Depiction of scientific principles, laws and theories in Chemistry textbooks used by students in Singapore

Abstract

In this study, we analyzed how scientific terms such as principle, law and theory are depicted in Chemistry textbooks used by students in Singapore. There are very few reports in the science or chemistry education literature that explicitly explore the term principle, although all three terms appear in a number of topics in the high school chemistry curricula. The textbooks’ definitions for the three terms were compared with key canonical attributes constituting these general terms. Findings indicate that most of the textbooks did not provide generic definitions of the three terms, and a number of attributes were also not apparent in the specific definitions of the three terms (except for principle). The relationship between laws and theories in textbooks was explored for three exemplars, and this provided useful insights. It is suggested that textbook authors, supported by curriculum developers and teachers, devote more attention to highlighting the relationships and distinctions among the three scientific terms. This can help students cultivate a better understanding of these terms, thus potentially leading to improved overall understanding of the nature of science.

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Introduction

Nature of science (NOS) has been an important area of research in the science and chemistry education literature. While a suitable definition of NOS seems to be elusive as different researchers have varying ideas on how it should be conceptualized, it broadly centers on the epistemology and sociology of science as well as the values and assumptions inherent in the value chain of knowledge creation in science (Abd-El-Khalick et al., 1998; Lederman et al., 2002). A recent approach in NOS studies is the family resemblance model (Erduran et al., 2019) in which clusters or categories are used to represent ideas about science. To foster interest and curiosity in the scientific tradition, the emphasis on NOS has expanded beyond academic research to its practical incorporation into chemistry and other science subjects in the classroom (e.g., Larison, 2018).

Reform efforts in science education have also emphasized the need for students to acquire good understanding of NOS (e.g., NGSS, 2013; Olson, 2018). This can help them to appreciate how knowledge is created in science when learning it via textbooks and in the classroom. Also, knowledge of NOS can contribute further towards enhancing science literacy levels (Lederman et al., 2014). Other reasons for students to know more about NOS include the following: (1) they can recognize that scientific knowledge has a developmental journey during which scientists build over what others have found; (2) the process of inquiry in science involves questioning, reasoning, and decision-making, all of which are important attributes to promote in students; and (3) there is the influence of creativity and imagination along the value chain from experimental design to interpretation of results, and this is also important in the production of scientific knowledge (see earlier references).

In the literature, students’ views of NOS have been ascertained via the use of various instruments – for example, views of NOS questionnaire (Lederman et al., 2002) and views on science and education questionnaire (Chen, 2006). The instruments comprise a series of questions for students to answer, with one of the questions focusing on the distinction between laws and theories.

In conventional NOS conceptualizations, the emphasis in one of the frameworks is on theories and laws, not surprisingly since these are key aspects of the scientific tradition. What seems to be missing is the emphasis on principles. This is also important as it operates across the natural sciences – for example, principle of moments in Physics as well as Le Chatelier's principle in Chemistry. Scientific principles, scientific laws and scientific theories are commonly considered in tandem in a number of scientific treatises (Dilworth, 1994; Krebs, 2001; Dilworth and Cohen, 2006).

In the field of Chemistry, which is the focus of this study, a number of principles are encountered in high school chemistry. We can cite Le Chatelier's Principle, Aufbau Principle and Pauli's Exclusion Principle in this regard. While the definitions of these specific terms are usually given in textbooks in Chemistry, inspection of a number of textbooks (see the Methodology section) in the educational dispensation, which the authors are familiar with, indicates that there is inadequate or no elaboration on what exactly is a principle, law or theory before introducing these. Does this mean that students are just applying these terms in problem-solving situations without appreciating the differences among these terms? The answer seems to be obvious.

We were able to locate one NOS study (Lin and Chen, 2002) that focused on scientific principles but in tandem with scientific laws and scientific theories; however, it constituted a very minor part (only one question out of eight questions in the instrument) of the overall NOS study involving pre-service teachers in Chemistry. The relevant question (Q6) was as follows:

“How do you think scientific laws, principles, and theories appeared”, for which three MCQ options were given:

(1) “Scientific laws, principles, and theories have existed in nature. Scientists discover them”.

(2) “Scientific laws, principles, and theories did not exist in nature. Scientists invented them and use them as tools to explain natural phenomena”.

(3) “Scientific laws, principles, and theories have existed in nature. Scientists discover some of them by chance and sometimes invent them”.

Since the terms were considered in unison in this question, it is difficult to unpack students’ individual conceptualization of the respective terms (including principle). Because principles, laws and theories represent distinct facets of scientific knowledge, which tend to evoke varied student responses, the current study therefore examined the important separation of these terms, as depicted in school Chemistry textbooks. Such a study has not only curricular implications but can also contribute to the corpus of knowledge related to the wider NOS studies on textbooks.

Theoretical frameworks

The first framework is on NOS. It has two versions which are commonly used: the consensual model (Abd-El-Khalick et al., 1998) and the family resemblance approach (Erduran et al., 2019). Both models include laws and theories.

The consensual model has several tenets, for example: (1) empirical nature of scientific knowledge – knowledge in science is obtained via laboratory experiments or observations of nature via the human perceptual apparatus; (2) distinction between observation and inference – the former represents what is observed, either via sensory organs or when augmented with instrumentation while the latter is concerned with what sense to make out of this; (3) theories and laws – the former has an explanatory basis that can account for a large number of observations while the latter represents descriptive statements of the relationships between variables; (4) role of creativity and imagination in the production of scientific knowledge – development of new scientific knowledge does not follow a template approach whereby even common folks can make discoveries; at some stage, human ingenuity, creativity and imagination come into play; (5) social and cultural aspects of scientific knowledge – since science is a human enterprise, it follows that it is subject to the social, political and economic imperatives or vagaries of society; (6) tentative nature of scientific knowledge – while knowledge on an aspect of a field in science is durable, there is no certainty that it will be so in the future when new developments come on board. For our study, we will focus only on the third NOS tenet as well as introduce the term ‘principle’. In the Family Resemblance Approach (Erduran et al., 2019), theories and laws are also some of the aspects but not principles.

We also draw on support from the literature on how scientific laws, scientific theories and scientific principles are conceptualized. The key reference that we consulted on this is Krebs (2001). This is for the second framework, where the attributes for laws, theories and principles are articulated. In his book, he documented several theories, laws and principles in sciences as well as came up with a framework for what encapsulates laws, theories and principles. We cannot discount the attributes for the three terms proposed by Krebs (2001) in his introduction to the book as these were presumably based after a comprehensive review of the hundreds of such terms in the sciences in his book. In the ensuing three paragraphs, we draw on ideas from Kreb's book.

Laws are “generalized descriptions of how things behave in nature under a variety of circumstances”. That is, “any phenomenon, event or action that occurs and behaves in the same manner under the same conditions, and is thus predictable, can be stated as a law” (Krebs, 2001). The laws are framed on the basis of empirical findings from repeat experiments and observations – key scientific traditions, over a period of time, and it is this currency that endows them with rigor. The law is “inferred from particular facts, applicable to a defined group or class of phenomena, and expressible by the statement that a particular phenomenon always occurs if certain conditions be present”. Krebs (2001) also noted that laws may or may not be exactly framed and that they are universal. Another feature of laws is that they can be framed mathematically. Though an exact formalism for a law in science exists under current thinking, it is subject to refinement as new research findings come on board in the future.

Theories represent “general explanatory statements of how things work in nature” and ‘they are the endpoint of scientifically gathered evidence about specific events that may incorporate other laws and hypotheses” (Krebs, 2001). That is, a theory is an attempt at coming up with an explanation for a process, based on available evidence. Krebs also indicated that “all theories are derived by humans and, as such, are linguistic constructions of assumptions made by scientists”. They are similar to, but much more than, educated guesses; they result from “critical observations, experimentation, logical inferences and creative thinking”. In common parlance, a theory can mean a conjecture but in science, it is more than a conjecture – the explanatory ballast that it provides has its basis on empirical evidence and/or observations.

A principle in science is similar to a law but is based on statements derived from it (Krebs, 2001). The statement, as framed, is referred to as a principle. There are, however, exceptions – for example, the Heisenberg uncertainty principle, encountered in quantum mechanics, can also be expressed mathematically, and it has its basis on physical laws (Krebs, 2001).

For the third framework, we consulted references in the philosophy of science literature and philosophy of chemistry literature on what constitutes laws, theories and principles. This aims to provide support for Kreb's framing of laws, theories and principles, which we would be using for our study, as well as see what other attributes could be included for the three terms.

