Scholarly article on topic 'Toward a durable prevalence of scientific conceptions: Tracking the effects of two interfering misconceptions about buoyancy from preschoolers to science teachers'

Toward a durable prevalence of scientific conceptions: Tracking the effects of two interfering misconceptions about buoyancy from preschoolers to science teachers Academic research paper on "Psychology"

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Academic research paper on topic "Toward a durable prevalence of scientific conceptions: Tracking the effects of two interfering misconceptions about buoyancy from preschoolers to science teachers"

Research Article

Toward a Durable Prevalence of Scientific Conceptions: Tracking the Effects of Two Interfering Misconceptions About Buoyancy From Preschoolers to

Science Teachers

Patrice Potvin and Guillaume Cyr

Departement de didactique, Universite du Quebec a Montreal, C.P. 8888, Succursale Centre-Ville,

Montreal, Quebec, Canada H3C 3P8

Received 31 March 2016; Accepted 8 March 2017

Abstract: While the majority of published research on conceptual change has focused on how misconceptions can be abandoned or modified, some recent research findings support the hypothesis that acquired scientific knowledge does not necessarily erase or alter initial non-scientific knowledge but rather coexists with it. In keeping with this "coexistence claim," this article presents an analysis of scientific understanding in four groups of individuals with varying degrees of expertise (preschoolers, elementary students, secondary students, and science teachers) using a cognitive task on buoyancy. This task allowed us to determine the prevalence of certain conceptions and the interference caused by two possible conceptual distractors with regard to producing accurate answers. Results describe the progression of the desired (scientific) conception with age/expertise as well as the evolution or regression of the statuses of two misconceptions. Results also show that misconceptions continue to interfere with performance even when there is a higher degree of scientific expertise, and that patterns of such interference can be studied. In keeping with these conclusions, we argue for the use of a model of conceptual learning called "conceptual prevalence." © 2017 The Authors. Journal of Research in Science Teaching Published by Wiley Periodicals, Inc. J Res Sci Teach 9999:XX-XX, 2017 Keywords: conceptual change; coexistence; prevalence; buoyancy

Despite a significant decrease in interest in conceptual learning among science education researchers in recent years (25% of publications [1998-2002] vs. 15% [2008-2012]) (Lin, Lin, & Tsai, 2014), it is still a very important and challenging topic and a major concern for science teachers. Indeed, conceptual change research could help educators understand the best ways to ensure students give scientifically inspired answers rather than intuitive or non-scientific ones.

The field has focused much of its efforts on identifying—and finding the roots—of the most common non-scientific ideas (oftentimes called "misconceptions") in various scientific disciplines (e.g., Arslan, Cigdemoglu, & Modeley, 2012; Tasdere & Ercan, 2011), describing

This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

Contract grant sponsor: Conseil de recherche en sciences humaines du Canada; Contract grant number: 435-2015-1376. Correspondence to: P. Potvin; E-mail: DOI 10.1002/tea.21396

Published online in Wiley Online Library ( © 2017 The Authors. Journal of Research in Science Teaching Published by Wiley Periodicals, Inc.

conceptual change (Vosniadou, 1994), and understanding which teaching operations can favor it (Duit & Treagust, 2003).

The earliest—sometimes labelled as classical—models (Nussbaum & Novick, 1982; Posner, Strike, Hewson, & Gertzog, 1982) of conceptual change were mostly derived from the Piagetian concept of accommodation (Piaget, 1974) or the Kuhnian notion of scientific revolution (Kuhn, 1962). In these models, misconceptions were most of the time seen as rigid, resilient structures caused by interactions with the physical world and/or that were socially transmitted or reinforced. The importance of provoking an initial "disequilibrium" or revealing "anomalies" through cognitive conflict was implicitly taken for granted and almost never questioned. If an initial non-scientific idea needed to be rejected, it appeared reasonable to think that the first step would be to try to weaken this idea, or question its ability to explain or predict so that it would be eventually replaced. The criterion of dissatisfaction (Posner et al., 1982) was believed to favor some sort of motivation to resolve the dissonance.

But, at the end, if deep conceptual changes were sometimes recorded, especially among learners with the most initial knowledge (Limón & Carretero, 1997), the levels of success were seldom high enough (Limón, 2001). Nevertheless, probably because the findings were mostly positive and the emerging prescriptions were simple, these models are still today among the most widely known and used, even though they require teachers to know about, respond to— and perhaps prevent—a number of possible misconceptions. This is no easy task given the potentially infinite number of personal ideas. In the research community, though, the models that observed this tradition remained criticized for their lack of satisfactory effectiveness and for not taking into consideration students' sincere efforts to understand the physical world. They also did not account for many answers that did not appear to be as strongly held but rather constructed "on the spot" (diSessa, 1993).

Then "second generation" conceptual change models appeared. These models progressively focused more and more on the constraints behind students' adherence to common conceptions than on the effect of cognitive conflicts or the ambition of "replacing" misconceptions (Amin, Smith, & Wiser, 2014). These constraints were sometimes called "intuitive rules," (Stavy & Tirosh, 2000) "ontological frameworks," (Vosniadou & Brewer, 1992) "p-prims," (diSessa, 1993) "core intuitions," (Brown, 1993), "common sense" (Talanquer, 2006), etc. and were sometimes presented as learning elements that were more fundamental than conceptions and therefore "responsible for a great number" (Talanquer, 2006, p. 812) of them. In other words, they coordinate complex performances and allow the production of answers, accurate or not.

Sometimes presented as adversaries of one another (knowledge as theory vs. knowledge in pieces), some of these models however shared an interest in—and a focus on—describing the processes that generate and modify conceptions, however sometimes slightly at the expense of concrete and generalizable prescriptions. Many of them could be characterized by their desire to compensate for the shortcomings of classical models in order to hope for a revision (Vosniadou, 1994), transformation (Amin et al., 2014; Heddy & Sinatra, 2013) or restructuration (Limón, 2001, p. 359) of learners' ideas and models. Second generation models of conceptual change have also given hope to many teachers who might have felt overwhelmed by the number of misconceptions to address because they proposed fewer conceptual objects (intuitive rules, p-prims, core intuitions, etc.) that could be involved in science learning. For example, when presenting their intuitive rule "More A-More B," Stavy and Tirosh (2000) suggested that "conceptions, apparently related to specific domains, are actually only specific instances of the use of this rule." (p. 2) Therefore, concentrating on the cognitive resources instead than on their specific instances promised to be more economic, and suggested that explanations and even predictions about the existence of some misconceptions could be made,

and also that the cognitive resources that constrain adherence to certain conception might be exploited by teachers. Second generation models also suggested that, to avoid certain possible negative effects of "extensively used" cognitive conflicts, teachers should make "moderate use" (Vosniadou, 2008, p. xix) of cognitive conflicts.

