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Evaluating Students' Conceptual Understanding of Isomers Based on a Four-Tier Diagnostic Tool in Upper Secondary Schools

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Title: Evaluating Students' Conceptual Understanding of Isomers Based on a Four-Tier Diagnostic Tool in Upper Secondary Schools
Language: English
Authors: Min Wu, Peiyao Tian, Daner Sun (ORCID 0000-0002-9813-6306), Dan Feng, Ma Luo
Source: International Journal of Science and Mathematics Education. 2025 23(4):907-947.
Availability: Springer. Available from: Springer Nature. One New York Plaza, Suite 4600, New York, NY 10004. Tel: 800-777-4643; Tel: 212-460-1500; Fax: 212-460-1700; e-mail: customerservice@springernature.com; Web site: https://link.springer.com/
Peer Reviewed: Y
Page Count: 41
Publication Date: 2025
Document Type: Journal Articles
Reports - Research
Education Level: Secondary Education
High Schools
Descriptors: Secondary School Science, High School Students, Scientific Concepts, Science Tests, Student Evaluation, Misconceptions, Mastery Learning, Scores, Chemistry
DOI: 10.1007/s10763-024-10494-y
ISSN: 1571-0068
1573-1774
Abstract: This study aimed to develop a comprehensive diagnostic tool for assessing upper-secondary school students' understanding of isomers, expanding upon existing two- and three-tier conceptual diagnostic methods. By incorporating 'Confidence Rating Factor' tiers within the answer and reason sections, a four-tier test was designed and developed. This test was utilized to evaluate students' comprehension of the isomeric conceptual framework and to identify prevalent misconceptions in terms of quantity, complexity, and typicality. The initial phase involved evaluating the reliability and content validity of the developed test before its distribution, resulting in a total of 385 effective test returned for analysis. Data analysis focused on descriptive statistics of students' scores across each tier and dimension, supplemented by unstructured interviews to gain deeper insights. Results indicated a general suboptimal mastery of isomer conceptual understanding among upper secondary school students. Notably, students exhibited higher scores and confidence ratings in the answer tier compared to the reason tier. At both tiers, there was a significant positive correlation between scores and their confidence ratings. Further examination revealed varying levels of proficiency across different content dimensions, with students demonstrating the strongest grasp on the concept of isomers but facing challenges, particularly in 'number judgment and writing'. The study identified eight misconceptions, classified as moderate, serious, and typical across four dimensions, offering valuable insights for teachers. These insights enable teacher to address students' specific learning challenges related to isomers promptly and effectively, ultimately enhancing their understanding and mastery of the subject.
Abstractor: As Provided
Entry Date: 2025
Accession Number: EJ1461684
Database: ERIC
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  Value: <anid>AN0183484467;[3d0g]01apr.25;2025Mar10.03:40;v2.2.500</anid> <title id="AN0183484467-1">Evaluating Students' Conceptual Understanding of Isomers Based on a Four-Tier Diagnostic Tool in Upper Secondary Schools </title> <p>This study aimed to develop a comprehensive diagnostic tool for assessing upper-secondary school students' understanding of isomers, expanding upon existing two- and three-tier conceptual diagnostic methods. By incorporating 'Confidence Rating Factor' tiers within the answer and reason sections, a four-tier test was designed and developed. This test was utilized to evaluate students' comprehension of the isomeric conceptual framework and to identify prevalent misconceptions in terms of quantity, complexity, and typicality. The initial phase involved evaluating the reliability and content validity of the developed test before its distribution, resulting in a total of 385 effective test returned for analysis. Data analysis focused on descriptive statistics of students' scores across each tier and dimension, supplemented by unstructured interviews to gain deeper insights. Results indicated a general suboptimal mastery of isomer conceptual understanding among upper secondary school students. Notably, students exhibited higher scores and confidence ratings in the answer tier compared to the reason tier. At both tiers, there was a significant positive correlation between scores and their confidence ratings. Further examination revealed varying levels of proficiency across different content dimensions, with students demonstrating the strongest grasp on the concept of isomers but facing challenges, particularly in 'number judgment and writing'. The study identified eight misconceptions, classified as moderate, serious, and typical across four dimensions, offering valuable insights for teachers. These insights enable teacher to address students' specific learning challenges related to isomers promptly and effectively, ultimately enhancing their understanding and mastery of the subject.</p> <p>Keywords: Confidence Rating; Four-tier Diagnostic Test; Isomer Conceptual Understanding; Upper Secondary Schools; Misconceptions; Education Specialist Studies In Education</p> <p>Article Note This research study was approved by the Ethics Committee of the School of Chemistry and Molecular Engineering, East China Normal University, Shanghai, China, where the first author is a faculty member and the fourth author is a high school chemistry teacher. Participants were well noticed in the research purpose and research methods. Signed consent was obtained for all participants and their parents. We have no conflicts of interest to disclose.</p> <hd id="AN0183484467-2">Introduction</hd> <p>The acquisition of disciplinary theory heavily relies on a profound grasp of the subject matter (MoE of China, [<reflink idref="bib47" id="ref1">47</reflink>]; National Academy of Sciences-National Research Council, [<reflink idref="bib50" id="ref2">50</reflink>]). Therefore, a central goal of teaching is to nurture students' deep understanding of concepts (Höft & Bernholt, [<reflink idref="bib30" id="ref3">30</reflink>]). In the upper secondary school chemistry, the nature and broad spectrum of concepts often leave students feeling bewildered, hampering their journey toward conceptual mastery. This confusion poses a barrier to recognizing connections and patterns, thus obstructing the establishment of a solid theoretical framework and impeding deep learning (Salame & Casino, [<reflink idref="bib56" id="ref4">56</reflink>]). To tackle this challenge and enrich students' chemistry learning experiences, numerous studies have emerged with a specific focus on enhancing students' conceptual understanding of the subject (Avargil & Piorko, [<reflink idref="bib7" id="ref5">7</reflink>]; Lin & Wu, [<reflink idref="bib43" id="ref6">43</reflink>]).</p> <p>Among the concepts covered in the chemistry curriculum, isomers stand out as crucial elements within the broader landscape of organic chemistry (Prasanson et al., [<reflink idref="bib52" id="ref7">52</reflink>]; Yeşiloĝlu et al., [<reflink idref="bib78" id="ref8">78</reflink>]). Proficiency in isomers and their related concepts is pivotal for students as it underpins a deeper comprehension of organic chemistry structures and functional groups. A solid grasp of these principles empowers students to discern the properties and structures of a wide array of substances, facilitating the construction of a robust foundation in organic chemistry during their secondary school education (National Academy of Sciences-National Research Council, [<reflink idref="bib50" id="ref9">50</reflink>]). Despite the pivotal role of isomers, students often grapple with their abstract nature and complexity (Klein, [<reflink idref="bib40" id="ref10">40</reflink>]; Pabuccu & Erduran, [<reflink idref="bib51" id="ref11">51</reflink>]; Prasanson et al., [<reflink idref="bib52" id="ref12">52</reflink>]; Schmidt, [<reflink idref="bib58" id="ref13">58</reflink>]; Wildayani et al., [<reflink idref="bib74" id="ref14">74</reflink>]). While teachers acknowledge these challenges and actively seek solutions, the outcomes have not always met expectations. A thorough review of existing literature reveals that studies related to isomers are often treated as a fractional component within the broader field of organic chemistry, with a noticeable lack of focus on the teaching and learning of isomers themselves (Hallal & Tlais, [<reflink idref="bib25" id="ref15">25</reflink>]; Isakovna, [<reflink idref="bib32" id="ref16">32</reflink>]).</p> <p>Moreover, existing research on isomers is predominantly entwined with studies on the broader teaching of organic compounds, emphasizing various strategies to facilitate the understanding of isomeric concepts (Isakovna, [<reflink idref="bib32" id="ref17">32</reflink>]; Kan et al., [<reflink idref="bib34" id="ref18">34</reflink>]). These strategies encompass a range of approaches including flowcharts (Yeşiloĝlu et al., [<reflink idref="bib78" id="ref19">78</reflink>]), learning games (Kavak et al., [<reflink idref="bib36" id="ref20">36</reflink>]; Prasanson et al., [<reflink idref="bib52" id="ref21">52</reflink>]), multimedia resources (Wildayani et al., [<reflink idref="bib74" id="ref22">74</reflink>]), teaching models (Treagust et al., [<reflink idref="bib70" id="ref23">70</reflink>]), and software applications (Esselman & Hill, [<reflink idref="bib18" id="ref24">18</reflink>]; Kurbanoglu et al., [<reflink idref="bib41" id="ref25">41</reflink>]). However, empirical studies specifically focusing on diagnosing conceptual understanding of isomers and dissecting students' challenges remain limited (Akkuzu & Uyulgan, [<reflink idref="bib2" id="ref26">2</reflink>]).</p> <p>Presently, various methods exist for assessing conceptual understanding, with one of the most widely employed being the two-tier diagnostic tool. This approach necessitates students to offer answers to questions and subsequently provide reasoning for their responses (Aronsson et al., [<reflink idref="bib4" id="ref27">4</reflink>]; Burrows & Mooring, [<reflink idref="bib10" id="ref28">10</reflink>]; Gericke & Wahlberg, [<reflink idref="bib21" id="ref29">21</reflink>]; He et al., [<reflink idref="bib27" id="ref30">27</reflink>]). By scrutinizing both students' answers and their accompanying reasoning, the two-tier diagnostic tool can roughly discern conceptual understanding and fundamental misconceptions (Singh, [<reflink idref="bib60" id="ref31">60</reflink>]). However, owing to its simplistic structure, it is susceptible to issues such as students guessing or speculating, which can undermine the reliability of assessment outcomes (Kılıç et al., [<reflink idref="bib37" id="ref32">37</reflink>]). Hence, the two-tier test is primarily suitable for the initial diagnosis of students' conceptual understanding (Yang, [<reflink idref="bib76" id="ref33">76</reflink>]).</p> <p>In contrast, the four-tier diagnostic tool encompasses answering the question, rating confidence in the answer, providing reasoning, and rating confidence in the reasoning (Atmaca Aksoy & Erten, [<reflink idref="bib6" id="ref34">6</reflink>]). This format not only evaluates whether students have selected the correct answer and reasoning but also gauges their confidence in their responses, aiding in distinguishing between guessing, lack of knowledge, and genuine misconceptions (Caleon & Subramaniam, [<reflink idref="bib11" id="ref35">11</reflink>]). The four-tier diagnostic tool furnishes more comprehensive and nuanced insights into students' conceptual understanding (Muna & Irawati, [<reflink idref="bib48" id="ref36">48</reflink>]). Moreover, it facilitates a deeper analysis of the interplay between students' content knowledge, reasoning abilities, and metacognitive awareness, yielding richer insights into the learning process (Habiddin & Page, [<reflink idref="bib23" id="ref37">23</reflink>]; Zhao et al., [<reflink idref="bib80" id="ref38">80</reflink>]).