Student Translations of the Symbolic Level of Chemistry

Abstract

The aim of the study was to explore students’ own translation of the symbolic level of a chemical reaction, including the information provided with the use of coefficients, indices, and signs, as well as the preservation of atoms. Students were asked to translate the symbolic level of the combustion of methane with the use of clay modelling. The students had to make active choices regarding the size, shape, two- or three-dimensional structure, and the number of atoms in the molecules included in the reaction using modelling clay. The analysis followed the three levels of analysis as presented by Hedegaard. The results highlight the variations in students’ answers and show the importance of investigating unrestricted translations of the symbolic level of chemistry. Including clay modelling in the educational process is helpful for both educators and students, as it fosters comprehension of underlying processes and enhances awareness of substance structure and atom redistribution across various substances.

1. Introduction

Chemistry as a school subject is important for learners of all ages as it provides the basis for understanding many of today’s societal challenges [1,2,3,4,5], especially the goals related to economic growth and active participation in issues in such as sustainability in the techno-scientific society [6]. Unfortunately, chemistry is not always an apparent and easily experienced science. Learning chemistry as a school subject can be viewed as learning multilevel thinking, as many of the levels are abstract because they are on a scale of one femtometre or smaller. This level is difficult to provide experience of, as we can only describe it by relating the size of something familiar. Few, if any, familiar things exist at such a small size to use them as a point of reference. It also becomes difficult to probe students’ understanding of the submicroscopic world, as the opposite is also an issue: How can a student express their understanding of a level so small that we have no familiar point of reference?

Chemists have circumvented the problem by using chemical symbols that exist on a macroscopic level, although they are intended to represent the submicroscopic level. The symbols can be viewed as the language of chemistry because, in the same way as a letter in the alphabet represents sounds, the chemical letters represent subatomic particles, atoms, charges, molecules, and chemical transformations. With the use of stoichiometry, the symbols change from being seen on a submicroscopic level to being seen on a macroscopic visual level. This study was designed to explore students’ own interpretations of the symbolic level of chemical transformations, including the submicroscopic–macro-level shift using stoichiometry. Clay modelling was used as it provides artistic freedom in terms of shape, size, two- or three-dimensionality, composition and distances between particles, and particle arrangement.

2. Background

2.1. The Knowledge Space of Chemistry as a School Subject

Learning chemistry is a complex educational journey that spans several years of compulsory and secondary school. Describing its complexity has been attempted for decades by educational researchers. The general point of agreement is that learning chemistry is a time-consuming process [7] that involves many abstract concepts, phenomena, and explanatory concepts on fundamentally different levels. The complexity of the subject has been described as a case of multilevel thinking [8]. Talanquer [9] attempted to describe the many aspects of the knowledge space of chemistry as a school subject (see Figure 1). The figure shows the many different levels of chemistry, ranging from the macroscopic experienced world to the subatomic level. Content is also described using different approaches such as visualisations, mathematics, concepts, and can be seen from both different contextual and historical perspectives. It includes knowledge of composition and structure, energy, and the speed of chemical processes—something that makes time an important factor for understanding natural chemical processes.

Another more general way to describe chemistry as a school subject was suggested by Johnstone [10], who described the three levels of chemistry as: descriptive, symbolic, and explanatory. The descriptive level represents the macroscopic level of observed phenomena, such as the melting of ice or boiling of water. The symbolic level is our translation of chemistry into symbols such as chemical formulas, symbols that represent atoms, atomic charges, stoichiometry, aggregation states, and chemical names [11]. The explanatory level is the submicroscopic level of chemistry, a level that cannot easily be visualised.

2.2. Models

The abstract level of chemistry as a school subject involves numerous forms of models and visual representations such as graphs, illustrations, games, animations, and models, among others. These are models/tools for communication are made to support learners in making sense of abstract content and solving problems. The word “model” is here used to describe a simplified model, which is a representation of a physical reality, used to explain, predict, or communicate natural science [12]. It can be an object, phenomena, process, idea, or system. Research suggests that one of the most important factors for scientific understanding is learning to reason with models [13]. Indeed, research shows that the translation between the learner and the representation is important. It is especially important for learners to translate the same content through many forms of representations [14], such as, for example, chemical formulae, animations, or drawings. Working with multiple representations [15] can invoke different stages of insights, e.g., what does each representation mean? Which part of the knowledge space is it related to? [16] How are the representations related to each other? What similarities and differences are there between representations? [17] This processes of connecting and integrating the different levels of the representation are important for developing deep and nuanced understanding [17,18].