Laws explain “why particular phenomena are what they are or occur as they occur” (Faye, 2005). Also, they are “statements that describe natural phenomena or relationships in the physical world that have been repeatedly observed and confirmed through empirical evidence and experimentations” (Singh, 2023). The mathematical nature of laws is underscored by Dilworth (1989): “Empirical laws in the exact sciences are most often expressed as equations representing relations between measurable parameters. These equations indicate mathematical functions relating quantities of certain properties, quantities which are themselves determined via the performance of specific mensural operations involving the use of particular instruments”. A large body of previously obtained data can also form the basis for the discovery of empirical laws as are also the findings from new experiments (Dilworth, 1989). Laws can also have its basis in facts of a scientific nature (Carey, 1994). The predictive nature of laws has been noted by Mitchell (2000), who further describes laws as “empirical truths”. That a scientific law is subject to refinement in the future as new findings challenge existing understanding is central to the scientific enterprise – for example, the ideal gas law is generally valid for real gases at normal temperatures and pressures but requires corrections in the ideal gas law equation for other conditions of temperature and pressure.

Dilworth (1989) stressed that “scientific theories explain phenomena or experimental laws by indicating the precise way in which they can be seen as being the result of particular causes, as this notion is understood in science”. A somewhat similar view is held by McMullin (1984): “Theory explains by suggesting what might bring about the explananda. It postulates entities, properties, processes, relations, themselves unobserved, that are held to be causally responsible for the empirical regularities to be explained”. Hempel (1970) characterized theories as follows: “Theories are normally constructed only when prior research in a given field has yielded a body of knowledge that includes empirical generalizations or putative laws concerning the phenomena under study. A theory then aims at providing a deeper understanding by construing those phenomena as manifestations of certain underlying processes governed by laws which account for the uniformities previously studied, and which, as a rule, yield corrections and refinements of the putative laws by means of which those uniformities had been previously characterized”. Theories also have predictive utility (Caldin, 2002).

The link between theory and law is also of interest. For example, “The discovery of the law of multiple proportions was the first great success of Dalton's atomic theory. This law was not induced from experimental results, but was derived from the theory, and then tested by experiments” (Pauling, 1964, p. 26).

While laws and theories are quite straightforward in terms of their basic tenets, that for principles may not be when we consulted the philosophy literature. Of the three principles encountered in school Chemistry textbooks – Pauli's Exclusion Principle, Aufbau Principle and Le Chatelier's principle, the school textbooks surveyed for this study did not go into the origins of these specific principles or indicate how these arise – whether from laws or theories, or vice versa. A very early reference (Lotka, 1922) indicates that Le Chatelier's Principle arises from the laws of thermodynamics – that is, from the first two laws of thermodynamics. In relation to the Aufbau Principle, it is thought to arise from the Bohr Theory (Park and Stetten, 2001). Bohr's version of the old quantum theory, while elegant to some extent, posed problems when issues such as the anomalous Zeeman Effect could not be satisfactorily explained. Pauli saw through the problem and proposed that electrons can have an additional degree of freedom of movement (on top of the earlier 3), which led to the emergence of his Exclusion Principle and its serving as a link between Bohr's earlier theory and the new quantum theory of Schrodinger and Heisenberg (Scerri, 1997). When Pauli framed the exclusion principle, he acknowledged two limitations: there was no logical basis for the principle and that it was not possible to derive it from more fundamental considerations; he further added that it could be due to some shortcomings in the theory (Pauli, 1964). It has to be noted that Pauli's Exclusion Principle was framed before the advent of formal quantum mechanics as a field. Now, it can be considered to follow from contemporary quantum theory. However, philosopher Massimi (2005) felt that “Pauli's principle emerged as a phenomenological rule 'deduced' from some anomalous phenomena and theoretical assumptions of the old quantum theory”. That is, this principle still follows from theory. Summing up, we note that scientific principles have their basis in either scientific laws or theories, depending on the specific scientific principle – at least in the context of those encountered in school chemistry. That is, the philosophical literature partially supports one of Kreb's postulates for a principle – when Krebs mentions that principles are based on statements derived from scientific laws, it can also include scientific theories as well. This means that the attribute for principles in Kreb's framework has to be slightly expanded. Furthermore, examining the background of the three scientific principles encountered in school chemistry, it can be noted that all these relate to phenomena or processes. For example, Le Chatelier's Principle relates to what happens when a chemical reaction in equilibrium is disturbed via a change in, for example, concentration or temperature. The Aufbau Principle describes what happens in the process of electrons filling up orbitals in an atom – they fill up the lower energy orbitals before filling up the higher energy orbitals. Pauli's Exclusion Principle emphasizes that in the occupancy of an orbital, no more than two electrons can occupy an orbital, and that they must have different spins. So, we can say that a scientific principle prescribes a rule or mechanism for a phenomenon or process to operate, and it is restricted in its operability to the specific process or phenomenon, as can be seen from the three specific terms encountered in school chemistry. Furthermore, it can be noted that it is qualitative in nature.

Summarizing, keeping the criteria proposed by Krebs (2001) for laws, theories and principles in mind, it is generally clear that the key criteria for laws and theories are also supported from the philosophy of science/chemistry literature. That for principle needs a slight amendment for one of the criteria – what is stated in Krebs (2001) as “Similar to a scientific law but is based on statements derived from it” needs to be reframed as “It is based on statements derived from scientific laws or theories”. Also, another attribute has been added for principle based on an examination of the three scientific principles encountered in school chemistry – its qualitative nature.

We must emphasize that in a study of this nature, we have to keep in mind the school chemistry context and be wary of digressions into philosophical aspects that are not germane to the central practice of chemistry, as taught in school and, by extension, what is covered in school Chemistry textbooks. For example, when comparing laws and theories in physics and chemistry, Christie (1994) and Christie and Christie (2000) argued that those in the former are precise while those in the latter are often approximate. In this context, it can be seen that gas laws are valid only for the ideal case and breaks down for real gases, especially at low temperatures and high pressures. In respect of the periodic table, Christie and Christie (2003) further noted that it is taxonomic in nature (even with the existence of the Periodic Law) and had little theoretical support until the advent of quantum mechanics, when concepts such as electronic structures of atoms came about. Van Brakel (2001) is critical about the criteria on what constitutes laws in chemistry, and argued that, strictly speaking, there are no laws in chemistry. Eastwell (2014) stressed that “A theory is not necessarily a well-supported explanation” and that “The most powerful knowledge in science is an embedded theory, defined as a theory that is supported by much convincing evidence and that has become central to the way scientists understand their world”. Nickles (2002), in his review of the book by Krebs (2001), called the depiction of laws by Kreb as “philosophically naïve”; however, he did not advance any justification for this assertion. As noted succinctly by Galili (2019), science educators are often faced with a dilemma when it comes to NOS – how to reconcile the claims of science education researchers with those working in the philosophy of science, especially when both sides have compelling arguments. It is the same when dealing with the three key scientific terms, two (law and theory) of which have been part of the NOS tradition thus far.

On the nature of scientific laws and theories Dilworth (1989) has provided useful perspectives: “Laws and theories constitute distinct and fundamental categories of science, an appreciation of the nature of which is a prerequisite to a proper understanding of science itself”; he mentioned a third category ‘principles’ as well though that was not the focus of his article. It must be reiterated that there is no hierarchical relationship among laws, theories and principles, and one does not transform into the other. These are different strands of knowledge in science that cannot be compared. A misconception that a theory can become a law or vice versa has been noted by NOS researchers (for example, Abd-El-Khalick, 2012).

Literature review on NOS aspects in Chemistry textbooks

As NOS is one of the key emphases in science (and chemistry) education research, several studies have focused on how NOS, overall, is depicted in Chemistry textbooks in a number of countries. Abd-El-Khalick et al. (2008) explored how NOS is represented in Chemistry textbooks used in high schools in the USA over four decades. It was noted that NOS representations (including laws and theories) were rather poor. There was little attempt in these books to present a nuanced viewpoint that could promote informed views about laws and theories and, at times, the depictions promote misconceptions. For example, some of the issues noted include the following: lack of consistency in portraying the terms, facts in science which hold true are labelled as laws, inadequate portrayal of the nature of laws, attributing certainty to law, “observation + imagination = new theory”, “theory is an unsupported notion about something”, etc. Another study (Niaz et al., 2011) evaluated 75 general Chemistry textbooks published in the USA and found that many of these textbooks presented little insight on overall NOS attributes, including that of theory and law. In exploring the integration of NOS elements in high school Chemistry textbooks in Turkey, Aydin and Tortumlu (2015) found that while there is a decrease in the number of NOS elements with grade progression, the emphasis seems to be more on the tentative nature of scientific knowledge, empirical nature of science and distinction between observation and inference; theories and laws were not covered in that study. Upahi et al. (2020) focused on senior high school Chemistry textbooks in Nigeria, and noted that depictions of overall NOS, including of laws and theories, are rather few. In an analysis of upper secondary Chemistry textbooks in Finland and Sweden, Vesterinen et al. (2013) covered several aspects of NOS but did not include laws and theories as the textbooks omitted discussion on these aspects. Senior high school Chemistry textbooks used in China were explored by Chen et al. (2022) for overall NOS representations, and it was found that the new textbooks covered more NOS aspects compared to old textbooks; however, the emphasis on theory and law was very low. Focusing on 11 aspects of NOS in middle school Chemistry textbooks in China, Zhu and Tang (2023) noted that, overall, the representations, including that of laws and theories, were roughly equal. On NOS emphases in high school Chemistry textbooks used in Iran, Zarei and Hossein Nia (2023) noted that several aspects, including laws, were covered but not theory. Marniok and Reiners (2017) explored how 11 aspects of NOS were covered in German Chemistry textbooks and noted that NOS aspects were represented rather poorly. While theories found resonance in the German textbooks, they were also conflated with models; also, no textbooks treated laws extensively. In one old textbook, it was even stated that any claim that is not refuted for a long time can be treated as a law.