</p> <p>Expanding upon this foundation, the present study utilized a four-tier diagnostic tool to undertake a comprehensive exploration of students' comprehension of the isomeric conceptual system in upper secondary schools. The study involved assessing overall conceptual understanding, evaluating performance at each tier and dimension, and scrutinizing the intensity, and typical characteristics of misconceptions within each dimension. Additionally, the study incorporated student interviews to explore the reasons of these challenges, with the intention of offering valuable insights to guide teachers in enhancing their instructional strategies of isomers conceptual system.</p> <hd id="AN0183484467-3">Literature Review</hd> <p></p> <hd id="AN0183484467-4">Conceptual Understanding of Isomer</hd> <p>Conceptual understanding encompasses a range of cognitive processes, including identifying and articulating concepts, grasping the connotation and extension of concepts, establishing connections between them, and applying these concepts in various contexts (Aydin et al., [<reflink idref="bib8" id="ref39">8</reflink>]; Holme et al., [<reflink idref="bib31" id="ref40">31</reflink>]). In alignment with existing research definitions, this study characterizes the conceptual understanding of isomers as the specific definitions students provide for the isomeric conceptual system, along with their opinions and perceptions regarding issues related to the application of isomeric concepts. Students encounter challenges in conceptual understanding, manifested as misconceptions (Goulart da Cunha et al., [<reflink idref="bib22" id="ref41">22</reflink>]; Schmidt, [<reflink idref="bib58" id="ref42">58</reflink>]), and alternative concepts (Abimbola, [<reflink idref="bib1" id="ref43">1</reflink>]; Driver & Easley, [<reflink idref="bib16" id="ref44">16</reflink>]). In this context, misconceptions in isomeric learning refer to students' conceptual understanding of isomers that deviate from accepted scientific explanations provided by researchers or textbooks. Specifically, when a student responds incorrectly with high confidence, it is deemed indicative of a developed misconception (Caleon & Subramaniam, [<reflink idref="bib12" id="ref45">12</reflink>]).</p> <p>Isomers are an essential component of secondary school chemistry education (Copolo & Hounshell, [<reflink idref="bib13" id="ref46">13</reflink>]). Students must master these concepts to deepen their understanding of chemical structures, functional groups, and the identification of properties and structures of various substances. Achieving this mastery is crucial for developing a comprehensive knowledge base in organic chemistry (Copolo & Hounshell, [<reflink idref="bib13" id="ref47">13</reflink>]; Quinkert et al., [<reflink idref="bib54" id="ref48">54</reflink>]). In the upper-secondary school chemistry curriculum standards, the concepts and learning objectives related to isomers are clearly outlined (Klein, [<reflink idref="bib40" id="ref49">40</reflink>]; MoE of China, [<reflink idref="bib47" id="ref50">47</reflink>]; Quinkert et al., [<reflink idref="bib54" id="ref51">54</reflink>]). As detailed in Table 1, the curriculum requires students to be well-versed in the basic concepts of isomers and to apply this knowledge to specific substances. This includes making judgments, distinctions, and practical applications based on these concepts. Nine specific learning objectives have been identified, which encompass understanding the definition and categories of isomers, distinguishing between similar concepts, and writing the structures of isomers.</p> <p>Table 1 Learning Objectives</p> <p> <ephtml> <table frame="hsides" rules="groups"><thead><tr><th align="left" colspan="2"><p>Curriculum standards</p></th><th align="left" rowspan="2"><p>Learning objectives</p></th></tr><tr><th align="left"><p>Themes</p></th><th align="left"><p>Contents</p></th></tr></thead><tbody><tr><td align="left"><p>Compulsory Courses Theme 4</p></td><td align="left"><p>1) Know that isomerism exists in organic compounds</p><p>2) can write the isomers of butane and pentane</p></td><td align="left"><p>1) Define isomerism, carbon chain isomerism, positional isomerism, functional group isomerism</p><p>2) recall the classification of simple organic substances (alkanes, cycloalkanes, alkenes, benzene and its homologs, alcohols, phenols, carboxylic acids, esters, halogenated hydrocarbons) and the functional groups they contain</p><p>3) briefly recall the writing of isomers</p></td></tr><tr><td align="left"><p>Selective Compulsory Courses Module 3 Theme 1</p></td><td align="left"><p>1) Recognise the existence of isomerism in organic compounds such as structural isomerism and stereoisomerism</p><p>(2) Be able to recognize isomerism, write isomers that meet specific conditions, and give examples of stereoisomerism</p></td><td align="left"><p>1) Be able to recall briefly the method of determining equivalent hydrogen</p><p>2) Distinguish between isomers and homologues</p><p>(3) Judge whether they are isomers or homologs of each other about specific substances, etc</p><p>(4) Classify isomers</p><p>(5) Write isomers based on simple chemical formulas, including alkanes, alkenes, halogenated hydrocarbons, alcohols, and esters</p><p>(6) Be able to write isomers of complex substances</p></td></tr></tbody></table> </ephtml> </p> <hd id="AN0183484467-5">Diagnosis of Conceptual Understanding</hd> <p>To effectively gauge students' conceptual understanding and identify potential issues, it is essential to use appropriate diagnostic methods (Soeharto et al., [<reflink idref="bib61" id="ref52">61</reflink>]). Various diagnostic approaches are currently available (Ates & Ceran, [<reflink idref="bib5" id="ref53">5</reflink>]; Temel et al., [<reflink idref="bib69" id="ref54">69</reflink>]).</p> <p>The survey method commonly employs questionnaires or tests to gather information about students' conceptual understanding (Sagala et al., [<reflink idref="bib55" id="ref55">55</reflink>]; Singh, [<reflink idref="bib60" id="ref56">60</reflink>]). This approach is the most prevalent due to its efficiency in collecting large amounts of data, facilitating statistical analysis (Supasorn & Promarak, [<reflink idref="bib64" id="ref57">64</reflink>]). However, surveys typically involve self-reporting by students or standardized tests, which may not reveal students' thought processes or underlying difficulties. The interview method involves face-to-face discussions with students (Aronsson et al., [<reflink idref="bib4" id="ref58">4</reflink>]). This approach can provide deeper insights into students' cognitive structures and underlying problems, but it is time-consuming and requires significant effort, making data analysis more complex. As a result, interviews are often used as a complementary diagnostic tool (Soeharto et al., [<reflink idref="bib61" id="ref59">61</reflink>]). The concept mapping method requires students to illustrate the relationships and hierarchical structures between concepts (Burrows & Mooring, [<reflink idref="bib10" id="ref60">10</reflink>]; Gericke & Wahlberg, [<reflink idref="bib21" id="ref61">21</reflink>]). Concept maps can clearly demonstrate students' conceptual understanding and knowledge construction (Gao et al., [<reflink idref="bib20" id="ref62">20</reflink>]). However, this method demands drawing skills from students and requires specific techniques for analysis, limiting its widespread use.</p> <p>The two-tier diagnostic method is a more recent development in conceptual understanding tests based on standardized assessments (Laliyo et al., [<reflink idref="bib42" id="ref63">42</reflink>]). This method includes two parts: a multiple-choice section and an open-ended explanation section (He et al., [<reflink idref="bib27" id="ref64">27</reflink>]). It requires students to not only select the correct answer but also explain their reasoning (Zakwandi et al., [<reflink idref="bib79" id="ref65">79</reflink>]). This approach allows teachers to assess both students' conceptual understanding and their reasoning processes. However, issues have emerged with the increased use of two-tier tests (Milenković et al., [<reflink idref="bib46" id="ref66">46</reflink>]). These include challenges in avoiding score overestimation due to correct guesses and difficulty in determining whether students achieved points through comprehensive understanding or partial grasp of the concepts (Caleon & Subramaniam, [<reflink idref="bib11" id="ref67">11</reflink>], [<reflink idref="bib12" id="ref68">12</reflink>]).</p> <p>In response to these challenges, Caleon and Subramaniam ([<reflink idref="bib11" id="ref69">11</reflink>]) introduced the Confidence Response Index in two-tier diagnostic tools, resulting in the development of a four-tier diagnostic tool that allows separate confidence ratings for both the answer and reason tiers. This enhancement aligns with the structure of the original two-tier diagnostic test and incorporates a Likert 6-point Confidence Rating scale. Specifically, the four-tier diagnostic test comprises the following components: 1) Answer-Tier (Tier-A)—Students select the answer they believe is correct; 2) Confidence Rating for Answer-Tier (Tier-CF<subs>A</subs>)—Students rate their confidence in their chosen answer from Tier-A using a Likert scale; 3) Reason-Tier (Tier-B)—Students explain the reasons for their choice of answer in Tier-A; 4) Confidence Rating for Reason-Tier (Tier-CF<subs>B</subs>)—Students rate their confidence in the reasons they provided in Tier-B. The structure of the four-tier diagnostic test is shown in Table 2.</p> <p>Table 2 The Structure of Four-Tier Diagnostic Tests for Conceptual Understanding</p> <p> <ephtml> <table frame="hsides" rules="groups"><thead><tr><th align="left" colspan="2"><p>Question</p></th></tr><tr><th align="left"><p>Tier</p></th><th align="left"><p>Option</p></th></tr></thead><tbody><tr><td align="left"><p>Tier-A</p></td><td align="left"><p>A. B. C. D</p></td></tr><tr><td align="left"><p>Tier-CF<sub>A</sub></p></td><td align="left"><p>A. B. C. D. E F</p></td></tr><tr><td align="left"><p>Tier-B</p></td><td align="left"><p>A. B. C. D</p></td></tr><tr><td align="left"><p>Tier-CF<sub>B</sub></p></td><td align="left"><p>A. B. C. D. E F</p></td></tr></tbody></table> </ephtml> </p> <p>By including tiers to gauge confidence levels and reasoning, the four-tier test can uncover misconceptions that traditional multiple-choice tests might overlook (Dewi et al., [<reflink idref="bib15" id="ref70">15</reflink>]). This deeper insight allows teachers to more accurately identify areas where students struggle and implement targeted interventions. Additionally, the structured format of the four-tier test facilitates the analysis of response patterns, helping to pinpoint the specific origins of students' conceptual difficulties (Fadhilatullathifi et al., [<reflink idref="bib19" id="ref71">19</reflink>]).</p> <hd id="AN0183484467-6">Confidence Rating Factor (CRF)</hd> <p>The Confidence Rating Factor refers to diagnostic questions where students are asked to choose an answer and assess their degree of certainty about that answer (Putica, [<reflink idref="bib53" id="ref72">53</reflink>]). Options such as 'very sure,' 'somewhat sure,' and 'not too sure' are typically used, allowing students to reflect on their subjective judgment (Hermita et al., [<reflink idref="bib28" id="ref73">28</reflink>]). In the field of education, Hasan et al. ([<reflink idref="bib26" id="ref74">26</reflink>]) introduced confidence ratings to interpret misconceptions. In Hasan's study, the 'degree of certainty in response' is referred to as the 'Confidence in Response Index,' which is intrinsic to students' self-assessment of conceptual mastery. Takahashi ([<reflink idref="bib65" id="ref75">65</reflink>]) states that high confidence in problem-solving and high scores indicate a good understanding of the concept, while low confidence and low scores indicate a lack of understanding. High confidence with low scores suggests some misunderstanding. This relationship between performance and confidence ratings helps identify students' misunderstandings and guesses (Tekin et al., [<reflink idref="bib68" id="ref76">68</reflink>]). If a student is 'very confident' about an incorrect answer, this indicates a potential deep-rooted misconception (Hasan et al., [<reflink idref="bib26" id="ref77">26</reflink>]). Conversely, if students choose the correct answer but are 'not quite sure,' it suggests they might have guessed correctly. This distinction helps differentiate between answers students understood and those they guessed (Tekin et al., [<reflink idref="bib68" id="ref78">68</reflink>]). Combining answer choices with confidence ratings allows teachers to gain a more comprehensive understanding of students' conceptual knowledge.