These models, that belong in our opinion to what Ohlsson (2009) calls the "transformation of knowledge" paradigm, are also characterized by a generalized lack of concern for what makes "change" durable even though, we believe, teachers might think of durability as an important educational preoccupation. Unfortunately, transformation models do not offer enough tools to tackle this question effectively. Resurrection of initial conception is most of the time merely presented as regrettable. We feel that this might simply be a natural consequence of believing that misconceptions can be transformed. Indeed, if some eventual costly transformation of knowledge has finally been successful, why should one worry about an eventual spontaneous—and presumably just-as costly—reverting to initial situations?

The Beginnings of the Idea of Coexistence

However, the idea of a transformation of initial conceptions does not necessarily imply that all elements of these conceptions must be modified or transformed during a conceptual change process. Indeed, if certain elements can be rejected, some of them that are useful might remain, and new ones, more locally relevant, be summoned. Indeed, it does not appear necessary, nor beneficial, that they be abandoned or forgotten, as they may remain useful in other contexts. Indeed, intuitive rules, core intuitions and p-prims have been judged to be "domain general," instead as "domain specific" (Brown, 1993). Their persistence is therefore implicit. In this context, conceptual change can be considered as shifts in the attention given to- and the mobilization of- such or such cognitive resources. These shifts have sometimes been called "refocusing" (Brown, 1993), "reprioritization" (Kaufman, Vosniadou, diSessa, & Thagard, 2000) or described as modifications of "cueing priorities" (diSessa, 1993).

Thus, as the classical models suggest rejection of monolithic conceptions, the second "transformation" models suggest the persistence and the coexistence within a learner's mind of certain cognitive resources: "Core intuitions are not changed, they are simply reorganized or refocused in relation to a particular context" (Brown, 1993).

But during the 80s and the 90s, we also find authors that have embraced the idea of coexistence and accepted that whole conceptions or representations (and not only domaingeneral cognitive resources) can coexist, but however most of them formulated such commitments in rather implicit ways (Hewson, 1981; Solomon, 1983). The idea of coexisting conceptions was formulated more explicitly in later articles (Chi, 1992; Galili & Bar, 1992; Linder, 1993; Mortimer, 1995, Tyson, Venville, Harrison, & Treagust, 1997) and doctoral theses (Ozdemir, 2004), and recommendations were formulated.

Nevertheless, we argue that the idea of coexistence of multiple conceptions within a learner's mind remains rather implicit or marginal in the conceptual change research tradition and never became a major trend, especially given that the methods used in the majority of research articles on the topic are inspired by early models like the one suggested by Posner.

Evidence of Coexistence

However, in recent years, a growing number of neuroimaging and mental chronometry studies have provided convincing experimental evidence that new knowledge does not necessarily nor completely alter or erase previous knowledge. These studies have gathered evidence that shows that when learners successfully solve counterintuitive problems, previous intuitive knowledge or heuristics continue to interfere in scientific and mathematical performance.

They reported that, all other things being equal, response times are significantly longer when subjects are asked to solve problems that have a possible conceptual or heuristic distractor. Evidence was provided with congruent/incongruent (or intuitive/counterintuitive) tasks on perimeters and area (Babai, Levyadun, Stavy, & Tirosh, 2006; Stavy & Babai, 2008), living things (Babai, Sekal, & Stavy, 2010), solids and liquids (Babai & Amsterdamer, 2008), buoyancy (Potvin, Masson, Lafortune, & Cyr, 2015), and even by testing in a number of scientific subdisciplines (Shtulman & Valcarcel, 2012). According to neuroimaging studies, overcoming intuitive or conceptual interference also increases the activity of the brain mechanisms that are usually associated with the cognitive function of inhibition, like when performing a Stroop task. These studies used scientific tasks on conservation (Houde et al., 2011), electric circuits (Potvin, Turmel, & Masson, 2014; Masson, Potvin, Riopel, & Brault Foisy, 2014), falling objects (Brault Foisy, Potvin, Riopel, & Masson, 2015), and so forth. For the authors of these studies, recording the activation of the anterior cingulate and the prefrontal (dorsolateral and/or ventrolateral) cortices in counterintuitive problems is evidence that something interfered—and was ultimately "neutralized" or inhibited—with the process of producing accurate (or expert) answers. These findings therefore further support the so-called "coexistence" claim as well.

These interesting findings therefore seriously challenge most of the research tradition of conceptual "change," in which misconceptions are considered to be abandoned, exchanged, or altered during learning (Potvin, 2013).

Conceptual Prevalence as a Response to Coexistence

We therefore believe that, the "conceptual change" field was for the most part unprepared for the idea of multiple coexisting ideas or for the possible "persistence" claim that naturally came with it. We therefore feel that an appropriate response to the coexistence claim might be to think in terms of "prevalence" rather than in terms of "change."

According to this perspective, many contradictory ideas of different granularities can compete inside a learner's head; a scientific conception might oppose common-sense knowledge; a socially transmitted myth could oppose the certain use of a p-prim, etc. Any conceptual object (heuristic, intuitive rule, p-prim, ontological framework, or conception) that could distract learners from producing scientifically correct answers or from performing in a given context could produce misconceptions; things that have been labelled as such in the past. Accordingly, we will thus consider that misconceptions are any visible and observable products (answers, justifications, performances) of the mobilisation of all sorts and combinations of cognitive resources and information. Every time we will hereafter use the term "(mis-)conception" it will implicitly refer to the combination of cognitive resources, information, beliefs, etc. that underlie its expression. In a sense, conceptions and (mis-)conceptions are thus phenotypical and can be considered as by-products of more profound and invisible mechanisms and processes. In the prevalence perspective, a conceptual change can thus only be an observable modification of performance, answers or justifications; and "change" does not refer to genotypical or fundamental exchanges of unitary elements or their transformation, but rather to a shift in prevalence of the use of one or more cognitive resources, in an overtaking process. In previous work (Potvin, 2017), we have proposed that this modification could, by analogy, be considered as "epigenetic," in the sense that the expression (phenotype) of the genotype (intuitive resources) changes while the genotype, or elements of it, can remain the same.

