Res Sci Educ DOI 10.1007/s11165-014-9400-7

Exploring Undergraduates’ Understanding of Transition Metals Chemistry with the use of Cognitive and Confidence Measures Bellam Sreenivasulu & R. Subramaniam # Springer Science+Business Media Dordrecht 2014

Abstract Compared to studies on school students’ understanding of various topics in the sciences, studies involving university students have received relatively less attention in the science education literature. In this study, we investigated university students’ understanding of transition metals chemistry, a topic in inorganic chemistry, which has been only scarcely explored in the science education literature. A four-tier diagnostic instrument was used. The instrument comprises 25 questions, and each question has an answer tier, a confidence rating for this tier, a reason tier and a confidence rating for this tier. Versions of the instrument were refined iteratively during the preliminary and pilot phases of the study. This study reports on the results obtained from the main phase of the study, using a sample of 140 students. Overall, the diagnostic test was difficult for the students. The students had a mean score of 38 %, based on correct responses for both answer and reason tiers for the questions. It was accompanied by a mean confidence of only 3.49 out of 6 (that is, 58.2 %) for the whole test. The results indicate that transition metals chemistry is a difficult topic for the students. Twenty-four alternative conceptions have been identified in this study, including some indication of their strengths. Some implications of the study are discussed. Keywords Transition metals chemistry . Alternative conceptions . Four-tier diagnostic test . Confidence ratings . University students

Introduction Students’ understanding of various topics in the sciences has been an active field of study in science education research. These studies have generated a wealth of knowledge about B. Sreenivasulu Department of Chemistry, National University of Singapore, 21 Lower Kent Ridge, Singapore 119077, Singapore e-mail: [email protected] R. Subramaniam (*) National Institute of Education, Nanyang Technological University, 1 Nanyang Walk, Singapore 637616, Singapore e-mail: [email protected] Present Address: B. Sreenivasulu Singapore University of Technology and Design, 20 Dover Drive, Singapore 138682, Singapore

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students’ alternative conceptions (ACs) in these topics. Identification of ACs in different topics is important as it provides instructors research-based evidence of students’ learning difficulties in these topics so that these could be used to inform the development of strategies for teaching. A large number of studies on students’ understanding of science topics have concentrated on school students, not surprisingly since access to samples is somewhat easier. There have been relatively fewer studies that have focused on students in higher education institutions. Aiming to contribute towards this, we investigated undergraduates’ understanding of transition metals chemistry, an important topic in inorganic chemistry. Learning Learning is a complex process which entails assimilation of information, linking of the incoming content to relevant conceptual frameworks in the mental schemata (West and Fensham 1974) and, more importantly, trying to make sense of the knowledge to be learnt. The latter is, of course, a challenge. When students are able to internalize coherently this sequence of processes, learning can be considered to have occurred meaningfully (Bodner 1986). There could also be situations when students are not able to harmonize effectively this sequence of processes, and rote learning then becomes the default mode for knowledge acquisition (Ausubel 1968). In the cognitive constructivist paradigm (Kalina and Powell 2009), there is a pronounced emphasis on activating prior knowledge in the process of learning. This is because such activation allows learning to be built up incrementally from what the student already knows. When prior knowledge is not activated, the efficacy of the process of knowledge acquisition becomes more difficult as there is no relevant content or conceptual framework on which to build students’ understanding of the new knowledge to be learnt. Alternative Conceptions Prior knowledge plays an important role in meaningful learning for it helps the learner to make some sense of the new information as well as organize these in his or her mental schemata. This prior knowledge can be in the form of concepts or conceptions. There is little consensus in the science education literature on what exactly constitutes a concept or conception as different authors have used varying interpretations to describe these terms. For the purpose of this study, we will use the formalism of Duit and Treagust (1995), who view concepts as being definitive in nature and which represent ideas that have garnered mainstream acceptance from the scientific community; they also view conceptions as representing students’ ideas that deviate from the tenets of scientific wisdom. These conceptions are known by various terms—for example, misconceptions (Amir and Tamir 1994), alternative conceptions (Wandersee et al. 1993), naïve conceptions (Champagne et al. 1983), pre-conceived ideas (Johansson et al. 1985) and alternative frameworks (Gilbert & Watts 1983). Whichever term is used, they represent stumbling blocks in the process of building a unified understanding of a topic. If these stumbling blocks can be identified, instructional intervention is possible. Not surprisingly, identification of ACs in various topics in the sciences has been a fruitful field of study in science education research. Duit (2009) has compiled a comprehensive bibliography of over 8,400 entries related to ACs and learning difficulties in various topics in the sciences for different levels. We use the term “alternative conception” (AC) in this study. Our preference for this term over other terms stems also from our conviction that since students would have invested some cerebral effort in coming up with this formulation, they need to be given

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some credit for this effort (Driver 1981). Also, the AC can be a starting point for the journey towards acquiring the concepts that are in line with the views of the scientific community (Wandersee et al. 1993). It has to be borne in mind that not all preconceptions harbored by students can be labeled as ACs (Clement et al. 1989). Some of these could be due to lack of knowledge. For example, in multiple choice questions, students can get an answer wrong through guesswork; this is not regarded as a misconception (Hasan et al. 1999). ACs in students can arise from various sources—for example, textbooks, teaching, native culture, and the media (Duit and Treagust 1995; Ivowi and Oludotun 1987), and from everyday experiences (Taber 2004). These can often be held tenaciously by students, which make these quite resistant to change via teaching or even instructional intervention (for example, see Gilbert et al. 1982; Duit and Treagust 1995). The resistance to change is linked to the extent to which an AC is anchored in the students’ mental schemata (Chinn and Brewer 1993). The more firmly it is held, generally, the greater is the effort needed to effect conceptual change. For the identification of ACs, the usual approaches that have been used in the literature include interviews (Voska and Heikkinen 2000), multiple choice questions (Tekin and Nakiboglu 2006), concept mapping (Ross and Munby 1991), open-ended questions (Reynolds et al. 2006) and two-tier questions (Tsui and Treagust 2010). Interviews are known to be effective in unraveling the nature of the understanding possessed by a student of a concept in significant depth; however, interviews are time consuming and are not practical for mass screening of students. Two-tier questions have been especially useful in documenting a range of ACs on various topics in the sciences, and this has contributed to their prevalent use among researchers (for example, Lin 2004; Caleon and Subramaniam 2009). Again, two-tier questions have a few drawbacks. For example, they are not able to differentiate mistakes in students’ responses due to existence of ACs from those due to lack of knowledge (Caleon and Subramaniam 2010a). Similarly, they are not able to indicate whether a correct response obtained by a student is due to content proficiency or guessing. Further, they are not able to provide some indication of the strength of the ACs harbored by students, which has instructional implications for intervention. The foregoing limitations can be addressed to a significant extent by adding a confidence rating to each tier or a mean confidence rating for both tiers—in the former case, it becomes a four-tier question (Caleon and Subramaniam 2010a) while in the latter case, it becomes a three-tier question (Caleon and Subramaniam 2010b). It thus becomes possible to get some numerical estimates of the strength of an AC held by a student. The strength of an AC can be regarded as the tenaciousness with which it is held by the student in his or her mental schemata. Though the notion of tenaciousness is rather subjective, some indication of it can be inferred from the certainty or confidence with which an incorrect response (answer) or response combination (answer/reason) is chosen by a student to an MCQ item or a two-tier MCQ item respectively. For example, an incorrect answer chosen with a high certainty of response can be considered as an AC (Hasan et al. 1999; Potgietera et al. 2010). The term, certainty of response, is similar to confidence rating, which is derived from the psychological literature. As ACs can be held by students with varying degrees of confidence, Caleon and Subramaniam (2010b) extended the idea further by classifying the ACs as either genuine or spurious—the former is held by at least 10 % of the sample with mean confidence exceeding 3.5 (on a confidence scale of 1–6) while the latter is held by at least 10 % of the sample with mean confidence less than 3.5. When students hold ACs with high levels of confidence, it suggests that the ideas are anchored in their mental models rather strongly (McClary and Bretz 2012), and therefore greater effort would be needed to wean them away

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from these towards the correct concepts. Owing to the complexity in the nature of ACs, the confidence rating of an AC arising from an incorrect response should be regarded as an approximation for the strength of the AC. General Observations on Literature Related to Alternative Conceptions The extensive bibliography by Pfundt and Duit (2009) indicates that much of the research into students’ understanding of ideas and topics in chemistry has focused on school-age pupils, with relatively less emphasis on tertiary level students. Nonetheless, there are reports of studies on ACs harbored by tertiary-level students on a number of chemistry topics (Table 1). It has also been reported that a majority of students have learning difficulties with fundamental chemistry concepts, and that many of their scientifically incorrect ideas will persist and be carried forward unchanged from their school level to university, and even up to adulthood (Nakhleh 1992). Although several studies have investigated students’ conceptions related to different chemistry topics, there is only one report dealing with students’ ACs related to transition metals chemistry. In fact, the topic of transition metals chemistry is an important module in inorganic chemistry, not only at the university level but also at leaving level examinations such as the Singapore-Cambridge General Certificate of Education (GCE) ‘A’ level examinations. The importance of the topic stems from the fact that transition metals find a range of applications; for example, owing to their high density and low susceptibility to corrosion, they are used as infrastructural materials in industry or as components of alloys, and because of their ability to exhibit multiple oxidation states, they are used as catalysts in various industrial processes. In particular, the chemistry of transition metals forms the basis for the synthesis and application of a wide variety of metal coordination polymers, metal organic frameworks as gas storage devices, and new bioinorganic anticancer and anti-arthritis compounds. As the area of transition metals chemistry has developed quite rapidly in recent years, it has also found

Table 1 Some studies on alternative conceptions at tertiary level Topic on which ACs have been found

Reference

General university chemistry/acids and bases

Cros et al. (1986); Cros et al. 1988; Zoller (1990).

Chemical bonding

Coll and Taylor (2001); Coll and Treagust (2001, 2002, 2003); Nicoll (2001); Robinson (1998); Taber (1998); Taber and Coll (2002).

Chemical equilibrium

Banerjee (1995); Thomas and Schwenz (1998).

Evaporation and condensation

Chang (1999); Canolat (2006); Gopal et al. (2004); Papageorgiou and Sakka (2000)

Solutions, solubility of salts and particulate nature of salts in solutions

Ebenezer and Fraser (2001); Smith and Metz (1996); Pinarbasi and Canpolat (2003); Bucat and Mocerino (2009); Kelly and Jones (2007, 2008); Kelly et al. (2008); Tien et al. (2007); Smith and Nakhleh (2011); Williamson and Abraham (1995). Kaper and Goedhart (2002); Kaper and Goedhart 2002; Lewis and Linn (1994).