</p> <p>When calculating confidence ratings, the Overall Confidence rating factor (CF) is most commonly calculated (Wahyuni et al., [<reflink idref="bib72" id="ref79">72</reflink>]). The CF is a measure of the overall level of student confidence. Besides, CFC (Confidence in Correct Answers) and CFW (Confidence in Wrong Answers) are also commonly calculated. CFC indicates the confidence of students who gave the correct answer to the question and CFW indicates the confidence of students who gave the wrong answer to the question (Yan & Subramaniam, [<reflink idref="bib75" id="ref80">75</reflink>]). Calculating these indices helps to identify students' misconceptions and helps to diagnose their cognitive status more accurately (Saputra, [<reflink idref="bib57" id="ref81">57</reflink>]). If a student expresses a high degree of confidence in an incorrect answer, it indicates that there may be a deep-rooted misconception (Zhao et al., [<reflink idref="bib80" id="ref82">80</reflink>]). Teachers can adopt appropriate teaching strategies for different situations, e.g., in cases where students are highly confident of incorrect answers, they need to focus on addressing misconceptions.</p> <hd id="AN0183484467-7">Research Purpose and Questions</hd> <p>Based on the research background, this study developed a four-tier comprehensive test focused on evaluating upper-secondary school students' conceptual understanding of isomers. The specific research questions addressed in this study are outlined below:</p> <p></p> <ulist> <item> What is the extent of students' overall conceptual mastery regarding their understanding of isomers?</item> <p></p> <item> Do variations and correlations exist in students' responses across different tiers of assessment?</item> <p></p> <item> To what extent do students demonstrate comprehension of the sub-conceptual dimensions of isomer understanding?</item> <p></p> <item> What is the prevailing moderate, severe, or typical misconceptions among students regarding their understanding of isomers?</item> </ulist> <hd id="AN0183484467-8">Research Methods</hd> <p></p> <hd id="AN0183484467-9">The Design and Development of the Four-Tier Diagnostic Tool of Isomers</hd> <p>The development of the four-tier isomer test in this study involved the following steps: (<reflink idref="bib1" id="ref83">1</reflink>) identifying the key concepts for the test, (<reflink idref="bib2" id="ref84">2</reflink>) designing preliminary two-tier items, (<reflink idref="bib3" id="ref85">3</reflink>) conducting a pilot test, (<reflink idref="bib4" id="ref86">4</reflink>) creating the formal four-tier test, and (<reflink idref="bib5" id="ref87">5</reflink>) assessing the quality of the four-tier test.</p> <hd id="AN0183484467-10">The Key Concepts Measured in the Four-Tier Test</hd> <p>The design of the conceptual content was based on the learning objectives outlined in the curriculum standard (Table 1). After identifying these learning objectives, the researcher conducted brief online interviews with eight chemistry teachers to gather insights on isomers and students' conceptual understanding of the test content. Details of the interviews are provided in Appendix 1. The responses to questions 1 and 2 were transcribed, and keywords from the teacher interviews were extracted and coded into a frequency table (Table 3). The analysis revealed that, from the teachers' perspective, when students study isomers, they not only need to understand the simple definition of the concept and grasp the connotation of the concept but also need to relate it to the understanding of other basic concepts and apply the concept.</p> <p>Table 3 Frequency of Teacher-Responses' Keywords</p> <p> <ephtml> <table frame="hsides" rules="groups"><thead><tr><th align="left"><p>No</p></th><th align="left"><p>Content</p></th><th align="left"><p>Frequency</p></th></tr></thead><tbody><tr><td align="left"><p>1</p></td><td align="left"><p>Write all possible isomers for the given chemical formulas</p></td><td align="left"><p>8</p></td></tr><tr><td align="left"><p>2</p></td><td align="left"><p>Writing isomers with ordered thinking</p></td><td align="left"><p>6</p></td></tr><tr><td align="left"><p>3</p></td><td align="left"><p>Reasons for the formation of isomers</p></td><td align="left"><p>6</p></td></tr><tr><td align="left"><p>4</p></td><td align="left"><p>Determining the types of isomers</p></td><td align="left"><p>6</p></td></tr><tr><td align="left"><p>5</p></td><td align="left"><p>Correctly identify isomers, homologues, identical substances, isotopes, and allotropes</p></td><td align="left"><p>5</p></td></tr><tr><td align="left"><p>6</p></td><td align="left"><p>Correctly determine which substances are isomers of each other</p></td><td align="left"><p>4</p></td></tr><tr><td align="left"><p>7</p></td><td align="left"><p>Integrated understanding of the concept of isomerism</p></td><td align="left"><p>4</p></td></tr><tr><td align="left"><p>8</p></td><td align="left"><p>Correct understanding of the meaning of 'structurally different'</p></td><td align="left"><p>4</p></td></tr><tr><td align="left"><p>9</p></td><td align="left"><p>Elaborate on this with examples</p></td><td align="left"><p>3</p></td></tr><tr><td align="left"><p>10</p></td><td align="left"><p>Build a physical model of isomerism</p></td><td align="left"><p>2</p></td></tr><tr><td align="left"><p>11</p></td><td align="left"><p>Knowing that isomerism is not limited to organic substances, but that inorganic substances can be isomers of each other, as well as inorganic and organic substances</p></td><td align="left"><p>2</p></td></tr><tr><td align="left"><p>12</p></td><td align="left"><p>Isomers with different physical properties and similar or completely different chemical properties</p></td><td align="left"><p>2</p></td></tr><tr><td align="left"><p>13</p></td><td align="left"><p>Isomers must be studied as compounds</p></td><td align="left"><p>1</p></td></tr></tbody></table> </ephtml> </p> <p>Additionally, the responses of teachers to Questions 3 and 4 were collected and analyzed. The key information from their responses was extracted and combined with relevant literature to create a conceptual map of isomers, as illustrated in Fig. 1.</p> <p>Graph: Fig. 1 Conceptual Map of Isomers</p> <p>Teacher interviews provided theoretical support for the content mapping of the diagnostic tool. Drawing from the definition of conceptual understanding in existing studies, the tool was constructed according to the content dimensions of isomerism. The conceptual system of isomerism was initially divided into four parts: F1 Definition of Isomer, F2 Differentiating Related Concepts, F3 Identifying the Type of Isomer/Isomerism, and F4 Identifying the Number of Isomers and Writing Isomer.</p> <hd id="AN0183484467-11">Initial Two-Tier Item Design</hd> <p>Based on the identified concepts requiring assessment and insights getting from teacher interviews, an initial two-tier test was designed. The design process adhered to specific guidelines:</p> <p></p> <ulist> <item> Both the Answer-Tier and the Why-Part should offer a minimum of n options, with n being no less than 4. Typically, each question presents no more than 8 options.</item> <p></p> <item> The Tier-B section should feature a blank item, affording students the choice to abstain from responding if none of the provided options resonate with their understanding. This fosters flexibility, allowing students to articulate alternative reasoning if the given options fail to align with their comprehension (Voska & Heikkinen, [<reflink idref="bib71" id="ref88">71</reflink>]). The initial two-tier diagnostic test was developed by the researcher, comprising 13 items, each containing 2 questions (answer and reason), as depicted in Table 4.</item> </ulist> <p>Table 4 Initial Two-Tier Test Item Distribution</p> <p> <ephtml> <table frame="hsides" rules="groups"><thead><tr><th align="left"><p>Dimension</p></th><th align="left"><p>Item</p></th></tr></thead><tbody><tr><td align="left"><p>F1 Definition of Isomer</p></td><td align="left"><p>Item 1, Item 2, Item 3, Item 4, Item 5, Item 6</p></td></tr><tr><td align="left"><p>F2 Differentiating Related Concepts</p></td><td align="left"><p>Item 7, Item 8, Item 9</p></td></tr><tr><td align="left"><p>F3 Identifying the Type of Isomer/Isomerism</p></td><td align="left"><p>Item 10, Item 11, Item 12</p></td></tr><tr><td align="left"><p>F4 Identifying the Number of Isomers and Writing Isomers</p></td><td align="left"><p>Item 13</p></td></tr></tbody></table> </ephtml> </p> <hd id="AN0183484467-12">Pilot Test and Item Adjustment</hd> <p>Following the determination of the initial two-tier test items, the pre-test was administered at a secondary school in Shanghai, China, targeting senior students. Out of the administered 42 tests, 8 were deemed invalid due to having more than half of the items unanswered or lacking confidence rating answers, resulting in an effective rate of 81.00%. Subsequently, the open-ended two-tier diagnostic test underwent analysis and categorization. Common error patterns were identified and compiled, as detailed in Appendix 2. Drawing from the insights garnered from the pilot test results and the error rationales among students, adjustments were made to the predictive version of the diagnostic tool under expert guidance, as outlined below:</p> <p></p> <ulist> <item> In item 5, a discrepancy was noted between the order of presentation for the melting and boiling points in the Tier B paragraph and the corresponding answer. Upon receiving guidance from both experts and teachers, the order was rectified to ensure consistency. Consequently, both sections were revised to feature the boiling point preceding the melting point. Additionally, adjustments were made to the language in Tier B, particularly in options C and D, to mitigate partial overlap with the answer paragraph.</item> <p></p> <item> During the administration of the actual test for item 9, it was observed that no students selected options C and D. Upon closer examination, it became evident that these options were not functioning as distractors nor were they inaccurately represented. As per recommendations from experts, the descriptions were subsequently modified.</item> <p></p> <item> During the administration of the actual test for Item 13, it was noted that no student selected reason A. This observation suggests that reason A either served minimally as a distractor or had negligible interference. However, in the blank space provided, some students offered the reason "There are 4 species with a degree of unsaturation of 4 and containing functional ester groups in the molecular structure." Consequently, this reason was incorporated into the item's options.</item> <p></p> <item> Integration and adjustment of some topics and expressions based on experts' opinions.</item> </ulist> <p>The content of the test remained unchanged; only certain statements were revised and enhanced, and a few items were consolidated.</p> <hd id="AN0183484467-13">Final Four-Tier Diagnostic Tool of Isomers</hd> <p>Building upon the framework of the four-tier test, the formal isomer diagnostic tool was formulated. The distribution of items is detailed in Table 5 and provided in Appendix 3 for reference.