It is important here to understand that such a reduction is essentially methodological and not epistemological. We acknowledge that it does not necessarily properly recognize the sometimes crucial distinctions between different intuitive objects or how conceptions or misconceptions are initially acquired. For the time being, this reduction nevertheless appeared to us as necessary in

order to better focus on analyzing the observable differences between initial and final answers. It also creates common ground to compare the different conceptions and to monitor their appearance.

Of course, each existing conception can be more or less "believed in" and therefore have varying credibility statuses. This status can be defined as the level of adherence or of perceived cognitive utility that a person attributes to a conception (or a misconception) in a specific context of performance or response in relation to other possible competing conceptions. It can be considered higher when a person succeeds more often at congruent/intuitive tasks and fails more often at incongruent/counterintuitive ones. We can also hypothesize that adherence could be evaluated by the feeling of certainty that a learner has towards each possible conception (Hemmerich, Van Voorhis, & Wiley, 2016; Potvin, Skelling-Desmeules, & Sy, 2015).

Accordingly, prevalence would be the special status of a (mis-)conception when its adherence is superior to the ones of all other presumably existing conceptions in a certain context. Most of the time, we are only conscious of our prevalent conceptions. And when learners have to defend their choices, justifications that support prevalent conceptions usually appear first and are often expressed with strength and sometimes with a feeling of certainty. Prevalence therefore constrains accuracy but cannot automatically be considered durable. Indeed, some successful educational experiences seem to have lasting effects, whereas others appear to be subject to "recency" effects (Baddeley & Hitch, 1993) and have more ephemeral apparent consequences. Thus prevalence can be temporary. The reader should note that we consider that there is a subtle but important difference between the concepts of prevalence and adherence. For example, a learner could have different adherence levels for many coexisting conceptions, but only one of them can be prevalent at the time.

In this view, it can also be expected that non-prevalent conceptions—if they actually persist in a learner's mind—will presumably participate in decision-making processes, even if they cannot be detected based on accuracies. Their presence can, however, be observed in response times. Interference can therefore be defined as the distracting effect of a non-prevalent conception on a particular performance or response. The greater the interference, the longer it will take to produce correct performances or answers. It can also be hypothesized that if the status of an interfering while non-prevailing conception is high enough, then it probably has to be inhibited in order to secure accurate performances. This inhibition process is one of the most likely explanations of delays in responses.

Tracking Prevalence and Interference: Research Questions

To our knowledge, there have been few research efforts, in a coexistence perspective, to track prevalence of- and the interference by- conceptions as learners get older or acquire knowledge. The recent article by Shtulman and Harrington (2015) is, in our opinion, one of the best there is. The authors used a consistent-inconsistent task (Shtulman & Valcarcel, 2012) with younger (M = 19 year olds) and older (M = 65 year olds) adults in scientific and non-scientific occupations and concluded that "older adults are no more immune to the conflict between science and intuition than are younger adults" (p. 14) and that "scientists are no more immune to [this] conflict [...]" (ibid.) even 40 years after they completed their initial scientific training.

As a complement to this study, we propose tracking the evolution of conceptual prevalence and interference. We will, however, not make this exploration in the years following scientific training but during the training itself. We also propose using our "sink/float" task (Potvin, Sauriol, & Riopel, 2015) to answer the following research questions: (1) what are the prevalent misconceptions that we can record at different ages/levels of expertise? and (2) what are the main conceptual interferences about buoyancy that we can record in each of these groups?

In providing answer elements to these research questions, we hope to illustrate that the prevalence of certain conceptions over others can be established using a single set of stimuli. The research may also provide a clearer picture of the coexisting conceptions (and misconceptions) that actively compete for cognitive utility in this context—not only the prevalent ones, but also their immediate competitors at different age levels. In doing so, we believe that we are contributing to the field by following up, in a more systematic way, the coexistence hypothesis that has been implicitly or indirectly suggested in conceptual change research in the past.



The participants consisted of 62 preschoolers (ages 5-6), 557 fifth- and sixth grade students (ages 10-11), 127 tenth- and eleventh-grade students (ages 14-15), and 22 secondary school science teachers (total N = 768). The participants were recruited from their respective schools, informed of the research objectives, and asked to perform the task. Informed consent and parental permission (when needed) were obtained for all participants. All participating students came from schools in Greater Montreal in Canada. Since the teachers were recruited at a province-wide conference on science education, they were from different parts of Quebec. No participants were deliberately excluded and they were all selected based on their willingness to participate. As a result, our sample may not be completely representative, especially in the case of preschoolers and science teachers (as there were fewer participants). Nonetheless, there is no particular reason to think that they are not, except for the possible effect of their (and their parents') willingness to contribute.

Over the years, a large number of frequent misconceptions have been recorded about buoyancy (Thouin, 2015; Unal, 2008). On reviewing these articles, we noted that the identification of misconceptions depended on the form and content of the problems presented to the students. For problems where buoyancy involved the concept of force (Cepni & Sahin, 2012), misconceptions were usually about the magnitude and behaviour of the force being studied. When the problem was not posed in Archimedes' terms, force was usually not among the recorded misconceptions. Of course, when problems focused on the submerged volume of objects (Tasdere & Ercan, 2011) instead, misconceptions about the effects of this volume were predominant, and so on. Displayed—and apparently prevalent—misconceptions therefore appear to be context-related and not necessarily prevalent per se. It thus seems important to ascertain the parameters of the contexts being studied, as well as the ability of these contexts to reveal different conceptions/ misconceptions (Kloss, Fisher, & Van Orden, 2010). The previously validated sink/float task (Potvin, Sauriol, & Riopel, 2015) offers a context that is easy to grasp and control. It also allows us to test three different conceptions, two of which have been recorded in previous studies. The first misconception can be expressed as "volume determines if an object will sink or float" (Unal, 2008, p. 140) and the second, as "weight determines if an object will sink or float" (ibid.). We will hereinafter refer to these two conceptions as VOLUME and MASS (with capital letters). Likewise, we will use the term SUBSTANCE to refer to the conception that "a specific density determines if an object will sink or float." In our task, the material (polystyrene, wood, and lead) was key to producing scientific and correct responses. SUBSTANCE is therefore the scientific conception that educators hope students will eventually adhere to at some point during their schooling. We also believe that the task is in keeping with other classical studies on buoyancy that focus on salient variables such as size, weight, and density (Smith, Carey, & Wiser, 1985,1992).

