenković et al., 2014a). Другим речима, да би ученици разумели зашто супстанца има одређена својства или зашто се мења на одређен начин (макроскопски ниво), потребна је истовремена примена субмикроскопских и симболичких приказа у хемијским објашњењима (Treagust et al., 2003). ...
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The aim of this research is to examine how students in the eighth grade of elementary school and the first grade of high school interpret the representations of the structure and composition of substances and how successful they are in transforming the representations of one level into another. A total of 193 students participated in the research, 81 students of the eighth grade of elementary school and 112 students of the first grade of high school. According to the aim of the research and research questions, a test was prepared whose requirements referred to different levels of representations related to the structure of atoms, molecules and ions, chemical bonds, pure substances and mixtures. The students in the first grade of high school achieved a statistically significantly better overall achievement on the test compared to the students in the eighth grade of elementary school. The results of the research show that submicroscopic level representations help the eighth-grade students less in understanding the structure of atoms, molecules and ions, as well as the composition of pure substances and mixtures, while the first-grade high school students are more successful in their interpretation. In addition, the research results have shown that there are problems in translating the meaning of one level of representations to another, especially when information is conveyed using submicroscopic-level representations.
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Concreteness fading has been proposed as a general instructional approach to support learning of abstract mathematics and science concepts. Accordingly, organizing external knowledge representations in a three-step concrete-to-idealized sequence should be more beneficial than the reverse, concreteness introduction, sequence. So far, evidence for the benefits of concreteness fading come mainly from studies investigating learning of basic mathematics concepts. Studies on learning natural science concepts are scarce and have not implemented the full three-step-sequence. In an experimental classroom study (N = 70), we compared concreteness fading and concreteness introduction in high school science education about electromagnetic induction using a detailed assessment. Furthermore, we explored whether these sequences differentially affect the use of the different representations during instruction. Both sequences were equally effective and there were no differences in using the representations. We discuss why our results question the proposed advantages of concreteness fading and highlight conceptual differences and learning goals across domains.
... Από όσο γνωρίζουμε, δεν υπήρχε κάποια έρευνα που να μελετά συστηματικά και ολοκληρωμένα σε ένα πακέτο βασικών εννοιών την ικανότητα αναπαράστασης και μετάφρασης και στα τρία επίπεδα διδασκομένων. Οι μέχρι τώρα έρευνες επικεντρώνονται είτε σε μία συγκεκριμένη έννοια (π.χ., χημική αντίδραση, φύλο, κ.ά.) ή σε συγκεκριμένο συνδυασμό επιπέδων αναπαράστασης (Chi et al., 2018;Lin et al., 2016;Ye et al., 2018). ...
Στην εργασία αυτή περιγράφονται τα ερευνητικά αποτελέσματα τριών θεματικών ενοτήτων που αφορούν στο τρίπτυχο Μαθησιακές Διεργασίες - Μέθοδοι Διδασκαλίας - Μέθοδοι Αξιολόγησης. Στην πρώτη ενότητα διερευνήθηκε με το εργαλείο VACT η μετάβαση ομάδων διδασκόμενων διαφορετικής εμπειρίας από τη χρήση οπτικών στην υιοθέτηση αναλυτικών στρατηγικών κατά την επίλυση προβλημάτων Οργανικής Χημείας. Διερευνήθηκαν, επίσης, τα χαρακτηριστικά των μαθητών που προβλέπουν τη χρήση αυτών των στρατηγικών. Στη δεύτερη ενότητα περιγράφεται η ανάπτυξη και η εφαρμογή μιας συστημικής διδακτικής μεθόδου για τη διδασκαλία και αξιολόγηση στο πεδίο της Οργανικής Χημείας, καθώς και η ανάπτυξη συστημικών ερωτήσεων με τα κατάλληλα χαρακτηριστικά για τη διερεύνηση της συστημικής σκέψης. Στην τρίτη θεματική ενότητα διερευνήθηκαν τα απαραίτητα χαρακτηριστικά που πρέπει να έχουν οι χημικές αναπαραστάσεις ώστε να διευκολύνεται η μάθηση με κατανόηση. Προτάθηκαν κριτήρια αξιολόγησης, με τα οποία αξιολογήθηκαν και οι αναπαραστάσεις σχολικού βιβλίου Β τάξης λυκείου. Εξετάσθηκε, επίσης, η ικανότητα μετάφρασης χημικών αναπαραστάσεων Ελλήνων μαθητών και φοιτητών.
... Students often have difficulties in understanding SMRs, and teaching about the world of particles is challenging, since particle theory is abstract. Therefore, the use of visualisation material is necessary for classroom presentation (Johnstone, 2001;Exerciseer and Dalton, 2006;Kautz, Heron, Shaffer and McDermott, 2005;Lin, Son and Rudd, 2016;Cheng and Gilbert, 2017). ...