The literature review on NOS aspects in Chemistry textbooks suggests that there are a number of gaps that are worth exploring:

1. While Chemistry textbooks from a number of countries have been explored for NOS depictions (including on laws and theories), a study focusing on the Singapore context has not been conducted. At grades 9–10, the Chemistry textbook used in the country was specially commissioned by the Ministry of Education for the prescribed curriculum. At grades 11–12, while there are no prescribed textbooks, three internationally recognized textbooks are used by teachers to curate notes for students. The study in the Singapore context can contribute further to the literature on NOS aspects in Chemistry textbooks – our interest is on scientific terms such as laws, theories, and principles.

2. Textbook analyses in the literature have focused more on general NOS aspects, with the tenets on laws and theories being one of them. However, laws and theories have not been the basis of extensive analyses in these studies.

3. Where laws and theories have been explored in analyses of textbooks, an analysis based on how the definitions match the canonical equivalents has not been done in the literature. This is important as it can unpack how these are framed in the textbooks – where this is not up to expectations, pointers can be suggested for future curricular reforms as well as see what can be done by teachers to promote the NOS attributes related to the scientific terms in the interim.

4. None of the Chemistry textbook analysis in the literature focused on scientific principles. Since the latter is commonly considered in tandem with laws and theories in a number of scientific treatises, it is worth exploring this on top of laws and theories.

The research questions that we wished to explore for the Chemistry textbooks used in Singapore were:

1. Are the terms law, theory and principle defined generically in Chemistry textbooks and, if so, are the canonical attributes of these terms apparent in the definitions?

2. For the specific laws, theories and principles defined in these textbooks, are the canonical attributes apparent?

3. How are the associations between related laws and theories portrayed in these textbooks?

Methodology

Textbooks and syllabi

The Chemistry textbooks currently used by students in Singapore were explored with reference to how the three terms were portrayed, both from a general perspective as well as from a specific perspective.

Table 1 presents details of the textbooks used for this study.

Table 1 Textbooks used for analysis

Textbook	Authors	Year of publication	Publisher
Chemistry Matters	M. Chang, A. Chew, J. Sadler, Y. T. Tan, H. V. Wong and C. H. Woo	2023	Marshall Cavendish Education, Singapore
Cambridge International AS and A Level Chemistry	P. Cann and P. Hughes	2015	Hodder Education, Cambridge
The Molecular Nature of Matter and Change (5th edition)	M. S. Silberberg	2009	McGraw-Hill Higher Education, Singapore
Chemistry: Introducing Inorganic, Organic and Physical Chemistry (2nd Edition)	A. Burrows, J. Holman, A. Parsons, G. Pilling and G. Price	2013	Oxford University Press, Oxford

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The textbook by Chang et al. (2023) for grades 9–10 was specially commissioned, with the local context in mind. In grades 11–12, no prescribed textbook is used (or required for purchase) as students are given curated notes prepared by teachers. However, students are provided references to the textbooks used by teachers in the preparation of the class notes. Students have also access to a few other Chemistry textbooks in the school library though it is not clear to what extent these are consulted.

The syllabi for Chemistry at grades 9–10 and grades 11–12 are available online, and indicated in the Reference section (SEAB, 2022a, 2022b).

Procedure

Prior to the analysis, we entered verbatim how the three terms were presented, both from a general perspective as well as from a specific perspective, into a table (Tables 2–4). The tabulations also indicate the numbers of the respective terms encountered in the Chemistry curricula at grades 9–10 and grades 11–12.

Table 2 General scientific terms used in Chemistry textbooks at grades 11–12 matched to attributes

Textbook	NOS term
	Law	Theory	Principle
Note: a tick (✓) besides the attribute indicates that it is apparent in the definition while a cross (✗) indicates that it is not apparent in the definition.
Cambridge International AS and A Level Chemistry by Cann and Hughes (2015)	Not stated	Not stated	Not stated
Chemistry: The Molecular Nature of Matter and Change (5th Edition) by Silberberg (2009)	“A summary, often in mathematical form, of a universal observation”.	“Formulating conceptual models, or theories, based on experiments is what distinguishes scientific thinking from speculation. As hypotheses are revised according to experimental results, a model generally emerges that describes how the observed phenomenon occurs. A model is not an exact representation of nature, but rather a simplified version of nature that can be used to make predictions about related phenomena. Further investigations refine a model by testing its predictions and altering it to account for new facts”.	Not stated
	A ✓  B ✗  C ✓	A ✓  B ✓  C ✓
	D ✗  E ✗
Chemistry: Introducing inorganic, organic and physical chemistry by Burrows et al. (2013)	Not stated	Not stated.	Not stated

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Table 3 Scientific terms used in Chemistry textbook at grades 9–10 (specific)

Term	Example	Definition given in textbook by Chang et al. (2023)	Attributes
Law	Law of conservation of mass	Not stated explicitly.	A ✓  B ✗  C ✗
		However, in the chapter on balancing of chemical equations, it is stated that “Atoms are conserved in physical and chemical reactions”.	D ✗  E ✗
	Avogadro's Law	“At the same temperature and pressure, equal volumes of gases contain the same number of particles”.	A ✓  B ✓  C ✗
			D ✗  E ✗
Theory	Kinetic-particle Theory	“All matter is made up of tiny particles and these particles are in constant random motion”.	A ✓  B ✗  C ✗
	Arrhenius Theory of acids and bases	Not stated explicitly.
		However, in the chapter on acids and bases, it is stated as “An acid is a substance that produces hydrogen ions, H^+, in aqueous solutions”.	A ✓  B ✗  C ✗
	Collision Theory	Not stated explicitly.
		However, in the chapter on rates of reactions, it is stated that “For an effective collision to occur, the reactant particles must collide with energy equal to or more than the activation energy”.	A ✓  B ✗  C ✗

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Table 4 Scientific terms used in Chemistry textbook at grades 11–12 (specific, with indication of attributes)