"Sink/float" is a computer-based cognitive task that presented a sequence of stimuli in the form of pairs of circular objects ("balls"). The balls were said to be made of one of the above-mentioned substances and came in three sizes. There were two possible answers: the left ball or the right ball, for a total of 81 possible answers (32 x 32). We excluded the 27 stimuli for which neither "left" or "right" were the correct answer (whenever the two balls were made of the same material) so that the final task consisted of 54 stimuli. They were presented in random order and participants were asked to indicate "which one of the two balls (left or right) will have a tendency to 'sink more'" by hitting the appropriate key (left or right) on a computer keyboard.

There are four possible conditions that can be attributed to our 54 stimuli:

• Incongruent (referred to as incongruent inverse in certain articles [Stavy & Babai, 2010]) is a condition that can be attributed to a stimulus in which a misconception is presumed to distract from the correct answer (example: if one of the objects has a higher specific density than the other but is believed to be lighter (ex: an iron needle vs. a battleship), then MASS adherents might answer the task of determining "which one will sink more" with less accuracy or slower);

• Equal (sometimes called incongruent equal) is a condition that can be attributed to a stimulus in which a considered conception does not help the participant decide (example: If an object is exactly as heavy as another, then MASS adherents might be troubled while answering and might delay their answer);

• Congruent is when a certain conception is presumed to help the participant produce a correct answer (example: If an object is both larger and made of a denser materiel than the other, then VOLUME adherents might answer faster or with more accuracy);

• Congruent salient is similar to congruent but when the considered conception is suspected to have an even stronger pull (toward the correct answer) because of a greater magnitude difference (example: a big rock will be considered as having a greater tendency to sink than a small pebble by both VOLUME and MASS adherents)

Since we are studying the potential presence of three possibly coexisting conceptions, one of the four conditions have been attributed to our 54 stimuli for each of these conceptions. Thus each stimulus has been labelled three times according to what it shows.

Figure 1 presents a subset of eight (out of 54) stimuli from the sink/float task and the conditions that they have been attributed to, according our two interfering misconceptions (VOLUME and MASS). For clarity, we have only chosen to present stimuli that have "left" as correct answer. However, it is important to keep in mind that it is not that case in the used task, where all stimuli have a "mirror" version [27 for which "left" is the correct answer and 27 for which "right" is the correct answer]).

When we will analyze the data for all subjects in terms of adherence to VOLUME (left column), we will consider that size will either interfere (A: incongruent), not interfere (C; equal), benefit (E: congruent) or benefit more [greater difference in sizes] (G: congruent salient) in the production of correct answers. When we will analyze the data for all subjects in terms of adherence to MASS (right hand side column), we will consider that size will either interfere (B: incongruent), not interfere (D; equal), benefit (F: congruent) or benefit more [greater difference in weight] (H: congruent salient) in the production of correct answers. And finally, when we will analyze the data for all subjects in terms of adherence to SUBSTANCE, we will consider that all 54 stimuli are congruent, because hypothetical "perfect" SUBSTANCE adherents would answers all stimuli correctly.

Note that, in Figure 1, stimuli C and F are the same. This does not mean that C appears twice in the task but rather illustrates that the same stimuli can have different

Figure 1. Examples of stimuli from the task and the corresponding conditions for each conception. [Color figure can be viewed at]

labels, depending on the studied (mis-)conception. This is how the sink/float task can be used not only to measure the adherence to one of the conceptions, but rather of all of them simultaneously. Thus it will also allow determination of prevalence as well as of interference.


Prevalence was established on the basis of accuracies. For each conception (and for every participant), we computed an adherence score that, according to the definition of prevalence provided above, was obtained by adding up the proportion of available congruent stimuli that were answered accurately plus the available incongruent stimuli that were answered incorrectly. Next, in order to associate each participant with a conceptual profile, a two-step cluster analysis was conducted by including all three adherence scores. Lastly, the percentage of participants in each profile was determined for each age group.

Interference of competing conceptions was calculated for accurate answers only. This allowed us to determine which interferences could be detrimental to performance. A multiple-factor analysis of variance (ANOVA) was used to confirm the difference in response times (RT) for each condition for each interfering conception, and we presented the mean scores for all distinct RTs for each age/expertise group.

Results and Interpretation Prevalence (Research Question No. 1)

Figure 2 shows the findings from the conducted two-step cluster analysis. The two-step Cluster Analysis procedure is an exploratory tool designed to reveal natural groupings (here: clusters of participants) within a dataset that would otherwise not be apparent. The groupings are established in order to minimize the within-cluster sum of squares. We ran the test using the three available adherence scores (SUBSTANCE, MASS, and VOLUME). The output (Figure 2) shows the adherence profiles of participants who belong to each one of the cluster that were obtained (each column). The best interpretable solution produced four distinct clusters, with a measure of cohesion and separation greater than 0.5, which is considered as "good."

Each row presents the distribution of adherence scores throughout clusters. For example, in the first row, the best scores of adherence to SUBSTANCE are found in participants that were attributed to cluster 1 (distribution is pushed to the right, for these participants) and the weakest went in cluster 4. Each column thus presents the distribution of all adherence scores of all participants that belong to each corresponding cluster.

The 370 participants who were gathered in column 1 (cluster 1) by the clustering procedure have the highest adherence to SUBSTANCE and a very low adherence to VOLUME. These participants differ from cluster 2 participants who all have adherence to MASS as their dominant characteristic. Since their adherence to SUBSTANCE if the strongest according to the answers they gave in the task, they have been labelled "Prevalence of SUBSTANCE" participants. Cluster 2 participants (N = 177) have the highest adherence to MASS. Therefore, they have been labelled "Prevalence of MASS". Cluster 3 gathers participants (N = 137) who have the highest adherence

Cluster 1 2 3 4

% of participants (N) 48.2% (370) 23.0% (177) 17.8% (137) 10.9% (84)

Adherence to SUBSTANCE i A A

Adherence to MASS A A

Adherence to VOLUME A * A

Label and colour Prevalence of SUBSTANCE Prevalence of MASS Prevalence of VOLUME Weak scores

Figure 2. Results from the two-step cluster analysis. [Color figure can be viewed at]

to VOLUME. They therefore have been labelled "Prevalence of VOLUME" participants. However some of them have a very distinct sub-profile (marked with an "*"); the adherence to VOLUME of these interesting participants is very weak—and not strong (as the rest of participants from this cluster), meaning that they might adhere to an unexpected misconception that "small volume makes objects sink." According to an additional cluster analysis that we conducted, this time only on the "prevalence of VOLUME subjects," we were able to determine that these "prevalence of negative VOLUME" adherents represent about 44 of the 137 participants in cluster 3. Cluster 4 (N = 84) includes the few participants with rather low adherence to any of the conceptions and who did not fit easily into other profiles. They have been labeled "weak scores" participants. Different colors (bottom of Figure 2) have been attributed to each prevalence profile and used in the following Figure 3.