2.3. Learning Chemistry

To learn chemistry, students need to move between the levels of chemistry [9], master the language of chemistry, i.e., the symbolic level and be able to imagine that the symbolic level represents the invisible world of atoms and molecules on a scale so small, it is not easily imagined. Research indicates that students often believe that atoms are on a scale big enough to be observed using regular microscopes or that textbook illustrations depict the actual atomic size [19]. So far, the scale of the subatomic level can only be accessed by relating size to something familiar or through animations. Unfortunately, the different possibilities for relating the size of an atom to something meaningful that can be experienced are few (if there are in fact any). Animations can provide a sense of transition between the macroscopic and submicroscopic world and give a bodily experience of just how small the submicroscopic level is through the time elapsed between the different levels [20]. Additionally, symbolic-level illustrations are often used without clarification, something that may obstruct students from making the connection between submicro- and symbolic representations. Other difficulties occur as the representations themselves are not consistent, and the same round circle may for example symbolise single atoms, a particle, or a group of particles [21,22,23,24].

2.4. Challenges When Learning about Chemical Reactions

The above-described challenges are valid for most of the areas of chemistry, including chemical transformations, which are the focus of this study. Only some chemical transformations can be experienced in real life, such as the denaturation of proteins while frying an egg; other examples are combustions or explosions [25]. Slower transformations such as the breakdown of matter in nature are so slow that most of us don’t even notice that the transformation is taking place. Also, many of the visual transformations are irreversible, such as exploding fireworks [25], something that may lead to assumptions that all chemical reactions are irreversible when, in fact, most chemical transformations are reversible.

In formal education, chemical transformations on the symbolic level are commonly described to students using either a basic particle theory or with the use of the atomic model. The particle theory uses particles generalized to the level of circles and shows the change in the form of straightforward reengagements of particles and sometimes collision theory. The second approach, the atomic model, is specific and makes use of electrons, protons, atoms, ions, and molecules, and shows, for example, the transition of electrons between different particles [26]. Research shows that both perspectives are useful for supporting learners and students that make use of the more generalized particle model can use it to support complex reasoning [26]. These two models can also be used as an intended student progressions in learning about chemical reactions; moving from rearrangement to describing the process based on specific particles.

When depicting a chemical reaction using the symbolic level, the level changes from submicroscopic to the macro level with the addition of stochiometric information [27]. With the addition of numbers, the chemical equation resembles a mathematical equation, and it is not uncommon for students to view a chemical reaction as math problem rather than a tool for explanation that is linked to phenomena or the submicroscopic level [28,29,30,31,32,33,34]. This is a reasonable assumption since mathematics and chemistry share signs, but the signs hold different meanings in different subjects. In a chemical reaction, the + sign between reactants does not refer to an addition; instead, it means “and” [25]. The arrow in the reaction formula signifies the direction of the conversion of reactants into products and can be translated to “forms”, but students commonly see it as an equal sign (=) leading to a view of a chemical reaction as being equal on both sides of the symbol; even though the total number of atoms of each type and the total mass are the same on both sides of the arrow, there are not an equal number of products and reactants during the reaction [25]. Considering the chemical reaction as a mathematical problem can also result in students memorising chemical reaction formulas symbolically or perceiving it as an implementation of a set of rules instead of as a transfer of atoms and the breaking and forming of chemical bonds [31,32,35,36,37,38,39,40].

Balancing chemical reaction formulas is also a challenge since a comprehensive understanding of stoichiometry also requires the students to separate coefficients from indices [41]. Examples of such challenges include understanding the two different meanings of the number 2 in the symbol 2Ag₂O, as well as determining when a symbol represents a mole of atoms or a mole of molecules. One common error in students’ illustrations of the products of a chemical transformation is combining multiple molecules into one molecule [35,42], or suggesting that mass can transform into some form of energy during a chemical or physical change [38,43,44,45]. Even though students commonly encounter submicroscopic representations in texts and animations, and during instruction, their understanding of these submicroscopic representations and their ability to draw accurate depictions themselves is less satisfactory [35]. Studies have highlighted the importance of engaging students with multiple representations to support learning [23,35,42,46,47,48].