</p> <p>Table 5 Item Distribution of The Four-Tier Test of Isomer</p> <p> <ephtml> <table frame="hsides" rules="groups"><thead><tr><th align="left"><p>Test Dimension</p></th><th align="left"><p>Item</p></th></tr></thead><tbody><tr><td align="left"><p>F1: Definition of isomer/isomerism</p></td><td align="left"><p>1, 2, 5</p></td></tr><tr><td align="left"><p>F2: Differentiating related concepts</p></td><td align="left"><p>6, 9</p></td></tr><tr><td align="left"><p>F3: Identifying the Type of isomers</p></td><td align="left"><p>3, 4, 7, 8</p></td></tr><tr><td align="left"><p>F4: Identifying the Number of Isomers and Writing Isomers</p></td><td align="left"><p>10</p></td></tr></tbody></table> </ephtml> </p> <p>For the F1 Definition of isomer/isomerism, Item 1 introduces students to two substances featuring typical functional groups (carboxyl and ester groups). By prompting students to discern whether these substances exhibit isomerism, the item aims to gauge their conceptual grasp of isomers, particularly emphasizing the concept of "different structures", and their comprehension of isomerism itself. Item 2 presents fundamental concepts such as Relative Molecular Mass, Element Mass Fraction, and Empirical Formula. It tasks students with determining whether the given Molecular Formula A and B are identical. This approach aims to evaluate students' conceptual understanding of isomers from an inorganic chemistry perspective, employing alternative descriptions. Item 5 furnishes details regarding the variations in melting and boiling points between n-pentane and isopentane. Students are prompted to ascertain the data range for the melting and boiling points of neo-pentane and select the reasoning behind it. The objective is to assess students' capability to grasp the relationship between alkane structure (branching, symmetry) and properties (melting point, boiling point).</p> <p>For F2 Differentiating related concepts, Item 6 evaluates students' comprehension of the distinction between the 'structure' of isomers, emphasizing a three-dimensional structure over a planar one, and their capacity to differentiate between isomers and identical substances. Item 9 examines students' ability to distinguish confusing concepts using two chemical formulas, CH<subs>3</subs>CH<subs>2</subs>OH and HOCH<subs>2</subs>CH<subs>2</subs>CH<subs>2</subs>OH, where share the same functional group but differ in the number of functional groups.</p> <p>In F3 Identifying the Type of isomers, Item 3 combines common substances 1-butene and 2-butene to gauge students' basic understanding of functional group isomerism. Item 4 examines students' understanding of basic carbon chain structures. Item 7, through different representations of butane, tests students' understanding of carbon chain isomerism and their knowledge of simple alkane structures. Item 8 evaluates students' proficiency in distinguishing between the functional groups phenol hydroxyl and alcohol hydroxyl in complex compounds containing benzene rings.</p> <p>In F4 Identifying the Number of isomers and isomer writing, Item 10 employs the provided chemical formula C8H16O2 to ascertain the number of isomers featuring a benzene ring and only one type of functional group. This item aims to assess students' ability to accurately identify the quantity of isomers and articulate them correctly in writing.</p> <hd id="AN0183484467-14">Quality of the Four-Tier Test</hd> <p>After data collection, the test underwent assessment for reliability, validity, and discrimination utilizing SPSS 28.0 software.</p> <hd id="AN0183484467-15">Reliability</hd> <p>The reliability of the formal test results was initially examined. As depicted in Table 6, the test's reliability was assessed for students' responses at each tier and for each dimension. The Cronbach's alpha coefficient surpassed 0.7, indicating strong reliability for the test (Tavakol & Dennick, [<reflink idref="bib67" id="ref89">67</reflink>]).</p> <p>Table 6 Cronbach's Alpha Values of the Test</p> <p> <ephtml> <table frame="hsides" rules="groups"><thead><tr><th align="left" colspan="2"><p>Variables</p></th><th align="left"><p>α coefficient</p></th><th align="left"><p>Total Items</p></th></tr></thead><tbody><tr><td align="left" rowspan="6"><p>Tier</p></td><td align="left"><p>Tier-A</p></td><td align="left"><p>0.838</p></td><td align="left"><p>10</p></td></tr><tr><td align="left"><p>Tier-CF<sub>A</sub></p></td><td align="left"><p>0.880</p></td><td align="left"><p>10</p></td></tr><tr><td align="left"><p>Tier-B</p></td><td align="left"><p>0.801</p></td><td align="left"><p>10</p></td></tr><tr><td align="left"><p>Tier-CF<sub>B</sub></p></td><td align="left"><p>0.837</p></td><td align="left"><p>10</p></td></tr><tr><td align="left"><p>Tier-AB</p></td><td align="left"><p>0.835</p></td><td align="left"><p>10</p></td></tr><tr><td align="left"><p>Tier-CF<sub>AB</sub></p></td><td align="left"><p>0.912</p></td><td align="left"><p>10</p></td></tr><tr><td align="left" rowspan="4"><p>Concept Dimension</p></td><td align="left"><p>G1</p></td><td align="left"><p>0.835</p></td><td align="left"><p>3</p></td></tr><tr><td align="left"><p>G2</p></td><td align="left"><p>0.838</p></td><td align="left"><p>2</p></td></tr><tr><td align="left"><p>G3</p></td><td align="left"><p>0.888</p></td><td align="left"><p>4</p></td></tr><tr><td align="left"><p>G4</p></td><td align="left"><p>0.708</p></td><td align="left"><p>1</p></td></tr></tbody></table> </ephtml> </p> <hd id="AN0183484467-16">Validity</hd> <p>Regarding validity, the specific content of the test items was derived from secondary school chemistry curriculum standards and insights from teacher interviews. Additionally, the test underwent modifications based on pilot testing with students, expert reviews, and consultations with frontline teachers. Consequently, the test exhibits strong content validity. Furthermore, this study evaluated the structural validity of the test. Using students' overall scores of the four-tier test (Tier-AB) for analysis, the Kaiser–Meyer–Olkin (KMO) measure yielded a value of 0.590, indicating adequacy for factor analysis. Subsequently, an exploratory factor analysis (EFA) was conducted to further ascertain the validity of the test. Prior to the factor analysis, a principal component analysis was executed, selecting options based on eigenvalues exceeding 1 and employing the Varimax rotation option. The results of the factor analysis revealed four factors, aligning with the predefined content dimensions. The structural validity of the final test was deemed robust. Table 7 presents the factors and loadings of the items following factor analysis.</p> <p>Table 7 Factor loading coefficients after rotation</p> <p> <ephtml> <table frame="hsides" rules="groups"><thead><tr><th align="left" rowspan="2"><p>Item</p></th><th align="left" colspan="4"><p>Factor</p></th></tr><tr><th align="left"><p>1</p></th><th align="left"><p>2</p></th><th align="left"><p>3</p></th><th align="left"><p>4</p></th></tr></thead><tbody><tr><td align="left"><p>Item 1</p></td><td align="left"><p>0.087</p></td><td align="left"><p>0.735</p></td><td align="left"><p>-0.061</p></td><td align="left"><p>-0.132</p></td></tr><tr><td align="left"><p>Item 2</p></td><td align="left"><p>-0.003</p></td><td align="left"><p>0.641</p></td><td align="left"><p>0.044</p></td><td align="left"><p>0.362</p></td></tr><tr><td align="left"><p>Item 3</p></td><td align="left"><p>0.738</p></td><td align="left"><p>0.112</p></td><td align="left"><p>0.096</p></td><td align="left"><p>0.156</p></td></tr><tr><td align="left"><p>Item 4</p></td><td align="left"><p>0.598</p></td><td align="left"><p>-0.300</p></td><td align="left"><p>0.346</p></td><td align="left"><p>0.030</p></td></tr><tr><td align="left"><p>Item 5</p></td><td align="left"><p>0.055</p></td><td align="left"><p>0.817</p></td><td align="left"><p>0.039</p></td><td align="left"><p>0.081</p></td></tr><tr><td align="left"><p>Item 6</p></td><td align="left"><p>0.181</p></td><td align="left"><p>0.329</p></td><td align="left"><p>-0.411</p></td><td align="left"><p>0.428</p></td></tr><tr><td align="left"><p>Item 7</p></td><td align="left"><p>0.495</p></td><td align="left"><p>0.204</p></td><td align="left"><p>0.034</p></td><td align="left"><p>-0.279</p></td></tr><tr><td align="left"><p>Item 8</p></td><td align="left"><p>0.738</p></td><td align="left"><p>-0.077</p></td><td align="left"><p>-0.050</p></td><td align="left"><p>-0.006</p></td></tr><tr><td align="left"><p>Item 9</p></td><td align="left"><p>0.387</p></td><td align="left"><p>-0.165</p></td><td align="left"><p>0.366</p></td><td align="left"><p>0.405</p></td></tr><tr><td align="left"><p>Item 10</p></td><td align="left"><p>-0.162</p></td><td align="left"><p>0.067</p></td><td align="left"><p>0.752</p></td><td align="left"><p>0.033</p></td></tr></tbody></table> </ephtml> </p> <p> <emph>Extraction method: Principal component analysis. Rotation method: Varimax with Kaiser normalization</emph> </p> <hd id="AN0183484467-17">Discrimination Index (DI)</hd> <p>The discriminability (D) value serves as a crucial parameter for assessing a test's overall efficacy by scrutinizing participants' performance post-testing (Putica, [<reflink idref="bib53" id="ref90">53</reflink>]). The specific criteria are as follows: D < 0.19 indicates poor discriminability, warranting the elimination of the test item; 0.2 < D < 0.29 suggests acceptable discriminability, potentially necessitating modifications; 0.3 < D < 0.39 indicates good discriminability, rendering the item usable; and D > 0.4 signifies very good discriminability, affirming the item's suitability for use.</p> <p> <ephtml> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>D</mi><mo>=</mo><mo stretchy="false">(</mo><mover><mi>M</mi><mo>¯</mo></mover><mi>a</mi><mo>-</mo><mover><mi>M</mi><mo>¯</mo></mover><mi>b</mi><mo stretchy="false">)</mo><mo stretchy="false">/</mo><mrow><mi mathvariant="normal">Full</mi><mi mathvariant="normal">Score</mi></mrow></mrow></math> </ephtml> </p> <p>Graph</p> <p>Note: M̅a: The mean score of the top 27% of students, M̅b: the mean score of the bottom 27% of students.</p> <p>Using the above formula, the discriminability values for Tier-A, Tier-B, and Tier-AB are calculated as 0.418, 0.415, and 0.470, respectively. Considering the normal distribution of students' overall scores, the normal probability-probability (P-P) plots in Appendix 4 illustrate a close alignment of data points along the diagonal. This alignment signifies that the expected cumulative probabilities closely match the observed cumulative probabilities, indicating a well-conforming dataset with a normal distribution. Besides, the normal P-P plot of the residuals demonstrates that the residuals are uniformly distributed around Y = 0, with the majority of residuals within 0.04 of the absolute value. This observation suggests that the data exhibit good normality. Based on the calculated discriminability value and the normal distribution, it can be concluded that this test paper has good discriminability.</p> <hd id="AN0183484467-18">Data Collection</hd> <p>Conducted in secondary schools in Shanghai, China, this study involved the administration of a formal test to 423 senior students who had selected Chemistry for the National College Entrance Examination. Participants were drawn from 6 upper-secondary schools in Shanghai, with an average age range of 16–17 years (Mage = 16–17). The test, lasting 40 min, took place during self-study sessions overseen by class teachers and the researcher. All 423 tests distributed for the study were returned, yielding a 100% response rate. Following the exclusion of 38 invalid tests (Items in the test with more than half of them unanswered or without confidence rating answers), the analysis focused on 385 valid responses, accounting for 91.02% of the total.