Experienced Teachers’ Pedagogical Content Knowledgeof Teaching Acid–base Chemistry

Michal Drechsler & Jan Van Driel

Published online: 2 November 2007# Springer Science + Business Media B.V. 2007

Abstract We investigated the pedagogical content knowledge (PCK) of nine experiencedchemistry teachers. The teachers took part in a teacher training course on students’ difficultiesand the use of models in teaching acid–base chemistry, electrochemistry, and redox reactions.Two years after the course, the teachers were interviewed about their PCK of (1) students’difficulties in understanding acid–base chemistry and (2) models of acids and bases in theirteaching practice. In the interviews, the teachers were asked to comment on authentic studentresponses collected in a previous study that included student interviews about theirunderstanding of acids and bases. Further, the teachers drew story-lines representing theirlevel of satisfaction with their acid–base teaching. The results show that, although all teachersrecognised some of the students’ difficulties as confusion between models, only a few choseto emphasise the different models of acids and bases. Most of the teachers thought it wassufficient to distinguish clearly between the phenomenological level and the particle level.The ways the teachers reflected on their teaching, in order to improve it, also differed. Someteachers reflected more on students’ difficulties; others were more concerned about their ownperformance. Implications for chemistry (teacher) education are discussed.

Keywords Pedagogical content knowledge . Models . Acids and bases .

Upper secondary school

Introduction

It is widely acknowledged that chemistry is highly demanding for students. The topic ofacids and bases is one of the most fundamental in chemistry curricula. It is also recognisedfrom everyday life in the contexts of, for instance, food, industry, healthcare, environmental

Res Sci Educ (2008) 38:611–631DOI 10.1007/s11165-007-9066-5

DO9066; No of Pages

Submitted to Research in Science Education

M. Drechsler (*)Department of Chemistry, Karlstad University, Universitetsgatan 1, Karlstad, Swedene-mail: michal.drechsler@kau.se

J. Van DrielGraduate School of Teaching, ICLON, Leiden University, Leiden, The Netherlands

issues, and drugs. Further, acids are sometimes used in the media, such as in movies andhorror stories. The history of the scientific development of acids and bases goes mainly froma phenomenological to a particulate abstract level. At the phenomenological level, acid–basereactions can be described using formula equations as reactions between substances, and at anabstract particulate level using ionic equations as proton-transfer reactions, according toBrønsted’s model. Both levels are introduced in chemistry teaching at Swedish secondaryschools, which gives teachers a good opportunity to discuss the use of different models toexplain phenomena in a historical perspective. Research has shown, however, that acids andbases are difficult for students to understand (cf. Demerouti et al. 2004). Research has alsoshown that textbooks are unclear when describing this area (cf. Carr 1984). Little is knownabout how experienced teachers teach acids and bases. Even in the survey of chemistryteachers’ knowledge base by De Jong et al. (2002) the domain of acids and bases are notexplicitly mentioned. One notable exception is a study by Banerjee (1991) where chemistryteachers’ misconceptions in different areas of chemical equilibrium were investigated. Itwas found that the teachers had similar and widespread misconceptions as students in areasrelated to the prediction of equilibrium conditions, rate and equilibrium, applyingequilibrium principles to daily life, and to acid–base and ionic solutions in water. Further,research has also revealed that teachers’ knowledge about models in general in science anduse of these models varies (cf. Van Driel and Verloop 1999, 2002).

In secondary schools, teachers’ knowledge is strongly related to the subject taught (Meijeret al. 1999). In this respect, Shulman introduced pedagogical content knowledge (PCK) as aform of teachers’ special practical knowledge needed to help students understand specificcontent (Schulman 1987). According to Grossman (1990), there are three main domains –subject matter knowledge, pedagogical knowledge, and context knowledge – that influenceteachers’ PCK. Magnusson et al. (1999) developed the concept of PCK further, describingPCK as a “mixture” or “synthesis” of five different types of knowledge: orientation towardscience teaching, knowledge of science curriculum, knowledge of science assessment,knowledge of students’ understanding, and knowledge of instructional strategies.

In this study, nine experienced chemistry teachers were interviewed to explore their PCKabout acid–base chemistry. Below, the literature on the theoretical background to this studyis first discussed: this concerns the role of models in teaching acids and bases, as well as thenature of pedagogical content knowledge. Next, the context and the design of the study aredescribed. Finally, the empirical parts of the research project are reported.

Background

Models in Science Education

Models are an important aspect of the development of scientific knowledge. Models linktheories with a target – a system, an object, a phenomenon, or a process; they are parts oftheories scientists develop to explain some aspects of the world-as-experienced (Gilbertet al. 2000). In the course of history, scientists have come up with different answers to andexplanations of scientific questions. This has led to the development of different scientificmodels over time. These models are often the products which we aim to teach to students inupper secondary school. Knowledge of models and their use, and recognition of theirlimitations, would allow students to gain a better understanding both of scientificknowledge and of the nature of science; that is, how scientific knowledge is achieved.However, teachers and textbooks are not always explicit about the use of models. Van Driel

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and Verloop (1999, 2002) found that teachers’ views on models are often narrow andincongruous. Further, textbooks do not always use specific models, but transfer attributesfrom one model to another, resulting in hybrid models that might be difficult to teach and tolearn (Justi and Gilbert 2000).

A scientific concept is usually first explained to students using a simple, often older,model. Later, students are introduced to more sophisticated, often newer, models. Justi andGilbert (2002) report that students might be confused when a new model is introduced, andthus combine attributes from different models. It is, therefore, important to discuss thedifferences between the models presented and clearly explain why the new model isintroduced. According to Boulter and Gilbert (2000), it is also important that, in addition tolearning about models and their uses, students recognise their limitations in science. Thisallows students to gain a better understanding of both the facts and the nature of science.The students may realise that a phenomenon can be explained in different ways, that is, thatseveral models can be used for the same target.

Students’ Difficulties in Understanding Acid–base Models

The area of acids and bases is amongst the most fundamental in chemistry curricula. Duringthe development of chemistry, acids and bases have been explained in several ways. Newmodels have been introduced with the aim of giving better descriptions of naturalphenomena. The definitions of the concepts of acids and bases have evolved from aphenomenological level to an abstract level. In secondary school curricula, three distinctmodels can be identified. These models are (a) the ‘ancient’ model, (b) the Arrheniusmodel, and (c) the Brønsted model. In this section, first, these three models are brieflyreviewed. Second, the literature on students’ difficulties in understanding especially theBrønsted model is discussed. Finally, a possible cause of students’ difficulties, thepresentation of acids and bases in chemistry textbooks, is discussed.

