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Gestalt and Functionality as Independent Dimensions of Mental Models in Science

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Malte Ubben at Leipzig University
Malte Ubben
Stefan Heusler at University of Münster
Stefan Heusler
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In teaching sciences, models are often used to introduce, elaborate or simplify real-world phenomena or concepts. It is, however, often the case that misconceptions arise from or are facilitated by these teaching models during their transition to mental models of the individual learners. For instance, models are often seen as direct replicas of something real—scaled versions of reality. Even though for architectural models, this approach is sufficient, in physics, other model types must also be taken into account. In particular, in quantum physics, the ability for abstract model building is essential. In our exploratory study with 3108 participants, the dispositions towards models in physics in general and models of the atomic hull in particular were analysed. Based on this quantitative data, two independent dimensions of the participants’ mental models were extracted: (i) Functional Fidelity and (ii) Fidelity of Gestalt. Based on these empirical findings, four main types of mental models are proposed.
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Gestalt and Functionality as Independent Dimensions
of Mental Models in Science
Malte S. Ubben
1
&Stefan Heusler
1
#Springer Nature B.V. 2019
Abstract
In teaching sciences, models are often used to introduce, elaborate or simplify real-world
phenomena or concepts. It is, however, often the case that misconceptions arise from or are
facilitated by these teaching models during their transition to mental models of the individual
learners. For instance, models are often seen as direct replicas of something real—scaled
versions of reality. Even though for architectural models, this approach is sufficient, in physics,
other model types must also be taken into account. In particular, in quantum physics, the ability
for abstract model building is essential. In our exploratory study with 3108 participants, the
dispositions towards models in physics in general and models of the atomic hull in particular
were analysed. Based on this quantitative data, two independent dimensions of the partici-
pants’mental models were extracted: (i) Functional Fidelity and (ii) Fidelity of Gestalt. Based
on these empirical findings, four main types of mental models are proposed.
Keywords Mental models .Quantum physics .Model building in science education .Cognitive
development
Introduction
The creation of mental models is essential for learning and therefore understanding the
generation of mental models is important for education research in general and physics
education in particular (Dutke 1994). They are the depictions and meanings our mind gives
to phenomena and their underlying structures (Rickheit and Sichelschmidt 1999). Mental
models that are deemed insufficient by the scientific community are the subject of many
studies (e.g. for an overview see Schecker et al. 2018). This holds true—again—in a general
sense and particularly in physics education.
https://doi.org/10.1007/s11165-019-09892-y
*Malte S. Ubben
malte.ubben@uni-muenster.de
1
Institut für Didaktik der Physik, Westfälische Wilhelms-Universität Münster, Wilhelm-Klemm-Str.
10, 48149 Münster, Germany
Published online: 16 September 2019
Research in Science Education (2021) 51:1349–1363
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
... Egy 3108 középiskolás diákot vizsgáló német tanulmányban feltártak egy kétdimenziós struktúrát, amely alkalmas a tanulók atomokról alkotott gondolati modelljeinek leírására [73]. ...
... • Az alaki ragaszkodás leírja, hogy a gondolati modellek mennyire a kinézetre összpontosítanak, és mennyire tekinthetőek a jelenségek vizuális ábrázolásának [73][74]. Az erős alaki ragaszkodású diákok vizuális képeket építenek fel fejükben, és gyakran hiszik, hogy ezek a valóság hű, nagyított képei. ...
... • A funkcionális ragaszkodás azt skálázza, hogy a gondolati modellek mennyire a jelenségek leírására törekednek, és erre milyen elvont fogalmakat használnak [73][74]. Például a Bohrmodell jó közelítéssel írja le a hidrogénatom spektrumát. ...
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... Additionally, how models are understood by learners has been at the core of several studies [9][10][11]. Previous research points towards a two-factorial structure of students' perceptions of quantum models that has been shown to explain a significant amount of the variance [11,12]: These two factors were coined 'Fidelity of Gestalt' and 'Functional Fidelity, ' and will be described and contextualized in the existing body of literature on students' conceptual development in the research background Sect. 2 of this paper. ...
... One of the more recent endeavors to describe how learners understand models in science, refers to what we summarize as the Gestalt-Function-hypothesis according to which (quantum) models are perceived depending on the degrees of 'Fidelity of Gestalt' and 'Functional Fidelity' in students' thinking: The Gestalt-Function-hypothesis was first in principle proposed by Ubben and Heusler [12,17] and was based on an exploratory factor analysis of students' statements about physics models in general and about statements of various models for the atomic shell in particular. The results indicated a latent two-factor structure describing the ideas about models held by the 3108 participants surveyed. ...
... The results indicated a latent two-factor structure describing the ideas about models held by the 3108 participants surveyed. The two factors extracted were summarized as follows [12] . However, the results of this first study were only a description of how models of a very minor part of quantum physics (namely atoms) were perceived by learners, and it was thus by no means clear that the two-factor structure reported was generalisable to other areas of quantum physics, or even physics and sciences in general. ...