Science and technology continue to develop rapidly, which leads to the need for all-encompassing science education, starting in the early years (Lloyd et al., 1998; Millar, 2006). All students should benefit from the science education provided, which includes an understanding of the scientific dimension of phenomena and events, critical recognition of the possibilities and limitations of science, its role in society and its contribution to citizenship, as well as the development of critical thinking, oral communication, and writing skills (BSCS, 2008; ICSU, 2011; Vieira & Tenreiro-Vieira, 2014). In addition, Harlen (2010) suggested that science education should enable everyone to make informed choices and take appropriate action that will affect their well-being and the well-being of society and the environment.
... De uma forma geral, os recursos utilizados vão ao encontro do que estudos têm demonstrado acerca de como o uso de representações 3D pode contribuir para a eficácia do ensino (Lin, Son & Rudd, 2016). O uso de simulações e animações computacionais é amplamente citado nas pesquisas (Kozma & Russell, 2005;Wu, Krajcik & Soloway, 2001), com resultados animadores, e, mais recentemente, o uso de modelagem molecular tem mostrado resultados promissores (De Farias Ramos & Serrano, 2015). ...
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The obstacles faced in learning stereochemistry include difficulties related to visualization, problems in the acquisition and mastery of concepts that are prerequisites for understanding and differentiating stereoisomers. It is important to highlight that cognitive learning contributions consider that the student learns what is meaningful to him; for this reason, contextualization has a fundamental role in the conceptualization process. This work aims to present a systematic review of the literature on teaching of stereoisomerism seeking to identify strategies and themes used. The search method consisted of the selection of studies published in journals in the last 20 years, in Portuguese and Spanish, with Qualis A1 and A2 in the teaching area, in addition to the articles from Química Nova na Escola. Those that included stereoisomers in organic compounds were included as the central theme, presenting strategies or themes for their contextualization in teaching. Based on Content Analysis, the analytical process of the sixteen articles selected based on the criteria resulted in the creation of categories: scope of the article, teaching strategies, didactic resourcesfor visualization and themes used. The results indicate the focus on the publication of teaching proposals, strategies for the development of visual skills using molecular kits and applications, and the drugs theme being the most used for contextualization. As a general synthesis, we found the use of resources for visual literacy, in addition to the contextualization that privileges a variety of situations in which the concept of stereoisomerism is applied, having the potential to make it meaningful for students
Conference Paper
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Band 39 aus Tagungsband der Gesellschaft für Didaktik der Chemie und Physik
Conference Paper
It has been acknowledged that chemistry learning involves macroscopic, submicroscopic, and symbolic representations that should be comprehended by both students and teachers. Since very little research was geared toward investigating high school teachers’ understanding and practices of multiple representations in chemistry learning in Indonesia, this study was carried out to explore such knowledge gap. The method used was descriptive quantitative. Seventy-five chemistry teachers in East Java province participated in this study. They were surveyed using a validated questionnaire asking their understanding of multiple representations. The findings suggest that 49.33% of the participants do not know multiple representations, although, in fact, they practiced these representations in the classroom and employed media that explain chemistry macroscopically, sub-microscopically, and symbolically in learning. Chemistry teachers involved more macroscopic and symbolic representations in learning rather than submicroscopic. Therefore, there is a mismatch between teachers’ understanding and classroom practices with regard to the enactment of multiple representations in chemistry learning.
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For biological researchers, systems thinking is a basic conceptual framework, and many educationalists consider systems thinking as a metacognitive skill that enables students to understand and cope with the new scientific advancements that reach our society. With this in mind, we investigated the implementation of systems thinking in upper secondary biology education in several studies. In this chapter, we report a critical appraisal of our systems modeling approach that emerged from these studies. We first lay a theoretical foundation under our emergent modeling approach which prescribes the sequence in which multiple representations should be placed in a bottom-up educational strategy. Second, we articulate two studies that both designed and evaluated the development of a learning and teaching strategy that engaged students in developing multiple representations of living systems with increasing complexity. One study focused on the development of an initial systems model in cell biology, and the other addressed the use of computer modeling as a tool in the understanding of the dynamics in ecosystems. We conclude by critically looking back at these study results in the formulation of some general recommendations about the use of multiple representations in the development of systems thinking.