Heat, temperature and energetics of chemical reactions Chemical thermodynamics

Carson and Watson (1999, 2002); Granville (1985); Linda and Carl (2010); Sözbilir et al. (2010).

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applications in areas such as environmental chemistry, water and oil purification, metal cleaning, ore flotation, germicides, and metal ion control in biological systems, Thus, it has become inevitable that teaching and learning in undergraduate inorganic chemistry curriculum include transition metals chemistry as a major topic. Pedagogical studies exploring learning difficulties and problems associated with undergraduate students’ understanding of the chemistry of transition metals are thus essential. The topic also allows students to integrate concepts from multiple domains in chemistry—for example, stoichiometry, bonding, catalysis, and periodic table. Literature Review on Transition Metals Chemistry Except for a single study on complex ions using college students at university level (Barke et al. 2009, pp238–240), we found no other references to ACs on transition metals chemistry in the available literature or in bibliographies such as Pfundt and Duit (2009). In the above study done at the University of Muenster, a questionnaire was constructed on the reactions of complexes (both transition metals and other metals) while focusing on concepts such as ‘composition and reactions of copper complexes, the stability of the tetraamminecopper complex, the equilibrium of aquacobalt (II) and chlorocobalt (II) complexes, and the solubility of silver chloride, silver bromide and aluminum hydroxide’ (p238). Students’ responses were in the form of formulae, equations and sketches of mental models. Examination of these responses indicated that their understanding of complex reactions is rather limited. The important misconceptions identified were: –

–

The number of molecules of water of crystallization in the formula of copper sulfate pentahydrate was mistaken for the coordination number of Cu2+, even though the students were taught about its octahedral coordination in lectures. Some even thought that each ‘CuSO4’ group is surrounded by five water molecules Many students could not provide the right reasoning behind the color changes observed in the reaction when hydrochloric acid is added to cobalt (II) chloride and then diluted; also they were not able to write the equation for the reaction.

There is also a report on textbook mistakes associated with crystal field stabilization energy (CFSE, Δ) calculations for some transition metal ions (Tudela 1999). In this report, Tudela points out a common mistake observed in some well-known inorganic chemistry textbooks on the expressions for CFSE in the case of octahedral complexes with d6-d10 configurations, in which the pairing energy (P) component is incorrectly included. For example, in the case of high-spin d6 complexes, CFSE is expressed as P 0.4Δo. However, as P > Δo for high-spin complexes, this expression would lead to a rather high positive value of CFSE, which would tend to destabilize the system for an octahedral field relative to a spherical field. Furthermore, as knowledge of d-orbitals is essential for students starting to learn crystal field theory and splitting of d-orbitals, there is also a report on undergraduates’ conceptual difficulties associated with the shapes of d-orbitals (Johnstone 1971). The author reported that students found it difficult to conceptualize how splitting of the d-orbitals occurs for a species in an octahedral field. Obviously, there is very scant literature on students’ ACs in the area of transition metals chemistry. Studies on students’ ACs in this direction seem to be essential so as to provide some pointers on how to improve teaching and make instructional intervention via conceptual change strategies possible, and hence addressing learning difficulties in transition metals

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chemistry (including coordination chemistry) at the university level. Also, from our experience, we note that many students possess rather superficial understanding of a number of aspects of transition metals chemistry. There is also a lack of conceptual understanding as well as difficulties in applying relevant concepts to solve questions, even after lectures and tests are conducted on these topics. Examination of the literature reveals the following: 1. For an important topic in inorganic chemistry, the topic of transition metals chemistry, which is covered at advanced (high school) and university levels, has attracted very little attention from researchers. 2. Based on the very limited studies in the literature, there are very few ACs reported that relate specifically to transition metals chemistry. This has limited utility for university instructors and high school teachers. 3. There is no diagnostic instrument on transition metals chemistry that can be used by teachers and researchers to document students’ understanding in this area. 4. For identifying ACs, the common approaches used in the literature include interviews, open-ended questions and two–tier tests. With respect to the latter, while it has the advantages of easy administration and convenience, as mentioned earlier, it is not able to explicitly indicate whether an incorrect response is a genuine AC or arises from lack of knowledge. Also, some indication of the strength of the ACs cannot be known from these tests. Knowledge of the strengths of the ACs would be useful for instructors to prioritize intervention. To a significant extent, these shortcomings can be addressed by the use of a four-tier question format—since the publication on it by Caleon and Subramaniam (2010a), there have been only two other studies done using it (McClary and Bretz 2012; Sreenivasulu and Subramaniam 2013). Odom and Barrow (2007) used a similar format but they did not label it as 4-tier. Clearly, there is a need for further work to assess the utility of this new instrument format in diverse settings. Pursuant to the foregoing, the principal objectives of this study were to develop a four-tier diagnostic instrument on transition metals chemistry and document the prevalence and strengths of university students’ ACs on this topic, thus helping to assess their understanding on this topic. An additional objective of this study is to assess the utility of the four-tier diagnostic format for use in such studies owing to the presence of only a few studies in the literature using this type of instrument. The research questions which guided our study are: 1. What are the ACs harbored by undergraduate students in the topic of transition metals chemistry? 2. What are the strengths of the ACs harbored by these students? Identification of ACs on transition metals chemistry would be useful for a number of reasons: it would provide instructors with useful pointers to keep in mind when teaching this topic; it would address a shortcoming in the research literature that has documented ACs on various topics in university level chemistry but very few on transition metals chemistry; it would provide scope for instructors to use conceptual change strategies to address some of these ACs; and it would encourage researchers to explore further aspects of this topic. It is to be noted that the presence of ACs can come in the way of students achieving a good understanding of the topic and, if not addressed, some of these may persist even after graduation or when they become educators.

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Methodology Our approach in addressing the research questions is to first develop a diagnostic instrument on transition metals chemistry in an iterative manner and then administer the final version of it to a sample of undergraduates in order to ascertain the prevalence and strengths of the ACs on this topic through suitable data analyses. As mentioned earlier, a four-tier diagnostic format addresses some of the limitations of the two-tier diagnostic format, and hence it would be used in this study. More importantly, by requesting students to not only indicate their choice of answer and reason for each question but also their confidence levels for the accuracy of their responses, there would be more scope to enhance the robustness of the test and extract measures beyond cognitive scores, as well as documenting ACs in the process. Development of Transition Metals Chemistry Diagnostic Instrument (TMCDI) The sequence of steps involved in the development of the TMCDI is similar to that documented by Treagust (1988) for two-tier tests but with some modifications. Owing to the paucity of studies on learning difficulties and ACs related to transition metals chemistry, the journal literature was only minimally helpful. Thus, we embarked on a two-step process to come up with the final version of the TMCDI. Based on the propositional knowledge statements generated, questions for the preliminary version of the instrument were prepared after consulting a number of sources besides the limited literature on this topic–for example, reviews of past years’ university examination questions, tutorial questions set at the university level, Singapore-Cambridge GCE “A” level questions in Chemistry, Cambridge examiners’ reports on A-level Chemistry, questions set by other examination boards, assessment books, magazines such as Chemistry Today, conversations with teaching staff who have taught the topic, and our own teaching experience. The questions were all in multiple choice format and for each question, there are typically 4 -5 responses followed by a blank space for students to provide written justification for their choice of response. Questions of different types are set – for example, conceptual questions, those that involve calculations, those that require the identifying of an incorrect or correct statement from the given statements, those that require an affirmation or refutation of the problem statement in the stem of the question, and those that need a response from the given options that are not phrased as sentences, For example, Q2 asks for which one of the given complex ions is optically active, and here the options require students to examine the structures of the ions before arriving at the correct answer. It is expected that the reasoning for their choice of answer in such questions would provide useful insights on the students’ thinking, which may lead to the possible identifying of ACs. The use of different types of questions can be helpful in probing students’ understanding in a nuanced manner. There were 30 questions in total. It is a general practice in diagnostic testing to conduct interviews with a few students to ascertain some of the ACs harbored by them, and use these also in the framing of the distracters in the MCQs in the preliminary version of the diagnostic test. This was not done in our study as we note that interviews are generally time-consuming—for example, only a limited number of students can be selected and interviewed, recordings of the interviews have to be made, transcripts of the interviews have to be generated, and these transcripts have to be carefully studied in order to identify gaps in their understanding of the topic and the ACs harbored by them. We wanted to explore if practitioner knowledge and experience can instead be predominantly used in place of interviews. Teaching staff with experience in teaching this topic and who have interactions with students over tutorials over the years do represent a valuable source which can be harnessed for the purpose of finding out common ACs and learning difficulties. Their views on the topic were gathered over a period of time and

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collectively represent useful insights and perspectives which should not be underestimated. For example, the first author’s teaching and research experience also includes topics on transition metals and advanced coordination chemistry. On the other hand, generation of ACs from interviews of a few students (out of the hundreds in a cohort) represent the ACs prevailing among these students in that cohort—and it may not necessarily be representative of the entire cohort, though these would still be useful. This is, of course, not to discount the importance of interviews, which still represent a very important way to probe students’ understanding in a nuanced manner. It could be thought that a closed instrument was used to probe students’ understanding of the topic at this stage. Our stance is that ACs and learning difficulties of students, based to a good extent on the knowledge and experiences of a practitioner teaching the topic, can have more generalizability than those culled from interviews of a few students in the cohort. Additionally, it provides us with an opportunity to assess whether a preliminary version of the diagnostic instrument can be framed in good measure using this approach. Since such an approach generally differs from the usual approach used in the diagnostic literature, it would be of interest to explore and assess its use. Further, it has to be reiterated that when students were requested to provide an explanation for their choice of answer for each MCQ item in the test, examination of the justification responses for the existence of ACs and incomplete understanding would help us to frame the distracters for the reason tier in the next version of the instrument. It could be argued that the lack of interviews may be perceived as taking the easy way out in terms of constructing the instrument—our stance is that even without interviews, it is still possible to document ACs as long as the approach used is robust. More importantly, we wish to reiterate that in the preliminary version of the instrument, the additional requirement for justification responses from students can also provide rich insights into students’ thinking and, in the case of incorrect reasoning, can provide, in place of interviews, a good indication of the existence of ACs and learning difficulties in students’ own handwriting. The preliminary version of the TMCDI was administered to a sample of 123 university students who had completed a module on transition metals chemistry about two to three semesters earlier. They were informed about 2 weeks in advance of the test to revise this topic. Slightly more than 1 h was given for them to complete the test, and it was found that this time duration was adequate. As the students were helping out in the research, it was essential that some indication of the time required be intimated to them in advance as they may have other commitments after the test. Senior students were selected for the preliminary instrument because they have already completed the topic. It was relatively easy for them to revise the topic since they were also doing an advanced module on transition metals chemistry. The test papers were marked, and options chosen for the questions as well as the corresponding justification responses were keyed into an Excel file. Based on the prevalence of the incorrect responses, the distracters for the second tier for each question were carefully framed for the next version of the instrument. For some questions, where no reasons were given by the students or where the reasons given were not clear or did not make sense, the authors used their own teaching experience to finalize the choice of responses. For example, some students provided a reasoning using phrases such as “it is a fact”, “I feel so”, “by elimination of other choices”, “I guess” to support their answer that the magnitude of the crystal field stabilization energy in tetrahedral complexes is considerably less than that in octahedral complexes. These reasons do not make any use of the language of chemistry. Regarding one of the definitions of a ligand, some students selected their right answer as: a ligand can act as a Lewis base to form a metal complex, but their reason is in the form of phrases such as “by the elimination of other choices”, “the rest of the choices are wrong”, “this is obvious answer” “according to definition”, “memorizing from notes”, etc. We acknowledge that interviews would have helped us to probe their understanding further in this regard.