Term	Example	Definition given in textbook
		Cann and Hughes (2015)	Silberberg (2009)	Burrows et al. (2013)
Law	Law of conservation of mass	“The sum of the masses of all the products is always equal to the sum of the masses of all the reactants”.	“The total mass of substances does not change during a chemical reaction”.	Not stated
		A ✓  B ✓  C ✓  D ✗  E ✗	A ✓  B ✓  C ✗  D ✗  E ✗
	Dalton's Law	(Not mentioned as such).	“In a volume of unreacting gases, the total pressure is the sum of the partial pressures of the individual gases: Ptotal = P1 + P2 + …”	“The total pressure exerted by a mixture of gases is the sum of the partial pressures of each individual gas”.
		A statement under the equilibrium constant section states that “The sum of the partial pressures of gases will equal the total pressure”.
		A ✓  B ✓  C ✓  D ✗  E ✗	A ✓  B ✓  C ✓  D ✗  E ✗	A ✓  B ✓  C ✓  D ✗  E ✗
	Boyle's Law	“The volume V of a fixed mass of gas at constant temperature is inversely proportional to the pressure p on the gas: pV = constant”	“At constant temperature and amount of gas, the volume occupied by a gas is inversely proportional to the applied (external) pressure: V ∝ 1/P”	“At constant temperature, the volume of a fixed amount of gas is reduced in proportion as the pressure increases”.
		A ✓  B ✓  C ✓  D ✗  E ✗	A ✓  B ✓  C ✓  D ✗  E ✗	A ✓  B ✓  C ✓  D ✗  E ✗
	Charles Law	“The volume V of a fixed mass of gas at constant pressure is directly proportional to it temperature T: V ∝ T”	“At constant pressure, the volume occupied by a fixed amount of gas is directly proportional to its absolute temperature: V ∝ T”	“The volume of a fixed amount of gas, at constant pressure, is proportional to the absolute temperature.”
		A ✓  B ✓  C ✓  D ✗  E ✗	A ✓  B ✓  C ✓  D ✗  E ✗	A ✓  B ✓  C ✓  D ✗ E ✗
	Avogadro's Law	“Under the same conditions of temperature and pressure, equal volumes of all gases will contain equal number of molecules”.	“At fixed temperature and pressure, equal volumes of any ideal gas contain equal number of particles, and therefore, the volume of a gas is directly proportional to the amount (mol): V ∝ n”	“Equal volumes of gases at constant temperature and pressure contain equal numbers of molecules”.
		A ✓  B ✓  C ✓  D ✗  E ✗	A ✓  B ✓  C ✓  D ✗  E ✗	A ✓  B ✓  C ✓  D ✗  E ✗
	Ideal gas law	Not defined explicitly.	“An equation that expresses the relationships amongst volume, pressure, temperature and amount (mol) of an ideal gas: PV = nRT”	Not stated explicitly. Given as ideal gas equation: pV = nRT
		Stated as ideal gas equation: pV = nRT through combining the relationships between p, V and T.
		A ✗  B ✓  C ✓  D ✗  E ✗	A ✓  B ✓  C ✓  D ✗  E ✗	A ✗  B ✓  C ✓  D ✗  E ✗
	Hess Law	“The enthalpy change for a reaction, ΔH, is independent of the path taken”.	“The enthalpy change of an overall process is the sum of the enthalpy changes of the individual steps of the process”.	“The total enthalpy change for a chemical reaction is independent of the path by which the reaction occurs, provided the starting and finishing states are the same for each reaction path”.
		A ✓  B ✓  C ✓  D ✗  E ✗	A ✓  B ✓  C ✓  D ✗  E ✗	A ✓  B ✓  C ✓  D ✗  E ✗
Theory	Kinetic-Particle Theory	Not defined explicitly. Assumptions about ideal gas are stated.	“The model that explains gas behaviour in terms of particles in random motion whose volumes and interactions are negligible”.	“The theory is based on a simple model that describes gas behaviour in terms of the movement of molecules”.
			A ✓  B ✗  C ✗	A ✓  B ✗   C ✗
	Arrhenius Theory of acids and bases	“An acid is a substance that gives hydrogen ions in water”.	“A model of acid–base behaviour in which an acid is a substance that has H in its formula and produces H^+ in water, and a base is a substance that has OH in its formula and produces OH^− in water”.	“An acid is a substance that ionized in water to give H^+ ions and anions, and a base is a substance that ionized in water to give hydroxide ions (OH^−) and cations”.
		A ✓  B ✗  C ✗	A ✓  B ✗  C ✗	A ✓  B ✗  C ✗
	Brønsted–Lowry Theory of acids and bases	“An acid is a proton donor. A base is a proton acceptor”.	“A model of acid–base behaviour based on proton transfer, in which an acid and a base are defined, respectively, as species that donate and accept a proton”.	“An acid donates H^+ in a chemical reaction and the substance that accepts the H^+ is the base”.
		A ✓  B ✗  C ✗	A ✓  B ✗   C ✗	A ✓  B ✗  C ✗
	Lewis Theory of acids and bases	Not stated.	“A model of acid–base behaviour in which acids and bases are defined, respectively, as species that acquire and donate an electron pair”.	“A Lewis acid is an electron pair acceptor and a Lewis base is an electron pair donor”.
			A ✓  B ✗  C ✗	A ✓  B ✗  C ✗
	Collision Theory	“In order for a reaction to take place, the reactant molecules must first collide and secondly have sufficient combined energy to get over the activation energy barrier”.	“A model that explains reaction rate as the result of particles colliding with a certain minimum energy”.	“For a reaction to occur, two molecules must collide with a certain minimum kinetic energy along their line of approach”.
		A ✓  B ✗  C ✓	A ✓  B ✗  C ✓	A ✓  B ✗  C ✓
	Valence Shell Electron Pair Repulsion Theory	“The electron pairs in the outer (valence) shell of an atom will experience the least repulsion when they are as far apart from one another as possible and allow for the prediction of the shapes of simple molecules”.	“A model explaining that the shapes of molecules and ions result from minimising electron-pair repulsion around a central atom”.	“The VSEPR theory is used to predict the shapes of molecules by looking at the repulsions between electron pairs in the valence shell on the central atom in the molecule”.
		A ✓  B ✗  C ✓	A ✓  B ✗  C ✗	A ✓  B ✗  C ✓
Principle	Le Chatelier's Principle	“If the conditions of a system in equilibrium are changed, the position of equilibrium moves so as to reduce that change”.	“If a system in a state of equilibrium is disturbed, it will undergo a change that shifts its equilibrium in a direction that reduces the effect of the disturbance”.	“When an external change is made to a system in dynamic equilibrium, the system responds to minimize the effect of the change”.
		A ✓  B ✓  C ✓	A ✓  B ✓  C ✓	A ✓  B ✓  C ✓
	Pauli Exclusion Principle	“No more than two electrons can occupy the same orbital, and if the two electrons are in the same orbital, they must have opposite spins”.	“No two electrons in the same atom can have the same four quantum numbers”.	“No two electrons in an atom can have the same four quantum numbers”.
		A ✓  B ✓  C ✓	A ✓  B ✓  C ✓	A ✓  B ✓  C ✓
	Aufbau Principle	Not stated explicitly. Presented via an example of “filling up orbitals with electrons to predict the electronic configuration of atoms or ions”.	“The conceptual basis of a process of building up atoms by adding one proton (and one or more neutrons) at a time to the nucleus and one electron around it to obtain the ground state electronic configuration of the elements”.	“The Aufbau (German for “Building up”) Principle involves building up the electronic structure of an atom by filling the lowest energy orbitals first. This method can be used to determine the electronic configuration for a particular atom”.
			A ✓  B ✓  C ✓	A ✓  B ✓  C ✓

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Data analysis

The generic definitions of the terms in the textbooks were matched with the key canonical attributes constituting these terms. It was also done for the specific terms as well. This approach can help to ascertain what attributes of each term are present or missing in the definitions. Based on the theoretical frameworks, the key attributes which we chose to focus on for the three terms are:

Law. (A) Generalized descriptions of how things behave in nature under a variety of circumstances.

(B) It can be used to make predictions.

(C) It can be represented mathematically via equations.

(D) It is subject to refinement as new research findings come on board in the future.

(E) It is framed on the basis of empirical findings from repeat experiments and observations.

(All the above attributes are from Krebs (2001)).

Theory. (A) General explanatory statement of how things work in nature.

(B) It is the endpoint of scientifically gathered evidence about specific events that may incorporate other laws and hypotheses.

(C) It has predictive utility.

(All the above attributes are also from Krebs (2001)).

Principle. (A) It is based on statements derived from scientific laws or theories.

(B) It is a rule that is able to account for how a process is believed to operate.

(C) It is qualitative in nature.

(The first attribute is partially from Krebs (2001) while the other two attributes were inferred from an examination of the three scientific principles encountered in the high school chemistry syllabus.)

Though more attributes could have been included for each of the three scientific terms from the literature, we felt that the above attributes are adequate for a few reasons. First is that the focus of our study is on secondary and high school Chemistry textbooks, so the key attributes depicted above for each term would suffice. Second is that drawing on abstract concepts such as, for example, symmetry and conservation (Krebs, 2001) for depicting laws, etc., may not be relevant for the school chemistry context encountered in our study. Third is that the authors discussed at considerable length on what to include, and it was felt that the above key attributes would be adequate for the analysis of the school Chemistry textbooks.

The tabulations were done by one of the authors and the accuracy was checked by another author. There was very good agreement between both these authors on the analysis (inter-rater agreement = 0.95, but reached unity after discussions between the authors). In trying to match the attributes for each term with respect to the canonical equivalents (A, B, etc. as above) for each respective term in the tables, a tick (✓) was used when the attribute is present; if the attribute is not present, a cross (✗) was used.

Results and discussion

In this section, we present the results and discuss the findings according to the research questions.

Research question 1

The prescribed textbook for students at grades 9–10 does not elaborate on scientific laws and theories from a general perspective, even though these are part of the curriculum. Scientific principles are not encountered at these grade levels, and so are not found in the textbook. Thus, a separate table is not presented here for this purpose.