Interpretation. We believe that Figures 2 and 3 provide a rather convincing argument that a prevalence perspective, as we described above and operationalized, could provide an interesting framework for interpreting conceptual learning. In fact, the distribution shows an increasing prevalence among those with more expertise of the conception that substance is key to scientific answers. It also shows a steady decrease in the belief that buoyancy depends on volume alone. Lastly, it shows that the more unclear or unstable patterns (all weak scores) tend to decrease and virtually disappear.

The belief that mass is the key to understand buoyancy appears to be more prevalent in elementary students than any other age group. This suggests that, for certain students, it may play a role in the transition from VOLUME to SUBSTANCE. The model also gave an unexpected result: the non-negligible presence of a conception that links buoyancy to volume but in the opposite sense; that is, that smaller objects would sink more. A third of Cluster 3 participants seem to adhere to this conception (more than to SUBSTANCE). It also appears that all three of the 22 science teachers who show a prevalence of VOLUME fall into this "inverse VOLUME" category. It therefore appears that some of our greatest experts do not necessarily rely strictly on scientific models for their answers but possibly on understated considerations. Of course, not all our secondary teachers taught physics (some were biology teachers) so we could not expect them to have impeccable scientific knowledge of all scientific problems.

Comparing the statuses (adherences) of the various conceptions enabled us to identify prevalence among individuals at specific points in time. However, given that it is cross-sectional

Figure 3. Distribution of the participant profiles in the different groups. [Color figure can be viewed at]

and not longitudinal, this analysis cannot be used to prove that multiple conceptions coexist within these individuals. Indeed, having a majority of "prevalence of SUBSTANCE" students at the secondary level and more "prevalence of VOLUME" at the preschool level does not necessarily mean that there were shifts in prevalence between these two groups; it could indeed merely be a sign of conceptual restructuration or of conceptual exchange. As a result, up until this point, the analysis was only descriptive. To provide evidence of coexistence, we analyzed the reaction times and looked for interferences.

Interference (Research Question No. 2)

Figure 4 shows an analysis of the interference caused by adherence to VOLUME and Figure 5 presents the interference caused by an adherence to MASS. In each one of these figures, we show response times for each one of the conditions of stimuli (Incongruent, equal, congruent, and congruent salient) and for all age groups. We used a generalized linear model function in SPSS to perform a multiple-factor analysis of variance. Results show statistically significant differences for the "age group" [F(3.27) = 129.778, p = 0.000], VOLUME [F(3.27) = 15.202, p = 0.000], and MASS [F(3.27) = 32.809, p = 0.000] variables and interaction between age group and VOLUME [F(9.27) = 5.428, p = 0.000].

For the data presented in Figure 4, post hoc tests showed that differences between all possible combinations of two conditions are significant (p < 0.003), except for "congruent*congruent salient"(p < 0.199).

For the data presented in Figure 5, post hoc tests show that differences between all possible combinations of two conditions are significant (p < 0.003), except for "congruent*equal" (p = 0.040). The following interpretation of differences between all conditions is based on these findings.

Interpretation. According to the research tradition, if the only difference between the stimuli of different conditions is the presence or intensity of a conceptual distractor, then a difference between RT of correct answers given to congruent (red curves) and incongruent (blue curves)

Figure 4. RT means for VOLUME conditions for each age group. [Color figure can be viewed at]

Figure 5. RT means for MASS conditions for each age group. [Color figure can be viewed at]

stimuli should mean that the conception interferes in the production of correct answers. If this is the case, we must conclude, like Shtulman, that both misconceptions interfere in all age groups. However, the interference of VOLUME clearly decreases with acquired expertise. MASS also causes interference among all subjects although, when comparing differences, preschoolers seem to struggle with it less than they do with VOLUME. It is also worth noting that the interference caused by MASS does not appear to change much between elementary students and science teachers. Could it be that this misconception is not addressed systematically enough in school? Or is it that cognitive decision mechanisms invariably include a potential competitor in reflection (and that MASS remained the most useful- while incorrect- one)?

A second interesting observation is the evolution of the difference between congruent (red curves) and congruent salient (grey curves) stimuli. Congruent salient stimuli are logically presumed to be easier to process than merely congruent ones because of an easier-to-process encoding. When there is no difference between them, it may mean that salience simply remains unprocessed or that attention is merely focused on other considerations. If this interpretation is correct, we can infer that as expertise is acquired, MASS (Figure 5) is gradually disregarded as an interesting competitor after elementary school (while still interfering). As for VOLUME (Figure 4), since there was no statistically significant difference between the two conditions, we can suggest with caution (because absence of proof is not proof of absence) that VOLUME is not a challenge for any age group, except maybe (although not significantly) preschoolers who surprisingly seem to have slightly more difficulty (higher RT) with congruent salient than with congruent stimuli. We believe that this puzzling result could be due to a certain number of "small objects sink more" adherents in this cluster. In fact, for these subjects, salience might make it more difficult rather than easier, as it does for ordinary VOLUME adherents. It is also possible that the noise they bring prevented us from observing statistically significant differences between congruent salient and congruent. It is a little strange that VOLUME salience had no impact on the degree of difficulty yet MASS salience did.