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Questions which elicited above 75 % correct responses were left out for the next phase of the study as these were deemed to be rather easy for the students. It is a standard practice in item testing to leave out questions that exceed this percentage of correct responses (Rust and Golombok 1989). Additionally, facility index (FI) and discrimination index (DI) values as well as the % options chosen in the answer tier of the questions in the preliminary version of the test were further used to fine-tune the instrument for the pilot study. The FI for a question refers to the proportion of students who provided correct responses to a question—it is equal to the number of students who scored correctly for a question divided by the total number of students who attempted that question. The DI for a question refers to the extent to which a question can discriminate between the top 25 % of the sample and the bottom 25 % of the sample, based on overall test scores—it is the difference between the proportion of students who answered correctly in the top 25 % minus the proportion of students who answered correctly in the bottom 25 %. A DI value greater than 0.3 is recommended for inclusion of an item (Rust and Golombok 1989). In total, 27 questions in two-tier format were drafted for the pilot version of the TMCDI. The pilot version of the instrument was sent to two academics in the first author’s university for content validation. Both academics had at least 5 years of experience in teaching the topic at the university level and also have research interests in advanced transition metals chemistry and metal coordination chemistry, besides other areas. To guide them in validation, a checklist was attached to the TMCDI for them to complete. Items in the check list required them to tick columns with respect to the following: is the content of the test within the university syllabus in chemistry; are the answer keys given for both tiers correct; are the distractors plausible and do they represent possible ACs; overall, is the instrument appropriate for testing students’ understanding of key concepts in transition metals chemistry; etc. There was also space in the checklist for them to provide written comments. Additionally, they were encouraged to annotate on the instrument any comments related to the questions. The feedback given by the validators was very positive. Inter-rater agreement was better than 0.85, and this is considered good. Some minor comments given by them were taken into consideration in revising certain questions, including the distracters for the answer and reason tiers. Confidence ratings were then added to each tier of the questions—the six levels range from Just guessing to Absolutely confident. A six-point scale was also used by Caleon and Subramaniam (2010a) and Sreenivasulu and Subramaniam (2013) for their four-tier instruments, and it seems adequate for use in our study as well. The pilot version of the TMCDI in four-tier format was then administered to a different sample of students (N=120). Prior to the test, the students were briefed about the purpose of the study, the format of the instrument, and how to use confidence ratings in the answer and reason tiers of the questions. For this phase of the study, we sought to determine whether the questions and responses were phrased in a manner that did not pose misunderstandings; whether the students had any problems in answering questions set in four-tier format, including making use of confidence ratings to indicate their levels of confidence for their responses (as this is a new format which they have not encountered before); and whether the test could be completed within the allocated 1 h. While the pilot test was in progress, the students were also requested to clarify with the first author any ambiguities they came across in the phrasings of any of the questions—this can help us to fine-tune the instrument for the main study. At the end of the pilot test administration, it was noted that the 1 h allocated for the test was adequate and that no student asked for any clarifications in relation to the phrasing of any of the questions. They also had no issue with the use of confidence ratings to answer the questions—after all, they were undergraduate students who could be expected to make use of these in indicating the confidence of their responses.

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For the analysis of the pilot study results, the responses for each question were keyed into an Excel file. Statistics that were calculated included the following: % of options chosen for answer and reason tiers of a question, confidence level selected for each of these options, FI, DI, and Cronbach Alpha. Based on a review of these measures, two questions were deleted for the final version of the instrument as these were considered easy, and the distracters for a few questions were further improved to enhance the effectiveness of the questions. For this version, we did not include a blank option in the reason tier for students to write their own reason. This is due to a few reasons— the number of questions in the test seems to be on the high side, the time duration for the test was rather tight as it had to be completed during curriculum time, and the number of options for each question seemed to us to be sufficient with respect to the principal objectives of the study. Moreover, the cognitive processing required of students to answer the questions and indicate confidence levels is already somewhat on the high side—if a blank option is included, we felt that most students would not make use of it. A sample question in four-tier format is shown here: 1. The magnitude of the crystal field splitting in tetrahedral complexes (Δt) is significantly less than that in octahedral complexes (Δo). Is this statement true or false? Answer (a) True (*) (b) False Confidence Rating for Answer 1

2

3

4

5

6

Just Guessing

Very Unconfident

Unconfident

Confident

Very Confident

Absolutely Confident

Reason (a) There are only four ligands instead of six, so Δt = 4/9 Δo (b) The direction of the orbitals does not coincide with the direction of the ligands, thus reducing the crystal field splitting further (c) (a) and (b) are both correct (*) (d) (a) and (b) are both wrong

Confidence Rating for Reason 1

2

3

4

5

6

Just Guessing

Very Unconfident

Unconfident

Confident

Very Confident

Absolutely Confident

Correct responses (*)

The final version of the TMCDI comprised 25 questions in four-tier format, and it was used for the main study. Most questions have four distracters and a few have five or six distracters— in the case of the latter, the additional distracters were found to be plausible options for use, in view of the nature of the questions, to probe students’ understanding further. Provision of more distracters in these questions also serves to enhance the cognitive processing needed by students to sieve the correct answer from the responses and thus serve to enhance the

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robustness of these questions as well as possibly uncover further ACs. A copy of the diagnostic instrument can be obtained from the authors on request. Samples A total of 140 university students majoring in chemistry at the first author’s university participated in the main phase of the study on a voluntary basis. The students were in the second year of their B.Sc. program in Chemistry and were of 19–21 years of age. These students were not involved in the preliminary and pilot phases of this study, and they had all completed a course in transition metals chemistry. They were given 2 weeks advance notice to prepare for the test. Consent to participate in the study was sought via email 2 weeks before the test administration. The students were informed that it would be a diagnostic test, which seeks to determine their ACs and that the findings from the study would be used for research purposes. Further, only summarized findings would be reported and individual responses, if used, would not be identifiable. They were also informed that their grades in the test would not be counted towards their final course grade and that how they performed in the test is confidential to the researchers taking part in the study. During the test administration, the purpose of the study was further reiterated and confidentiality of their responses was further assured. An important reason why the students were willing to participate in the study was that it was a useful “class test” for them to see how well prepared they were in this topic before they sit for their semestral examination a few weeks later. Treatment of Data The following were the steps that we took: (a) All the test papers were marked, based on the answer and reason keys given (b) For each question, the following variables were ticked on an Excel file for each student— option selected for answer tier, confidence selected for answer tier, option selected for reason tier and confidence selected for reason tier. (c) Based on (b), the following measures were determined, as detailed in Caleon and Subramaniam 2010b: % of students who scored only answer correctly, % of students who scored only reason correctly, % of students who scored both tiers correctly, FI, DI, Confidence when correct (CFC) for each question—this is the mean confidence of students who provided correct response for a question and is calculated by totaling their confidence ratings and dividing it by this number of students; Confidence when wrong (CFW) for each question—this is the mean confidence of students who provided incorrect response/s for a question and is calculated by totaling their confidence ratings and dividing it by this number of students; Mean Confidence (CF) for each question—this is the confidence indicated for each question, irrespective of whether it is right or wrong, and is obtained by totaling the confidence ratings for a question and dividing it by the total number of students; Confidence Discrimination Quotient (CDQ)—this indicates whether students can distinguish between what they know and what they do not know, and is equal to CFC−CFW/standard deviation for CF; and Confidence Bas (CB)—this indicates how calibrated students are in the confidence of their responses with respect to the accuracy of their responses and is given by {(CF−1)/5}-proportion of students who gave correct responses. The % of students in the various scoring ranges was also determined. For assessing the internal consistency of the test, Cronbach Alpha and split-half reliability were determined, based on the cognitive scores. For the determination of FI and DI, the criterion used was that responses for both tiers of the questions must be correct. For

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determining reliability using split-half approach, the test papers were arranged serially and then sorted out into two piles on the basis of odd and even numbers. Reliability of the confidence ratings for the test was also determined. IBM SPSS Statistics (Version 19.0) was used for computing reliability statistics. For the identification of ACs, the approach of Tan et al. (2002) was used. In their approach, ACs were identified on the basis of incorrect answer/reason combinations selected by at least 10 % of the sample. For the strength of the ACs, the approach of Caleon and Subramaniam (2010b) was used (see earlier section).