How the three terms are portrayed from a general perspective in the three textbooks used by students in grades 11–12 is shown in Table 2. Additionally, we have also shown in the table which canonical attributes are apparent or not apparent for each definition. While principles are not defined in all the three textbooks, only one of the textbooks depicts laws and theories in a generic manner. The book by Silberberg (2009) defines a law as “A summary, often in mathematical form, of a universal observation”. This description highlights how things behave in nature (attribute A) and the possible mathematical nature (attribute C) but fails to present the predictive nature (attribute B), the possibility of modification in the face of new findings (attribute D), and that it has its basis on empirical findings from repeated experiments and/or observations (attribute E). In explaining theory, the same book states that “Formulating conceptual models, or theories, based on experiments is what distinguishes scientific thinking from speculation. As hypotheses are revised according to experimental results, a model generally emerges that describes how the observed phenomenon occurs. A model is not an exact representation of nature, but rather a simplified version of nature that can be used to make predictions about related phenomena. Further investigations refine a model by testing its predictions and altering it to account for new facts”. This definition can be considered to fulfil the three canonical attributes under theory. A point to note is that in this definition, theory is conflated with model. In science, theory and model are two distinct aspects, with the latter being a representation of an aspect of reality that may not be discernible. Especially the description for theory could have been clearer in this book. With one notable exception, the textbooks did not introduce the scientific terms, law and theory, from a generic context. All the textbooks also did not state the generic definition for the term principle. As a result, it is unlikely that teachers and students would be able to gain a good understanding of these terms, as well as the relationship between the terms, before delving into the specific definitions presented in the rest of the textbooks. There is also the likelihood that students may develop or deepen their misconceptions about the three terms. Our observations are not surprising as there are reports of less than satisfactory coverage of theories and laws even in textbooks used in other countries as well – for example, in the USA (Abd-El-Khalick et al., 2008) and in Turkey (Izci, 2017).

The misconception that a law can become a theory (or vice versa) has been noted in the NOS literature (Abd-El-Khalick, 2012). Can a principle become a law? Laws, theories and principles are unique terms, each with their own domain characteristics. That is, their depictions have terminological exactitude. It is thus not possible for a principle to become a law (or vice versa).

Research question 2

Across grade levels 9–12, there are seven occurrences of laws, six occurrences of theories and three occurrences of principles.

The specific definitions of laws and theories, extracted from the textbooks used in grades 9–10, are shown in Table 3. Scientific principles are not encountered at these grade levels, and so descriptions related to principles are not found in the textbook. By introducing Avogadro's Law as “At the same temperature and pressure, equal volumes of gases contain the same number of particles”, attributes A and B are revealed while attributes C, D, and E are not obvious. While the Law of Conservation of Mass is not stated explicitly, it has a replacement statement: “Atoms are conserved in physical and chemical reactions”. By failing to acknowledge that the said Law has its roots in experimental evidence where scientists measure and compare the masses of reactants and products, the de-contextualization of the replacement statement may unintentionally lead to misconceptions if interpreted incorrectly by students that scientists can actually see and count atoms during a reaction. Statements representing the Arrhenius Theory of acids and bases as well as the Collision Theory are given in the textbook despite not being framed as theories per se. Only the Kinetic-Particle Theory is presented as “All matter is made up of tiny particles and these particles are in constant random motion”. Although all three latter statements reveal how things behave in nature (attribute A), they do not provide any hint to students on the amount of work carried out by scientists to arrive at these intellectual summations, and hence the opportunities for students to associate with especially attributes B and C may be foregone.

The specific definitions of the three terms in the textbooks used in grades 11–12 are shown in Table 4. The definition for the Law of Conservation of Mass is not given in the textbook authored by Burrows et al. (2013), while Silberberg (2009) stated that “The total mass of substances does not change during a chemical reaction”. Using the term “mass”, as compared to the word “atoms” used in the textbook for grades 9–10, affords the definition a more quantitatively measurable perspective. Cann and Hughes (2015) defined the said law as “The sum of the masses of all the products is always equal to the sum of the masses of all the reactants”; the use of the words “sum” and “equal” further underscores a mathematical basis behind this law. This approach can also be seen in Silberberg's (2009) definition of the Hess Law, viz. “The enthalpy change of an overall process is the sum of the enthalpy changes of the individual steps of the process”, where the word “sum” is also present. Comparatively, both Cann and Hughes (2015) and Burrows et al. (2013) emphasized on the independence of the reaction path taken in their statement for the Hess Law, but omitting the use of distinct mathematical terms; however, the mathematical nature can be argued to be present if we treat ‘enthalpy change’ as the difference in energy between two paths within a reaction or the difference in energy between the initial and final states of the system.

Analysis of the specific definitions for the various laws across all three textbooks used at grades 11–12 indicate that attribute D (the law is subject to refinement as new research findings come on board in the future) is not apparent in all the descriptions. This could be a plausible reason why students, and even teachers, tend to confuse scientific laws with laws from a jurisprudence perspective. The latter are more commonly encountered in court settings and could be the source of the misconception that scientific laws are strict rules established by scientists that have to be obeyed, aligning with legal laws created by society and governments that students and teachers (as citizens) are subjected to. In court parlance, laws are not refutable and, by extension, it may be incorrectly perceived that scientific laws are absolute and not open to scrutiny.

With respect to specific theories, the definitions found in all three textbooks used at grades 11–12 fulfil attribute A (general explanatory statements of how things work in nature) but attributes B (they are the endpoint of scientifically gathered evidence about specific events that may incorporate other laws and hypotheses) and C (they have predictive ability) are not distinctly implied. Silberberg (2009) acknowledged that theories are the intellectual constructs of scientists by using the word “model” to frame the definition of each of these theories, while Burrows et al. (2013) used the word “model” only when presenting the Kinetic-Particle Theory. Similar to the discussion on laws earlier, students are likely to cultivate the mistaken belief that scientific theories are merely ideas conjured up by scientists without appreciating the rigorous scientific process that goes into their development and formulation, which is the result of misconstruction based on the common layman understanding of theory (an unproven conjecture or an abstract thought).

From the three specific definitions of principles extracted from the textbooks, all three attributes for scientific principle are obvious: it is based on statements derived from scientific laws or theories, it is a rule that can account for how a process is believed to operate, and it is qualitative in nature. That the statement is derived from the relevant law or theory is not stated in the background information for each of the principles in the textbooks. That is, the manner of phrasing of each of the scientific principles is still scientific.

We acknowledge that the three scientific terms used in specific contexts need to be depicted in a parsimonious manner in textbooks. This could be a reason why the three terms are couched in a somewhat simple manner in the textbooks. However, we argue that there is scope for enhancing the accuracy of these definitions to some extent. Especially, the mathematical nature of laws can be better reinforced – see for example, Appendix. By appending the mathematical formalism immediately after the definition, this can go some way in reiterating the mathematical nature of laws in Chemistry rather than having to infer it from the statements in textbooks.

In respect of the analyses of specific laws, theories and principles found in Chemistry textbooks, we find that there has been generally less emphasis in the literature as compared to generic aspects of laws and theories. Of course, no textbook analyses have focused on principles. To this extent, our findings in respect of unpacking the attributes for each specific term add on to the general NOS literature on Chemistry textbooks.

Research question 3

To investigate the manner in which the textbooks used in grades 11–12 introduce relationships between laws and theories, selected statements have been extracted from the textbooks, and three exemplars were studied in more detail. The first involved establishing the connection between Boyle's, Charles’ and Avogadro's Laws to derive the ideal gas law (Table 5). Each textbook first introduced the three laws separately and, in some cases, illustrated the graphical representation of the two variables involved for the respective law. The textbook by Cann and Hughes (2015) stated that “We can combine all three influences on the volume of the gas into one relationship”, while Burrows et al. (2013) surmised that “The three experimental laws of Boyle, Charles and Avogadro link together the four variable properties of a gas, n, p, V and T”. The use of the descriptors “combine”, “relationship” and “link” implies a progressive knowledge building up process, where the information gained through scientific experiments for each of the three laws are correlated and can be dovetailed into the formulation of a single entity. On the other hand, while Silberberg (2009) acknowledged the “relationship” amongst the variables, his textbook positions the three laws as “special cases” of the ideal gas law. In doing so, it could give rise to incorrect perceptions amongst students that the ideal gas law precedes the three said laws, and that the laws are exceptions of the “all-encompassing” ideal gas law. Referring to the canonical attributes ascribable to laws, it can be seen that while these statements found in the textbooks serve to reinforce the first three attributes (A, B and C), they do not serve to highlight attributes D and E. One reason for the absence of attribute D could be that at grades 11–12, only the ideal gas scenario is considered; modifications of the ideal gas law to take into account the fact that real gases do not occupy negligible volume, for example, are not introduced until the undergraduate level.

Table 5 How the ideal gas laws are associated with other laws in Chemistry textbooks used in grades 11–12

Textbook	Statement(s) extracted from textbook
Cann and Hughes (2015)	“We can combine all three influences on the volume of the gas (referring to Boyles Law, Charles’ Law and Avogadro's Law) into one relationship”.
Silberberg (2009)	“These three laws (referring to Boyles Law, Charles’ Law and Avogadro's Law) are special cases of an all-encompassing relationship among gas variables called the ideal gas law”.
Burrows et al. (2013)	“The three experimental laws of Boyle, Charles and Avogadro link together the four variable properties of a gas, n, p, V and T”.