Another interesting observation is the apparently strange behaviour of equal stimuli (green curves in Figures 4 and 5). Keeping in mind that these stimuli are hypothesized to cause no

conceptual interference whatsoever because there are no distractors based on VOLUME (the two balls have the same volume) or MASS (the two balls appear to weigh approximately the same), it could be hypothesized that these stimuli would be easier (faster) to answer. This was the case for our top experts (science teachers), confirming that VOLUME does not seem to cause much interference in problem resolution and that these experts truly focus on material. But as we go back in time (or regress in expertise), these stimuli become increasingly difficult to the point of being the hardest conditions for preschoolers. We suggest that our analysis of different age groups helps explain why: for the most radical "prevalence of VOLUME" adherents, these problems might at first appear unsolvable. After looking for a difference in volume, it would appear normal, a posteriori, for participants to take more time because they must first accept that the stimuli offers no basis for resolution before falling back on a secondary criteria to find an answer. This means that for certain learners, equal stimuli may have no distractors in them (as initially presumed) but for others, they simply do not provided the key that they were looking for. We therefore believe that, depending on the levels of expertise of the subjects, researcher should be very cautious about how they interpret the behaviour of stimuli for this condition. For example, the opposite happens for MASS. This conception does not seem to be associated with much interference for preschoolers (shorter RT) but it gradually becomes increasingly difficult as expertise is acquired. We believe this might be because the interference—and therefore the status—of MASS is very weak among our younger participants. For them, the true challenge is overcoming the interference caused by VOLUME. But the opposite holds true for our top experts. Having two balls of the same weight could first appear to be unsolvable and therefore take more time before MASS is ruled out and SUBSTANCE eventually prevails in finding the correct answer. As we can see, RT data from equal stimuli can be easy to interpret but requires knowing the statuses of participants' conceptions on a large spectrum of different age groups. Indeed, in both Figures 4 and 5, the green curve intersects with many other curves and is in very different positions for different age groups. This could not have been interpreted completely had we only looked at one age group.

Transversal Interpretation

Our method allowed us to track the development of three conceptions throughout schooling and identify the biggest (yet often undetected) conceptual obstacles and challenges faced by each age group.

Most preschoolers demonstrated a "prevalence of VOLUME" (Figure 3) and, when they produced correct answers, had a hard time overcoming the interference VOLUME created (Figure 4). They did not appear to be subject to much MASS interference (since in Figure 4, the difference between congruent and incongruent for preschoolers is large, whereas in Figure 5 this difference is negligible) and a few of them seemed to adhere to an unexpected conception that smaller objects sink more (the "8" in Figure 2). Perhaps they were inspired by the prototypical ideas of "beach balls" or "balloons", which clearly float. They may also adhere to the observed misconception that the presence of air (which could explain the bigger volume) in an object makes it float (Smolleck & Hershberger, 2011). Their adherence to VOLUME seemed to be so strong that they had most difficulty (longer RTs) when the stimuli presented balls of the same volume.

Most of our elementary students already fell into the "prevalence of SUBSTANCE" cluster; however, many of them were also MASS adherents, and MASS clearly interfered when they provided accurate answers (which was not the case for preschoolers). We therefore believe that the main challenge for them was overcoming MASS. The VOLUME conception did not seem to cause much interference for them (or any of the older participants) since no distinction was observed between congruent and congruent salient in Figure 4 from that point forward. We believe that this

suggests that elementary students could be as ready as most adults to have a scientific understanding of buoyancy. We can relate these results with (Smith)'s interpretation that there is an interesting difference between how children between ages 5 and 7 and children between ages 8 and 9 see weight in density problems, and that this is when the intuitive "heavy for size" concept (p. 178) (which can be considered an early form of the density concept) sometimes starts to appear. We believe that this comparison shows close similarities between the two studies, even though they use different methodologies.

At the secondary level, MASS and VOLUME became marginal as prevalent conceptions, but they still caused interference, when correct answers were produced. While the interference of VOLUME decreased, MASS appeared to remain as much of a challenge as it had been for elementary students (parallel congruent and incongruent curves). This seems strange since most of these students had learned about buoyancy between elementary school and the age of 14 (in Quebec's (Canada) school system). Are there things that school doesn't teach well? Are there developmental considerations to take into account?

This steady decrease was also observed in science teachers, while SUBSTANCE was prevalent for a very large majority of them, indicating that MASS still coexisted and caused interference for these experts. Also, based on the fact that equal stimuli for MASS had the highest RTs (Figure 5) and that equal stimuli for VOLUME were the easiest for them to answer correctly (Figure 4), we believe that science teachers do not struggle at all with VOLUME. They can, however, occasionally be thrown off by stimuli that show two balls of equal mass but wind up answering correctly. We believe that this interpretation suggests that MASS might have to be inhibited for SUBSTANCE to prevail.


Limitations and Strengths of Using the Sink/Float Task

In this research, we conducted a transversal analysis of adherence to certain conceptions about buoyancy among four groups of individuals of different ages. To optimize the analysis, we simplified the buoyancy problems and asked our subjects to choose between two objects. We realize that doing this limited our ability to understand our participants' deep comprehension of buoyancy (which can be rather complex), especially if the participants feel that they are under pressure to answer correctly. However, it can also be argued that when answers are given under pressure or to very simple questions, they might be more spontaneous, and the analysis would then not be influenced as much by "social desirability" and may therefore be more authentic. To secure a better focus, we decided to analyze just one context (comparison of two balls) using several similar questions. While this allowed us to statistically record differences, it may also have had negative task effects, the consequences of which are difficult to predict. Another limitation is that not all conceptual difficulties in science can be broken down into simple "visual" tasks like ours. Our methodology is therefore limited to scientific topics that can be addressed visually or reduced to binary questions. As a result, we were not able to analyze the nature or origin of the studied misconceptions. It is indeed sometimes considered unfortunate when misconceptions are reduced to mere answers counts. We acknowledge that our methodology has this limitation and suggest that, in the future, methods that concentrate more on the nuances of students' conceptions be used concomitantly.

Nevertheless, in the case of buoyancy, our analysis allowed us to produce prevalence and interference profiles that can be interpreted and that reveal a likely story as to what conceptions our participants adhere to. When answering so many similar—yet crucially different—stimuli, it is unlikely that participants could "cheat" on the task in a coherent and dishonest way. We therefore

believe that our data may have revealed participants' true, despite contextual, adherences, whether they prevail or not.

The task also allows us to effectively differentiate between the possible considered (mis-) conceptions. For example, with typical multiple-choice (MC) tasks and other paper-and-pencil formats, it can be rather difficult to distinguish between adherence to MASS or VOLUME and SUBSTANCE (the correct conception), especially if there are suggestions in the questions that can cause confusion. Indeed, MASS and VOLUME are intertwined within the correct scientific understanding (SUBSTANCE). In this line of thinking, Smith et al. (1985) argued that understanding buoyancy might in essence be a problem of differentiation. With the sink/float task, there is no explicit suggestion as to which properties of the balls are to be the focus of attention by the experimenter, allowing abetter differentiation of distinct adherences.