(a) At the phenomenological level, acids can be defined using the ancient model, or Boylemodel, in terms of their properties; for example, they have a sour taste, aqueoussolutions of acids turn blue litmus red, they neutralise bases. Acids have also beenknown to react with non-precious metals and carbonates. The opposite of acids, alkaliswere recognised by their soapy feeling and, most importantly, their ability to destroy(neutralise) the properties of acids in a reaction where salts were formed. Alkalis couldalso turn red litmus blue. At the end of the 18th century, bases were defined as anysubstance that formed a salt during a reaction with an acid (Oversby 2000).

(b) The Arrhenius model explains acids on the phenomenological level and on the particlelevel. In this model, acidic properties are connected with the hydrogen ion (H+); thehigher the concentration of H+ ions, the more acidic the solution. Acids are defined assubstances that can produce H+ ions in a water solution. Bases are definedanalogously as substances that in water solution produce hydroxide ions (OH−). In areaction between an acid and a base – neutralisation – hydrogen ions from the acidreact with hydroxide ions from the base, forming water (Arrhenius 1903):

Hþ þ Cl�ð Þ þ Naþ þ OH�ð Þ ! Naþ þ Cl�ð Þ þ HOH ð1Þ

or, simplified, (when hydrogen and hydroxide ions have already been produced)

Hþ þ OH� ! HOH ð2Þ

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(c) At the abstract level, or particle level, acidic properties are explained as proton transferbetween particles, that is, molecules or ions. Brønsted defined acids and bases asparticles, such as molecules or ions. Further, the Brønsted model is not limited towater as a solvent. In this model, acids are defined as particles that donate protons,while bases are defined as particles that accept protons. Hence, the Brønsted modelcan be used to explain more bases and is more generally applicable than the Arrheniusmodel. When an acid donates a proton it becomes a base. An acid and a base that areconnected in this way are said to be conjugating, or are termed an acid–base pair. If,for example, the acid HA donates a proton, the base A− remains. If the base B− acceptsa proton, the acid HB is formed. This makes it easier to interpret the acidity of theresulting solution in an acid–base reaction. According to Brønsted, a proton transfercan be written in general terms as follows:

acid1 þ base2! base1 þ acid2 ð3Þ

or as an ionic equation

HAþ B�! A� þ HB ð4ÞResearch has shown that students have difficulties in understanding the Brønsted model.

For instance, Ross and Munby (1991) and Nakhleh (1994) reported that upper secondarystudents were unable to fully understand the acid–base chemistry because they haddifficulties in understanding acids and bases as ions. Rayner-Canham (1994) and Demeroutiet al. (2004) showed that students, although they were expected to understand Brønstedmodel, were more familiar with the Arrhenius model, and that they did not use the Brønstedmodel to explain the properties of acids and bases. Schmidt and Volke (2003) found thatstudents had problems accepting water as a base. These difficulties might be the result of afailure to inform students clearly about the benefits of introducing the more complexBrønsted model, such as the concept of conjugating acids and bases. Drechsler and Schmidt(2005b) reported that students confused attributes from different models when asked toexplain an acid–base reaction. Further, they did not understand the differences between theArrhenius and the Brønsted model.

Carr (1984) suggested that students’ difficulties in understanding acids and bases mayoriginate from confusion about the models used in teaching. He pointed out that universitytextbooks confused the Arrhenius and the Brønsted acid–base models without discussing thatthey are actually two different models. No explanation was provided in the introduction of a newmodel, and it was not shown how the newmodel differed from the previous one. Oversby (2000)stated that the three textbooks for A-level (age 16) in his survey explained different acid–basemodels but lacked a discussion about the strengths and limitations of each model. Further, inthe application sections, the books did not refer to any specific model, and the models wereused as facts. De Vos and Pilot (2001) divided the acid–base concept into six different layers orcontexts: craft, synthesis, analytical, Arrhenius, Brønsted, and application contexts. Theauthors showed that, in many modern textbooks, these layers are not well connected and aresometimes inconsistent with each other. As a result, chemistry teachers and students areconfronted with incoherent acid–base models which are difficult to teach and to learn.

Drechsler and Schmidt (2005a) showed that textbooks used these models implicitly.Further, different models were used indiscriminately, and hybrid models were oftenconstructed. Further, since Drechsler and Schmidt (2005a) and Furió-Más et al. (2005)showed that teachers use textbooks as a source of knowledge, the confusion about themodels in the textbooks may be propagated in teaching, causing students difficulty in

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understanding this area. Furió-Más et al. (2005) and Gericke and Drechsler (2006) alsoshowed that textbooks introduce new models in a non-problematic way, and have a linear,cumulative view of models of acids and bases, as if there were no conceptual gaps betweenthe different models. This suggests that scientific knowledge grows linearly and isindependent of context, and no progression between the models can be seen. Instead, theway models are used suggests that different models of a phenomenon constitute a coherentwhole; that is, different models are seen as different levels of generalisation. In this way,attributes from a simpler or older model would be valid in all later models as well.According to Justi (2000), this idea could lead to learning problems among students.

Teachers’ Pedagogical Content Knowledge

Pedagogical content knowledge (PCK) was first introduced by Shulman (1986) as a form ofteachers’ special practical knowledge; describing teachers’ capacity to help studentsunderstand specific content. According to Shulman, the key elements of PCK are (a)knowledge of representations of subject matter and (b) understanding of specific learningdifficulties. In a later article, Schulman (1987) included PCK in “the knowledge base forteaching.” This knowledge base consisted of three content-related categories (contentknowledge, PCK, and curriculum knowledge) and four categories related to generalpedagogical knowledge (learners and their characteristics, educational contexts, andeducational purposes). In terms of the features integrated, the concept of PCK has beenfurther elaborated by several scholars. Grossman (1990) identified three main domains –subject matter knowledge, Pedagogical knowledge, and Context knowledge – that influenceteachers’ PCK. Magnusson et al. (1999) proposed that the concept of PCK could bedescribed as a “mixture” or “synthesis” of five different types of knowledge: (a) orientationtoward science teaching, (b) knowledge of science curriculum, (c) knowledge of scienceassessment, (d) knowledge of students’ understanding, and (e) knowledge of instructionalstrategies. Carlsen (1999) suggests that the dynamic nature of PCK should be emphasisedand that PCK should not be seen as a static body of knowledge. According to Van Driel et al.(1998), two key elements of PCK are essential in all research about teachers’ knowledge.These elements are (1) teachers’ knowledge about specific conceptions and learningdifficulties with respect to particular content and (2) teachers’ knowledge aboutrepresentations and teaching strategies. These are the same as Shulman’s key elementsand are also the components of PCK that were investigated in this study. According to DeJong et al. (2005), these two components are intertwined and should be used in a flexiblemanner. The more teachers know about students’ difficulties with a certain topic, and themore strategies they have at their disposal, the more effectively they can teach the topic.