The structure of learners’ perceptions of models (not only) in quantum physics: spotlight on Fidelity of Gestalt and Functional Fidelity
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In previous research, it has been argued that many of the student (mis-)conceptions of quantum concepts described in the literature as widespread among learners can be traced back to poorly developed (quantum) model perceptions that hinder the learning of quantum physics. In particular, it has been shown that the degrees of two cognitive dimensions, namely Functional Fidelity and Fidelity of Gestalt, in students’ thinking account for a substantial amount of the variance in students’ model perceptions in quantum physics and may therefore be useful for describing and understanding the (development of) students’ conceptions of quantum physics topics. So far, however, the cognitive dimensions Functional Fidelity and Fidelity of Gestalt have only been investigated in exploratory studies. In this article, we report the results of a confirmatory factor analysis of data collected from N = 179 secondary school students using an instrument adapted from the literature to assess learners’ perceptions of the photon model. The results of our study provide empirical evidence that the two-factor model of learners’ model perceptions in the quantum context is indeed a good fit to the data. Together with literature from science education research on students’ conceptual development, and taking into account earlier findings on Fidelity of Function and Gestalt Fidelity we derive a plausible description of students’ conceptual development in the context of quantum physics – leading to what we call the Fidelities-Model of Conceptual Development. We discuss this framework in the light of previous research and argue for its potential generalisability beyond the teaching and learning of quantum physics topics. The implications of our findings for both science education research and practice are presented.
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... Instead, the preparation, time evolution, and measurement of a particular quantum state are described (e.g., using Dirac notation) [26]. Functional fidelity is used to describe the mental models of students in QP [27,28]. It indicates "how far the mental models [...] were thought of as appropriate descriptions of how phenomena work-what abstract concepts underly the corresponding models" [27] (p. ...
... Functional fidelity is used to describe the mental models of students in QP [27,28]. It indicates "how far the mental models [...] were thought of as appropriate descriptions of how phenomena work-what abstract concepts underly the corresponding models" [27] (p. 1356). ...
... If a mental model is not useful for providing an adequate explanation of a given phenomenon or process, an individual will modify their underlying mental model to better align with the observed reality. Progress on the research into the nature of learners' mental models was achieved in a recent study by Ubben and Heusler [27]: They uncovered a twodimensional structure underlying students' mental models of the atomic hull, with one dimension being functional fidelity and the other dimension being fidelity of Gestalt [27]. Fidelity of Gestalt describes "how far the mental models [...] were understood as exact visual representations of phenomena of exact depictions of how things look" [27] (p. ...
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Evidence from physics education research suggests that the introduction of a formalistic description of quantum phenomena can be beneficial to student learning, particularly in terms of helping students move away from naive realist views of quanta or space-time descriptions of quantum phenomena. However, the mathematical requirements for mastering quantum formalism are typically far beyond the scope of secondary school education. Therefore, in previous research, we have proposed a reduced Dirac notation tailored to the capabilities of secondary school students, which is included in a novel teaching-learning sequence. However, the cognitive processes of students when confronted with an introduction to quantum physics via a reduced Dirac notation have not been thoroughly investigated: In particular, it seems important to investigate whether this approach is actually beneficial to students’ learning and to explore the learning difficulties students are likely to encounter in such a setting. This paper contributes to this research gap by reporting the findings of an acceptance survey: N = 14 learners participated in one-on-one interviews following a protocol consisting of four cyclical phases (information phase, acceptance evaluation, paraphrasing phase, and application phase). The findings of our study indicate that the instructional elements within our new teaching-learning sequence were generally well accepted by students but also revealed learning difficulties that students may encounter. Thus, on the one hand, the findings of this study pave the way for future research on students’ learning of quantum physics using Dirac notation. On the other hand, the in-depth findings reported here may guide teachers in designing learning environments that introduce Dirac notation at the upper secondary school and introductory university levels. Published by the American Physical Society 2024
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... 2.1). Ubben and Heusler investigated students' conceptions about the atomic shell, and identified a two-dimensional structure of the mental models held by students and designated these two dimensions as "Fidelity of Gestalt" and "Functional Fidelity" [19]. Subsequent studies have evidenced that this twodimensional structure can be used to describe learners' mental models of the photon [17], and that there is a correlation between the conceptual understanding of QP and the degree of Functional Fidelity in students' thinking about photons [20]. ...
... A variety of theoretical frameworks have been developed with the purpose of describing mental models and the manner in which they are constructed (e.g. [18,19]). One of these frameworks has been developed within the context of QP [19]. ...
... [18,19]). One of these frameworks has been developed within the context of QP [19]. In their research, Ubben and Heusler identified a two-dimensional structure that underlies learners' mental models of the atomic shell [19]. ...
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... Through the analysis of students' mental representations, it is possible to identify alternative conceptions and plan better teaching strategies to facilitate students' cognitive development (Ubben et al., 2022). Therefore, mental representations and mental models are essential for learning, and their investigation is crucial for science education research (Ubben & Heusler, 2021). ...