2.5. Models for Teaching the Symbolic Level of Chemistry

Teaching methods become important in the chemistry classroom where multilevel thinking and the abstract language and symbols of chemistry meet students’ everyday experiences and macro-level understanding. There are models for teaching that can be used for illustrating what occurs at the submicroscopic level, such as visual aids like drawings, diagrams, animations, illustrated narratives, gestures, bodily representations, and symbolic representations through formulas. Also, molecular models that visualise the 3D molecules that represent the current consensus models of molecules and chemical bonds are traditionally used in the chemistry classroom. Research has explored how teaching tools can enhance chemistry learning, and a combination of using symbols alongside the submicroscopic models has shown promise in enhancing students’ ability to assess their own understanding and for teachers to address student questions. For example, visualisations of the molecular level have been shown to be important as helps students combining the three levels of chemistry in a holistic manner [49,50,51,52]. However, only allowing students to interpret and understand presented models provides limited insight into their thoughts and comprehension of concepts and models.

2.6. Students Expressed Models

Student-generated models are another way to provide teachers with a deeper understanding of student thinking [21,35,53,54,55,56,57]. Allowing students to express their own ideas can be a way for teachers to make sense of student ideas [55,56], work with the multiple levels of chemistry [58] and support discussions of temporal, spatial, and casual relationships.

Different approaches for generating student models i.e., students’ own interpretation of a chemical content have been explored. The material utilized imposes limitations on the representation of models. For instance, drawings are primarily confined to a two-dimensional format, while the use of items like pasta [59] restricts the range of shapes that can be created. Here, the inclusion of gestures (embodied actions), and verbal support can be support an otherwise static expression [56]. A discrepancy arises between the expressed and intended forms, as students may face difficulty in visually expressing the intended goal. Drawing in three dimensions can, for example, be challenging for some students. The opposite is also true—not all students can express what they intend using words. One example of the latter was a student who gave a written explanation of the hydrogen nucleus by stating that “hydrogen has a proton in the nucleus”, a statement that most teachers would have accepted as the consensus model until the student made a ball and referred to as the nucleus, then added another ball firmly pushed into the nucleus, symbolising that the proton was in the nucleus (see Figure 2) [53].

Studies indicate that many students struggle with the transition from the symbolic to the particulate nature of chemistry. The purpose of this study was to investigate the aforementioned transition, which encompasses both the conservation of atoms and the application of indices and coefficients using clay modelling. The study aims to:

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Explore student translations between the symbolic and the particulate nature of chemistry.

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Analyse how students creatively interpret chemical processes when given total artistic freedom.

2.7. Design of Study

The students included in this study were provided with the opportunity to illustrate molecules using clay models. An example of this includes allowing students to transition from molecular to structural formulas and switch between line formulas and drawings to show the tetrahedral structure of carbon compounds.

3. Method

3.1. Context

The case study involved 68 voluntary participants enrolled in the first of two chemistry courses during a foundational year within a university program. This year offers preparatory science education at a level equivalent to upper secondary education, for admission to higher education in science. This program includes students completing required courses for eligibility and others improving grades. The students included in this study were formed into groups and included students that had not previously studied chemistry (39 students), called Group 1, and students that had previously studied chemistry (29 students), called Group 2. The participants in this study spanned a wide age range, from 20 to 50 years old, with the majority being between 20 and 25 years old. Given that the course is being offered at the university level, the inclusion of students from the uptake area is predominantly from the southern regions of Sweden, which comprises both rural and urban localities. The data analysis was comprehensive but did not incorporate gender considerations.