To promote teachers’ development of their PCK over time, the most important aspectsreported are disciplinary education (Sanders et al. 1993) and classroom teaching experience(Van Driel et al. 2002). The impact of teachers’ classroom teaching experience is enhancedby reflections on their own teaching (Osborne 1998). In order to capture the complexity anddiversity of teachers’ PCK for specific subjects, several authors have suggested that a multi-method design with triangulation should be applied (e.g., Kagan 1990; Baxter andLederman 1999). Narrative methods such as the story-line method were used to capture thedevelopment of teachers’ knowledge by Beijaard et al. (1999). Loughran et al. (2004)developed a combination of Content Representation (CoRe) and Pedagogical andProfessional-experience Repertoires (PaP-eRs). These should help experienced teachers toenhance their understanding of their own practice and pre-service teachers to better linkteaching and meaningful learning.

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Context and Research Questions

In a previous study, we reported that not all chemistry teachers in our sample were aware ofmodels of acids and bases older than the Brønsted model (Drechsler and Schmidt 2005a).Since the aim of this study was to examine the use of Brønsted and older acid–base modelsin teaching practice, we needed a sample of teachers that were aware of these variousmodels. Upper secondary chemistry teachers that had participated in a teacher trainingcourse arranged by our university 2 years earlier were interviewed. In that course, students’difficulties and the use of models in acid–base chemistry, electrochemistry, and redoxreactions had been discussed. Several papers reporting students’ difficulties in these areaswere discussed (e.g., Schmidt 1997). Further, a paper by Van Driel and Verloop (1999) wasused in discussions about the characteristics of a model. The teachers also analysedtextbooks in order to find examples of model confusion in the chapters about acids andbases, and redox reactions. The aim was not to provide the teachers with new teachingstrategies, but to make them aware (a) that students’ difficulties in understanding sometimesresulted from inconsistencies in their teaching, and (b) of the role of models in science andscience education. The teachers were interviewed about 2 years after the course. Nointerventions took place in these 2 years, but each school year the teachers had at least oneopportunity (perhaps more, depending on their school) to try out new ways of teachingacids and bases, using ideas they got from the course.

The aim of this study was to investigate (1) teachers’ knowledge of students’ difficultiesin understanding acid–base chemistry and (2), teachers’ knowledge of teaching strategies,especially their use of models of acids and bases in their teaching practice. Several studieshave, however, reported discrepancies between teachers’ intentions and what actuallyhappens in the classroom. For instance, Matthijsen (2006) suggested two different aspectsthat might explain these differences: (a) the nature of the belief, the more abstract a belief is,the more likely there will be discrepancy with practice, (b) educational context and personalcharacteristics, including general factors and resources such as time available which mayplace serious constraints on the way teachers translate their beliefs into practice.

Research Questions

1. What is the content of experienced teachers’ PCK about students’ difficulties inunderstanding acids and bases?

2. What is the content of experienced teachers’ PCK of teaching strategies they consideruseful to help students overcome such difficulties; in particular, do they intend to usemodels of acids and bases in their teaching?

3. How did the teachers perceive their PCK of teaching acids and bases develop untilnow?

Materials and Methods

Sample

All teachers from the course mentioned above were contacted by the first author, and nine(out of 11) volunteered to be interviewed. They were from different parts of southern andcentral Sweden. They are referred to here as T1–T9. The descriptions of the teachers aresummarised in Table 1.

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Procedure

A semi-structured interview was designed according to Kvale (1996). It consisted of threedistinct phases: the briefing and warm-up phase at the beginning, the main phase, and thedebriefing phase at the end. Briefing and debriefing were not tape-recorded. In the briefingphase the interviewer explained the purpose and the procedure of the interview (duration,use of audio recorder, etc.). The teachers gave permission for use of the tape recordings forresearch purposes and were assured about their right to withdraw from the interview at anytime. In the warm-up phase the teacher training course was discussed. The teachers werequestioned about what they remembered from the course, why they remembered thoseparticular parts, and if and how the material from the course was implemented in their dailywork. The latter part of the warm-up phase constituted a natural transition to the mainphase, which consisted of four parts. First, the teachers were asked about their planning ofan acid–base lecture sequence and about how they changed their teaching from year to year.Second, the textbooks the teachers used were discussed, and the teachers were asked tocomment on excerpts from the books (see Appendix 2). The teachers were asked if theyused the paragraph/equation/example in their teaching. They were also asked to explainwhy they used it and how they thought students understood it. Third, students’ thoughts anddifficulties regarding acids and bases were discussed. The teachers were asked to commenton authentic responses from students that were collected in an earlier study (Drechsler andSchmidt 2005b). The teachers were asked (a) if they recognised the statements from theirown teaching, (b) how they would handle a student who came up with such statement, and(c) how they thought the student had got these ideas. The teachers were also asked whetherthey thought students understood why different models are used and if students knew thedifferences between the models (see Appendix 1). Finally, to complement the data, theteachers were asked to draw story-lines in which they described how their level ofsatisfaction with teaching acids and bases had developed over the years. The story-linemethod (Gergen 1988) has been used before to address teachers’ PCK (Beijaard et al.1999). By reviewing the use of the story-line method in studies on experienced teachers’practices and events in their careers Beijaard et al. (1999) concluded that the story-linemethod was helpful in respect of evaluating changes through individual teachers’ careersregarding a certain aspect of teaching. In the present study, teachers were asked to drawstory-lines in connection with the main phase of the interviews. In the story-lines, theteachers described how their level of satisfaction with teaching acids and bases had

Table 1 Description of the teachers interviewed in this study

Teacher Sex Age Years ofexperience

Type ofschool

Number ofcolleagues

Also teaching secondsubject

T1 Male 35–40 10 Small 0 MathematicsT2 Male ∼50 20–25 Medium 3 MathematicsT3 Female >60 >25* Medium 3 MathematicsT4 Male >60 >25 Medium 3 BiologyT5 Male ∼50 20–25 Large 8 MathematicsT6 Male 35–40 10 Medium 3 MathematicsT7 Female ∼50 20–25 Medium 2 BiologyT8 Male >60 >25 Medium 3 BiologyT9 Female 35–40 10 Medium 2 Mathematics