</p> <p>Following the culmination of data collection, coding, and scoring, the analysis delved into assessing students' overall mastery of isomer concepts and their proficiency at each tier and dimension. Moreover, to gain deeper insights into the underlying causes of students' misconceptions and to elicit their responses to these misunderstandings, 4 students (Student A: female, low achievement level; Student B: male, medium achievement level; Student C: female, medium achievement level; Student D: male, high achievement level), each harboring misconception about isomers, were purposefully selected. This selection was based on their test results, gender, and academic achievement level for unstructured interviews. The primary objective of the interview was to elucidate students' problem-solving approaches and thinking processes when addressing the questions, providing valuable supplementary information to the misconception's analysis. The exemplar interview questions were: <emph>How would you approach a question that involves relative molecular mass and its relationship with isomerism? Do you think these concepts are inherently linked, or do you see them as separate concepts? Can you share any experiences or examples that may have influenced your understanding of this relationship? What are your challenges?</emph></p> <hd id="AN0183484467-19">Data Analysis</hd> <p>This study employed a mixed-methods approach, combining both quantitative and qualitative methods for data analysis (Creswell & Creswell, [<reflink idref="bib14" id="ref91">14</reflink>]; McMillan & Schumacher, [<reflink idref="bib45" id="ref92">45</reflink>]).</p> <hd id="AN0183484467-20">Students Overall Performance Analysis</hd> <p>Quantitative analyses were conducted to assess students' overall proficiency in conceptual understanding of isomers. Initially, students' performances were quantified through point allocation. The overall score (Tier-AB) was determined as follows: a student earned one point if they answered both Tier-A and Tier-B questions correctly for a given item. For Tier-A, one point was assigned for each correct answer, and the same method was applied to Tier-B. The maximum scores for Tier-A, Tier-B, and Tier-AB were all 10.</p> <p>In addition, to fully assess students' overall confidence ratings, descriptive results were derived by calculating mean confidence ratings (Yang, [<reflink idref="bib76" id="ref93">76</reflink>]). The formula for calculating Confidence Ratings is CF= <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mfrac><mn>1</mn><msub><mi mathvariant="normal">n</mi><mn>1</mn></msub></mfrac><msubsup><mo>∑</mo><mrow><mi mathvariant="normal">j</mi><mo>=</mo><mn>1</mn></mrow><mi mathvariant="normal">n</mi></msubsup><msub><mi mathvariant="normal">C</mi><mi mathvariant="normal">j</mi></msub></mrow></math> </ephtml> (n<subs>1</subs> = number of students, C = confidence rating). Since CF was examined on a 6-point scale, the full score for CF was 6. In this study, Tier-CF<subs>A/B</subs> = CF of Tier-A/B; Tier-CF<subs>AB</subs> = (CF<subs>A</subs> + CF<subs>B</subs>)/2.</p> <p>Students' overall performance in Tier-A, Tier-B, Tier-AB, Tier-CF<subs>A</subs>, Tier-CF<subs>B</subs>, and Tier-CF<subs>AB</subs> was evaluated using the scoring methods outlined earlier. Following the scoring process, descriptive statistics were computed for the average scores of students at each tier. These statistics were based on the established reliability and validity of the test, along with considerations of differentiation index and data distribution normality.</p> <hd id="AN0183484467-21">Difference and Correlation Analysis of Students' Performances Across Tiers</hd> <p>To assess variances in students' performance across tiers, paired-sample t-tests were utilized to compare differences between Tier-A and Tier-B, as well as Tier-CF<subs>A</subs> and Tier-CF<subs>B</subs>. Furthermore, for a deeper examination of students' confidence ratings, the study calculated and compared CFC (mean confidence rating for correct answers) and CFW (mean confidence rating for incorrect answers). The calculation method is outlined as follows:</p> <p></p> <ulist> <item> CFC= <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mfrac><mn>1</mn><msub><mi>n</mi><mn>2</mn></msub></mfrac><msubsup><mo>∑</mo><mrow><mi mathvariant="normal">j</mi><mo>=</mo><mn>1</mn></mrow><mi mathvariant="normal">n</mi></msubsup><msub><mi mathvariant="normal">D</mi><mi mathvariant="normal">j</mi></msub></mrow></math> </ephtml> (n<subs>2</subs> = number of students who provide correct responses, D = confidence rating by students who provide correct responses)</item> <p></p> <item> CFW= <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mfrac><mn>1</mn><msub><mi>n</mi><mn>3</mn></msub></mfrac><msubsup><mo>∑</mo><mrow><mi mathvariant="normal">j</mi><mo>=</mo><mn>1</mn></mrow><mi mathvariant="normal">n</mi></msubsup><msub><mi mathvariant="normal">E</mi><mi mathvariant="normal">j</mi></msub></mrow></math> </ephtml> (n<subs>3</subs> = number of students who provide wrong responses, E = confidence rating by students who provide wrong responses).</item> </ulist> <p>In this study, CFC<subs>A/B</subs> = CFC in Tier-A/B; CFW<subs>A/B</subs> = CFC in Tier-A/B; CFC<subs>AB</subs> = (CFC<subs>A</subs> + CFC<subs>B</subs>)/2. CFW<subs>AB</subs> = (CFW<subs>A</subs> + CFW<subs>B</subs>)/2. After the calculation, paired-sample t-tests are also used to compare the differences between CFC<subs>A</subs>-CFW<subs>A</subs>, and CFC<subs>B</subs>-CFW<subs>B</subs>.</p> <p>Moreover, Pearson correlation analysis was used to explore the correlations and relationships between scores at Tier-A, Tier-B, Tier-CF<subs>A</subs>, and Tier-CF<subs>B</subs>.</p> <hd id="AN0183484467-22">Students' Performance in Each Dimension</hd> <p>Based on the overall performance analysis, descriptive statistics were used to describe students' understanding of each dimension. Firstly, this research calculated students' mean scores of Tier-A, Tier-B, Tier-AB, Tier-CF<subs>A</subs>, and Tier-CF<subs>B</subs> in each dimension. The maximum score for Tier-CF<subs>A</subs>, and Tier-CF<subs>B</subs> is 6. When calculating the mean scores for Tier-A and Tier-B, since the number of items in each dimension is different, they are transformed into mean scores per individual item. Thus, the maximum mean score for Tier-A, Tier-B, and Tier-AB in each dimension is 1. The calculation of students' mean scores of Tier-A/B/AB in each dimension can be seen as follows.</p> <p></p> <ulist> <item> F1: <emph>M</emph> (Tier-A/B/AB) = [Tier-A/B/AB (Item 1) + Tier-A/B/AB (Item 2) + Tier-A/B/AB (Item 5)]/3; <emph>M</emph> (Tier-CF<subs>A/B/AB</subs>) = [Tier- CF<subs>A/B/AB</subs> (Item 1) + Tier- CF<subs>A/B/AB</subs> (Item 2) + Tier- CF<subs>A/B/AB</subs> (Item 5)]/3</item> <p></p> <item> F2: <emph>M</emph> (Tier-A/B/AB) = (Tier-A/B/AB of Item 6) + Tier-A/B/AB of Item 9)/2; <emph>M</emph> (Tier-CF<subs>A/B/AB</subs>) = (Tier-CF<subs>A/B/AB</subs> of Item 6 + Tier-CF<subs>A/B/AB</subs> of Item 9)/2</item> <p></p> <item> F3: <emph>M</emph> (Tier-A/B/AB) = (Tier-A/B/AB of Item 3 + Tier-A/B/AB of Item 4 + Tier-A/B/AB of Item 7 + Tier-A/B/AB of Item 8)/4; <emph>M</emph> (Tier- CF<subs>A/B/AB</subs>) = (Tier- CF<subs>A/B/AB</subs> of Item 3 + Tier- CF<subs>A/B/AB</subs> of Item 4 + Tier- CF<subs>A/B/AB</subs> of Item 7 + Tier- CF<subs>A/B/AB</subs> of Item 8)/4</item> <p></p> <item> F4: <emph>M</emph> (Tier-A/B/AB) = Tier-A/B/AB of Item 10; F4: <emph>M</emph> (Tier- CF<subs>A/B/AB</subs>) = Tier- CF<subs>A/B/AB</subs> of Item 10</item> </ulist> <p>Scores for each dimension at every tier were computed, offering a comprehensive overview of students' understanding across various aspects of the subject matter.</p> <hd id="AN0183484467-23">Students Misconceptions Analysis</hd> <p>To identify and assess students' misconceptions, determining their severity and typicality, description statistics were employed. Students were deemed to have developed corresponding misconceptions in an item if they chose incorrectly in Tier-B with a Confidence Rating for Tier-B (Tier-CF<subs>B</subs>) of ≥ 4, irrespective of their responses in Tier-A and Tier-CF<subs>A</subs> (Hoe & Subramaniam, [<reflink idref="bib29" id="ref94">29</reflink>]; Tan et al., [<reflink idref="bib66" id="ref95">66</reflink>]). The severity of misconceptions was evaluated based on the mean confidence rating (Tier-CF<subs>AB</subs>) encompassing both Tier-CF<subs>A</subs> and Tier-CF<subs>B</subs>. Students with a Tier-CF<subs>AB</subs> value between 3 and 4 were considered moderately misconceived, while those with a value exceeding 4 were categorized as seriously misconceived (Yan & Subramaniam, [<reflink idref="bib75" id="ref96">75</reflink>]). Typicality of misconceptions was ascertained by establishing a threshold for the percentage of individuals with a specific misconception. Each of the 10 items presented two tiers of answering (Tier-A) and explaining (Tier B), each involving right and wrong options. With two options in Tier A and four options in Tier B, there were a total of 8 possible combinations of options (2*4 = 8). Each combination had a 12.5% random chance of selection. If a combination was chosen by more than 10% of the sample, exceeding the percentage expected by chance (12.5% + 10%), the misconception was deemed typical. Therefore, the typicality of a misconception was defined as the percentage of individuals selecting that combination of options for the misconception being greater than 22.5% (12.5% + 10%).</p> <p>Besides, the 4 interviewed students (coded as A, B, C, and D) provided valuable insights into their misconceptions. Their interview results were analyzed to complement the quantitative analysis of misconceptions, assessing their severity and typicality. This qualitative data, combined with quantitative findings, facilitated an exploration of the reasons behind students' misconceptions, their problem-solving approaches, and the underlying factors contributing to these misconceptions.</p> <hd id="AN0183484467-24">Results</hd> <p></p> <hd id="AN0183484467-25">Students' Overall Performances in the Conceptual Understanding of Isomer</hd> <p>First, a descriptive statistics analysis was conducted to assess students' overall performance and performance across four tiers—Tier-A, Tier-B, Tier-CF<subs>A</subs>, and Tier-CF<subs>B</subs>. The data presented in Table 8 offers insights into their overall test performance, revealing a mean score (Tier-AB) of 5.60 (SD = 1.59), indicating a moderate level, and a Mean Confidence Rating (Tier-CF<subs>AB</subs>) of 4.17 (SD = 0.88), signifying a relatively high confidence level. Upon further examination of performance across the four tiers, it becomes apparent that students exhibited varying levels. Specifically, students performed better in Tier-A than in Tier-B. Similarly, students' confidence in Tier-CF<subs>A</subs> was higher than in Tier-CF<subs>B</subs>.