Results and Discussion Prior to the administration of the four-tier diagnostic test, the students had completed a module on transition metals chemistry, which comprised lectures (plus a few tutorials) that focused on topics such as variable oxidation states, formation of colored compounds, magnetic properties, formation of complexes, catalytic properties, etc. Furthermore, the properties of complexes such as color and magnetic nature were also highlighted in light of crystal field theory while applying to various examples of octahedral, tetrahedral and square planar complexes. Unless these fundamental concepts are properly understood, topics related to structure-bonding and structure-property relationships in transition metals chemistry can become arduous. Despite all these, some learning difficulties seemed to persist among the students. Test Statistics Mean FI for the test was 0.59 for the answer tier, 0.46 for the reason tier, and 0.38 for both tiers. These values indicate that the test was more on the difficult side. Mean DI for the answer tier was 0.39. This shows that the test was able to reasonably discriminate the top 25 % from the bottom 25 % of the samples on the basis of the answer tier. The reliability of the test with respect to cognitive scores, based on Cronbach Alpha, was 0.54 for the answer tier and 0.48 for the reason tier (Table 2). If based on split-half reliability, the respective values were 0.53 and 0.50. If both tiers are considered, the alpha values are relatively higher. The somewhat modest values of Cronbach Alpha are due to the fact that the test was on the difficult side, as reflected by the low test scores (Mehrens and Lehman 1991). However, the values obtained are considered to be satisfactory for criterion-referenced tests (Popham and Husek 1969), which the TMCDI is. Caleon and Subramaniam (2010a) and Sreenivasulu and Subramaniam (2013) also obtained modest alpha values for their four-tier instruments for the cognitive scores when both tiers are considered. In particular, the increase

Table 2 Reliability statistics for four-tier test on transition metals chemistry for main study (N=140) Reliability statistic

Answer Score

Reason Confidence

Score

Both Confidence

Score

Confidence

Cronbach alpha

0.54

0.67

0.48

0.64

0.60

0.70

Split-half method

0.53

0.68

0.50

0.63

0.61

0.71

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in reliability when both tiers are considered attests to the importance of using the reason tier in tandem with the answer tier in assessing students’ understanding. The reliabilities for the confidence ratings are higher: 0.67 and 0.64 for the answer and reason tiers respectively according to Cronbach Alpha, and 0.68 and 0.63, respectively, according to split-half reliability (Table 2). If both tiers are considered, the reliability is slightly higher. Test Scores Though the focus of the study is on ACs, it is of interest to consider how the students performed on the diagnostic test. Table 3 shows the results of the test according to two different scoring schemes. If the test were to be marked as a typical MCQ test, that is, taking into consideration only the answer tier, 15.7 % of the students would have a score of 70 and above. The number of students in this scoring range drops to zero if correct responses for both tiers are mandated. Likewise, for the other scoring ranges, students fared better in the answer tier than for both tiers. For the scoring range below 50, 22.1 % of the students got the A-tier correct while 82.1 % got both tiers correct—the latter is more due to the fact that these students got only a few questions correct for both tiers; these were accompanied by generally low confidence ratings. Table 4 shows how students performed for each question in the 25-item diagnostic test. The test was generally difficult—the mean score for the test was 0.38 (that is, 38 %), based on correct responses for the answer and reason tiers of the questions. If only the answer tiers were considered, the mean score for the test is 0.59 (that is, 59 %). This finding further reiterates the point that traditional multiple choice questions have some drawbacks—students can get some of the questions correct through guessing, use of partial knowledge or elimination of unlikely options. If they are mandated to justify their choice of answer in the reason tier, there is better scope for checking on their understanding, thus enhancing the efficacy of the test. The low test scores are not surprising and are consistent with other studies in the diagnostic literature where students, even those at the university level, do not score highly in such tests. Confidence in Answering Questions Students’ confidence in answering questions can shed some light on whether the correctness of their response matches their confidence. For example, if a response to a question is correct but is assigned the lowest confidence rating, it indicates lack of knowledge rather than content proficiency. In traditional MCQ tests, the correct response would be treated as content proficiency! Likewise, if the response for a question is incorrect but assigned the highest possible confidence rating, then it indicates an AC—in traditional MCQ tests, the incorrect response would probably be treated as lack of understanding or lack of knowledge of the concept tested. Where students’ confidence comes in between the interval from Just guessing to Absolutely confident, it has to be interpreted accordingly. The above interpretations follow from the work of Hasan et al. (1999); Klymkowsky et al. (2006), and Caleon and Subramaniam (2010a). Table 3 Cognitive scores for fourtier test

Scores (%)

% students (A-tier correct)

% students (Both tiers correct)

70 and above 60–69

15.7 39.3

0 7.9

50–59

22.9

10

Below 50

22.1

82.1

0.61

0.11

0.35

0.51

0.75

0.75

0.91 0.59

0.37

0.79

0.66

0.63

0.22

0.20

0.75 0.79

11

12

13

14

15 16

17

18

19

20

21

22

23 24

0.85 0.38

7 8

10

0.56

6

9

0.99

0.73

0.16

3

4

0.88

5

0.69

2

0.45 0.57

0.17

0.24

0.57

0.52

0.75

0.29

0.75 0.49

0.48

0.44

0.66

0.41

0.10

0.36

0.25 0.22

0.34

0.75

0.78

0.19

0.60

0.45

0.36

0.44 0.51

0.16

0.14

0.44

0.51

0.66

0.23

0.69 0.39

0.46

0.33

0.36

0.30

0.09

0.27

0.19 0.21

0.33

0.69

0.78

0.14

0.56

4.06 4.26

3.40

3.84

2.39

3.21

3.99

2.81

4.52 2.84

3.40

4.15

3.46

2.87

2.94

3.40

3.91 3.11

3.92

3.85

5.09

3.98

3.44

3.84

CF

Both

A

R

A tier

Proportion correct

1

Question

4.23 4.47

3.18

3.84

2.56

3.43

4.35

2.98

4.57 2.98

3.57

4.53

3.90

3.37

3.13

3.58

4.04 3.09

4.06

4.29

5.12

3.96

3.64

4.25

CFC

3.57 3.48

3.50

3.81

2.04

2.79

2.67

2.63

4.08 2.50

2.69

3.11

2.88

2.60

2.94

3.15

3.14 3.11

3.59

2.53

3.00

3.94

2.29

2.88

CFW

0.54 0.82

0.18 0.15

0.32

2.31

−0.16

−0.28

3.31

−0.07

2.86 3.06

3.49

3.61

3.62

0.43

2.63

−0.06

4.01 2.86

3.11

3.96

3.40

2.57

2.72

3.36

3.90 2.68

0.13

0.01 −0.02

0.02

0.30

0.13

0.07

0.30

0.21

0.39 0.21

3.97

3.92

−0.12 0.26

4.68

0.04

3.84

3.48

0.45

3.51

−0.07

CF

0.21

CB

0.03

0.36

0.50

1.12

0.30

0.49 0.38

0.70

1.01

0.75

0.59

0.13

0.33

0.64 −0.02

0.39

1.12

2.19

0.02

1.15

0.96

CDQ

R tier

2.83 3.30

2.79

3.45

2.49

3.42

4.04

3.02

4.02 3.15

3.66

4.30

3.72

3.02

2.43

3.82

3.66 2.48

4.08

4.43

4.82

3.62

3.77

3.94

CFC

2.84 2.75

3.60

3.68

2.10

3.24

2.37

2.39

4.11 2.49

2.64

3.62

2.63

3.29

2.76

3.11

3.95 2.72

3.91

2.40

4.19

3.92

3.02

3.05

CFW

0.01

0.34 −0.06 −0.10

−0.66

0.38

−0.17 −0.01 0.37

−0.17

−0.05

−0.13 0.29

0.14

1.19

0.10

−0.09 −0.01

−0.08 0.51 0.50

3.25

−0.04

3.46 3.66

3.45

3.73

2.35

3.26

3.80

2.72

4.27 2.85

4.05

0.26

0.47

3.43

2.72

2.83

3.38

3.90 2.89

3.95

0.79

0.12

−0.21 0.84

0.20 0.26

0.52

0.39 0.13

−0.25 −0.19 −0.26

0.27

0.15

3.89

4.89

−0.11

−0.04

1.36

0.62

3.91

0.42

−0.31

3.46

3.68

CF

−0.06

0.15

CB

0.60

0.74

CDQ

B tiers

3.58 3.89

3.05

3.48

2.51

3.42

4.29

3.27

4.08 3.03

3.66

4.47

3.80

3.29

2.42

3.93

3.48 2.64

4.03

4.43

4.91

3.73

3.79

4.35

CFC

3.37 3.42

3.52

3.77

2.23

3.09

2.88

2.56

4.69 2.74

2.90

3.85

3.21

2.48

2.87

3.27

4.00 2.96

3.90

2.65

4.81

3.94

3.03

3.30

CFW

0.33 0.06 0.03

−0.40 0.16 0.32

0.40

−0.17

−0.06

−0.10

0.12

−0.04 −0.02

−0.01

0.28

0.12

0.04

0.28

0.20

0.39 0.17

0.26

−0.12

0.00

0.44

−0.07

0.18

CB

−0.23

0.20

0.25

0.97

0.58

−0.55 0.22

0.59

0.43

0.45

0.61

−0.33

0.49

−0.40 −0.24

0.11

1.16

0.10

−0.16

0.44

0.58

CDQ

Table 4 Proportion of students who gave correct responses, with values of relevant confidence variables per question (A: Answer tier; R: Reason tier; B: Both tiers)

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0.41

0.59

0.24

Mean

SD

0.19

0.46

0.56

0.19

0.38

0.24

0.60

3.61

3.47

CF

Both

A

R

A tier

Proportion correct

25

Question

Table 4 (continued)