All students had formally studied chemistry during lower secondary years, approximately ages 13 to 16. This curriculum covered matter’s structure, elements, molecular and ionic compounds, and chemical reactions, including atoms, electrons, and nuclear particles. Prior to undertaking the task in this study, the students were introduced to the following concepts: atomic model, chemical compounds, molecules, chemical symbols, the periodic table, mass number and atomic mass calculation, VSEPR (for diatomic molecules, methane, ammonia, water, and carbon dioxide), mass conservation, calculation of the amount of substance and molar mass, chemical reactions, and balance chemical equations. The students had previously practiced using the particle model by drawing atoms, protons, neutrons, electrons, and molecules, and calculated the quantities of substances, determined molar masses, and balanced chemical equations.

3.2. Data Collection

The study investigated students’ translation between the symbolic and particulate level of chemistry, where they were required to transfer the symbolic level into 3D models using clay modelling. This transfer has also been described as modelling ability, and have been defined as: “the understanding of spatial molecular structures and the ability to transfer between molecular representations and chemical understanding levels” [60].

Working on students’ skills to draw and transfer between a molecular formula, a structural formula, and a model are seen as sub-skills in a hierarchy developed by Dori and Kaberman [60]. In this hierarchy, molecular formulas are transformed to structural formulas then computer-generated models. In this study, students were familiarized with molecular formulas and then asked to create a 3D model using clay for modelling. The purpose of taking the reverse path in this hierarchy was to concretize the symbols used in molecular or structural formulas. In order to achieve the purpose, the students were asked to build a balanced chemical equation of methane reacting with oxygen forming carbon dioxide and water, using modelling clay. The task also included presenting a balanced reaction formula using modelling clay, providing drawn images of the built models, showing molecular formulas below the images of the models, and explaining the process using their own words. The student received the following instructions;

“First, you are required to illustrate the transformation by constructing the various molecules involved in the reaction. Then, you depict the chemical conversion by moving atoms, which is accomplished by disassembling the molecular models and then reassembling the atoms in a new configuration. Show a balanced chemical reaction”.

The time they had available was 60 min, and the study was conducted with approximately 34 students at a time, working individually. Additional information provided were as follows:

“When methane gas (CH₄), is burned, carbon dioxide (CO₂) and water (H₂O) are formed if the combustion is complete. Combustion involves a reaction with oxygen (O₂) in the form of oxygen gas.

• Different molecules are built using modelling clay. Models are shaped into spheres.

• Build methane and oxygen molecules using modelling clay.
• Depict the reaction of methane and oxygen molecules. This should produce carbon dioxide and water.
• Arrange your molecular models to correctly illustrate a balanced chemical equation.
• Draw the balanced reaction process (using the particle model). These drawings are placed directly below the models built with clay models. Below each particle model, write the chemical symbols and names of the substances.
• Write an explanation of the process. This is done below the chemical symbols.
• Take a photo of your illustration of the reaction and your explanation. The following should be included in your photo: clay models, the drawn models, the chemical symbols beneath each model, your explanation of the reaction process”.

3.3. Data Analysis

Data were analysed using mixed methods. Clay models, depictions of the symbolic level, and written explanations were analysed independently by two researchers using Hedegaard’s three levels of qualitative analysis [61] where the first level is called “commonsense interpretation”. At this level of interpretation, data from the 68 students were merged into individual illustrations of molecular models (clay models + symbolic level illustrations), and an explanation of the process. The second level of analysis, called “situated interpretation”, was then applied to the data set. At this level of analysis, focus was placed on students’ written explanations and common structural and functional patterns of the symbolic level representations as well as for their models of the particulate level. Specifically, differences between the formal content and the student-expressed model in literal appearance, structure, and images were analysed and then sorted into four different categories, depending on their closeness to the formally introduced content. Following that, the frequency of answers in each category was determined. Analysis from the perspective of the two different student groups was also performed. The third level of analysis, called thematic and conceptual interpretation, was performed here with an analytical focus on identifying general connections between the results and the existing research literature.

4. Results

The analysis of the difference between the instructional model and the student model focused on the conservation of atoms, use of the lowest coefficients of reactants and products, the symbols + for “and” together with the arrow showing the direction of the reaction process and the three-dimensional structure of the clay models according to the VSEPR model. The students’ answers were divided into four different categories:

• Both the symbolic level and the particulate models were in accordance with the formally introduced content. An example of a representation from category A can be found in Figure 3a.
• The symbolic level was correct, but the translation to particulate models was incorrect. An example can be found in Figure 3b.
• The symbolic level was incorrect, but the translation to particulate models was correct. Examples can be found in Figure 3c,d.
• Neither the symbolic level nor particulates were correct. Examples from Category D can be found in Figure 4 and Figure 5.