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For the second case, the link between gas laws and Kinetic-Particle Theory was examined (Table 6). Cann and Hughes (2015) continued from their introduction of an ideal gas by articulating that the assumptions of an ideal gas lay the foundation for the Kinetic Theory. Taking a different approach, Burrows et al. (2013) contrasted the law, which is supported by observable and measurable experiments, with theory, which is presented as based on a model developed by scientists to better understand what is happening in a molecular (and hence non-observable) manner. Differing slightly from the two previous authors, Silberberg (2009) asserted that “…the kinetic molecular theory was able to explain the gas laws that some of the great scientists of the century before had arrived at empirically”. This viewpoint embraces the relationship between the gas laws and the theory from a historical perspective; the experimentally determined gas laws preceded the mental conceptualization of the theory, with the theory further strengthened through supporting the validity of the experiments. The explanatory flow provided by Silberberg (2009) lends itself to strongly supporting attribute B (they are the endpoint of scientifically gathered evidence about specific events that may incorporate other laws and hypotheses), although all the statements from the textbooks fulfil attribute A (general explanatory statements of how things work in nature).

Table 6 How the gas laws are associated to the Kinetic-Particle Theory in Chemistry textbooks used in grades 11–12

Textbook	Statement(s) extracted from textbook
Cann and Hughes (2015)	“It is possible to derive the ideal gas from the basic principles of mechanics. The Kinetic theory of gases starts by making the following assumptions about an ideal gas…”.
Silberberg (2009)	“Developed by some of the great scientists of the 19th century, most notably James Clerk Maxwell and Ludwig Boltzmann, the kinetic molecular theory was able to explain the gas laws that some of the great scientists of the century before had arrived at empirically”.
Burrows et al. (2013)	“The ideal gas equation was obtained using an empirical approach by combining laws derived from experimental measurements. Although it allows you to look at what happens when the conditions are changed, the approach does not tell you what is happening to the molecules in the gas. Chemists need to understand process on a molecular level.
	A common approach in science is to set up a model. The first stage in developing a model is to define the basic properties of the system and then make some assumptions about its behaviour. You can use models to derive equations and develop a theory that describes the situation under study in mathematical terms – then test whether the theory matches the experimental observations. The real test of a model is that it can be used to make predictions that can be tested experimentally.
	The kinetic molecular theory of gases (often called more simply the kinetic theory) is a good example of such an approach. The theory is based on a simple model that describes gas behaviour in terms of the movement of molecules. It was developed during the nineteenth century by a number of scientists including Ludwig Boltzmann and James Clerk Maxwell”.

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The third example compares how the three theories of acids and bases are showcased relative to one another (Table 7). The limitation of the Arrhenius Theory was initially stated by Cann and Hughes (2015), who then went on to indicate the Brønsted–Lowry Theory as an improvement that overcomes the limitation. Similarly, Silberberg (2009) claimed that the Lewis definition “greatly expands the classes of acids” with respect to the Brønsted–Lowry definition. The Lewis definition is also acknowledged by Burrows et al. (2013) to be “more general” than that proposed by Brønsted and Lowry. In all three textbooks, the descriptions have a commonality of positioning the introduced theories as an entity that gives a broader perspective of the observed natural phenomenon. It is also equally important to note that in these statements, the other two acid–base theories are neither discredited nor abandoned; instead, they serve as a springboard for scientific statements that hold true under different conditions to be formulated. From the discussion of the three acid–base theories in the textbooks, it can be discerned that theories are able to explain the workings of a natural phenomenon (attribute A), albeit under different conditions where these three theories are concerned. However, attributes B and C may not be obvious to students, as the authors did not delve deeply into the context in which the three theories were derived.

Table 7 How the various acid–base theories are associated in Chemistry textbooks used in grades 11–12

Textbook	Statement(s) extracted from textbook
Cann and Hughes (2015)	“The Arrhenius Theory can only be applied to reactions in aqueous solutions. Many similar reactions take place in solvents other than water or under anhydrous conditions.
	The Danish chemists Johannes Brønsted and the English chemist Thomas Lowry were working independently but both realised that the important feature of an acid–base reaction was the transfer of a proton from an acid to a base. They therefore defined an acid as a substance that could donate a proton and a base as a substance that could accept a proton”.
Silberberg (2009)	“Obviously, an acid–base reaction (also called a neutralization reaction) occurs when an acid reacts with a base, but the definitions of these terms and the scope of this reaction class have changed considerably over the years.
	The Lewis definition, like the Brønsted–Lowry definition, requires that a base have an electron pair to donate, so it does not expand the classes of bases. However, it greatly expands the classes of acids”.
Burrows et al. (2013)	“A more general definition of acids and bases than that given by Brønsted and Lowry was proposed by Gilbert Lewis in the same year, 1923. He defined a Lewis acid as an electron pair acceptor and a Lewis base as an electron pair donor”.

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The foregoing mode of analysis with respect to RQ3 has not been reported in the NOS literature, and so is a contribution to the literature in relation to analyses of Chemistry textbooks.

Summarizing comments

Overall, the findings from our study add on to other works reported on analysis of Chemistry textbooks from different countries on NOS. While other studies focus on several tenets of NOS, including the distinction between theories and laws in some cases, those related to these terms had somewhat limited emphasis in the overall studies. In respect of laws and theories, several of the studies reinforce the point that the depiction is less than optimal (see the literature review). Our study focused solely on laws and theories, as well as principles; the latter was not covered in the textbook analyses reported in the literature.

The theoretical frameworks used in this study have been helpful in answering the RQs. The first draws on two larger NOS frameworks – that is, it relates specifically to the distinction between laws and theories (which are already there in the two common NOS frameworks) (Abd-El-Khalick et al., 1998; Erduran et al., 2019), as well as principles (which is not there in the common NOS frameworks). With the key attributes for these terms being further elucidated from Krebs (2001), and further generally supported/augmented from the philosophy literature, these have helped in the parking of the terms from the textbooks with respect to the appropriate attribute for each term. Note that two of the attributes for scientific principles (B and C) were inferred from an examination of the three specific terms (it is a rule that is able to account for how a process is believed to operate; and it is qualitative in nature). Overall, this has allowed us to see what attributes are or are not populated in the respective definitions.

The rubric used for evaluating the attributes for each term, predominantly based on Krebs (2001) and further supported/augmented from the literature (and, in the case of principle, two from an examination of the three scientific principles found in the textbooks), was found to be adequate for analysing the components constituting the three scientific terms in the school textbooks in our study, though from a philosophical perspective, there may be scope for adding a few more attributes. For example, we did not focus on the attribute that theories are constructed while laws are discovered (Dilworth, 1989) as these can be argued to be quite subjective. In any case, none of the textbooks surveyed brought out this point in relation to laws and theories. Likewise, the common perception that scientific laws are universal (Krebs, 2001) was not framed as an attribute for law as this point is debatable – see for example, Reutlinger (2011), who noted that most philosophers consider that laws in physics are universal while those in other disciplines are not. Please also see McComas (2003) for a perspective on laws and theories in Biology.

Implications

The findings from this study can possibly provide information to Chemistry textbook authors, curriculum developers and teachers about the areas for concern, as well as the support required for high school students to achieve higher NOS literacy levels, in particular deepening their understanding of the scientific terms law, theory and principle. Textbooks remain a prominent part of science instruction and play an integral role in helping students and teachers develop their overall perceptions of NOS. Our study has also highlighted that relatively few of the Chemistry textbooks used by high school students and teachers in the country represent laws, theories and principles at a generic level adequately. There appears to be a high emphasis on scientific terminology and definitions, with little or no elaboration on how a particular term is embedded in the wider scientific context. Hence, there is a need for textbook authors to consider incorporating a structure to help readers better understand the underpinnings behind laws, theories and principles. For example, it could be highlighted that the various laws under the topic of gases such as Boyle's Law, Charles’ Law, and Avogadro's Law have permitted the quantitative relationship among the number of moles, volume, temperature, and pressure (along with Molar Gas Constant) of a gas to be established into an equation that has also predictive utility. A deeper comprehension of how theories and principles are developed also plays an important role – for example, understanding the behaviour of gases in terms of the Kinetic Theory as well as predicting shifts of equilibrium between two gases (such as N₂O₄ and NO₂) in response to an external imposition, with the use of Le Chatelier's Principle. Importantly, some background information on the origins of the various laws, theories and principles would be useful and indeed can help students better connect with the content taught. This need not be comprehensive but can be expressed succinctly in a paragraph or so.