*(15 in upper secondary school)

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developed over the years. A rudimentary form of a story-line consists of progressive, flatand/or regressive lines, with which many combinations and variations can be constructed.The teachers graded (on a five-point scale where 1 was considered very dissatisfied, 3neutral, and 5 very satisfied) how satisfied they were with their teaching of acids and bases,at the present. Then the teachers constructed the story-line from the present to the past. Bystarting from the present, it is easier for the respondent to start thinking about the aspect ofteaching in question and draw lines towards the past. A reverse procedure appears to bemore difficult for the respondents (Beijaard et al. 1999). Finally, the teachers were asked tocomment on the story-lines, explaining what had caused the direction or the change ofdirection or incline.

During the debriefing phase, the research project was described in more detail. After thetape recorder was turned off, the teachers were given the opportunity to comment on boththe content and the procedure of the interview. The teachers again gave permission for useof the tape recordings for research purposes.

Analysis

The interviews were analysed in the following seven steps.

1. The interviews were transcribed in full.2. The transcripts were read repeatedly to get an overview of the interviews.3. Using the transcripts, summaries per question and per teacher were written in English.4. From these summaries main categories and subcategories were identified by both

authors separately. The categories and subcategories were then discussed untilconsensus was reached.

5. The categories were applied to the full interview transcripts by the first author. If acategory was mentioned several times by a teacher, in response to different questions orin different contexts, the category was marked for every time it was mentioned. In thisway, the teachers were given scores on the different categories. A third researcher wasasked to apply the categories to one of the interviews and also to check the pattern ofscores for each category. The results from this interrater check showed minordifferences, and after discussion consensus was reached.

6. When the final list of scores was developed, relations and patterns for every teacherwere looked for, again by both authors. Further, the categories were compared to theteachers’ statements from the story-lines.

7. Finally, all categories and scores for each teacher were listed in tables (see Tables 2, 3,and 4 below). In this way, patterns of categories amongst the teachers could becompared and analysed. Similarities and differences between the teachers’ PCK aboutacids and bases were identified to explore if subgroups could be found.

Some of these steps were performed in Swedish, since the interviews were carried out inSwedish, and some steps were done in English in order to make discussion between theauthors possible. For this reason, steps 1, 2, 3, and 5 were done individually by the firstauthor in Swedish and steps 4, 6, and 7 were done jointly by both authors in English. Inorder not to overlook important categories and to validate the list of categories, a thirdresearcher was called in for step 5. The analysis of the story-lines was done in the sameway. The categories from the teachers’ comments on the different parts of their story-lineswere listed separately and compared with the list of categories from the rest of theinterviews in step 6 above.

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Results

Interviews

Specific Research Question 1 What is the content of experienced teachers’ PCK aboutstudents’ difficulties in understanding acids and bases?

In this section, first the teachers’ general ideas about students’ difficulties are presented,followed by teachers’ comments on the excerpts from interviews with students.

In the warm-up phase of the interview, three teachers (T3, T4, and T8) mentioned thatstudents understood the concept of acids and bases quite well. According to the teachers,the main difficulties for students were calculations (T1, T2, T7, T8, and T9), and writingand interpreting equations (T1, T4, and T5); some said that bases were more difficult tounderstand than acids (T1 and T6).

In the main phase of the interview, excerpts from interviews with students werediscussed. The teachers were asked if they could relate the statements to their own studentsand how they thought the students might have got these ideas.

Most teachers recognised from their own teaching all of the student statements in theexcerpts. However, their explanations of the students’ misunderstandings, as well as themeasures, differed. The teachers’ explanations of the students’ misunderstandings wereclassified in the following four categories: (a) students’ misinterpretations of acid/basereaction equations, (b) students’ preconceptions, (c) model confusion, and (d) students’difficulties in distinguishing between explanations at the phenomenological (macroscopic)

Table 2 Teachers’ categories from Research Question 1

Students’ difficulties T1 T2 T3 T4 T5 T6 T7 T8 T9

GeneralCalculations x x x x xWriting and interpreting equations x x xBases x xComments on excerptsInterpreting the equation x xxxx xxx x x xPre-conceptions x xx xx x x x xx xx xxModel confusion xx x x xx x x xx x xxLevel confusion xx xx xx xxx xxx xx xx x

The more marks (x) a teacher has on a category, the more the teacher emphasised this category in differentquestions or in different excerpts.

Table 3 Teachers’ categories from Research Question 2

Models T1 T2 T3 T4 T5 T6 T7 T8 T9

Students accept that different models coexist x x x x x xTeachers’ use of models of acids and bases xxx x x x x x x xxxThree models are introduced x xTwo models are introduced x x xSpecific models are not introduced. Emphasis on micro-and macro- levels

x x x x

The more marks (x) a teacher has on a category, the more the teacher emphasised this category in differentquestions or in different excerpts.

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level and at the particle (microscopic) level. The distribution of the categories among theteachers is presented in Table 2.

Regarding category a (misinterpretations of the equation), a variety of examples werediscussed, such as, ‘Students do not realise that the products they suggest will react further’,or ‘Students make up alternative paths for the reaction’. For instance, T1 and T2 said thatstudents were satisfied when they came up with one idea of how the reactants could react,and they managed to balance the atoms and did not reflect further about whether theirsuggestion were possible. Students were also said to use the wrong charge for ions, or toforget to check the balance of the charges (T2, T3, and T7). Further, students were said toprefer water and salt amongst the products in an acid–base reaction (T2, T3, and T5).Finally, students did not take aggregation state or charge of ions into account when writingequations (T2, T3, and T4). T4 said that this could result in solutions that were impossible,for instance, solid sodium metal in water.

They forget to balance the charges. For instance, they can write an equation asNaOH+HCl → Na+Cl+H2O. Then they get angry because they don’t get full creditfor the task since they just forgot a little plus and a minus. They don’t realise that whatthey wrote is impossible; solid sodium will instantly react with the water.