Figure 3. The students’ clay modelling and answers of combustion of methane were divided into four different categories: listed as (a) Both the symbolic level and the particulate models were in accordance with the formally introduced content; (b) The symbolic level was correct, but the translation to particulate models was incorrect; (c) The symbolic level was incorrect, but the translation to particulate models was correct. Oxygen (O₂) and water (H₂O) are repeated twice in the reaction formula instead of using coefficients; (d) Coefficients are missing in the reaction formula.

Figure 3. The students’ clay modelling and answers of combustion of methane were divided into four different categories: listed as (a) Both the symbolic level and the particulate models were in accordance with the formally introduced content; (b) The symbolic level was correct, but the translation to particulate models was incorrect; (c) The symbolic level was incorrect, but the translation to particulate models was correct. Oxygen (O₂) and water (H₂O) are repeated twice in the reaction formula instead of using coefficients; (d) Coefficients are missing in the reaction formula.

Figure 4. Category D: Neither the symbolic level nor particulates were correct. (a) It is not possible to distinguish between reactants and products; (b) It is not possible to distinguish between reactants and products as the connection between molecular formula and clay models is inadequate.

Figure 4. Category D: Neither the symbolic level nor particulates were correct. (a) It is not possible to distinguish between reactants and products; (b) It is not possible to distinguish between reactants and products as the connection between molecular formula and clay models is inadequate.

Figure 5. Category D: Neither the symbolic level nor particulates were correct. (a) Models built for CO₂ and H₂O but does not use them in the reaction formula. Presents CH₄O₂ as a product; (b) Shows 2CH₂O as a product in the reaction formula, but the connection between molecular formulas and the clay models is inadequate; (c) Neither the reaction formula nor the clay models are balanced; (d) Uses drawn symbols instead of molecular formulas in the reaction formula.

Figure 5. Category D: Neither the symbolic level nor particulates were correct. (a) Models built for CO₂ and H₂O but does not use them in the reaction formula. Presents CH₄O₂ as a product; (b) Shows 2CH₂O as a product in the reaction formula, but the connection between molecular formulas and the clay models is inadequate; (c) Neither the reaction formula nor the clay models are balanced; (d) Uses drawn symbols instead of molecular formulas in the reaction formula.

4.1. Preservation of Atoms in Chemical Reactions and Writing Chemical Equations

There was a significant difference between the two student groups for Category A and D (

Table 1. The four different categories A–D concern the students’ responses regarding the balanced reaction formula and its representation in clay. Data is provided for two different groups: 1. Students who have not previously studied chemistry (Group 1); 2. Students who have previously studied chemistry 1 (Group 2), and part of all. The responses are indicated in percentages. The number of participating students is indicated in parentheses. The analysis of the students’ translation difficulties between the two levels revealed specific challenges in symbols, molecular formula, and conservation of mass.

Category	Group 1 (%) (39)	Group 2 (%) (29)	Part of All (%) (68)
A. Both the symbolic level and the particulate models were in accordance with the formally introduced content	41	72	54
B. The symbolic level was correct, but the translation to particulate models was incorrect.	13	7	10
C. The symbolic level was incorrect, but the translation to particulate models was correct.	10	17	13
D. Neither the symbolic level nor particulates were correct	36	3	22

). For Category A, 72% in Group 2 (the students who had previously studied chemistry) correctly illustrated the conservation of atoms on both the symbolic and particulate levels, while only 41% of the students in Group 1 (the students who had not previously studied chemistry) could be categorized into this category. For Category D, only 3% of the students in Group 2 were classified as belonging to this category, while 36% of the students in Group 1 showed significant deviations from the formally introduced content in their expressions.

A closer comparison between the two groups was made by merging Category A and C. When these two categories were merged, Group 2 (89%) had a greater tendency to preserve atoms at the particulate level than Group 1 (51%). In an analysis of how many students presented a balanced reaction formula at the symbolic level, Category A and B were combined. The results showed that 79% of the students in Group 2, compared to only 51% of the students in Group 1, were able to write a balanced reaction formula.