It is understandable for textbook authors to opt for simple treatments of NOS terms such as theories, laws and principles than to focus on rigorous exploration of these terms. However, we feel that the level of rigor needed would be rather modest if one considers that these would help students to better connect with the terms.

Curriculum developers and teachers play an important role in upholding science as a manner of thinking, emphasizing on how scientists develop and improve scientific knowledge, including how laws, theories and principles are established and evolved as part of the scientific endeavour. For the latter objective to succeed, getting students to distinguish between laws, theories, and principles in Chemistry from more fundamental considerations needs to be embedded as a core part of the syllabus as well as promoted as an integral part of teaching and learning. By doing so, curriculum developers and teachers would then be sending a clear message to textbook authors that such content must be included in future editions. Our study has indicated that this content is currently not included in most of the textbooks, presumably because textbook authors feel that it is the teachers’ role to fulfil this objective, or that this is the responsibility of authors of textbooks meant for higher grade levels. The nature of textbooks is to document the content in a systematic and coherent manner, but this is also a clear disadvantage as knowledge is not constructed and internalized in a methodical fashion. Teachers will have to use materials from textbooks more judiciously and provide additional support to help students establish relationships between specific terms that may cut across pre-designated content chapters – for example, by intentionally drawing students’ attention to previously covered content (for example, the ideal gas law) so as to associate with, or compare and contrast, with material that is just being learnt (Le Chatelier's Principle involving gaseous systems).

Understanding the differences among laws, theories, and principles can help to better support students' development of chemistry concepts. Students should not have the impression that chemistry concepts are merely a bunch of facts to memorise and regurgitate in examinations but develop an appreciation that many of these concepts have fundamental underpinnings under the ambit of laws, theories and principles. For example, under the topic of gases, it's the various laws such as Boyle's Law, Charles’ Law, and Avogadro's Law that have permitted the quantitative relationship between moles, temperature, and pressure (along with gas molar constant) of a gas to be established into an equation that has predictive utility. By getting students to distinguish among laws, theories and principles in Chemistry from more fundamental considerations, teachers can help to ensure that students do not just apply these terms from a textbook perspective in problem-solving situations but also more from an informed perspective.

Teachers face considerable challenges in infusing NOS concepts in students, chief of which is curriculum time. It seems to us that since the full suite of scientific terms such as laws, theories and principles have been part of the Chemistry curricula, especially at high school, for a long time, it would require incremental effort of a nominal nature to explicate the differences among these terms from a general perspective to students. Lederman et al. (2014) have suggested that while NOS is complex in nature, the key considerations, especially for K-12 education, are to see what relevant contexts can be included in the curricula. Inspection of the attributes for scientific laws, theories and principles in the Methodology section suggests that these are short and concise, and can be included in textbooks when describing laws, theories and principles from a general perspective. Perhaps occupying a page or so in textbooks, they are generally within the comprehension level of students and afford opportunities for further instructional elaboration during classroom teaching.

The literature suggests that even teachers’ understanding of NOS (for example, Demirel et al., 2023), including terms such as laws and theories, is not adequate. This indicates that professional development programs on NOS which focus in some depth on the three terms can equip them to be more effective when teaching these concepts to students.

In the frameworks of NOS studies, there is pronounced emphasis on theories and laws. The findings from our study suggest that scientific principles can also be included in these frameworks since it is part of the scientific tradition.

Limitations

When interpreting the results of this study, two limitations need to be taken into consideration. Firstly, this study analyzed only four Chemistry textbooks commonly used in the country. Therefore, the results and discussion are not extendable to other textbooks, which may give a more different range of definitions. Future research could explore analysis of textbooks used at the undergraduate level. Secondly, the focus of this research is on content drawn from the textbooks and does not investigate how the content is used by teachers and students. Thirdly, at high school, teachers have also the flexibility to use other textbooks to curate notes; examining these is beyond the scope of our study. Teachers play an important role in the interpretation of instructional materials which, in turn, will affect how students perceive and learn about NOS. How teachers utilize and present the content found in the textbooks to their students can be the scope for further work.

Conclusions

While other chemistry education studies have explored how the general NOS framework is represented in textbooks, our study has focused on investigating how scientific laws, theories and principles are depicted in Chemistry textbooks used by students in grades 9–12 in Singapore. While scientific principles are an integral part of the Chemistry curriculum at the high school level, this term has not been well studied in the literature. By matching the generic and specific definitions found in the textbooks to the canonical attributes for this and the other two terms, we found that the textbooks do not provide generic definitions, and some of the attributes are not apparent even in the specific definitions. As a result, students may develop inadequate conceptions or even misconceptions about these terms. Also, interesting insights have been obtained when we explored associations between related laws and theories in the textbooks, even though we used only three examples. Textbooks remain one of the most important science teaching resources, and our study indicates a need for textbook authors, allied with curriculum developers and teachers, to reflect on the relationships and distinctions between scientific laws, theories and principles more clearly in future editions so as to promote greater NOS literacy for students and teachers.

In summary, the contributions of this study to the Chemistry (and science) education literature are as follows:

1. It explored the scientific terms laws, theories and principles generically as well as specifically from the perspective of Chemistry textbooks used by students in Singapore. This complements previous literature on analysis of NOS (including on laws and theories) in textbooks used by students in other countries such as the USA, China and Finland.

2. Despite scientific principles being considered in tandem with laws and theories in standard scientific treatises, scientific principles have not really been explored in NOS studies in the chemistry (and science) education literature, either in textbook analyses or as part of overall NOS studies. Our study sought to bridge this gap in the literature.

3. The analysis of the terms in the textbooks was matched with the key canonical attributes for these terms to uncover the extent of mapping. This approach, which has not been utilized in the chemistry education literature, has led to a deeper understanding of how these are portrayed.

4. The associations between related laws and theories portrayed in the textbooks, through the examination of three examples, is another aspect that has shed useful insights.

Conflicts of interest

There is no conflict of interest to disclose.

Appendix

Suggested approach for framing laws in high school Chemistry textbooks

Term	Name	How it is stated or defined
Law	Law of conservation of mass	Mass can neither be created nor destroyed but it can be transformed from one form to another. For example, in the case of a chemical reaction, mass of reactants = mass of products
	Dalton's Law	The total pressure (Pt) exerted by a mixture of gases is equal to the sum of the partial pressures (P1, P2, ….) of each of the constituent gases. That is, Pt = P1 + P2 +
	Boyle's Law	At constant temperature, the pressure (P) of a gas varies inversely with its volume (V). That is, P ∝ 1/V.
	Charles Law	At constant temperature, the volume of a gas (V) will be directly proportional to its absolute temperature (T). That is, V ∝ T.
	Avogadro's Law	Equal volumes of all gases, at the same temperature and pressure, contain the same number of molecules. That is V ∝ n, where n is the number of moles (also proportional to number of molecules)
	Ideal gas law	The product of pressure (P) and volume (V) of one mole of an ideal gas is equal to the product of absolute temperature (T) of the gas and universal gas constant (R). That is, PV = RT
	Hess Law	The overall enthalpy change (ΔH) for a chemical reaction is equal to the sum of the enthalpy changes of the individual steps (ΔH1, ΔH2, ΔH3,…). That is, ΔH = ΔH1 + ΔH2 + ΔH3 + ….

Acknowledgements

We thank the two reviewers for useful comments on an earlier version of this manuscript. This research received no funding. The views expressed in the paper are those of the authors and do not necessarily represent the views of the institutions to which the authors are affiliated with or any of the national agencies mentioned.