Regarding category b (preconceptions), the teachers said that the students seemed tounderstand the Brønsted definition when learning acid/base chemistry in upper secondaryschool. However, from the excerpts, the teachers said it appeared as though the students hadfallen back into their old beliefs, that is, the definitions of acids and bases that they learnedin lower secondary school or from everyday life. The most mentioned preconceptions werethe following: acids and bases are hazardous or poisonous (T1, T2, T3, and T8), only strongacids were taken into account (T4, T5, T6, T7, and T9), only substances containing ahydroxide ion were considered bases (T3, T7, and T9), and acids and bases were defined assubstances (T2 and T8). Finally, all teachers but T7 said that students treated weak acids asif they were strong. Because of these preconceptions the students might have difficultiesunderstanding, for instance, water acting as an acid.

Table 4 Teachers’ categories from Research Question 3

T1 T2 T3 T4 T5 T6 T7 T8 T9

Reasons for changing the method of teaching acids and basesa. Reflection on students’ difficulties xxx xx xx xx x x xxx x xxb. Collegial x x x xx x xxxc. Research xx x x x xd. Reflection on teaching x x x xx xx xxe. Textbook xx xxx xx xx xf. Stimulation x xx x xg. The media x xx xxh. Simpler experiments x xx x xWhat is changedExperiments xx xx xx x x x x xExplanations x x x x x xCalculations x x x xMore explicit explanation of models xx x x xMore explicit explanation of micro- and macro- levels x x x x x x x

The more marks (x) a teacher has on a category, the more the teacher emphasised this category in differentquestions or in different excerpts.

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The students seem to remember only what they learned in lower secondary school.The first definitions they learn in school are the ones they remember and believe in. Inthis case, the student forgot all about weak acids and equilibrium, thinking all acidsreact like strong acids. (T3’s response to excerpt 6 in Appendix 1)

Regarding category c (model confusion), only five of the interviewed teachers (T1, T3,T4, T7, and T9) said that they discussed the different models of acids and bases explicitlywith their students. All teachers, however, saw that students had confused different modelsof acids and bases in the excerpts. T5, for instance, said that students started working on aproblem using one model and changed when they realised the first model was not working.T5 did not think the students were aware of their behaviour. Further, T1, T3, T4, T7, and T9(the five teachers who discussed the different models explicitly) thought that most of theirstudents would recognise the limitations and scope of each model. T2, T5, T6, and T8 werenot aware of this problem in their own teaching because the different models were used atdifferent times or in different contexts. Most teachers, however, recognised the students’idea that only the best ‘true’ model should be taught (excerpt 4, Appendix 1).

My students can not realise that different models are used, since I don’t teach it thatway. I don’t think it confuses them since they are used from different chapters whichare taught at different times. In the first chapter we teach the phenomenological leveland in the second we explain what is really happening on a particle level. (T5)

Regarding category d (level confusion), T3, T4, T6, T8, and T9 said that studentsconfused what they saw at a phenomenological level with explanations on a particle level.Students were said to have a preference for using substances instead of particles in theirexplanations. They often confused acidic solution with acid, and basic solution with base.The teachers said it was important to be clear about which level was being discussed at aparticular moment, and why.

They have difficulties understanding the difference between an acid and an acidicsolution. You have to be very explicit about these things. I’m afraid it’s not very clearin the textbook either. First they define acids and then they only talk about acidicsolutions. (T2)

Specific Research Question 2 What is the content of experienced teachers’ PCK of teachingstrategies they consider useful to help students overcome such difficulties; in particular,how do they use models of acids and bases in their teaching?

In this section the teachers’ use of models of acids and bases, based on their comments onthe excerpts from textbooks and interviews with students, is presented. The distribution ofthe categories among the teachers is presented in Table 3.

Six of the interviewed teachers (T1, T2, T4, T5, T6, and T9) thought that studentsaccepted the use of models in chemistry. To explain this, T1 said, “Students accept thatsince the target is beyond reach, it is represented by a simplification instead.” The teachersalso thought that students accepted that different models could be used to explain the sametarget. However, only five of the interviewed teachers (T1, T3, T4, T7, and T9) said thatthey discussed the use of models of acids and bases in their teaching. Of the three teachers(T3, T7, and T8) who did not believe that most students understood the use of models, T3and T7 said they tried to teach it anyway. They did this to help the better students in theirunderstanding, and hoped that other students would at least grasp the simpler models whilerecognising it was not the whole truth. T1 and T9 defined three different models (ancient,

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Arrhenius, and Brønsted) in their teaching. T1 also mentioned an early alchemist model inwhich he defined acids as consisting of sharp particles and bases as smooth particles. T3,T4, and T7 defined two models in their teaching: “an old model” and Brønsted’s model. Inthe old model, the teachers combined attributes from the ancient model and Arrhenius’model. Acids were explained as hydrogen-containing substances that could producehydrogen ions in water solution. They had a sour taste, and could corrode metal andneutralise bases. Bases were explained as hydroxide-containing substances that couldneutralise acids. The result of a neutralisation reaction was a salt and water. The reason forintroducing the ancient model was that students recognised it from lower secondary schooland from everyday life. The students were also supposed to recognise the Arrhenius modelso the teachers could start a discussion about the use of models of acids and bases rightfrom the beginning of the chapter. The reason for introducing “the old model” was that theteachers did not think that students would understand the differences between the Arrheniusand the ancient model. Instead, they combined some attributes of these to form a newmodel. All of the above teachers thought that students understood the differences betweenBrønsted’s model and the older model(s). The teachers explained a new model as providinga deeper (more complex) explanation, and they told students that models are neededbecause it is impossible to see what is happening at the particular level. T1, T7, and T9 alsosaid that it was important to explain that some attributes from the older model could not beused in the new one.

Most of the students understand that different models are used to explain, for instance,acids and bases. Of course there are always some who want to know which of themthe true model is, or why they have to learn several models instead of concentrating onthe “best” one. Then you have to explain again that the models explain differentaspects of the target, or that we had to concentrate on a simpler model first since wehadn’t learned about particles yet. (T1)

Few teachers had seen their students confusing models, as the different models were taughtat different times and in different contexts. For instance, when dealing with neutralisation, theyused the Arrhenius model or the old model; later, in discussing buffer systems, Brønsted’smodel was used. The teachers agreed that more time should be spent on discussing thelimitations and scope of models, especially when new models were introduced.

The remaining four teachers (T2, T5, T7, and T8) did not explain the use of models ofacids and bases. They were all aware of the different acid–base models from the course, andmost of them used different models in explaining other areas of chemistry, for instance,atoms, bonding, and redox reactions. One reason for not using models to explain acids andbases was that they thought it was sufficient to differentiate between the phenomenologicallevel and the particle level. These teachers defined acids and bases as particles according toBrønsted, but at the phenomenological level the emphasis was not on the acids and basesthemselves but on the acidic or basic solutions.