We also believe that having simple instructions favors that most participants understand the task the same way, regardless of their age, expertise, and reading level. We believe that this supports the value of our transversal analysis.

Support for the Prevalence Claim

By analyzing reaction times (RT), our analysis went beyond the primary adherence to certain conceptions. As with certainty scores and the possibility of having a second round of answers (like with two-tiered voting systems), RTs are an interesting way to measure relative adherences to multiple conceptions. We also believe that it can be less subjective or susceptible to strategic considerations from participants than certainty indexes or tiered answers, therefore more accurate in quantifying and distinguishing levels of adherence.

It allowed us to better understand how much specific conceptions can interfere in teaching at different levels. For instance, it allowed us to see that our youngest participants hardly struggle at all with MASS and that science teachers do not seem to adhere much to VOLUME, but that this last misconception seems to be a challenge up to the end of secondary education.

We believe that such observations can help educators plan misconception-anticipating lessons—for students who do not initially produce correct answers but also for those who initially can but still have to consolidate their learning benefits. It might indeed be easier to consolidate knowledge when a teacher knows which competing misconception is for its students the most threatening at certain points in time, even if this misconception is not revealed in accuracies. Unlike classical or second-generation models of conceptual change, the prevalence perspective is, we believe, through its centration on relative adherences, the one that better allows such vigilance.

Most of all, we believe that the conceptual story depicted by our transversal design best supports the coexistence claim and possibly the prevalence perspective and not as much the conceptual change paradigms that implicitly suppose that only one conception can be adhered to at a time.

Our claims about the virtues of the prevalence perspective however require further discussion. Indeed, it would be possible that in a different interpretation, conceptual "change", if considered as an exchange or a disappearance of initial conception, would still require a temporary cohabitation of competing misconception with the more scientific one (until a definitive "change" occurs). In this perspective, coexisting conceptions could still, as we have, be recorded because of a recent exposure to lessons about buoyancy. However, we believe that this hypothesis would not fundamentally challenge the general idea of coexistence. This may have been the case had we recorded no interference with certain age groups, like the preschoolers, who had no training that we know of about buoyancy. But according to the interference data (Figures 4 and 5), we can see that there is always at least one interfering conception, regardless of age or recent exposure to lessons about buoyancy or density. Shtulman & Harrington (2015) also recorded interference with all ages. This suggests that (at least) two conceptions coexisting is more a rule than an exception,

and not limited to periods where learners consciously hesitate between two ideas. On the contrary, it is possible that the constant presence of a conceptual "plan B" proves to be an advantage, given the complexity of existence and the requirement to function and perform at all times, including when there is uncertainty or under other kinds of pressure, or when the context changes.

Further, we have to acknowledge that our results do not disqualify many "transformation" second-generation models. Indeed, in diSessa's perspective, as in Brown's, core intuitions are not destroyed in the process of conceptual change. Rather, it is the choice of the involved fundamental conceptual elements or intuitive resources that changes. Change thus becomes a question of re-focusing (or re-attributing) (Brown, 1993) or changing the cuing priority (diSessa, 1993) from certain p-prims (or elements that coordinate them) to others. When cuing priorities may be reduced, or when intuitions are de-focused, these objects may still be preserved. Thus they persist and while not prevailing, continue to coexist with other resources, waiting to be used later, in other situations. If, like in such perspectives, change (or transformation) happens at the scale of complex "coordination classes", and not on unitary conceptions, then the results we recorded in this research would not contradict these transformative perspectives, because the recorded lags in answers could then be attributed to hesitations between coexisting intuitive and more-fundamental-than-conceptions resources.

However, the prevalence perceptive and its centration on interference suggest methodologies that allow us to go further in the analysis of changes in answers. We believe that the qualification of the prevalence perspective within the conceptual "change" field of research thus largely depends on what we consider as a conception. Here, we have chosen to reduce the idea of conception to the external, visible phenotype of comprehension; and we assume that a change in answers would be based on educationally crucial changes at more fundamental levels, even thought we could- and did not- pushed our analysis as deep. We here refer our readers to the analogy with genetics that we proposed (Potvin, 2017) when we insisted on the difference between the phenotype (visible performance), genotype (available cognitive resources) and the epigenotype (the cognitive resources that ultimately get mobilized and prevail or interfere in certain contexts).

As presented in the Context section, we see our research as a follow-up of Shtulman and Harrington's work (2015). While these authors recorded an increase in conceptual interference with age after exposure to education, our study suggests a decrease of "misconceptual" interference during education. We find it interesting but not surprising that education appears to ensure the prevalence of scientific conceptions over misconceptions and that interference caused by misconceptions may nevertheless gradually come back over time despite previous education, especially in cases where these misconceptions can be more economic in certain local contexts.

Suggestion for the Next Steps

Keeping in mind that our design is cross-sectional, we feel that our task and analytic method could further be used to track the evolution of prevalence within these participants. The next logical step would therefore be to do so at different moments and supplement the analysis with RTs for correct answers. This kind of longitudinal approach could potentially allow us to observe shifts in prevalence and track the evolution of conceptual interference. We have previously proposed such designs in the past (Potvin, Sauriol, & Riopel, 2015), while notpushing our analysis as deep as we have done here.