References

1. Abd-El-Khalick F., (2012), Examining the sources for our understandings about science: enduring conflations and critical issues in research on nature of science in science education, Int. J. Sci. Educ., 34(3), 353–374 DOI:10.1080/09500693.2011.629013.
2. Abd-El-Khalick F., Bell R. L. and Lederman N. G., (1998), The nature of science and instructional practice: making the unnatural natural, Sci. Educ., 82, 417–437 DOI:10.1002/(SICI)1098-237X(199807)82:4[double bond splayed right]417::AID-SCE1[double bond splayed left]3.0.CO;2-E.
3. Abd-El-Khalick F., Waters M. and Le A. P., (2008), Representations of nature of science in high school Chemistry textbooks over the past four decades, J. Res. Sci. Teach., 45(7), 835–855 DOI:10.1002/tea.20226.
4. Aydin S. and Tortumlu S., (2015), The analysis of the changes in integration of nature of science into Turkish high school Chemistry textbooks: is there any development? Chem. Educ. Res. Pract., 16(4), 786–796 10.1039/C5RP00073D.
5. Burrows A., Holman J., Parsons A., Pilling G. and Price. G., (2013), Chemistry: Introducing Inorganic, Organic and Physical Chemistry, 2nd edn, Oxford: Oxford University Press.
6. Caldin E. F., (2002), The structure of chemistry, Int. J. Phil. Chem., 8, 103–121.
7. Cann P. and Hughes P., (2015), Cambridge International AS and A Level Chemistry, Cambridge: Hodder Education.
8. Carey S. S., (1994), A Beginner's Guide to Scientific Method, Belmont, CA: Wadsworth Publishing Company.
9. Chang M., Chew A., Sadler J., Tan Y. T., Wong H. V. and Woo, C. H., (2023), Chemistry Matters, Singapore: Marshall Cavendish Education.
10. Chen S., (2006), Development of an instrument to assess views on nature of science and attitudes toward teaching science, Sci. Educ., 90(5), 803–819 DOI:10.1002/sce.20147.
11. Chen B., Chen S., Liu H. and Meng X., (2022), Examining the changes in representations of nature of science in Chinese senior high school Chemistry textbooks, Sci. Educ., 1–20 DOI:10.1007/s11191-022-00383-7.
12. Christie M., (1994), Philosophers versus Chemists concerning “Laws of Nature”, Studies in History and Philosophy of Science, 25, 613–629 DOI:10.1016/0039-3681(94)90050-7.
13. Christie M. and Christie J. R., (2000), Laws and theories in chemistry do not obey the rules. Of Minds and Molecules: New Philosophical Perspectives on Chemistry, 34–50.
14. Christie J. R. and Christie M., (2003), Chemical laws and theories: a response to Vihalemm, Found. Chem., 5(2), 165–174 DOI:10.1023/A:1023631726532.
15. Demirel Z. M., Sungur S. and Çakıroğlu J. (2023), Science teachers’ views on the nature of science and its integration into instruction, Sci. Educ., 32(5), 1401–1433 DOI:10.1007/s11191-022-00409-0.
16. Dilworth C., (1989), On the nature of scientific laws and theories, Zeitschrift für Allgemeine Wissenschaftstheorie, 20, 1–17 DOI:10.1007/BF01801399.
17. Dilworth C., (1994), Principles, laws, theories and the metaphysics of science, Synthese, 101(2), 223–247.
18. Dilworth C. and Cohen R. S., (2006), The Metaphysics of Science: An Account of Modern Science in Terms of Principles, Laws, and Theories, Dordrecht: Springer.
19. Eastwell P., (2014), Understanding hypotheses, predictions, laws, and theories, Sci. Educ. Rev., 13(1), 16–21.
20. Erduran S., Dagher Z. R. and McDonald C. V., (2019), Contributions of the family resemblance approach to nature of science in science education: a review of emergent research and development. Sci. Educ., 28, 311–328 DOI:10.1007/s11191-019-00052-2.
21. Faye J., (2005), How nature makes sense, Nature's Principles, Dordrecht: Springer Netherlands, pp. 77–102.
22. Galili I., (2019), Towards a refined depiction of nature of science: applications to physics education, Sci. Educ., 28(3–5), 503–537 DOI:10.1007/s11191-019-00042-4.
23. Hempel C. G., (1970), On the standard conception of scientific theories, Analyses of theories and Methods of Physics and Psychology, Minnesota studies in the philosophy of science, 4, pp. 142–163.
24. Izci K., (2017), Nature of science as portrayed in the middle school science and technology curriculum: The case of Turkey, Journal of Education in Science, Environment and Health, 3(1), 14-28.
25. Krebs R. E., (2001), Scientific Laws, Principles, and Theories: A Reference Guide, London: Greenwood Press.
26. Larison K. D., (2018), Taking the scientist's perspective. Sci. Educ., 27, 133–157 DOI:10.1007/s11191-018-9957-z.
27. Lederman N. G., Abd-El-Khalick F., Bell R. L. and Schwartz R. S., (2002), Views of nature of science questionnaire: toward valid and meaningful assessment of learners' conceptions of nature of science, J. Res. Sci. Teach., 39(6), 497–521 DOI:10.1002/tea.10034.
28. Lederman N. G., Bartos S. A. and Lederman J. S., (2014), The Development, Use, and Interpretation of Nature of Science Assessments, in M. R. Matthews (ed.), International Handbook of Research in History, Philosophy and Science Teaching. Dordrecht: Springer Science + Business Media, pp. 971–997 DOI:10.1007/978-94-007-7654-8_29.
29. Lin H. S. and Chen C. C., (2002), Promoting preservice chemistry teachers' understanding about the nature of science through history, J. Res. Sci. Teach., 39(9), 773–792 DOI:10.1002/tea.10045.
30. Lotka A. J., (1922), The general conditions of validity of the Principle of Le Chatelier, Proc. Amer. Acad. Arts Sci., 57 (2), 21–37.
31. Marniok K. and Reiners C. S., (2017), Representations of nature of science in German school chemistry textbooks, in Mcdonald C. V. and Abd-El-Khalick F. (ed.), Representations of nature of science in school science textbooks, Routledge, pp. 201–214.
32. Massimi M., (2005), Pauli's Exclusion Principle: The Origin and Validation of a Scientific Principle, Cambridge University Press.
33. McComas W. F., (2003), A textbook case of the nature of science: Laws and theories in the science of biology, Int. J. Sci. Math. Educ., 1, 141–155.
34. McMullin E., (1984), Two ideals of explanation in natural science, Midwest Stud. Phil., 9, 205–220.
35. Mitchell S. D., (2000), Dimensions of scientific law. Philos Sci., 67(2), 242–265.
36. Next Generation Science Standards (NGSS), (2013), The next generation science standards. Retrieved from https://www.nextgenscience.org/next-generation-science-standards.
37. Niaz M., Maza A., Niaz M. and Maza A., (2011), Nature of science in general Chemistry textbooks, Netherlands: Springer, pp. 1–37.
38. Nickles T., (2002), Scientific Laws, Principles, and Theories: A Reference Guide, Chicago: University of Chicago Press, pp. 172–173.
39. Olson J. K., (2018), The inclusion of the nature of science in nine recent international science education standards documents, Sci. Educ., 27(7–8), 637–660 DOI:10.1007/s11191-018-9993-8.
40. Park B. S. and Stetten Jr D., (2001), A principle written in diagrams: The Aufbau principle for molecules and its visual representations, 1927–1932, Tools and Modes of Representation in the Laboratory Sciences, Dordrecht: Springer Netherlands, pp. 179–198.
41. Pauli W., (1964), Nobel Lecture, in Nobel Lectures, Physics, Amsterdam: Elsevier, pp. 1942–1962.
42. Pauling L., (1964), General Chemistry, San Francisco: Freeman.
43. Reutlinger A., (2011), A theory of non-universal laws, Int. Stud. Phil. Sci., 25(2), 97–117.
44. Scerri E. R., (1997), Has the periodic table been successfully axiomatized? Erkenntnis, 47(2), 229–243.
45. SEAB (Singapore Examinations and Assessment Board), (2022a), Singapore–Cambridge General Certificate of Education Ordinary Level; Chemistry (Syllabus 6092). Access from https://www.seab.gov.sg/docs/default-source/national-examinations/syllabus/olevel/2022syllabus/6092_y22_sy.pdf.
46. SEAB (Singapore Examinations and Assessment Board), (2022b), Singapore–Cambridge General Certificate of Education Advanced Level Higher 2; Chemistry (Syllabus 9729). Access from https://www.seab.gov.sg/docs/default-source/national-examinations/syllabus/alevel/2022syllabus/9729_y22_sy.pdf.
47. Silberberg M. S., (2009), Chemistry: The Molecular Nature of Matter and Change, 5th edn, Singapore: McGraw-Hill Higher Education.
48. Singh K., (2023), Science Laws and Their Applications, Cambridge Scholars Publishing.
49. Upahi J. E., Ramnarain U. and Ishola I. S., (2020), The nature of science as represented in Chemistry textbooks used in Nigeria, Res. Sci. Educ., 50, 1321–1339 DOI:10.1007/s11165-018-9734-7.
50. Van Brakel J., (2001), The world: an unruly mess, Found. Chem., 3(3), 251–262.
51. Vesterinen V. M., Aksela M. and Lavonen J., (2013), Quantitative analysis of representations of nature of science in Nordic upper secondary school textbooks using framework of analysis based on philosophy of chemistry, Sci. Educ., 22, 1839–1855 DOI:10.1007/s11191-011-9400-1.
52. Zarei E. and Hossein Nia R., (2023), Analysis of high school Chemistry textbooks used in Iran for representations of nature of science, Interchange, 54(2), 253–270 DOI:10.1007/s10780-023-09490-y.
53. Zhu Y. and Tang A., (2023), An analysis of the nature of science represented in Chinese middle school Chemistry textbooks, Int. J. Sci. Educ., 45(4), 314–331 DOI:10.1080/09500693.2022.2160939.

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