Hydrogen chloride is a gas, but when you dissolve it in water there are no HClmolecules left. You now have an acidic solution. The dissolved oxonium ions makes itacidic. Accordingly, sodium hydroxide is a salt. When it is dissolved in water you geta basic solution with hydroxide ions in it. (T8)

These teachers considered it difficult enough for the students to differentiate betweenthese two levels, and believed that introducing more models would make the topic evenmore difficult for students to understand. T5 and T8 thought that the two levels werecomparable with two models, one phenomenological and one particulate; however, they did

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not refer to these levels as models in their teaching. The main difficulty for students indistinguishing between macroscopic and microscopic definitions was believed to be that thedefinitions use the same terms.

Specific Research Question 3 How did their PCK of teaching acids and bases develop overtime?

In this section results are presented from (a) interviews in which teachers were asked toexplain how and why they changed their teaching methods year after year and (b) story-lines in which teachers were asked to grade their level of satisfaction with their teaching ofacids and bases from the beginning of their careers to the present.

Regarding how and what the teachers changed in their teaching methods from year toyear, three main activities were mentioned: (1) how a topic was explained, (2) newexamples for calculation, and (3) new laboratory work. Several teachers mentionedexplicitly that the time allotted to teaching acids and bases and the content taught were wellestablished and were not changed.

The teachers’ reasons for changing how they taught acids and bases were classified intoeight categories, referring to (a) reflection on students’ difficulties, (b) collegial discussions, (c)research, (d) reflection on teaching, (e) textbook, (f) stimulation, (g) the media, and (h) simplerexperiments. The distribution of the categories among the teachers is presented in Table 4.

All teachers mentioned reflection on students’ difficulties (category a) as a reason forchanging how they taught a topic; however, T5, T6, and T8 were vague in their descriptions ofhow this was done. Other teachers said they tested students to determine which questions theydid not understand. Listening to students’ questions and statements during lessons, and havingstudents evaluate the lessons, were also mentioned as ways of identifying difficulties.

T1, T5 T6, T7, T8, and T9 mentioned that discussions with colleagues (category b) werean important reason for changing their teaching. Students’ difficulties and new experimentsaiming at challenging students’ “misconceptions” were said to be discussed.

T1, T4, T5, T7, and T9 mentioned that they occasionally were in contact with research(category c) in chemistry education. T1 and T7 occasionally participated in courses orworkshops at universities near their schools. They both said that this had mainly influencedtheir teaching at the beginning of their careers. They gained new insights into students’difficulties, and also increased their knowledge of the history and philosophy of science. Inrecent years, however, they attended university less often: they lacked time, and also feltthey did not need the courses to the same extent. T5 also mentioned that he had had somecontact with a university in the past, and had read journals that include articles on researchin science education. However, he found it difficult to implement what he learned in histeaching and, therefore, did not continue this path of education. T4 and T9 said theyoccasionally searched the universities’ web sites and this in way found new experimentalwork. The course the teachers had followed was said by most to have had some impact ontheir method of teaching acids and bases. T3 and T6, however, barely remembered thescope of the course. T2, T4, and T8 said that their ideas regarding, for instance, students’difficulties were confirmed, and T2, T4, T6, and T8 said that they put more emphasis onexplaining the differences between the micro- and the macro-scale in their teaching sincethe course. T5 said that he had learned much about students’ difficulties but not about howto help these students. Finally, T1, T4, and T9 said that, following the course, they hadchanged their teaching of acids and bases by using models.

T2, T3, T5, T6, T7, and T8 mentioned that they reflected on their own teaching(category d) in order to improve. They analysed what they did and how they did it, and if it

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was “right” and clear. T3 and T7 focused on the students’ understanding when changing ateaching strategy. For T2, T5, T6, and T8, the focus was directed on the teachers’ ownactions; for instance, they compared the lesson plan with what they actually did in theclassroom, or considered whether the results of an experiment were as expected.

T3, T6, T7, T8, and T9 mentioned that new textbooks (category e) could result inchanges in the way they taught acids and bases. The changes mentioned were newexperiments and new examples for calculations.

T1, T2, T5, T6, T8, and T9 also mentioned that they introduced changes because a newway of teaching was more stimulating (category f). T2, T5, and T8 said that it could beboring to do the same experiments year after year, and it was more stimulating to varythem. T1 aimed to make his classes stimulating for the students. He said that someexperiments were boring for the students and he searched for new, more interesting ones.T6 and T9 mentioned that teaching should be fun for both students and teachers.

Three teachers, T2, T6, and T8, said that the media (category g) provided a great sourceof context that was familiar to the students and, therefore, made the topic of acids and basesmore interesting for them. Three specific cases were mentioned: an article aboutacidification in the local newspaper, an advertisement on television for anti-corrosives,and an advertisement, also shown on television, in which mention was made of pH in bodylotions.

Regarding simpler ways of teaching (category h), T2, T4, T5, and T8 said that they oftenchanged the experimental work if they found a new experiment that was cheaper and lesstime consuming to perform and prepare.

Story-lines

Four patterns in teachers’ satisfaction with teaching acids and bases were identified in thestory-lines: (1) increasing satisfaction, (2) increasing followed by decreasing satisfaction,(3) decreasing satisfaction, and (4) decreasing followed by increasing satisfaction.

Six of the teachers described increasing satisfaction (pattern 1) with their teaching ofacids and bases in their story-lines. T1 and T7 had the steepest slopes, and both said theyhad felt very insecure in their teacher’s role at the beginning of their careers. They both alsosaid that they had followed the textbook strictly in the beginning. T1 mentioned that he wasnot sure about how the students could cope with advanced explanations. T7 said that,initially, she had had no idea about students’ difficulties. T1 said that he had learned aboutstudents’ difficulties and teaching strategies (from, e.g., research), and had become moreconfident about teaching in his own way instead of following the textbook. T7 said thatafter a while she knew the textbook and was able to adjust the content to fit her way ofteaching. In addition, she said that she had found a way of teaching that most studentsappreciated. The rest of the students would perhaps have to make a greater effort. T4, T5,and T6 had high starting points and, therefore, a moderately rising slope. T4 and T6 bothhad the highest raise at the beginning of their careers, and both said that they learned veryquickly about how well students understood them. T5 added that his idea of teaching acidsand bases had changed during the interview; that is, during the interview he learned muchabout students’ difficulties and also about teaching strategies aiming at solving thesedifficulties. With these new ideas in mind, he did not feel as satisfied with his teaching asbefore the interview, and thought that he perhaps should lower his curve. T3 said that shehad never been dissatisfied with her teaching. Her level of satisfaction had increased overthe years owing to her improved insight into students’ learning and her increasedknowledge about how to use the group more effectively. She could never be completely

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satisfied, however, as she felt that she often had to move to the next section without beingsure all students had understood the concepts.