0.61

3.79

3.53

CFC

0.51

3.05

3.43

CFW

0.51

0.57

0.09

CDQ

0.17

0.14

0.25

CB

0.56

3.37

3.28

CF

R tier

0.61

3.51

3.56

CFC

0.60

3.11

3.00

CFW

0.49

0.30

0.44

CDQ

0.18

0.09

0.21

CB

0.55

3.49

3.38

CF

B tiers

0.61

3.64

3.51

CFC

0.63

3.31

3.33

CFW

0.42

0.22

0.15

CDQ

0.17

0.12

0.23

CB

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The mean confidence of the students for the whole test was 3.49 (out of 6)—this means students were, overall, only about 58.2 % confident in the veracity of their responses to the questions! The mean confidence for the answer tier (3.61) was numerically higher than that for the reason tier (3.37); however, the difference is not statistically significant: t(139)=2.57, p>.05. These observations on confidence measures are not to be interpreted as students having difficulties in expressing their confidence—after all, university students are well able to express their confidence for responses to questions in diagnostic instruments (McClary and Bretz 2012; Sreenivasulu and Subramaniam 2013), but that their own judgments on the correctness of their responses to the questions indicate less than confident understanding of the topic. As a result, they were not able to assign the highest possible rating for the confidence scale if they think they have answered a question correctly. Students need to have good understanding of the topic before they can sieve through the responses and arrive at the correct answer in such tests. The test on transition metals chemistry is not meant to be an achievement test but rather a diagnostic test—students usually do better in the former than in the latter. The literature on diagnostic tests, irrespective of topic or level, show that they are generally difficult by nature as it requires good conceptual understanding of the topic in order for students to do well. Previous studies on two-tier tests have reported that students generally find the reason tier more difficult than the answer tier. It might therefore be expected that the confidence levels will also show this trend. Selecting the correct answer in the first tier requires content knowledge while selecting the correct reason in the second tier draws on students’ explanatory knowledge. The findings from the analyses of the confidence ratings (CFC) in this study are generally consistent with observations about the relative difficulty levels of the respective tiers in two-tier tests in previous studies. Similar results were also obtained by Caleon and Subramaniam (2010a) in their study on waves using secondary students and by Sreenivasulu and Subramaniam (2013) in their study of thermodynamics using university students. For the answer tier, the mean confidence when correct (CFC) for the test was 3.79, while the mean confidence when wrong (CFW) was 3.05; the difference is statistically significant: t(139)=2.85, p<.05. That is, when students are able to get an answer correct but are not able to assign the highest possible confidence rating, it indicates that there are some gaps in their conceptual understanding of the topic—also the mean CFC value, being just above the midpoint of the scale, indicates that students’ responses are generally unlikely to be due to guessing. As for the mean CFW, its value just below the mid-point of the scale indicates that it is unlikely to be due to guessing. The respective values for the reason tier are 3.51 and 3.11. If both tiers are considered together, the respective values are 3.64 and 3.31. Generally, the mean values of CFC and CFW, being at about the mid-point range, show that students’ understanding has not reached a level which can indicate mastery of content. For eight of the items, the confidence bias (CB) was negative when both tiers are considered— that means that students were underconfident in the accuracy of their responses to these questions. Only one question out of the 25 questions elicited a value of zero for CB—that is, students’ confidence matches the accuracy of their responses. This was a question which was generally done well by the students—78 % of the students got both tiers correct. For 16 of the questions, CB was greater than zero, that is, students were overconfident in the accuracy of their responses. The psychological literature indicates that students are generally not well calibrated—that is, their confidence is typically greater than that dictated by the accuracy of their responses (for example, Boekaerts and Rozendaal 2010). This is generally borne out by the results of our study as well. Values of confidence discrimination quotient (CDQ) reveal interesting findings. When both tiers are considered, seven of the questions have negative values—this arises as a result of the CFW for these questions being greater than the CFC. What this means is that for these questions, students displayed greater confidence in their answers when they were actually

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wrong than when they were actually correct! With the mean CDQ values of 0.57 for the answer tier, 0.30 for the reason tier and 0.22 for both tiers for the test, it is clear that the students have rather modest discriminating power between what they think they know and what they think they do not know! It is expected that students will indicate higher confidence when they are correct than when they are incorrect (Lundeberg et al. 2000). What these findings indicate is that the topic of transition metals chemistry poses considerable difficulty even for university students. They were generally not able to indicate high levels of confidence for their correct responses in the test. The students were also generally more confident when they were wrong—that is, they harbored ACs. It is the use of psychometric measures related to confidence ratings such as CFC, CFW, CDQ and CB that has enabled useful perspectives to be obtained. There is thus a need to also look at these measures besides cognitive scores in order to get a better picture of students’ understanding in a topic. Alternative Conceptions Table 5 shows a list of 24 ACs on transition metals chemistry documented in our study. The mean confidence for the ACs ranges from 2.51 to 3.93. Based on the classification scheme of Caleon and Subramaniam (2010b), eight of these can be described as genuine ACs while the remaining can be described as spurious ACs. The classification scheme of Caleon and Subramaniam, based on their study on the topic of waves using secondary students, is quite rigorous, and it is likely that some of the spurious ACs in our study can well be labeled as genuine ACs. A commentary on some general trends in relation to the ACs observed is now presented. For convenience, we classify the ACs into a few categories. Only the more important ACs are discussed. (i) Crystal field theory Concepts related to crystal field theory find considerable importance in the study of transition metals chemistry in relation to the geometry around the metal ion, bonding, magnetic properties, color, stability (as predicted by ligand field stabilization energy) and reactivity of their complexes. However, one fundamental inadequacy of crystal field theory is that the point charge and electrostatic model do not represent the actual situation of a metal ion in the electrostatic field of ligands approaching it. Learning difficulties related to appreciating the nuances of this theory can lead to the development of ACs, which can complicate further understanding of the topic. A number of ACs related to crystal field theory was diagnosed for the students in the test. Question 6 listed a number of complexes, where the students were asked to identify the one that has the highest crystal field splitting energy. This led to the confirmation of an AC: The magnitude of the crystal field splitting in a transition metal complex is highest when a strong- field ligand is coordinated to the central metal ion, irrespective of the geometry of the complex—expressed by 16.4 % of the sample with mean confidence of 3.75. In addition to this, it was noted that in a few tutorial classes, some students have tried to generalize a few inconsistent ideas—for example, octahedral complexes have higher crystal field splitting because of six ligands around the central metal ion. In contrast to this, some students were able to recognize that a square planar complex with four ligands around the central metal ion can exhibit higher crystal field splitting compared to an octahedral complex with six ligands (here the ligands are considered as monodentate ligands). Another AC found from this question is: The highest crystal field splitting occurs when a complex has the metal ion in a higher oxidation state, irrespective

Res Sci Educ Table 5 Alternative conceptions on transition metals chemistry S/n

Question number

Alternative conception

% of sample with alternative conception

Mean confidence

1

Q2 dd

25.0

2.66

2

Q3 aa

30.0

3.93

3

Q3 ad

Compared to complexes of monodentate ligands, those of bidentate ligands are more asymmetric and so are optically active The complex [Co(C2O4)3]3− is diamagnetic because the central metal ion is coordinated to a strong-field ligand The complex [Co(C2O4)3]3− has zero magnetic moment because of the (strong-field) ethanedioate ligand

11.4

3.93

4

Q6 ab

16.4

3.75

5

Q6 cd

The magnitude of the crystal field splitting in a transition metal complex is highest when a strong field ligand is coordinated to the central metal ion, irrespective of the geometry of the complex The highest crystal field splitting occurs when a complex has the metal ion in a higher oxidation state, irrespective of the geometry of the complex

20.7

3.75

6

Q6 ec

For a complex to show the highest crystal field splitting, it should have CN– ligands coordinated to it in a square planar geometry

21.4

3.75

7

Q8 ab

A metal ion in d5 configuration in a complex with octahedral geometry results in more crystal field stabilization energy

10.0

2.92

8

Q8 cd

When the ligand is larger, the metal complex adopts tetrahedral geometry

38.6

2.92

9

Q9 de

A complex with high crystal field splitting energy has the least magnetic moment

29.3

3.13

10

Q10 aa

In solid copper sulfate crystals, there are five water molecules coordinated to Cu2+

32.1

2.85

11

Q10 dd

In solid copper sulfate crystals, each copper (II) is coordinated to only one sulphate since water molecules have been lost due to dehydration

16.4

2.85

12

Q11 ca

A transition metal in zero oxidation state cannot attract ligands, and hence cannot form complexes

25.0

2.95

13

Q11 dd

The tendency for transition metals to involve all 3d-electrons in bonding will not decrease once the d5 configuration is exceeded because beyond this configuration the metal center can use its d-electrons even further to achieve a more stable state

16.4

2.95

14

Q12 ad

The color of vanadyl sulphate is not due to d-d transitions but to charge transfer process

10.7

2.76

15

Q12 bb

Cu+ has unpaired d-electrons which can take part in d-d transitions

17.9

2.76

16

Q14 ac

Transition metals are more electronegative than alkali metals due to partially filled d-orbitals

12.1

2.67

17

Q14 ba

Transition metals are more electropositive compared to alkali metals due to screening effect

10.0

2.67

Res Sci Educ Table 5 (continued) S/n

Question number

Alternative conception

% of sample with alternative conception

Mean confidence

18

Q17 ac

Cu and K are expected to have the same ionization energy for the loss of their 4s electron due to similar screening effect

19.3

2.51

19

Q17 bd

Reactivity of transition metals increases from left to right across a period due to increasing number of electrons

19.3

2.51

20

Q19 ab

Ligand-ligand steric repulsion will increase for small metal ions and large ligands in tetrahedral complexes

11.4

3.02

21

Q21 dd

Ionization energies of transition metals down a group in the periodic table parallel that of alkali metals

54.3

3.75

22

Q22 bb

Only transition metals are colored since electronic transitions involving d orbitals are possible

23.6

3.55

23

Q22 cc

Transition metals are very good oxidants as they can readily accept electrons from reductants

50.0

3.55

24

Q25 ca

Transition metals are good catalysts because they have partially filled d-orbitals that can accept and donate electrons readily

11.4

3.22

of the geometry of the complex, which is expressed by 20.7 % of the sample with mean confidence of 3.75. Yet another AC confirmed from this question is that for a complex to show the highest crystal field splitting, it should have CN– ligands coordinated to it in a square planar geometry—21.4 % of the sample expressed this AC with mean confidence of 3.75. These ACs indicate that students could not correctly apply overall factors such as nature of the ligand, geometry around the metal ion, oxidation state of metal ion, etc. that affect the crystal field splitting energy when it comes to comparing the extent of splitting of d-orbitals in the given complexes. However, in view of the electrostatic approach of crystal field theory, students wrongly correlated the splitting factor with the number of ligands instead of correlating it with the direction of approach of the ligands and their strength, whether strong-field or weak-field. It would be reasonable to argue that there will be lesser magnitude of interaction between the d-orbitals and ligands, and hence low crystal field splitting of d-orbitals in the case of tetrahedral complexes because there are only four ligands around the central metal ion, as compared to six ligands in octahedral complexes. Also, students could not apply the reasoning that Δsp >Δo >Δt, from which it is evident that the crystal field splitting energy in square planar complexes (Δsp) having only four ligands is higher than that in an octahedral complex (Δo) having six ligands (we know that Δsp =1.3 Δo). The nature of the ACs and their confidence values above the mid-point suggests that some instructional effort would be needed by the teacher to remediate these. Further, based on Question 8, 10 % of the sample with mean confidence of 2.92 had an AC: a metal ion in d5 configuration in a complex with octahedral geometry results in more crystal field stabilization energy. The origin of this misinterpretation seems to be rooted in their prior knowledge that half-filled d5 orbitals are stable in Mn2+, which can thus form an octahedral [MnBr6]4- complex with high crystal field stabilization energy. It