The data suggest that the students who had previous experience in chemistry found it easier to comprehend the particulate level than the symbolic level. An analysis of individual translation reveals that difficulties revolve around the utilisation of symbols, molecular formulas, and the preservation of mass.

One of the most common issues concerned the direction of the reaction process were some students struggled with the use of the arrow symbol. Two of these examples are illustrated in Figure 4, where students seem to understand that the arrow symbol is indicative of a change but is sometimes used between each molecular formula, so it is not possible to separate reactants from products.

The molecular formulas themselves were also difficult for some, and alternative models such as CH₄O₂ and ₂CH₂O (see Figure 5a,b) were suggested. Some students used parentheses around each molecular formula in the reaction formula, and one student only used parentheses around the molecules where the coefficient 2 was indicated, such as 2(O₂) and 2(H₂O).

Several students also failed to consider the conservation of atoms in the chemical reaction. One typical example is shown in Figure 3d, where only the molecular formulas for the reactants and products are specified. Others illustrated the conservation of atoms by repeating the molecular formula for a substance instead of using coefficients (Figure 3c).

Most students (94% of 68 students) had the same number of atoms in the clay model for each substance as in their corresponding molecular formula. In Figure 3a, an example is presented where the number of atoms in each molecule in the clay model corresponds to the number of atoms in the respective molecular formula. However, in 4b, examples are presented where the number of clay balls in the models does not correspond for each molecular formula presented under the models.

The use of modelling clay also placed another difficulty on the chemical equations themselves. The student needed to be creative in their constructions in order to distinguish between different types of atoms (

Table 2. Constructed clay models showing which products and reactants have been built, how they adhere to the teaching model regarding composition and choice of colour for different types of atoms. (A) Built correct reactants and products following the teaching model and choice of colour. (B) Did not build correct reactants and products following the teaching model and/or where the choice of colour for the types of atoms cannot distinguish the different types of atoms or where the same type of atom is illustrated with different colours. The responses are indicated in percentages. The number of participating students is indicated in parentheses.

Participating Students	A	B
Part of all (%) (68)	85	15
Part of Group 1 (%) (39)	85	15
Part of Group 2 (%) (29)	86	14

) allowing them to show the redistribution of atoms in the chemical reaction (Figure 3a). A large proportion of students (85%) used colours or other markers to distinguish the different types of atoms (Table 2). Among the remaining 15%, it was not possible to follow the redistribution of the different types of atoms. Either the same colour was used for two different types of atoms, or the same colour was not used for the same type of atom in the reactants and products. For examples, see Figure 6a,b.

Upon closer analysis of those who did not present a correctly balanced reaction formula, there was a significant variation between the two different groups of students. In Group 2 the most common issue (14%) was that they did not use the coefficient 2 in front of O₂ and H₂O. Instead, they repeated the molecular formulas for these twice in their reaction formula, such as O₂ + O₂ and H₂O + H₂O (see

Table 3. Compilation of the diversity of incorrectly presented reaction formulas. The responses are indicated in percentages. The number of participating students is indicated in parentheses.

Answers	Group 1 (%) (17)	Group 2 (%) (7)	Part of All (%) (24)
Students who wrote O2 + O2 and H2O + H2O instead of 2 O2 and 2 H2O.	3	14	5
Did not apply the lowest coefficient to the molecular formulas	5	3	4
Did not specify any coefficients in front of any of the molecular formulas.	18	0	10
Incorrectly balanced reaction formula.	0	3	1
Did not present correct molecular formulas in the chemical reaction formula and/or used -> between each molecular formula	18	3	12

). The most common errors in the Group 1 were either to only indicate each molecular formula once and without coefficients (18%) or to specify incorrect molecular formulas (18%).

One student wrote C₂O instead of CO₂, and another student wrote OH₂ instead of H₂O. These students were in Group 2. Five students correctly presented the molecular formula for H₂O but then presented an incorrect structural formula or clay model of the water molecule by including two oxygen atoms and one hydrogen atom (Figure 6b), missing the index. Three of these students were in Group 2.