T2’s curve had a steep rise at the beginning, followed by a slight decrease (pattern 2). He saidhe had found it difficult to teach chemistry at the beginning of his career. He thought that it wasmore difficult to learn how to teach chemistry than to learn how to teach other subjects, forinstance, mathematics, which was his second subject. After approximately 10 years of teaching,he said that he had found a way to teach that was acceptable to both the students and himself.

T8 drew a decreasing curve (pattern 3). The reason he gave for this was that the more helearned about students’ difficulties, the more he understood that he could never make themunderstand the concepts. He had a flat curve at the beginning of his career which he described asa period when he was not aware of students’ difficulties and was, therefore, quite satisfied.

Finally, T9 drew a curve that first decreased, and after some years increased (pattern 4).She explained that, at the beginning of her career, she thought that she knew what was best forthe students, because she considered herself a chemistry expert. She said that she soon entereda period of desperation because her teaching was not appreciated by the students. After someyears, she accepted that perhaps her method of teaching was not so clear, and as she learnedmore about students’ ideas, she began to be more satisfied with her teaching again.

Discussion and Conclusions

All teachers recognised (from the excerpts) that the students had confused models of acidsand bases and had also confused the macroscopic level and the microscopic level. Allteachers could also identify some conceptions of acids and bases that students usually havewhen they start upper secondary school. The teachers expected, however, that theseconceptions would have been dealt with during upper secondary education and that thestudents would have accommodated the Brønsted acid–base model. Although the excerptsfrom the students’ interviews were from interviews with other students, the teachersrecognised the statements from their own students, with the exception that the teachers whodid not teach the different models of acids and bases explicitly had not considered thatstudents could confuse attributes from different models.

In order to find patterns of categories amongst the teachers, Tables 2, 3 and 4 were mergedtogether. This allowed the whole pattern of scores amongst the categories for the teachers tobe more easily interpreted. Similarities and differences between the ways teachers taughtacids and bases were identified, resulting in two main categories of teachers’ methods ofteaching acids and bases. T1, T3, T4, T7, and T9 were categorised as student and modeloriented. These teachers seemed to reflect more on students’ difficulties when planning aseries of lessons, and they focused on making their explanations clearer. In their teaching,these teachers also tended to concentrate more on the concept of models of acids and bases.All discussed two or three models in their classes. They were also likely to blame students’mistakes on their pre-conceptions of acids and bases. T2, T5, T6, and T8, on the other hand,were categorised as teacher oriented and micro/macro-level oriented. These teachersreflected more on their own teaching when planning a series of lessons and focused onmaking the lessons more stimulating for them to teach. The sources of inspiration were to agreater extent said to be the media (news and commercials). They focused on searching forsimpler and cheaper demonstrations and experimental material, as well as simplercalculations. They did not explicitly address models of acids and bases in their classes,but, instead, they discussed acids and bases at two levels: a macroscopic or phenomeno-logical level, and a microscopic or particulate level.

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Only two of the teachers, T1 and T9 (see Table 3), defined three distinct models. Threeof the teachers (T3, T4, and T7; see Table 3) defined only two models: an old model andthe Brønsted model. In this respect, these teachers might be compared to the micro/macro-level oriented teachers who defined only one model, but emphasised the difference betweenthe microscopic properties (particle level) and macroscopic properties (phenomenologicallevel) of acids and bases. Reducing the concept of acids and bases to a phenomenologicallevel and a particle level, or reducing the models explained to a macroscopic and a particlemodel, suggests that different scientific models constitute a coherent whole; that is,different models are seen as different levels of generalisation. Attributes from a simpler orolder model would be valid in all later models as well. According to Justi (2000), this ideacould lead to learning problems among students. Further, it suggests that scientificknowledge grows linearly and is context independent, and that there is no progressionbetween the models. Furió-Más et al. (2005) argued that teachers must know the conceptualmodels that have been invented through history and justify the introduction of new models.Teachers need to guide students epistemologically in the interpretation of these models, thatis., they need to demonstrate that models are human constructions and only limitedrepresentations of reality (Harrison and Treagust 2000). The teachers in this study wereexpected to have knowledge about the scope and limitations of different acid–base modelsfrom the teacher training course they participated in. It transpired that not all of the teachershad developed teaching strategies for this issue.

Regarding the story-lines, some teachers found it difficult to consider only acids andbases when reflecting on their early years of teaching. They did not remember the teachingof acids and bases as being outstanding in any way. Acids and bases were not moredifficult, or easier, than other topics to teach, and, therefore, the teachers assumed that theline describing their level of satisfaction with teaching acids and bases would be similar to aline describing their level of satisfaction with teaching chemistry in general. The discussionabout the story-lines confirmed some of the teachers’ statements. T1 and T7 both mentionedresearch as a source of learning about students’ difficulties and teaching strategies in thebeginning of their careers. The role of research was confirmed in the discussion about thestory-lines. T3, T4, and T9 mentioned other ways to learn about students’ understanding,both in the interview and when explaining their story-lines. Further, T2, T5, T6, and T8reflected much on their own teaching, which they also discussed when they drew theirstory-lines. Finally, the large impact of textbooks on T6 and T7’s ways of teaching wasconfirmed by the discussion about the story-lines.