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is very likely that students reasoned that octahedral complex will have a metal ion, preferably in d5 configuration, and hence show high crystal field splitting. Rather than this to be labeled as a spurious AC, it is likely to be a genuine AC. When assessing whether a given complex is paramagnetic or diamagnetic, crystal field theory tells us that strong-field ligands give low spin complexes (also when P<Δo) whereas weak-field ligands form high spin complexes (when P>Δo). Question 9 listed a number of complexes formed by transition metals with various ligands and asked which one of these has the least magnetic moment. It uncovered an AC: a complex with high crystal field splitting energy has the least (or zero) magnetic moment. This was harbored by 29.3 % of the students, with mean confidence of 3.13. Here, surprisingly, these students did not know that low spin complexes are formed when the ligands are strongfield—it need not be diamagnetic in nature always. For a low spin complex, it does not mean that its magnetic moment has to be zero. But for a diamagnetic complex, the magnetic moment is expected to be zero. With the mean confidence exceeding the midpoint, it is clear that this AC is quite strongly held by the students and can be considered to be a genuine AC. (ii) Geometry of complexes The geometry around a metal ion in a complex is an important aspect in the study of transition metals chemistry. The stereochemistry of metal complexes is governed by electrostatic and electronic factors. The former concerns the ligand-ligand repulsions that tend to stabilize the most energetically favored geometry. The latter refers to the stability of each possible geometry for a given electronic configuration, that is, d n. Thus, the choice of ligands determines the preferred and most favorable geometry of the complex formed. From our teaching experience, we already know that students harbor quite a number of inconsistencies related to this aspect of the topic. It would be of interest to see whether the diagnostic questions would be able to further confirm this. An AC derived from question 2, where students were asked to choose an optically active complex from the given choices, is: compared to complexes of monodentate ligands, those of bidentate ligands are more asymmetric and so are optically active. 25 % of the students have this AC, and it was expressed with mean confidence of 2.66. This spurious AC can easily be rectified by targeted instruction. Question 8 confirmed an AC: when the ligand is larger, the metal complex adopts tetrahedral geometry. This was possessed by 38.6 % of the students with mean confidence of 2.92. For this question, the students answered that the complex formed between Mn2+ and Br− is tetrahedral [MnBr4]2− because of the larger size of the Br−, although some of them were able to correctly answer this based on the preliminary concept of sp3 hybridization (although hybridization theory is considered less important in bonding in metal complexes) in Mn2+. It seems to be true that tetrahedral complexes are favored when the ligands are larger and owing to the minimization of steric and electrostatic effects, such as ligand-ligand repulsions, but this may not be generalized as such and always. For instance, when the ligands are bulky or larger—as in the case of Cl−, Br− and I−, the ligand-ligand repulsions override the energy advantage of forming more metalligand bonds. Also, tetrahedral complexes are common, as in MnO4−, [MoO4]2−, [VO4]3−, [CrO4]2−, [FeCl4]2−, [CoCl4]2−, [CuBr4]2−, etc. But it is important to note that tetrahedral complexes are favored over higher coordinated complexes, based not just on the factor of larger ligands. There is another condition required: the metal ion should be in a higher oxidation state and, hence, be smaller—that is, when the metal ion is larger, tetrahedral geometry will be destabilized even though it is surrounded by larger ligands. Furthermore, electronic effects related to the d n configuration of the metal ion are also

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important and need to be considered. For example, more tetrahedral complexes have been identified for Co2+ with d 7 configuration, and d 4 and high-spin d 7 metal ions with halides. Though the confidence level for the AC is below the mid-point mark, it is likely to need careful instructional intervention as it is held by a significant number of students. (iii) Some general properties of transition metals Here, we focus on some ACs identified in relation to general properties of transition metals—for example, ionization energy, colors, magnetic properties etc. While interacting with students during instruction, it has been observed that some students had problems in correctly applying crystal field theory to interpret the magnetic properties of complexes in relation to the nature of the ligands (strong-field versus weakfield). For example, some students indicated that complexes formed by strong-field ligands are diamagnetic, which means such complexes have zero magnetic moment. For question 3, students were required to choose a complex that is diamagnetic (if any) from the listed complexes. It uncovered an AC: the complex [Co(C2O4)3]3− is diamagnetic because the central metal ion is coordinated to a strong-field ligand. This was expressed by 30 % of the sample, with mean confidence of 3.93. Another AC found from this question is: the complex [Co(C2O4)3]3− has zero magnetic moment, because of the (strong-field) ethanedioate ligand. This was possessed by 11.4 % of the sample, with mean confidence of 3.93. For both these ACs, students were not able to decipher the correct reasoning that while strong-field ligands lead to low spin complexes, the magnetic moment need not be zero for all low spin complexes. For example, [Fe(CN)6]3− is a low spin complex and has one unpaired electron due to t2g5eg0 configuration in Fe3+, for which the magnetic moment is non-zero due to the unpaired electron. Actually, a low spin complex becomes diamagnetic when all the electrons are paired, leading to zero magnetic moment. For both these ACs, which are rather similar, the mean confidence is quite high—obviously interventions to address these ACs would need more instructional attention. A transition metal can exhibit different oxidation states in different compounds, as for example, iron showing Fe2+ and Fe3+ states respectively in [Fe(CN)6]4− and [Fe(CN)6]3−. One of the interesting properties of transition metals is their ability to form complexes in which their oxidation state is apparently zero—for example, metal carbonyls such as [Ni(CO)4] and [Fe(CO)5], in which nickel and iron respectively are in zero oxidation states. Despite the apparent zero oxidation state, bonding is possible because each carbonyl ligand donates a pair of electrons to form one bond while the metal ion backdonates an electron pair to form a second bond. In such complexes, π-bonding between the metal atom and the ligand is believed to play an important role. Question 11 presented four statements about transition metals and students were required to choose an incorrect one. Several students could not extend the idea to the possibility of zero oxidation state. It revealed an AC: a transition metal in zero oxidation state cannot attract ligands, and hence cannot form complexes. This was possessed by 25 % of the sample, with mean confidence of 2.95—as the AC is held with relatively low confidence, it is due more to lack of knowledge and can be rectified quite easily. Question 17 tested students’ understanding on the trend in the reactivity of transition metals in the periodic table. When students attempted to choose the correct statement from the choices given, it allowed the following AC to be confirmed: reactivity of transition metals increases from left to right across a period due to increasing number of electrons. This was possessed by 19.3 % of the sample, with mean confidence of 2.51—the low confidence suggests that it would be easy to address this AC through simple instructional intervention. In general, transition metals vary widely in their

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reactivity. Many of them can dissolve in mineral acids. These metals are moderately reactive and combine to give binary compounds when heated with dioxygen, sulfur or halogens (for example, reaction product stoichiometry depends, in part, on the available oxidation states). Combination with H2, B, C or N2 may lead to interstitial hydrides borides, carbides or nitrides. Metals of low reactivity appear to be located toward the end of the transition series, particularly those of the third and fourth series. In general, there is a decrease in electropositive nature across a period as well as decreasing atomic size, causing electrons to be held more tightly. Students thought that colored compounds are formed only by transition metals. Also, that the transition elements are very good oxidants. Question 22 posed four statements about transition metals and asked for which one is true: it showed that 23.6 % of the students have the AC that only transition metals are colored since electronic transitions involving d orbitals are possible—mean confidence is 3.55. Another AC confirmed through this question was: transition metals are very good oxidants as they can readily accept electrons from reductants—half of the sample had this AC, and the mean confidence was 3.55. Actually, many of the transition metals can dissolve in mineral acids although some of them are ‘noble’—that is they have such low electrode potentials that they are unaffected by simple acids. Nevertheless, a few metals in the beginning of the series (for example, Sc3+/Sc couple, for which E° = −2.08 V) are powerful reducing agents. Perhaps, students thought that the transition metal ions act as Lewis acids while accepting electrons from the ligands (Lewis bases), which imply to them that these metal ions are oxidizing the ligands while getting reduced during complexation reactions. Not all but the first series of transition metals in higher oxidation states are strong oxidants and thus are readily reduced. On the other hand, M (II) and M (III) compounds are common among the first series of transition metals; these oxidation states are generally uncommon in compounds of the second and third series of transition metals. Even though the ACs have confidence values above the mid-point, instructional intervention should not be difficult to remediate these. For Question 21, to choose an incorrect statement regarding general properties of transition elements, about 54.3 % of the sample (with mean confidence of 3.75) chose to interpret that ionization energies of transition metals down a group parallel that of alkali metals as they seem to apply the general trend that they learnt in school regarding the periodicity in values of ionization energy as a supporting reason or explanation that ionization energy decreases down a group because outer electrons are further away from the nucleus, and thus easier to be removed. Further, along similar lines, while answering Question 17 regarding general properties of transition metals, about 19.3 % of the sample with a confidence level of 2.51 thought that Cu and K are expected to have the same ionization energy for the loss of their 4s electron due to similar screening effect. In fact, the first ionization energy for copper (Z=29) is higher (744 kJ/mol) than that for potassium (418 kJ/mol; Z=19). As copper has a higher nuclear charge, its nucleus pulls the valence electron more closely than potassium can. Hence, more energy is needed to ionize copper than potassium. Also, the less shielding offered by the d-electrons in Cu leads to high effective nuclear attraction for the 4s1 electron, which results in higher first ionization energy in Cu as compared to K. But students wrongly conceptualized that copper and potassium would have similar screening effects and hence have the same ionization energy for the loss of their 4s electron as the valence electron to be lost (that is, to get ionized) is in the same 4s energy level. Actually, in the case of transition metals, the ionization energy is found to be between 6 to 8 eV. As the electrons are filled in the inner d-orbitals, the electrons that are lost via ionization come from the outer s-orbitals instead (for example, 4s

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orbitals in the case of 3d series of transition elements in period 4). This results in relatively the same effective nuclear charge (Zeff) for the s-orbital electrons across the period and hence the increase in nuclear charge gets significantly offset by the screening provided by the electrons that are added to the inner d-shell. Although the first ionization energy, in general, increases from left to right, the ionization energy of neighboring elements are very nearly the same in the series. While comparing the periodicity of the properties such as ionization energy of the transition elements in the 4th, 5th and 6th periods, it is important to consider the unique observations regarding their atomic radii. Although there is a significant increase in the radius on moving from the 4th to 5th period, the atomic radii of the 5th period transition metals are not that different from those of 6th period due to lanthanide contraction, which is a consequence of a low shielding effect caused by 4f electrons. This lanthanide contraction significantly offsets the normal increase in size due to moving from period 5 to period 6. Thus, the 5th period metals, instead of getting significantly larger than 4d elements, show a small increase in size and are relatively identical to them in atomic size. Thus, the small increase in size, combined with the large increase in effective nuclear charge, explains why the first ionization values generally increase down a transition group. This trend runs counter to that observed in any main group, where heavier members at the bottom of a group are much larger and hence ionization energies are lower.