</p> <p>Table 8 Descriptive Statistics of Student Scores and Confidence Rating</p> <p> <ephtml> <table frame="hsides" rules="groups"><thead><tr><th align="left"><p><italic>Tier</italic></p></th><th align="left"><p><italic>M</italic></p></th><th align="left"><p><italic>SD</italic></p></th><th align="left"><p><italic>M</italic></p></th><th align="left"><p><italic>SD</italic></p></th></tr></thead><tbody><tr><td align="left"><p>Tier-A</p></td><td align="left"><p>6.01 (Out of 10)</p></td><td align="left"><p>1.75</p></td><td align="left" rowspan="2"><p>5.60 (Out of 10)</p></td><td align="left" rowspan="2"><p>1.59</p></td></tr><tr><td align="left"><p>Tier-B</p></td><td align="left"><p>5.20 (Out of 10)</p></td><td align="left"><p>1.85</p></td></tr><tr><td align="left"><p>Tier-CF<sub>A</sub></p></td><td align="left"><p>4.30 (Out of 6)</p></td><td align="left"><p>0.87</p></td><td align="left" rowspan="2"><p>4.17 (Out of 6)</p></td><td align="left" rowspan="2"><p>0.88</p></td></tr><tr><td align="left"><p>Tier-CF<sub>B</sub></p></td><td align="left"><p>4.04 (Out of 6)</p></td><td align="left"><p>0.92</p></td></tr></tbody></table> </ephtml> </p> <hd id="AN0183484467-26">Difference and Correlation of Students' Performances Across Tiers</hd> <p></p> <hd id="AN0183484467-27">Difference in Students' Performances Across Tiers</hd> <p>As can be seen from Table 8, the score of Tier-AB was 5.60 out of 10, which was almost at the medium level. However, students' confidence rating in Tier-CF<subs>AB</subs> is at a high level (4.17 out of 6). It indicates that students performed better in the Tier-CF<subs>AB</subs> than the Tier-AB. Students were slightly confident in their correctness but were relatively not good at answering and justifying questions. To get more specific differences, further paired samples t-tests were also conducted on the students' scores in Tier-A and Tier-B, and the confidence rating in Tier-CF<subs>A</subs> and Tier-CF<subs>B</subs>, respectively. The paired sample t-test results (t = 9.572, p = 0.000 < 0.05) indicate that students scored significantly higher in Tier-A than the Tier-B, which shows that students are significantly more likely to write answers correctly compared to reasons explanations. Students' mean confidence ratings for Tier-CF<subs>A</subs> and Tier-CF<subs>B</subs> are 4.30 and 4.04 (out of 6). The further paired sample t-test results (t = 13.195, p = 0.000 < 0.05) indicate that students were more confident in their responses to Tier-A significantly. That is, students were significantly more confident in the answers they filled than in the explanations they wrote. This also aligns with the above finding that a significantly higher score of Tier-A than Tier-B.</p> <p>In addition, the CF of students who solved the problem correctly (CFC) and computationally wrong (CFW) were counted separately (Table 9). The results showed that students who answered and interpreted the questions correctly had relatively high confidence, however, students who answered and interpreted the questions incorrectly also had higher-than-average confidence ratings. However, overall, students who answered and explained correctly were more confident than those who answered and explained incorrectly (CFC<subs>AB</subs> = 4.51 > CFW<subs>AB</subs> = 3.77). From the results of the paired-sample t-test, it can be found that in Tier-A, CFC<subs>A</subs> (4.48) > CFW<subs>A</subs> (3.77) and <emph>t</emph> = 4.09 (<emph>p</emph> = 0.007 < 0.05), indicating that students who answered the question correctly are more significantly confident. However, in Tier-B, CFC<subs>B</subs> (4.36) > CFW<subs>B</subs> (3.56), but t = 1.09, (p = 0.29 > 0.05), indicating that although students who explained the reason correctly were more confident than those who explained the reason incorrectly, there was no significant difference. It was initially evident that students did not have a sufficient degree of a correct grasp of Tier-B, because even though the students' explanations were correct, they were not confident in his or her explanations.</p> <p>Table 9 Mean Score of CFC and CFW</p> <p> <ephtml> <table frame="hsides" rules="groups"><thead><tr><th align="left"><p>Confidence Rating Type</p></th><th align="left"><p>Tier-CF<sub>A</sub></p></th><th align="left"><p>Tier-CF<sub>B</sub></p></th><th align="left"><p>Tier-CF<sub>AB</sub></p></th></tr></thead><tbody><tr><td align="left"><p>CFC (<italic>SD</italic>)</p></td><td align="left"><p>4.48 (0.37)</p></td><td align="left"><p>4.36 (0.77)</p></td><td align="left"><p>4.51 (0.44)</p></td></tr><tr><td align="left"><p>CFW (<italic>SD</italic>)</p></td><td align="left"><p>3.77 (0.36)</p></td><td align="left"><p>3.56 (0.44)</p></td><td align="left"><p>3.77 (0.25)</p></td></tr></tbody></table> </ephtml> </p> <p> <emph>Tier-CF</emph> <subs> <emph>AB</emph> </subs> <emph> is the mean confidence rating of the Tier-CF</emph> <subs> <emph>A</emph> </subs> <emph> and Tier-CF</emph> <subs> <emph>AB</emph> </subs> </p> <hd id="AN0183484467-28">Correlation of Students' Performances Across Tiers</hd> <p>To further explore the correlation among students' performance in different tiers, Pearson correlation analysis was conducted (see Table 10). The results of the correlation analysis unveiled a significant and strong positive correlation between Tier-CF<subs>A</subs> and Tier-CF<subs>B</subs>, indicating a close connection between students' confidence in answering questions correctly and their confidence in providing the correct reasoning for those answers. Moreover, a moderate and significant positive correlation was observed between scores in Tier-A and Tier-B, suggesting that the accuracy of answers is closely tied to the correctness of explanations provided by students. In essence, students were more likely to furnish correct explanations when they answered questions accurately, and vice versa. Additionally, a significant and moderate positive correlation was identified between Tier-A and Tier-CF<subs>A</subs>, as well as between Tier-B and Tier-CF<subs>B</subs>. This implied a moderate positive correlation between the accuracy of answers and students' confidence ratings in both answering questions and providing explanations.</p> <p>Table 10 Correlation of Students' Scores Across Tiers</p> <p> <ephtml> <table frame="hsides" rules="groups"><thead><tr><th align="left"><p>Tier</p></th><th align="left"><p>Tier-A</p></th><th align="left"><p>Tier-B</p></th><th align="left"><p>Tier-CF<sub>A</sub></p></th><th align="left"><p>Tier-CF<sub>B</sub></p></th></tr></thead><tbody><tr><td align="left"><p>Tier-A</p></td><td align="left"><p>1</p></td><td align="left" /><td align="left" /><td align="left" /></tr><tr><td align="left"><p>Tier-B</p></td><td align="left"><p>0.561<sup>***</sup></p></td><td align="left"><p>1</p></td><td align="left" /><td align="left" /></tr><tr><td align="left"><p>Tier-CF<sub>A</sub></p></td><td align="left"><p>0.403<sup>***</sup></p></td><td align="left"><p>0.268<sup>***</sup></p></td><td align="left"><p>1</p></td><td align="left" /></tr><tr><td align="left"><p>Tier-CF<sub>B</sub></p></td><td align="left"><p>0.388<sup>***</sup></p></td><td align="left"><p>0.322<sup>***</sup></p></td><td align="left"><p>0.911<sup>***</sup></p></td><td align="left"><p>1</p></td></tr></tbody></table> </ephtml> </p> <p> <emph>***. Significant correlation at the 0.001 level (two-tailed); Correlation value</emph> < <emph>0.3, weak correlation, Correlation value</emph> = <emph>0.3–0.6, moderate correlation</emph></p> <p>These analyses indicate a relationship between students' confidence ratings, the correctness of answers, and the correctness of explanations. When students answered correctly and provided accurate explanations, their confidence ratings tended to be higher. Likewise, when students were more confident, they were more likely to answer correctly and provide correct explanations.</p> <hd id="AN0183484467-29">Students' Conceptual Understandings in Each Dimension</hd> <p>Based on the overall performance results, the mean scores of each item in every dimension and the mean confidence rating of each item in every dimension were documented. As depicted in Table 11, students exhibited the highest mean score (0.683) and the highest confidence rating (CF<subs>A</subs> = 4.829, CF<subs>B</subs> = 4.413) in the F2 dimension, while registering the lowest mean score (0.140) and the lowest confidence rating (CF<subs>A</subs> = 2.816, CF<subs>B</subs> = 2.683) in the F4 dimension. This suggests that students demonstrated a strong understanding of concepts related to isomerism and other related topics, yet encountered the most challenges in discerning and articulating isomer numbers.</p> <p>Table 11 Overall Conceptual Understanding in Each Dimension</p> <p> <ephtml> <table frame="hsides" rules="groups"><thead><tr><th align="left"><p>Dimension</p></th><th align="left"><p>Tier-A</p></th><th align="left"><p>Tier-B</p></th><th align="left"><p>Tier-AB</p></th><th align="left"><p>Tier-CF<sub>A</sub></p></th><th align="left"><p>Tier-CF<sub>B</sub></p></th></tr></thead><tbody><tr><td align="left"><p>F1</p></td><td char="." align="char"><p>0.432</p></td><td char="." align="char"><p>0.339</p></td><td char="." align="char"><p>0.281</p></td><td char="." align="char"><p>4.279</p></td><td char="." align="char"><p>3.896</p></td></tr><tr><td align="left"><p>F2</p></td><td char="." align="char"><p>0.809</p></td><td char="." align="char"><p>0.712</p></td><td char="." align="char"><p>0.683</p></td><td char="." align="char"><p>4.829</p></td><td char="." align="char"><p>4.413</p></td></tr><tr><td align="left"><p>F3</p></td><td char="." align="char"><p>0.691</p></td><td char="." align="char"><p>0.586</p></td><td char="." align="char"><p>0.503</p></td><td char="." align="char"><p>4.409</p></td><td char="." align="char"><p>4.205</p></td></tr><tr><td align="left"><p>F4</p></td><td char="." align="char"><p>0.278</p></td><td char="." align="char"><p>0.346</p></td><td char="." align="char"><p>0.140</p></td><td char="." align="char"><p>2.816</p></td><td char="." align="char"><p>2.683</p></td></tr></tbody></table> </ephtml> </p> <hd id="AN0183484467-30">Students Misconceptions in Each Dimension</hd> <p>Expanding on the comprehensive analyses of the aforementioned dimensions, the four dimensions persist in offering insights into student misconceptions, particularly focusing on those occurring in samples exceeding 15 percent. These analyses explored the nature of student misunderstandings, encompassing their frequency, severity, and typicality. Furthermore, unstructured student interviews were conducted to get insights into individual students' challenges.</p> <hd id="AN0183484467-31">Students' Misconceptions in the Definition of Isomer</hd> <p>The F1 dimension comprises three items, and Table 12 details the misunderstandings observed among students in this dimension. In Item 1, which examined the simple definition of isomers, students performed well. For Item 2, assessing the expression of concepts related to isomers, two misconceptions were identified among students. Item 5 evaluated the derivation of isomeric properties, revealing one identified misconception. In total, three misunderstandings were found as students engaged with the comprehension of isomers and related concepts. Among these three misunderstandings, two were categorized as moderate, one as severe, and all three were considered typical misconceptions.</p> <p>Table 12 Students Misconceptions in the Definition of Isomer</p> <p> <ephtml> <table frame="hsides" rules="groups"><thead><tr><th align="left"><p>Item</p></th><th align="left"><p>Options</p></th><th align="left"><p>Misconception</p></th><th align="left"><p>Percentage (%)</p></th><th align="left"><p>Degree</p></th><th align="left"><p>Typicality</p></th></tr></thead><tbody><tr><td align="left" rowspan="2"><p>2</p></td><td align="left"><p>B, A</p></td><td align="left"><p>All isomers are organic compounds</p></td><td char="." align="char"><p>38.18</p></td><td align="left"><p>Moderate</p></td><td align="left"><p>Yes</p></td></tr><tr><td align="left"><p>B, D</p></td><td align="left"><p>Compounds are not necessarily isomers if their molecular formula and structures are different, even though their Relative Molecular Mass and Element Mass Fraction may be the same</p></td><td char="." align="char"><p>26.49</p></td><td align="left"><p>Moderate</p></td><td align="left"><p>Yes</p></td></tr><tr><td align="left"><p>5</p></td><td align="left"><p>D, B</p></td><td align="left"><p>The melting point and boiling point of a compound are related to its branched chains</p></td><td char="." align="char"><p>47.53</p></td><td align="left"><p>Serious</p></td><td align="left"><p>Yes</p></td></tr></tbody></table> </ephtml> </p> <p>In Item 2, 38.18% of students held the misconception that discussions about isomerism are exclusive to organic substances (BA), constituting a moderate and typical misunderstanding. During the interview, Student C expressed, "<emph>I didn't really understand the question. I can grasp the Structural Differences, but the concepts of Relative Molecular Mass, although I've learned them before, do they have anything to do with isomerism? I've never seen it before."