... Moreover, this research contributes to the understanding of mental representation formation in complex scientific topics like GR (Ubben et al., 2022). The results presented emphasize the importance of using multiple external mediations to support conceptual understanding, thereby extending existing theories on mental model development in science education (Ubben & Heusler, 2021). By examining how students construct and apply mental representations of curved spacetime, we have provided insights into the cognitive processes involved in learning abstract scientific concepts. ...
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... Using exploratory factor analysis, Treagust et al. identified five factors, namely models as "multiple representations", as "exact replicas" and as "explanatory tools", the "uses of scientific model", and the "changing nature of models". Later, Ubben and Heusler [12] combined these instruments with context-specific questions related to models of the atomic shell. Using exploratory factor analysis, two main factors were identified with regard to this context: The first factor is Fidelity of Gestalt (FG), which describes the extent to which models are understood to be accurate visual representations of phenomena or accurate representations of how things look, and the extent to which the gestalt of the models is perceived to be accurate. ...
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Article
  • Jan 2009
Atomic theory or the nature of matter is a principal concept in science and science education. This has, however, been complicated by the difficulty students have in learning the concept and the subsequent construction of many alternative models. To understand better the conceptual barriers to learning atomic structure, this study explores the troublesome nature of this fundamental scientific concept. In order to illustrate the distinction of student understanding by threshold barriers, this study chose three particularly high-achieving students from an original interview sample of 20 students who were selected from an introductory college chemistry course. The pre-course and post-course interview responses were examined and compared in detail. This study considers the concepts of 'probability' and 'energy quantization' to both describe the structure of the threshold of understanding students' need to negotiate in their construction of the target model of atomic structure. In this respect, this study suggests atomic structure as a possible threshold concept for further study in science. Identifying the nature and structure of the threshold of understanding confronting students, and analyzing the troublesomeness of atomic structure, provides valuable information for understanding student learning difficulties, and insight into how they may be addressed.
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Compounding quanta—Probing the frontiers of student understanding of molecular orbitals
Article
  • May 2002
College level students are expected to be able to make sense of, and explain, aspects of chemical bonding and structure in terms of molecular orbital concepts. The present paper derives from in-depth research into the thinking of a small sample of college chemistry students. This study in one UK college revealed the ways in which students found the orbital concept problematic. A previous paper (“Conceptualizing quanta: illuminating the ground state of student understanding of atomic orbitals”) reports how these students struggled to make sense of atomic structure in orbital terms. The present paper considers the students’ understanding of the molecular orbital concept. It is suggested that when learners are introduced to ideas about molecular orbitals before they have mastered ideas about atomic systems, then their learning difficulties may be ‘compounded’ in the more complex context. For example, it was found that students often identified the orbitals involved in two-centre bonds as atomic orbitals. Representations of delocalised bonds invoked various alternative interpretations: but were seldom conceptualised as implying poly-centred molecular orbitals. These findings suggest that students are not given sufficient time to construct acceptable models of atoms and molecules as ‘quanticles’. [Chem. Educ. Res. Pract. Eur.: 2002, 3, 159-173]
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Conceptualizing quanta—Illuminating the ground state of student understanding of atomic orbitals
Article
  • May 2002
This paper presents and discusses data relating to student understanding of the orbital concept and related ideas at college level (i.e. between secondary and university level education). The data derives from in-depth research into the thinking of a small sample of U.K. students. Students enter this level of study having been explicitly taught a quantum theory of matter (i.e. the particle model), and implicitly introduced to the quantization of charge. The key principles of quantization of energy and angular momentum are important at the college level when students are taught about orbitals, energy levels and quantum numbers. Interview extracts provide insights into the students’ attempts to make sense of these unfamiliar and abstract ideas. It is suggested that this is an area where there is a genuine pedagogic problem: capable and motivated students struggle to learn from experienced and knowledgeable teachers. The present paper describes how students conceptualized these key aspects of the atomic model. A subsequent paper (“Compounding quanta: probing the frontiers of student understanding of molecular orbitals”) considers how the same group of students applied their thinking in the more complex context of molecular systems. [Chem. Educ. Res. Pract. Eur.: 2002, 3, 145-158]
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1 Mental Models: Some answers, some questions, some suggestions
Article
  • Dec 1999
This chapter reviews the mental model construct in cognitive science. The chapter discusses the definitions and aspects of mental models. To demonstrate the usefulness of the mental conceptualization, the chapter presents applications in the domain of discourse comprehension and production. Mental models play a central and unifying role in representing objects, states of affairs, sequences of events, the way the world is, and the social and psychological activities of daily life. The major problem of the mental model approach lies in the fact that the external world is to be represented in a highly specific way. Representing indeterminacy in terms of mental models, thus, poses difficulties, casting some doubt on the contention that mental models can do without variables. The major advantage of the mental model approach lies in the fact that the influence of individual knowledge can be handled with relative ease. Mental models provide a straightforward explanation of several phenomena that are difficult to explain by more traditional accounts.
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