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In this historical and observational study, we describe how scientists use representations and tools in the chemistry laboratory, and we derive implications from these findings for the design of educational environments. In our observations we found that chemists use representations and tools to mediate between the physical substances that they study and the aperceptual chemical entities and processes that underlie and account for the material qualities of these physical substances. There are 2 important, interrelated aspects of this mediational process: the material and the social. The 1st emphasizes the surface features of both physical phenomena and symbolic representations, features that can be perceived and manipulated. The 2nd underscores the inherently semiotic, rhetorical process whereby chemists claim that representations stand for unseen entities and processes. In elaborating on our analyses, we • Examine the historical origins and contemporary practices of representation use in one particular domain - chemistry - to look at how developments in the design of representations advance the development of a scientific community, as well as the understanding of scientists engaged in laboratory practice. • Examine representations spontaneously generated by chemists, as well as those generated by their tools or instruments, and look at how scientists - individually and collaboratively - coordinate these 2 types of representations with the material substances of their investigations to understand the structures and processes that underlie them. • Draw implications from the study of scientists to make recommendations for the design of learning environments and symbol systems that can support the use of representations by students to understand the structures and processes that underlie their scientific investigations and to engage them in the practices of knowledge-building communities.
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A T I O N 2 0 0 0 , 4 (1) research' approach. In this approach, a small-scale curriculum development is linked to in-depth research on social, content and context specific teaching and learning processes. The structure of the research activities involves repeated cycles (a spiral) of activities, in which each cycle includes the following stages • an evaluation of a current educational situations; • formulation of research questions in conjunction with reflection on chemistry and chemistry education; • development and implementation of new teaching strategies and materials; • investigation of teaching and learning processes during classroom and laboratory sessions (important research instruments are audio/video-tapes for producing records of laboratory /classroom discussions); • repetition of the cycle. The cyclical approach is crucial to the individual teacher and can be used by professional research teams. It allows practitioners to link small-scale curriculum development to more in-depth research. Furthermore, if developmental research is carried out and published by practitioners at secondary level as well as at university level, the results can also help to bridge the gap between chemical education at this interface. References 1. De Jong O Schmidt H J Burger N and Eybe H 1999 Empirical research into chemical education UChem.Ed 3 28-30 2.
Chemistry seeks to provide qualitative and quantitative explanations for the observed behaviour of elements and their compounds. Doing so involves making use of three types of representation: the macro (the empirical properties of substances); the sub-micro (the natures of the entities giving rise to those properties); and the symbolic (the number of entities involved in any changes that take place). Although understanding this triplet relationship is a key aspect of chemical education, there is considerable evidence that students find great difficulty in achieving mastery of the ideas involved. In bringing together the work of leading chemistry educators who are researching the triplet relationship at the secondary and university levels, the book discusses the learning involved, the problems that students encounter, and successful approaches to teaching. Based on the reported research, the editors argue for a coherent model for understanding the triplet relationship in chemical education.
We describe a set of two computer‐implemented models that solve physics problems in ways characteristic of more and less competent human solvers. The main features accounting for different competences are differences in strategy for selecting physics principles, and differences in the degree of automation in the process of applying a single principle. The models provide a good account of the order in which principles are applied by human solvers working problems in kinematics and dynamics. They also are sufficiently flexible to allow easy extension to several related domains of physics problems.
Much scholarship in chemical education draws upon the model of there being three ‘levels’ at which the teaching and learning of chemistry operates, a notion which is often represented graphically in terms of a triangle with the apices labelled as macroscopic, submicroscopic and symbolic. This model was proposed by Johnstone who argued that chemistry education needs to take into account ideas deriving from psychological research on cognition about how information is processed in learning. Johnstone's model, or the ‘chemistry triplet’, has been widely taken-up in chemistry education, but has also been developed and reconceptualised in diverse ways such that there is no canonical form generally adopted in the community. Three decades on from the introduction of Johnstone's model of the three levels, the present perspective article revisits both the analysis of chemical knowledge itself, and key ideas from the learning sciences that can offer insights into how to best teach the macroscopic, submicroscopic and symbolic aspects of chemical knowledge.
This study sought to uncover memorized algorithms and procedures that students relied on in responding to questions based on the particulate nature of matter (PNM). We describe various memorized algorithms or processes used by students. In the study, students were asked to balance three equations of chemical reaction and then draw particulate representations of the compounds in the reactions. Students were then interviewed to uncover their understanding of underlying chemistry, taking note of any memorized algorithms that students were using. In addition to specific algorithms that students used, two trends were apparent from our analysis: (1) students successfully applied algorithms (in operations such as equation balancing) without necessarily understanding why they used the particular operations or processes. (2) Students have memorized processes and ideas which they incorrectly applied. Implications for assessment, research and instruction are also suggested.
Analogy and similarity are often assumed to be distinct psychological processes. In contrast to this position, the authors suggest that both similarity and analogy involve a process of structural alignment and mapping, that is, that similarity is like analogy. In this article, the authors first describe the structure-mapping process as it has been worked out for analogy. Then, this view is extended to similarity, where it is used to generate new predictions. Finally, the authors explore broader implications of structural alignment for psychological processing. (PsycINFO Database Record (c) 2012 APA, all rights reserved)