Conclusion and Implications Compared to school students’ understanding of topics in the sciences, there have been relatively fewer studies devoted to undergraduate students in the science education literature. Especially, in the area of chemistry, the topic of transition metals chemistry has received scarce attention from researchers despite the fact that it is an important topic in the chemistry curriculum. The undergraduate students sat for the diagnostic test after they had completed a module on transition metals chemistry. Generally, the test was on the difficult side, as reflected by the rather low mean scores. If the instrument is marked as a typical MCQ test, that is, taking into consideration only the correct responses for the answer tiers, students would have scored an average of about 59 %. If correct responses for both the answer and reason tiers are mandated, the mean score for the test drops to 38 %, and this is accompanied by a mean confidence of about 58.2 %—this does not reflect particularly good understanding among the sample. The foregoing observations further reinforce the limitations of traditional MCQ tests for use in assessment. There is more scope for checking students’ understanding if they are required to justify their choice of answers. Even then, a better picture of student understanding does not emerge—there could still be elements of guessing, use of partial knowledge or test-taking strategies at work. The incorporation of confidence ratings can help to elicit a more nuanced appreciation of students’ confidence in the accuracy of their responses. As mentioned earlier, there are very few studies done on transition metals chemistry and, as a result, the number of ACs reported in this topic is rather few. The four-tier diagnostic instrument from this study has helped to confirm the existence of 24 ACs after students have undergone a module on transition metals chemistry. It has to be reiterated that the topic is also covered in some depth in the Singapore-Cambridge GCE “A” level examinations in Chemistry, and that a number of the ACs could be a carry-over from their school years. This is in line with other studies on ACs on various topics, where it has been reported that many ACs are resistant to instruction and some are rather tenacious, even at the university

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level. To what extent some of the ACs confirmed in this study are resistant to instruction would need further research. Besides the prevalence of the ACs, data on their strengths are also presented. Some knowledge of the strengths of the ACs is desirable for use by instructors for prioritization purposes, either during teaching or for intervention using conceptual change strategies. Generally, the higher the confidence rating assigned to the AC, it is likely that the more strongly it is held. While two-tier tests are effective in documenting the prevalence of ACs, they are not able to differentiate incorrect answers arising from lack of knowledge from those due to ACs (Caleon and Subramaniam 2010a). By incorporating confidence ratings to two-tier tests, the effectiveness of such tests in identifying students’ ACs can be enhanced significantly. Another limitation of two-tier MCQs is that they are not able to quantify the strengths of the ACs found— knowledge of the strengths of the ACs would be useful for instructors to prioritize intervention to address ACs. ACs held by students with relatively low confidence are more likely to be due to lack of knowledge and can be more easily addressed by students on their own while those held with relatively higher confidence may require some work on the part of the instructor as well. Again, the incorporation of confidence ratings to two-tier questions can help in this regard. In studies involving the development of diagnostic instruments, it is customary to make use of interviews at the early stage to detect gaps in students’ understanding as well as the existence of ACs, all of which can come in useful to frame distracters for the questions. In this study, we did not make use of interviews and instead relied, to a significant extent, on practitioner knowledge and experience to come up with the preliminary version of the instrument in MCQ format in good measure. As mentioned earlier, ACs and learning difficulties uncovered during the interview stage represent those of a few students (among the few hundreds in a cohort) and may not necessarily be generalized for the entire cohort in question. Practitioner knowledge on ACs and learning difficulties on transition metals chemistry, culled from teaching a number of cohorts as well as interactions with students over tutorials, cannot be discounted and has been put to good use in this study. The results of this study show that this approach is also useful in coming up with a preliminary version of the instrument in good measure. When students provide reasons for their choice of answer, the responses can be further analyzed for framing the ACs as distracters for the reason tier of the question. Also, the use of different types of questions, such as conceptual, those involving calculations, those involving the identification of correct/incorrect statements, etc, in the diagnostic instrument has been helpful in obtaining a good picture of students’ understanding on the topic. The 25-item diagnostic instrument in four-tier format developed in the present study can be used to assess students’ understanding of transition metals chemistry and identify areas for intervention. Indeed, many teachers recognize the importance of identifying students’ ACs but lack the means to do this (Morrison and Lederman 2000). In this context, the diagnostic instrument (TMCDI) can be useful. Based on the results of our study, it is clear that the four-tier diagnostic format is suitable for use in AC studies. Besides documenting the prevalence of ACs harbored by the students, it also provides some indication of the strengths of these ACs. As mentioned earlier, knowledge of the strengths of the ACs can be of use during teaching as well as in instructional intervention. There is a need to go beyond documenting ACs to looking at other measures as well—psychometric measures such as CFC, CFW, CDQ, and CB can help to inform teachers about other aspects of learning. With this in mind, the four-tier test format shows significant promise. Use of multiple measures can help to paint a more comprehensive picture of students’ understanding (Boekaerts and Rozendaal 2010).

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Further work The results of this study suggest a few pointers for further research. Firstly, the instrument developed can be used by instructors in other universities to diagnose ACs on transition metals chemistry harbored by their students and determine the extent to which remedial instruction is needed. Secondly, we intend to use the instrument for a cross-national study involving university students—there has been very little research reported in the literature on such areas at the tertiary level. Thirdly, for the ACs harbored rather strongly by students, we aim to develop instructional resources that can help to remediate these ACs so that conceptual change can be promoted.

Limitations The results of our study need to be interpreted in light of the following limitations: (a) It is assumed that the students conscientiously answered the questions in the diagnostic test, including indicating their confidence levels for each tier of the questions. (b) The performance of the students in this test on some aspects of a single topic cannot be used to predict their overall proficiency on the topic of transition metals chemistry or on their performance in the subject of chemistry at the undergraduate level. (c) The diagnostic test used with the students is not a typical achievement test that they are used to. Hence, their scores in the former test would necessarily be lower—in line with other studies in the literature. (d) The performance of the students in this test cannot be used to generalize the performance of all chemistry undergraduates in their cohort or to extrapolate to other cohorts of students. (e) The diagnostic instrument on transition metals chemistry is not a comprehensive test on this topic—there would obviously be other ACs harbored by the students which we have not uncovered in our study. Also, there is scope for improving the items in the instrument.

Acknowledgments We express our gratitude and appreciation to the reviewers who spent considerable time and effort in going through our manuscript, making detailed comments, and providing several suggestions for improvement. The assistance of Honours student Lim Ting Liang and PhD student Ramakrishna Mallampati in this study is gratefully acknowledged. Financial support in the form of a Teaching Enhancement Grant (C-143000-019-001) from the Center for Development of Teaching and Learning at the National University of Singapore is also gratefully acknowledged.

References Amir, R., & Tamir, P. (1994). In-depth analysis of misconceptions as a basis for developing research-based remedial instruction: the case of photosynthesis. The American Biology Teacher, 56(2), 94–100. Ausubel, D. P. (1968). Educational psychology: a cognitive view. New York: Holt, Rinehart and Winston. Banerjee, A. C. (1995). Teaching chemical equilibrium and thermodynamics in undergraduate general chemistry classes. Journal of Chemical Education, 72, 879–881. Barke, H. D., Hazari, A., & Yitbarek, S. (2009). Misconceptions in chemistry: addressing perceptions in chemical education (pp. 235–259). Berlin: Springer. Bodner, G. M. (1986). Constructivism: a theory of knowledge. Journal of Chemical Education, 63, 873–878.

Res Sci Educ Boekaerts, M., & Rozendaal, J. R. (2010). Using multiple calibration indices in order to capture the complex picture of what affects students’ accuracy of feeling of confidence. Learning and Instruction, 20(5), 372–282. Bucat, R., & Mocerino, M. (2009). Learning at the Sub-Micro Level: Structural Representations. In J. K. Gilbert & D. F. Treagust (Eds.), Multiple representations in chemical education. The Netherlands: Springer. Caleon, I., & Subramaniam, R. (2009). Exploring students’ conceptualization of the propagation of periodic waves. The Physics Teacher, 48, 55–59. Caleon, I., & Subramaniam, R. (2010a). Do students know what they know and what they do not know? Using a four-tier diagnostic test to assess the nature of students’ alternative conceptions. Research in Science Education, 40, 313–337. Caleon, I., & Subramaniam, R. (2010b). Development and application of a three-tier diagnostic test to assess secondary students’ understanding of waves. International Journal of Science Education, 32, 939–961. Canolat, N. (2006). Turkish undergraduates’ misconceptions of evaporation, evaporation rate and vapour pressure. International Journal of Science Education, 28(15), 1757–1770. Carson, E. M., & Watson, J. R. (1999). Undergraduate students’ understanding of enthalpy change. University Chemistry Education, 3, 46–51. Carson, E. M., & Watson, J. R. (2002). Undergraduate students’ understanding of entropy and Gibbs free energy. University Chemistry Education, 6, 4–12. Champagne, A. B., Gunstone, R. F., & Klopfer, L. E. (1983). Naive knowledge and science learning. Research in Science and Technological Education, 1(2), 173–183. Chang, J. Y. (1999). Teacher college students’ conception about evaporation, condensation, and boiling. Science Education, 83, 511–526. Chinn, C. A., & Brewer, W. F. (1993). The role of anomalous data in knowledge acquisition: a theoretical framework and implications for science instruction. Review of Educational Research, 63(1), 1–49. Clement, J., Brown, D., & Zeitsman, A. (1989). Not all preceptions are alternative conceptions. International Journal of Science Education, 11, 554–565. Coll, R. K., & Taylor, N. (2001). Alternative conceptions of chemical bonding held by upper secondary and tertiary students. Research in Science and Technological Education, 19, 171–191. Coll, R. K., & Treagust, D. F. (2001). Learners’ mental models of chemical bonding. Research in Science Education, 31, 357–382. Coll, R. K., & Treagust, D. F. (2002). Exploring tertiary students’ understanding of covalent bonding. Research in Science and Technological Education, 20, 241–267. Coll, R. K., & Treagust, D. F. (2003). Investigation of secondary school, undergraduate, and graduate learners’ mental models of ionic bonding. Journal of Research in Science Teaching, 40, 464–486. Cros, D., Amouroux, R., Chastrette, M., Fayol, M., Leber, J., & Maurin, M. (1986). Conceptions of first year university students of the constitution of matter and the notions of acids and bases. European Journal of Science Education, 8, 305–313. Cros, D., Chastrette, M., & Fayol, M. (1988). Conceptions of second year university students of some fundamental notions in chemistry. International Journal of Science Education, 10, 331–336. Driver, R. (1981). Pupils’ alternative frameworks in science. European Journal of Science Education, 3(1), 93–101. Duit, R. (2009). Bibliography—students’ and teachers’ conceptions and science education. Available at http:// www.ipn.uni-kiel.de/aktuell/stcse/stcse.html Duit, R., & Treagust, D. F. (1995). Students’ conceptions and constructivist teaching approaches. In B. J. Fraser & H. J. Walberg (Eds.), Improving science education (pp. 49–60). Chicago, Illinois: University of Chicago Press. Ebenezer, J. V., & Fraser, M. D. (2001). First year chemical engineering students’ conceptions of energy in solution process: phenomenographic categories for common knowledge construction. Science Education, 85, 509–535. Gilbert, J. K., & Watts, D. M. (1983). Concepts, misconceptions and alternative conceptions: changing experiences in science education. Studies in Science Education, 10, 61–98. Gilbert, J. K., Osborne, R. J., & Fensham, P. J. (1982). Children’s science and its consequences for teaching. Science Education, 66, 523–633. Gopal, H., Kleinsmidt, J., Case, J., & Musonger, P. (2004). An investigation of tertiary students’ understanding of evaporation, condensation and vapor pressure. International Journal of Science Education, 26(13), 1597–1620. Granville, M. F. (1985). Student misconceptions in thermodynamics. Journal of Chemical Education, 62(10), 847–848. Hasan, S., Bagayoko, D., & Kelley, E. L. (1999). Misconceptions and the certainty of response. Physics Education, 34, 294–299. Ivowi, U. M. O., & Oludotun, J. S. O. (1987). An investigation of sources of misconceptions. In J. Novak (Ed.), Proceedings of the second international seminar: misconceptions and educational strategies in science and mathematics (vol. 3, pp. 252–257). Ithaca, NY: Cornell University.