4.2. Analysis of the VSEPR Model

The teaching models for VSEPR theory (3D structure of molecules) included tetrahedral methane, double-bonded, linear oxygen, linear carbon dioxide, and angled water molecules (see Figure 3a).

Only about one-third (32%) of students made clay models in accordance with the VSEPR theory. There was also very little difference between the two student groups (

Table 4. The proportion of models focusing on whether they adhere to or do not adhere to the VSEPR theory. The responses are indicated in percentages. The number of participating students is indicated in parentheses.

Participated Students	According to VSEPR Theory	Not According to VSEPR Theory
Part of all (%) (68)	33	68
Part of Group 1 (%) (39)	33	67
Part of Group 2 (%) (29)	31	69

).

The most common deviating model, according to the VSEPR theory, was the model of CO₂. 46% of the students built an angular, not linear CO₂ (Figure 3b–d, Figure 5a,c,d, and Figure 6a,b). In Group 2 almost half of the students (48%) built an angular CO₂ molecule (

Table 5. Distribution of models that do not follow the VSEPR theory. Methane (CH₄)—built in 2D, carbon dioxide (CO₂)—built as angled. Other: oxygen (O₂) built as split or four together, built together 2 H₂O, built a hybrid model. The responses are indicated in percentages. The number of participating students is indicated in parentheses.

Participating Students	CH4 (2D)	CO2 (Angular)	Other
Part of all (%) (68)	41	46	10
Part of Group 1 (%) (39)	36	44	13
Part of Group 2 (%) (29)	48	48	6

). Within this group almost half of the students did not construct CH₄ in tetrahedral form (Figure 3b,c, Figure 4a and Figure 5c) they instead used the 2D structure (see Table 5). In Group 1, the proportion of angled CO₂ and CH₄ in 2D was lower, which can be explained by the fact that in this group, it was much more common for them to present molecular models that deviated regarding the composition of types of atoms in the molecules. Despite oxygen’s simplicity, some students imaged separate oxygen atoms (Figure 5d) and put four atoms close together. Another student placed two water molecules close to each other (Figure 5c).

In a deeper analysis of the shapes and structures of the molecular models, the relative sizes of the atoms were also examined. When assessing the relative size, slightly over one-third (34%) of the built models closely resembled the teaching model, where carbon and oxygen are similar in size, while hydrogen is roughly half their size (Table 4). However, there was a division among student groups. Among Group 2, 38% of the students’ models closely aligned in relative sizes, compared to 31% in Group 1 (

Table 6. Size of the different types of atoms: A—relative size according to the teaching model, B—same size for all types of atoms, C—sizes of the atoms do not match the teaching model or have different sizes for the same type of atom. The responses are indicated in percentages. The number of participating students is indicated in parentheses.

Participating Students	A	B	C
Part of all (%) (68)	34	31	35
Group 1 (%) (39)	31	26	44
Group 2 (%) (29)	38	38	24

). Figure 3a shows a model closely aligned in relative sizes. A common deviation was using the same atom size for all atom types (31%), as exemplified in Figure 3b, Figure 5d and Figure 6b, and in Group 2, this was the most common deviation (38%). In Group 1, it was more common (44%) to use different sizes for their atoms, but they did not follow the rules for the relative sizes (see Figure 4a,b) where the carbon atom is twice the size of hydrogen and oxygen atoms), or they were not consistent in using the same size for the same types of atoms.

5. Discussion

To present a balanced chemical reaction formula, one must have a comprehensive understanding of the symbolic level of chemistry, as well as the particles that are represented by the symbols. This study sought to analyse students’ ability to translate between two levels in a chemical transformation. In order to attain the objective, the study participants were instructed to illustrate the combustion of methane through symbolic representation and subsequently transform these symbols into particles using modelling clay. The application of clay modelling prompts students to make choices pertaining to size, shape, dimensionality, and distinguishing among various atom models. A method to guide students away from using letters and towards an alternative form of abstraction.

The study included two distinct groups of students: a group with prior knowledge of chemistry and another group new to the subject. It is reasonable to assume that the students who decided to repeat their chemistry course did not excel on their first try. Substantial variations were found among the student groups, indicating the specific areas where repetition is highly advantageous for learning. An illustrative case was found in the association between the 2D written equation and the clay model, where students with a background in chemistry showed enhanced performance, indicating that the experienced students had less difficulty in linking the two.