</emph> Meanwhile, Student B mentioned t<emph>hat isomers are associated with organic substances, not inorganic ones, and all organic compounds are covered in textbooks and exercise books</emph>. This indicates that students find the information presented in the question challenging to comprehend, and they lack clarity regarding the relationship between Relative Molecular Mass, and Element Mass Fraction of isomerism. Moreover, during their organic chemistry learning stage, they primarily encountered organic compounds, leading them to naturally assume that isomerism only applies to the organic category. Additionally, examinations typically did not cover this knowledge point, so teachers may not emphasize it in the classroom. However, it's crucial to note that isomers exist among various inorganic substances, especially coordination compounds, such as cyanuric acid (HOCN) and isocyanic acid (HNCO), as well as ammonium cyanate (NH<subs>4</subs>CNO) and urea (CO (NH<subs>2</subs>)<subs>2</subs>).</p> <p>Moreover, 26.49% of students believed that "<emph>when the Relative Molecular Mass and the Element Mass Fraction are the same, the molecular formulas may be different, and when the structures are different, they may not be isomers of each other</emph>" (BD), representing a moderate and typical misconception. Interviews with four students to explore the reasons behind this misconception revealed that some students (Students A, B, and C) struggled to deviate from the textbook definition of the concept, finding it challenging to comprehend it from an alternative perspective. While it's true that teachers may not have emphasized this knowledge in their lectures, it remains essential for educators to convey such information to students. Without proper instruction, students may easily develop an inadequate conceptual understanding.</p> <p>Regarding Item 5, a considerable 47.53% of students erroneously believed that the melting and boiling points are solely determined by branched chains. Specifically, they thought neopentane has a lower boiling and melting point due to having more branched chains (DB), constituting a severe and typical misconception. During the interview, Student A initially referred to the teaching material, asserting that it states, "<emph>the more branched chains, the lower the melting and boiling point, and neopentane has more branched chains, so it has a lower melting and boiling point.</emph>' However, upon the researcher's prompting, the student realized the need to specify that "lower" refers to the boiling point. When pressed further to explain why the boiling point decreases, Student D admitted to <emph>not paying enough attention to the distinction between boiling and melting points and chose the answer based on a general impression</emph>. Another student, Student C, indicated that <emph>the relationship between boiling point and branched chains is extensively discussed in books and classes, leading to the misconception that the melting point follows the same pattern.</emph> This suggests that while the student accurately understood the association between boiling point and branched chains, there was ambiguity regarding the relationship between melting point and symmetry. When prompted to elaborate on this judgment, Student C struggled to provide a complete answer.</p> <hd id="AN0183484467-32">Students' Misconceptions in the Differentiating Related Concepts</hd> <p>Table 13 provides an overview of the challenges faced by students in discerning and distinguishing concepts related to isomerism. Within the two items in F2, Item 6 assessed the differentiation between Isomers and Identical Substances, while Item 9 focused on distinguishing between Isomers and Homologs. Students demonstrated proficiency in Item 9 but encountered difficulties in Item 6, resulting in the development of two misconceptions. Both misconceptions were categorized as moderate misunderstandings and were considered typical.</p> <p>Table 13 Misconceptions in the Differentiating Related Concepts</p> <p> <ephtml> <table frame="hsides" rules="groups"><thead><tr><th align="left"><p>Item</p></th><th align="left"><p>Options</p></th><th align="left"><p>Misconception</p></th><th align="left"><p>Percentage (%)</p></th><th align="left"><p>Degree</p></th><th align="left"><p>Typicality</p></th></tr></thead><tbody><tr><td align="left" rowspan="2"><p>6</p></td><td align="left"><p>B, B</p></td><td align="left"><p><inline-graphic href="MediaObjects/10763_2024_10494_Figa_HTML.png" /> and <inline-graphic href="MediaObjects/10763_2024_10494_Figb_HTML.png" /> are isomers because they have different structures with different positioned Cl </p></td><td char="." align="char"><p>15.58</p></td><td align="left"><p>Moderate</p></td><td align="left"><p>No</p></td></tr><tr><td align="left"><p>B, C</p></td><td align="left"><p>Isomers are of the same substance only differ in molecular structures. Isomers are of the same substance in essence</p></td><td char="." align="char"><p>17.15</p></td><td align="left"><p>Moderate</p></td><td align="left"><p>No</p></td></tr></tbody></table> </ephtml> </p> <ulist> <item>15.58% of the students held the misconception that two substances with different positions of chlorine atoms and distinct structures are isomers (BB), representing a moderately atypical misunderstanding. During the interview, Student A asserted that <emph>since the chlorine atoms are in different positions, the structures are different</emph>. However, when probed about whether the structures were considered from a planar or three-dimensional perspective, Student A acknowledged that <emph>they were viewed from a planar perspective</emph>. This error highlights students' insufficient understanding of the structure of common substances, especially the spatial stereo structure (methylene chloride). It underscores the need to help students identify confusing concepts, even if the curriculum does not demand an in-depth exploration of stereoisomerism. Despite dichloromethane being a common substance in upper-secondary school, using it as an example can aid in addressing such misconceptions. When asked about the teaching style, Student A mentioned that <emph>the teacher used PowerPoint with three-dimensional pictures of substance structures but lacked animations or physical models</emph>. This suggests a correlation between students' conceptual understanding and the teacher's teaching methods. Abstract knowledge, especially in organic chemistry, requires more than words and pictures; physical models provide students with a tangible understanding.</item> <item>17.15% of the students believed that isomers are substances with different structures, but essentially remain the same substance (AC), constituting a moderately atypical misconception. In the interview, Student B argued that <emph>both chemical formulas represent methylene chloride, they are identical substances, while the given two structural formulas differ.</emph> When prompted to differentiate between the concepts of Identical Substances and Isomers, Student B persisted, claiming that <emph>isomers can also be the same substances and that the same substances are special isomers</emph>. This question shows that some students have difficulty in fully distinguishing between the concept of Isomers and the concept of Identical Substances. Identical substances must have the same structure, while isomers must be different substances.</item> </ulist> <hd id="AN0183484467-33">Students' Misconceptions in the Identifying the Type of Isomer/Isomerism</hd> <p>The F3 dimension encompasses four items. Items 3 and 8 assess students' comprehension of Functional Group Isomerism, while Item 4 examines Positional Isomerism, and Item 7 evaluates Carbon Chain Isomerism. Table 14 provides an overview of students' misconceptions related to various types of isomers and tautomerism. Among these items, two misconceptions were identified in Items 3 and 4, featuring one moderate misconception, one severe misconception, and one typical misconception.</p> <p>Table 14 Misconceptions in the Identifying the Type of Isomer/Isomerism</p> <p> <ephtml> <table frame="hsides" rules="groups"><thead><tr><th align="left"><p>Item</p></th><th align="left"><p>Options</p></th><th align="left"><p>Misconception</p></th><th align="left"><p>Percentage (%)</p></th><th align="left"><p>Degree</p></th><th align="left"><p>Typicality</p></th></tr></thead><tbody><tr><td align="left"><p>3</p></td><td align="left"><p>A, D</p></td><td align="left"><p>Functional Group Isomerism indicates the type or number of Functional Groups is different</p></td><td char="." align="char"><p>19.70</p></td><td align="left"><p>Moderate</p></td><td align="left"><p>No</p></td></tr><tr><td align="left"><p>4</p></td><td align="left"><p>B, A</p></td><td align="left"><p>Position Isomerism indicates the position of the substituent is different</p></td><td char="." align="char"><p>23.64</p></td><td align="left"><p>Serious</p></td><td align="left"><p>Yes</p></td></tr></tbody></table> </ephtml> </p> <p>In Item 3, 19.70% of the students believed that CH<subs>3</subs>-CH<subs>2</subs>-CH = CH<subs>2</subs> and CH<subs>3</subs>-CH = CH-CH<subs>3</subs> are Functional Group Isomorphisms, and Functional Group Isomorphism refers to a different type or number of Functional Groups (AD), which is a moderate and atypical misconception. During the interview, Student B stated that <emph>they all have double bonds in different positions.</emph> When the researcher asked: <emph>"do you think that Functional Group Isomerization means that the positions of the Functional Groups are different</emph>"<emph>,</emph> the student said:" <emph>yes, from the name, the Functional Group Isomerization must be related to the Functional Group, and then over here (referring to the reason tier) there is a reference to Functional Group Isomerization and Positional Isomerization, both of which are related to the functional group</emph>". When the researcher further inquired: "<emph>So do you think that whatever is related to the three words Functional Group can refer to Functional Group Isomerism?</emph>" Student B stated: "<emph>Maybe, not sure</emph>". From the interview, it is clear that the student, when understanding Functional Group Isomerization, would simply define it wrongly literally, thinking that as long as it is related to the word Functional Group, it can be expressed as Functional Group Isomerization, and it is the wrong understanding of the concept that leads to the wrong judgment of the specific substance in the answer tier.</p> <p>Item 4 examined the definition of the concept of Positional Isomerism. 23.64% of the students thought that the methyl groups of the two substances were in the same position, whereas positional isomerism means that the substituents are in different positions (BA), which is a serious and typical misconception. The options show that this group of students can correctly determine whether the structures of substances are the same or not, i.e. they use the principle of equivalence correctly, but they have a misunderstanding of the target of Positional Isomerism. In the interview, Student C was adamant that the <emph>hydroxyl group is in the same place, so the substituent is in the same place, and positional isomerization means that the substituent is in a different place in this item</emph>. Again, the error was due to the student's failure to clarify the inclusion relationship.</p> <hd id="AN0183484467-34">Students' Misconceptions in the Identifying the Number of Isomers and Writing Isomers</hd> <p>The F4 dimension, represented by Item 10, aimed to evaluate students' proficiency in generating and making numerical judgments about isomers. Table 15 reveals that misconceptions arose when students endeavored to produce and document all potential isomers. One misunderstanding was identified in this item, characterized as a severe and typical misconception.