Res Sci Educ Johansson, B., Marton, F., & Svensson, L. (1985). An approach in describing learning as change between qualitatively different conceptions. In L. H. T. West & A. Pines (Eds.), Cognitive structures and conceptual change (pp. 235–255). Orlando, FL: Academic Press. Johnstone, A. R. (1971). Conceptual problems associated with d-orbital models. Journal of Chemical Education, 48(1), 74. Kalina, C., & Powell, K. C. (2009). Cognitive and social constructivism: developing tools for an effective classroom. Education, 130(2), 241–250. Kaper, W. H., & Goedhart, M. J. (2002). Forms of energy, an intermediary language on the road to thermodynamics? International Journal of Science Education, 24, 81–95. Kelly, R. M., & Jones, L. L. (2007). Exploring how different features of animations of sodium chloride dissolution affect students’ explanations. Journal of Science Education and Technology, 16, 413–429. Kelly, R. M., & Jones, L. L. (2008). Investigating students’ ability to transfer ideas learned from molecular animations to the dissolution process. Journal of Chemical Education, 85, 303–309. Kelly, R. M., Phelps, A. J., & Sanger, M. J. (2008). The effects of a computer animation on students’ conceptual understanding of a can-crushing demonstration at the macroscopic, microscopic, and symbolic levels. Chemical Educator, 9, 184–189. Klymkowsky, M. W., Taylor, L. B., Spindler, S., & Garvin-Doxas, K. (2006). Two- dimensional, implicit confidence tests as a tool for recognizing student misconceptions. Journal of College Science Teaching, 36, 44–48. Lewis, E. L., & Linn, M. C. (1994). Heat, energy and temperature concepts of adolescents, adults and experts: Implications for curricular improvements. Journal Research in Science Teaching, 31(6), 657–677. Lin, S. W. (2004). Development and application of a two-tier diagnostic test for high school students; understanding of flowering plant growth and development. International Journal of Science and Mathematics Education, 2(2), 175–199. Linda, C. H., & Carl, E. W. (2010). Student interpretations of equations related to the first law of thermodynamics. Journal of Chemical Education, 87(7), 750–755. Lundeberg, M. A., Fox, P. W., Brown, A. C., & Elbedour, S. (2000). Cultural influences on confidence: country and gender. Journal of Educational Psychology, 92(1), 152–159. McClary, L. M., & Bretz, S. L. (2012). Development and assessment of a diagnostic tool to identify organic chemistry students’ alternative conceptions related to acid strength. International Journal of Science Education, 34(15), 2317–2341. Mehrens, W. A., & Lehman, I. J. (1991). Measurement and evaluation in educational psychology (4th ed.). Forth Worth, TX: Holt, Rinehart and Winston. Morrison, J.A. & Lederman, N.G. (2000). Science teachers’ diagnosis of students’ perceptions. Presented at the annual meeting of the National Association for Research in Science Teaching, New Orleans, LA Nakhleh, M. (1992). Why some students don’t learn chemistry. Journal of Chemical Education, 69(3), 191–196. Nicoll, G. (2001). A report of undergraduates’ bonding misconceptions. International Journal of Science Education, 23, 707–730. Odom, A. L. & Barrow, L. H. (2007). High school biology students' knowledge and certainty about diffusion and osmosis concepts. School Science and Mathematics, 107(3), 94–101. Papageorgiou, G., & Sakka, D. (2000). Primary school teachers’ views of fundamental chemical concepts. Chemistry Education: Research and Practice in Europe, 1, 237–247. Pfundt, H., & Duit, R. (2009). Bibliography: students’ alternative frameworks and science education (5th ed.). Kiel, Germany: IPN, University of Kiel. Pinarbasi, T., & Canpolat, N. (2003). Students’ understanding of solution chemistry concepts. Journal of Chemical Education, 80(11), 1328–1332. Popham, W. J., & Husek, T. R. (1969). Implications of criterion-referenced measurement. Journal of Educational Measurement, 6(1), 1–9. Potgietera, M., Malatjeb, E., Gaigherc, E., & Venterd, E. (2010). Confidence versus performance as an indicator of the presence of alternative conceptions and inadequate problem-solving skills in mechanics. International Journal of Science Education, 32(11), 1407–1429. Reynolds, C. R., Livingston, R. B., & Willson, V. (2006). Measurement and assessment in education. Boston: Pearson. Robinson, W. R. (1998). An alternative framework for chemical bonding. Journal of Chemical Education, 75, 1074–1075. Ross, B., & Munby, H. (1991). Concept mapping and misconceptions: a study of high school students’ understandings of acids and bases. International Journal of Science Education, 13(1), 11–23. Rust, J., & Golombok, S. (1989). Modern psychometrics: the science of psychological assessment. Florence, KY: Taylor & Francis/Routledge.

Res Sci Educ Smith, K. J., & Metz, P. A. (1996). Evaluating student understanding of solution chemistry through microscopic representations. Journal of Chemical Education, 73, 233–235. Smith, K. C., & Nakhleh, M. B. (2011). University students’ conceptions of bonding and melting and dissolving phenomena. Chemistry Education Research and Practice, 12, 398–408. Sözbilir, M., Pınarbaşı, T., & Nurtaç Canpolat, N. (2010). Prospective chemistry teachers’ conceptions of chemical thermodynamics and kinetics. Eurasia Journal of Mathematics, Science & Technology Education, 6(2), 111–120. Sreenivasulu, B., & Subramaniam, R. (2013). University students’ understanding of chemical thermodynamics. International Journal of Science Education, 35(4), 601–635. Taber, K. S. (1998). An alternative conceptual framework from chemistry education. International Journal of Science Education, 20(5), 597–608. Taber, K. S. (2004). Intuitive physics: but whose intuition are we talking about? Physics Education, 39, 123–124. Taber, K. S., & Coll, R. K. (2002). Bonding. In J. K. Gilbert, O. De Jong, R. Justi, D. F. Treagust, & J. H. Van Driel (Eds.), Chemical education: towards research-based practice (pp. 213–234). Dordrecht, The Netherlands: Kluwer. Tan, K. C. D., Goh, N. K., Chia, L. S., & Treagust, D. (2002). Development and application of a two-tier multiple choice diagnostic instrument to assess high school students’ understanding of inorganic chemistry qualitative analysis. Journal of Research in Science Teaching, 39(4), 283–301. Tekin, B. B., & Nakiboglu, C. (2006). Identifying students’ misconceptions about nuclear chemistry. A study of Turkish high school students. Journal of Chemical Education, 83(11), 1712–1718. Thomas, P. L., & Schwenz, R. W. (1998). College physical chemistry students’ conceptions of equilibrium and fundamental thermodynamics. Journal of Research in Science Teaching, 35(10), 1151–1160. Tien, T. L., Teichert, A. M., & Rickey, D. (2007). Effectiveness of a MORE laboratory module in prompting students to revise their molecular-level ideas about solutions. Journal of Chemical Education, 84, 175–181. Treagust, D. F. (1988). Development and use of diagnostic tests to explore students’ misconceptions in science. International Journal of Science Education, 10, 159–170. Tsui, C. Y., & Treagust, D. (2010). Evaluating secondary students’ scientific reasoning in genetics using a twotier diagnostic instrument. International Journal of Science Education, 32(8), 1073–1098. Tudela, D. (1999). A common inorganic chemistry textbook mistake: incorrect use of pairing energy in crystal field stabilization energy expressions. Journal of Chemical Education, 76(1), 134–135. Voska, K. W., & Heikkinen, H. W. (2000). Identification and analysis of student conceptions used to solve chemical equilibrium problems. Journal of Research in Science Teaching, 37(2), 160–176. Wandersee, J. H., Mintzes, J. J., & Novak, J. D. (1993). Research on alternative conceptions in science. In D. Gabel (Ed.), NSTA handbook: research in science teaching (pp. 177–209). New York: Macmillan. West, L. T. H., & Fensham, P. (1974). Prior knowledge and the learning and science: a review of Asubel’s theory of the process. Studies in Science Education, 1(1), 61–81. Williamson, V. M., & Abraham, M. R. (1995). The effects of computer animation on the particulate mental models of college chemistry students. Journal of Research in Science Teaching, 32, 521–534. Zoller, U. (1990). Students’ misunderstandings and misconceptions in college freshman chemistry (general and inorganic). Journal of Research in Science Teaching, 27, 1053–1065.