To demonstrate the conservation of atoms and the redistribution of atoms students need to translate symbols to particles and assign different colours to different atom types, while using the same colour for the same atom type. Most students (85%) succeeded in this, regardless of whether they previously had studied chemistry or not.

The conservation of atoms during the transformation was also evident in the clay’s molecular models. Several students successfully constructed clay models with the accurate composition of atoms and molecules, but their written formulas were sometimes not balanced in terms of coefficient usage. Another frequent error observed within this group was the use of O₂ + O₂ and H₂O + H₂O instead of the correct 2O₂ and 2H₂O. The results indicate either that utilising particles or clay models was more convenient compared to symbols, or that the students had not yet started employing abbreviations and found it more logical to think in terms of distinct species. A significant number of students failed to indicate any coefficients in their reaction formula, or mistakenly placed parentheses around the molecular formulas and subsequently inserted the coefficients as 2(O₂) and 2(H₂O). This could potentially indicate that they perceive the chemical reaction formula as a mathematical formula, as stated by [28,29,30,31,32,33,34]. Due to the complex nature of converting between symbolic and particulate models, it is recommended that the integration of modelling be introduced early on in chemistry education.

The findings also highlight the significance of prioritising the relationship between molecular formulas by utilising coefficients to signify the quantity of formula units as well as emphasising the use of arrows in reaction formula. Although the use of the arrow symbol indicated that these students understand that some kind of transformation occurs during the process.

By enabling students to utilise modelling, they can visually represent chemical transformations and make the thought process behind molecules and chemical reactions more apparent. This method can be useful for students to practice differentiating between particle levels (atomic and molecular), atom redistribution in chemical reactions, physical transformations, as well as for differentiating between indices and coefficients. Differentiation between indices and coefficients is a frequently encountered challenge [41]. Models can also provide an understanding of the different representations of molecular models and how they relate to each other in a chemical transformation [15,16]. The various representations of matter pose several challenges as they can represent individual atoms, molecules, and large clusters of molecules [21,22,23,24].

The VSEPR model serves as the fundamental basis for predicting the three-dimensionality of molecules, which is crucial for comprehending various aspects of chemistry, such as chemical bonding and steric hindrance.

Out of all the models built by the students, only one-third followed the principles of the VSEPR model. There was no difference between the two different groups of students (Table 4). Among the various molecules, carbon dioxide (CO₂) posed the greatest challenge for the students in terms of its three-dimensional structure. Regardless of the presence of a double bond between carbon and oxygen resulting in a linear shape, the structure of the molecule was commonly perceived as having an angular shape. The utilisation of an angular shape by numerous students implies a disregard for the VSEPR model, as they chose to rely on their familiarity with the shape of the water molecule to estimate the three-dimensional arrangement of carbon dioxide. The findings demonstrate the significance of facilitating the translation of symbolic representations into three-dimensional particles that are not predetermined molecular models and using multiple representations sparks insights: their meanings, connections, related knowledge areas, and similarities and differences [15,16,17,18]. This method enables students to actively manipulate and contemplate the distinction between two-dimensional and three-dimensional dimensions while also considering the molecular structure. It serves as a valuable tool for instructors to observe first-hand how students apply their comprehension of molecular formulas at both the symbolic and particle levels. An important part of the VSEPR theory is atomic size; it is noteworthy that only 39% of students with a background in chemistry were able to identify discrepancies in atom size. Results also suggest that learning these concepts is a time-consuming process. This could be attributed to the fact that the symbols in the chemical reaction formula do not convey atom size.

6. Conclusions

This approach facilitates the exploration of the translation between the symbolic level of chemistry and the particles they symbolize. The results demonstrate the significance of investigating the range of interpretations that emerge when students are granted artistic autonomy to actively select size, shape, and two- or three-dimensionality in their translations of the symbolic aspect of chemistry. The development of a deeper understanding of the stoichiometry field centres around the accuracy of the translation [15,17,18].

The incorporation of clay modelling in the learning process yields benefits for both instructors and students, as it fosters an understanding of the interpretations of underlying processes and promotes a heightened awareness of substance structure and the redistribution of mass within different substances.