Implications

Though only a few teachers mentioned research as a source of learning, most of theteachers said that they had made, or at least tried to make, changes in their teaching of acidsand bases after the course about students’ difficulties and the use of models. T5 said that hehad learned much about models in the course, but felt that a part about how to implementthese ideas in teaching would have been useful. He wished for a new course on this. Inaddition, when drawing his story-line, T5 said that his level of satisfaction with his teachingof acids and bases had changed during the interview. This indicates that a teacher trainingcourse should be followed up with additional discussions about, for instance, how teachersimplemented their new ideas and the difficulties that arose when doing so, and new ideasshould be generated for developing their teaching further. Gilbert et al. (2002) refers to thework of Kempa who suggested six different levels of impact of existing chemical education

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research on classroom teaching. These levels vary from teachers’ unawareness of relevantresearch findings to teachers’ decisions to use these findings in order to improve classroomteaching. The highest level is said only to be reached when teachers has extensiveconsultancy or collaborative support from a mediator, for instance, a researcher withclassroom experience. Discussing authentic student statements from other teachers wasfound to be a pleasant and relaxed way of discussing these issues with teachers. This mightalso be a fruitful way to enhance pre-service teachers’ PCK of both (a) students’understanding and (b) teaching strategies to help students overcome their difficulties.Textbooks also play an important part in teachers’ planning of lessons, at the beginning oftheir careers and also later on. Pre-service teachers should learn to critically reviewtextbooks. This might also help them to develop new teaching strategies.

This study has several limitations and more research is needed for a better understandingof the role of acid–base models in teaching and learning. One clear limitation of this studyis that, during the interviews, teachers described how they taught and developed newstrategies for teaching acid–base chemistry. It is not clear from the results, however, whatreally happened in the classroom. Further, this study is limited to a small sample of teachersthat had participated in a teacher training course arranged by our university. It would bevaluable to address these issues to a large sample of teachers. Finally, it is unclear howSwedish teachers apply their general view of models to other concepts in chemistry.

Acknowledgements The authors wish to thank Onno de Jong for his assistance in preparing the paper andNiklas Gericke for his assistance in the development of the categories.

Appendix

Excerpt from Interviews with Students

Acid–base Reactions

1. Students were asked to write a reaction equation between an acid and a base.

HAcþ NaOH! NaAcþ H2O;

Since water is formed, it becomes neutral.

HClþ NaOH! NaClþ H2O;

In an acid–base reaction, it becomes neutral.

HClþ NaOH! NaH2Oþ Cl�

The base NaOH takes a proton from the acid HCl.

2. Students were asked what an acid–base reaction is.

In a reaction there is always one [particle] acting as a base. Even if you have twoacids, for example HCl and H2SO4, one is a base.Acids and bases are very difficult for me...Acids donate protons and bases aresubstances that accept these protons. It is pretty tricky, because, if you look atwater, it is both an acid and a base. If a water molecule is first a base, it takes a

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proton from another water molecule, so that the water molecule that was first abase suddenly becomes an acid. It is quite difficult to keep up with that, how itturns around. In an acid–base reaction the result will be neutral... They consumeeach other depending on their concentrations. Hydrogen ions or oxonium ions andhydroxide ions form water in a neutralisation.

Water is an Acid

3. Students were asked to identify acids and bases in the equation:

NH3 þ H2O! NHþ4 þ OH�

When they hesitated to define water as an acid, they were asked why.

It is difficult to think about water as sour...Because water is not really...it is both an acid and a base, as I recall it...but... I donot know...water is water, right? It makes me think of something neutral,something that is not extreme in any way.You can’t imagine drinking an acid, but you drink water.

Model Confusion

4. The students were asked to explain the differences between the following two equations.

acidþ base! saltþ wateracid1 þ base2 ! base1 þ acid2

Some substances, for example, water, can act both as an acid and as a basedepending on the substance with which they react.Salt and water are formed... there should be an acid and a base as well...perhapsyou can identify NaCl as an acid, I am not too familiar with that.It would have been better to learn Brønsted from the beginning. It gets messychanging models when you’ve already learned it one way.

HClþ NaOH

5. Students were asked to explain, on a particle level, the reaction between the substancesHCl and NaOH.

Perhaps it strives to turn into water. If these two (Na+ and Cl−) are attracted moreto each other and NaCl is a salt, right? Perhaps it has something to do with a metaland a non-metal attraction. They want to form a salt. And if OH and H have astronger attraction to each other, I do not know.

Buffer Solutions

6. Students were asked to explain how buffer solutions work.

How can it work? You cannot have an acid and a base in the same solution. In thatcase the acid and the base should consume each other.

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Excerpts from Textbooks

Since the teachers used different books, different excerpts were discussed. As the excerptsfrom the different books were quite similar, however, an example from each type of excerptis presented below.

1. The books define acids according to their general properties, e.g., sour taste, colouringlitmus, reaction with non-precious metals, etc (for example, textbook 1, page 103).

The substances that for many years were called acids have many common properties.For instance, they have a sour taste and it is said that their reactions are sour.

2. The books define acids according to Brønsted (for example, textbook 2, page 79).

A reaction in which protons are donated or accepted is called a proton transferreactions. The substance or ion that donates protons is an acid, according toBrønsted’s definition of acids.

3. The books’ explain acidic solution/basic solution (for example, textbook 2).

The oxonium ions give water solutions their sour taste and sour reaction. In colloquialspeech, that sour solution is called an acid (page 78)...The rule is to pour the acid intowater (page 80; with acid, the authors refer to a water solution of an acid.)

4. The books use redox reactions, e.g., reactions with non-precious metals (for example,textbook 3, page 161).

Now that we know that acids are proton acceptors, we can write formulas for acidicsolutions’ reactions with carbonate compounds and with non-precious metals....

Reaction with carbonate

CaCO3 sð Þ2Hþ aqð Þ ! Ca2þ aqð Þ þ CO2 gð Þ þ H2O lð ÞReaction with non-precious metal

Mg sð Þ þ 2Hþ aqð Þ ! Mg2þ aqð Þ þ H2 gð Þ5. The books use formula equations and ionic equations according to, for instance,

neutralisation (for example, textbook 1, page 112).

Naþ þ OH� þ H3Oþ þ Cl� ! 2H2Oþ Naþ þ Cl�

We can see that the ions Na+ and Cl− do not participate in the reaction. They arecalled counter ions or “spectator ions.” Thus, only the following reaction takes place.

OH�baseþH3O

þacid

! H2Oþ H2O

“The reaction between an acid and a base is called neutralization. A salt is formed.”

None of the textbooks explained the following about acids and bases:

That models are usedWhat model is in use at the momentWhy different models are used in parallelThe scope and limitations of each model.

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Textbook 1: Andersson, S., Sonesson, A., Stålhandske, B., & Tullberg, A. (2000).Gymnasiekemi A. Stockholm: Liber.

Textbook 2: Borén, H., Larsson, M., Lif, T., Lilleborg, S., & Lindh, B. (2000).Kemiboken A 100p. Stockholm: Liber.

Textbook 3: Henriksson, A. (2000). Kemi kurs A. Malmö: Gleerups Förlag.

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