Possible Prescriptions for Teaching

Since it supports the coexistence view, we believe that our research also supports previous models that incorporate this idea. In earlier publications, we proposed a model called "conceptual prevalence" that is based on three main ideas. The first idea is to fully

accept that contradictory conceptions can possibly coexist within individual's minds and therefore acknowledge that the internal race between them may never definitively be won. This suggests that it is crucial to have strong reinforcement programs once the scientific conceptions have been acquired. The second idea is that the brain appears to actively avoid contradictory evidence (Fugelsang & Dunbar, 2005), especially when there is little previous experience with the topic. It is therefore important to secure a minimal acquisition of knowledge about a topic if we want learners to perceive possible conflicts. Without this knowledge, attempts to generate conflicts appear to be less fertile. As a result, students without enough previous knowledge should not be exposed to conflicts at the beginning of teaching sequences. Conflicts should rather come later, when learners are able to minimize the effects of what Ohlsson calls the "assimilation paradox" (Ohlsson, 2009), in which learners can only interpret new information with the available and possibly "misconceptual" schemes, therefore possibly reinforcing them before they can even be challenged. The third idea is that, if misconceptions continue to interfere (even with experts), it may be useless and even counter-productive to try to discredit them. Conflicts should essentially be used to help learners identify the contexts in which their misconceptions are useless, and not to necessarily "attack" the conceptions themselves. Attempts to trigger conflicts could then be made when the availability of the scientific conception is secured so that there is the possibility of having a fertile competition for cognitive utility. Ohlsson (2009) had already demonstrated the superiority of "concept-concept" conflicts over "anomalies-concept" conflicts. We argue that securing the presence of the desired conceptions (fall-back solutions) before generating opportunities for conflict may allow the learners to build their understanding on successes. This type of proposition for the specific and exclusive use of conflicts requires disregarding the misconceptions themselves and concentrating on the pedagogically fertile contexts in which they are effective or not. We believe that this approach also minimizes possible personal prejudice. Indeed, learners may perceive attacks on conceptions as being attacks on their intelligence, which may be detrimental to self-esteem.

In the particular case of buoyancy problems, since we recorded the presence of multiple coexisting misconceptions at most expertise levels, it could appear appropriate to always begin teaching sequences by presenting the desired conception first, in a classical direct instruction initiative, in order to secure its availability or, if already available, to temporarily increase its status. Learners could then avoid contamination with irrelevant ideas, like VOLUME or MASS, which can happen if we instead initially concentrated on trying to discredit these misconceptions. Then it could be possible to suggest a series of simple buoyancy problems, like in our task, in which students could develop inhibitive reflexes for their remaining errors, provided that efficient and immediate feed-back is provided. It could then be interesting to discuss and analyse in class the cases (like our incongruent stimuli) where possible conceptual interference can lead to errors, maybe with real life floating or sinking objects, in order to secure and automatize inhibitive responses. Teaching further could imply a rigorously distributed in time program of reinforcement that imply all sorts of questions, congruent or not, in order to ensure that durable prevalence can be obtained. Indeed, prevalence remains fragile, and the race between conceptions may never be definitely won.

Such an intervention would be fundamentally different from earlier approaches that would, for example, begin teaching sequences by triggering cognitive conflicts (discrepant or surprising events), and then hope for accommodation when desired conceptions are presented. Usually, classical approaches would neither insist on ulterior practice programs, because correct answers are often considered as evidence of a definitive transformation or rejection.

Prevalence VersusOther Comparable Models

The prevalence model shares common aspects with other coexistence models in psychology, such as dual-process theory models (Evans, 2003; Evans & Stanovich, 2013) and the inhibitory-control theory (Houde & Borst, 2014, 2015). We feel, however, that these models are somewhat too insensitive to the reality of science teaching/learning, and for three reasons.

First, these models generally place heuristics and algorithms in opposition and often present them as belonging to "systems 1 and 2" respectively. On the one hand, unsatisfying heuristics are thought of as being intuitive, unconscious, and fast, like when many people respond incorrectly to the Wason selection task (Evans & Stanovich, 2013). Some well-known conceptual objects of the conceptual change field, like p-prims and core intuitions, might be understood as this kind of heuristics. On the other hand, algorithms, which favour correct answers in such tasks and could be associated with some systematic uses of scientific definitions, rules, or models, are presented as being often counterintuitive, conscious, slow, and more demanding. We believe that while models that use these labels may be appropriate for logical and some mathematical-problem solving, it is inadequate to think of correct answers as necessarily requiring more cognitive effort in the context of scientific reasoning. In fact, one of the ambitions in science is to develop simpler models. From a constructivist point of view, scientific models, laws, and principles are essentially tools that are only interesting if they help better explain/predict natural phenomena. Science does not always evolve on a simple/complex continuum, nor does it necessarily suppose a higher psychological load as most logical or mathematical problems do. We therefore believe that in many cases conflicts between scientific misconceptions and scientific conceptions are merely conflicts between conceptions and not conflicts between heuristics and algorithms. In fact, misconceptions have not necessarily prevailed because they are cognitively simpler but maybe or also because they are merely more familiar or automatic.

Second, we believe that dual-process and inhibitory-control models might not be sensitive enough to the issues of durability in learning. They use labels such as heuristic or algorithms to qualify certain functions, often implicitly suggesting that these labels cannot be changed. But, from an educational standpoint, teachers should cultivate the ambition to make some initially demanding ideas become, at the end, automatic and intuitive, instead of merely hoping that students will choose heavy ideas over economic ones. For example, Newton's laws have always been conceptually difficult for most students because there frequently are initial misconceptions about movement (Brown & Hammer, 2008; Clement, 1993; Dykstra, Boyle, & Monarch, 1992). But some students are capable of overcoming these difficulties and eventually become familiar enough with Newton's laws to use them rapidly and effortlessly. In these cases, we can hardly speak of Newton's laws as being necessarily algorithmic. In education, we strive to develop students' expertise. We do not see why (or how) this expertise should remain cognitively heavy for their entire lives.

Third, dual-process theory might have trouble to describe what happens when more than two conceptions are competing in a certain context. We believe that our demonstration has showed a tension between three distinct conceptual tendencies is possible. Thus a model that can integrate more than two competitors might be more successful in describing the reality of science teaching.

Accordingly, we believe that there is a need for a prevalence model that is exclusive to science education and teaching. A possible prevalence teaching model (Potvin, 2013,2017) was described at length in previous studies, and we suggested it be broken down into three steps: 1) favour the availability of the desired conception; 2) install inhibitive "stop signs;" and 3) work for durable prevalence of the desired conception. We also successfully tested this model in comparison with more classical applications of conceptual change teaching models for buoyancy problems

(Potvin et al., 2015). We therefore hope for more science education research and teaching efforts that accept and include the idea of coexistence.

We would like to thank all the participants (N = 768) to this study. Many thanks also to Lorie-Marlene BraultFoisy, Martin Riopel, Guillaume Malenfant-Robichaud and Francois Thibault for their insights on conceptual prevalence. This research was made possible because of a grant from the Government of Canada through the Conseil de Recherche en Sciences Humaines (SSHRC/CRSH) [GrantNo. 435-2015-1376].


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