</p> <p>Table 15 Misconceptions in Identifying the Number of Isomers and Writing Isomers</p> <p> <ephtml> <table frame="hsides" rules="groups"><thead><tr><th align="left"><p>Item</p></th><th align="left"><p>Options</p></th><th align="left"><p>Misconception</p></th><th align="left"><p>Percentage (%)</p></th><th align="left"><p>Degree</p></th><th align="left"><p>Typicality</p></th></tr></thead><tbody><tr><td align="left"><p>10</p></td><td align="left"><p>C, D</p></td><td align="left"><p>The degree of unsaturation of C<sub>8</sub>H<sub>8</sub>O<sub>2</sub> is 5. The number of isomers with benzene rings and only one functional group is 8, and 4 of them are esters</p></td><td char="." align="char"><p>16.58</p></td><td align="left"><p>Serious</p></td><td align="left"><p>Yes</p></td></tr></tbody></table> </ephtml> </p> <p>16.58% of the students believed that the degree of unsaturation of C<subs>8</subs>H<subs>8</subs>O<subs>2</subs> is 5. There are 8 isomers containing benzene rings, with only one functional group. which there are 4 esters (CD), which is a serious and typical misconception. During the interview, Student D stated that <emph>the calculated degree of unsaturation is 5, and the benzene ring has an unsaturation of 4, leaving 1 unsaturation, which can form either a carboxyl group or an ester group due to the presence of two oxygens</emph>. Analysis of the structural formulae already written by the 4 students revealed that the students first wrote four carboxylic acids in the order of mono-substituted phenylacetic acid to disubstituted o-phenylene carboxylic acid, and then four esters in the order of mono-substituted phenol ethyl ester to disubstituted phenol methyl ester in the order of o-phenylene carboxylic acid, omitting the rest of the types.</p> <hd id="AN0183484467-35">Discussions</hd> <p>In this study, a novel four-tier diagnostic tool was developed based on existing two- and three-tier diagnostic tools (Mutlu & Şeşen, [<reflink idref="bib49" id="ref97">49</reflink>]; Widiyatmoko & Shimizu, [<reflink idref="bib73" id="ref98">73</reflink>]). This tool not only evaluates students' selections in the "answer" and "reason for answer" tiers but also assesses their confidence levels in the "Answer-Tier" and "Reason Tier" levels (Putica, [<reflink idref="bib53" id="ref99">53</reflink>]; Sreenivasulu & Subramaniam, [<reflink idref="bib63" id="ref100">63</reflink>]; Yang, [<reflink idref="bib76" id="ref101">76</reflink>]; Yang & Lin, [<reflink idref="bib77" id="ref102">77</reflink>]). The incorporation of confidence ratings enables a more comprehensive understanding of students' conceptual mastery, helping identify the type, degree, and typicality of misconceptions (Ammase et al., [<reflink idref="bib3" id="ref103">3</reflink>]; Kaltakci-Gurel et al., [<reflink idref="bib33" id="ref104">33</reflink>]; Kiray et al., [<reflink idref="bib39" id="ref105">39</reflink>]; Sreenivasulu & Subramaniam, [<reflink idref="bib62" id="ref106">62</reflink>]).</p> <p>Analyzing students' mastery of isomers in the answer and reason tiers, it was found that, on average, students scored 5.60 out of 10, indicating the challenging nature of isomeric understanding. This aligns with previous research highlighting students' difficulties with isomerism (Akkuzu & Uyulgan, [<reflink idref="bib2" id="ref107">2</reflink>]; Eastwood, [<reflink idref="bib17" id="ref108">17</reflink>]; Prasanson et al., [<reflink idref="bib52" id="ref109">52</reflink>]) and consistent with diagnostic studies showing students, across age groups, tend to score moderately (Habiddin & Page, [<reflink idref="bib24" id="ref110">24</reflink>]; Sreenivasulu & Subramaniam, [<reflink idref="bib62" id="ref111">62</reflink>]; Yan & Subramaniam, [<reflink idref="bib75" id="ref112">75</reflink>]). The variability in scores revealed higher performance in the answer tier compared to the reason tier, suggesting students might guess or employ incorrect reasoning processes to achieve correct answers. This underscores the importance of the reason tier to enhance test validity.</p> <p>Considering students' confidence ratings, both in the answer and reason tiers, it was observed that students were generally confident in their choices, with higher confidence in the answer tier than in the reason tier. This trend is in line with previous studies (Caleon & Subramaniam, [<reflink idref="bib11" id="ref113">11</reflink>], [<reflink idref="bib12" id="ref114">12</reflink>]; Yang & Lin, [<reflink idref="bib77" id="ref115">77</reflink>];). Further analysis revealed that correctly answered questions correlated with higher confidence levels, affirming findings from previous studies (Kapoor & Natarajan, [<reflink idref="bib35" id="ref116">35</reflink>]). Interestingly, students who answered correctly in the answer tier exhibited significantly higher confidence levels than those who answered incorrectly. However, in the reason tier, while correct answers were associated with higher confidence, the difference was not significant.</p> <p>Comparing overall student scores and confidence levels, a positive correlation emerged, suggesting that higher scores in both tiers corresponded to elevated confidence ratings. This aligns with other studies (Putica, [<reflink idref="bib53" id="ref117">53</reflink>]). Additionally, a positive correlation was identified between scores in the answer and reason tiers, indicating consistency in performance and confidence across both tiers.</p> <p>Based on the investigation of students' conceptual understanding in four dimensions, this study found that their abilities are strongest in the recognition of isomers and confused concepts, while 'numerical judgment and writing' is the biggest challenge. The recognition of isomers and confused concepts focuses on understanding and analyzing structures, which is more in line with students' previous learning experiences and thinking habits. Through previous learning and training, they may have accumulated certain relevant knowledge and analytical abilities, and therefore perform better in this aspect. However, judging and writing the number of isomers demand observation and potentially involve more intricate analyses, particularly when confronting complex molecular structures and recording numerical details. Hence, students may encounter difficulties in this aspect.</p> <p>In addition, the study found a total of 8 misconceptions, including 5 moderate misconceptions, 3 serious misconceptions, and 3 typical misconceptions. Students have a good ability to distinguish isomers and easily confused concepts, but they find it difficult to master the deeper connotations of isomers, such as the substitution definition and the relationship between structure and properties, which may be because these concepts are more abstract and require deeper understanding and analysis (Barber, [<reflink idref="bib9" id="ref118">9</reflink>]; Schwanenflugel, [<reflink idref="bib59" id="ref119">59</reflink>]). Furthermore, compared to functional group isomers and position isomers, students have a more thorough understanding of carbon chain isomers, especially in terms of phenol hydroxyl and alcohol hydroxyl, indicating that students have a good grasp of some specific types of isomers, but their general conceptual understanding still needs to be strengthened (Kim, [<reflink idref="bib38" id="ref120">38</reflink>]). In addition, students performed well in understanding the complete writing of simple alkane isomers but faced challenges when dealing with isomers containing benzene rings, which may be because the molecular structure of those with benzene rings is more complex, requiring students to have stronger spatial visualization and writing skills (Lowrie et al., [<reflink idref="bib44" id="ref121">44</reflink>]). Consequently, teachers should prioritize fostering students' in-depth understanding of the concept of isomers, rather than merely imparting superficial knowledge. This entails reinforcing the connection between structure and properties, encouraging active thinking, and nurturing independent problem-solving abilities. Moreover, given the varying levels of mastery among students, differentiated teaching strategies should be employed, with particular emphasis on addressing weak areas through targeted training initiatives.</p> <hd id="AN0183484467-36">Conclusions</hd> <p>In this study, a four-tier diagnostic test was meticulously crafted to evaluate students' grasp of isomeric concepts. The analysis indicated that students performed more proficiently in the Answer Tier compared to the Reason Tier, showcasing a corresponding elevation in confidence ratings. Notably, a positive and significant correlation was observed between students' scores and their confidence levels, affirming that higher scores were associated with greater confidence. A nuanced examination of students' conceptual understanding across four dimensions unveiled their strongest command over isomer and confusing concept recognition, while "number judgment and writing" presented the greatest challenges. The study identified and diagnosed 8 misconceptions within these four dimensions, featuring 5 moderate, 3 severe, and 5 typical misconceptions.</p> <p>It's important to acknowledge that the study's population was limited to 12th grade students from local schools in Shanghai, which, while sufficiently sized, may restrict the generalizability of findings. Future research endeavors should extend the study to encompass a broader demographic, including varied regions, school sections, or subject areas. This expansion will facilitate a more comprehensive evaluation of students' comprehension of target concepts, paving the way for in-depth exploration of pedagogical strategies geared towards enhancing conceptual understanding and supporting robust student learning.</p> <hd id="AN0183484467-37">Appendix 1 Interview Outline for Teachers on Conceptual Understanding of Isomers</hd> <p>Note: The interviewees were eight chemistry teachers from various secondary schools in Shanghai, with teaching experience ranging from 2 to 25 years.</p> <p></p> <ulist> <item> Please talk about the concept of 'isomer' in your perspective.</item> <p></p> <item> How do you think students should judge that they understand the concept of 'isomer'?</item> <p></p> <item> What knowledge base must students have before they can learn the concept of 'isomer'? The more detailed the better.</item> <p></p> <item> The concept of 'isomer' is used throughout organic chemistry. What problems do you think students will have in learning this concept?</item> </ulist> <hd id="AN0183484467-38">Appendix 2 Misconceptions of students on the pilot test</hd> <p></p> <p> <ephtml> <table frame="hsides" rules="groups"><tbody><tr><td align="left"><p>1.1</p></td><td align="left"><p>If hydrocarbons have the same M, then their chemical formulas are the same. Since their properties and structures are different, they are considered to be isomers</p></td></tr><tr><td align="left"><p>1.2</p></td><td align="left"><p>If the properties are different, then the functional groups are different. If the structures are different, then they are not the same substance. Therefore, they are isomers</p></td></tr><tr><td align="left"><p>1.3</p></td><td align="left"><p>Isomers are substances that have the same elemental mass fractions, but have different structures</p></td></tr><tr><td align="left"><p>1.4</p></td><td align="left"><p>Hydrocarbons contain only C and H elements. If the M is the same, then the number of C and H atoms must be equal</p></td></tr><tr><td align="left"><p>2.1</p></td><td align="left"><p>If the constituent elements are the same, and the elemental mass fractions are the same, then the molecular formula is the same</p></td></tr><tr><td align="left"><p>2.2</p></td><td align="left"><p>The determination of whether compounds are constitutional isomers can only be made when it is specified that the substances are organic compounds</p></td></tr><tr><td align="left"><p>2.3</p></td><td align="left"><p>If the empirical formulas are the same, the relative molecular masses are the same, but the structures are different, then they must be isomers."</p></td></tr><tr><td align="left"><p>3.1</p></td><td align="left"><p>For example, NO<sub>2</sub> and N<sub>2</sub>O<sub>4</sub> have the same elemental mass fractions, but they are not constitutional isomers</p></td></tr><tr><td align="left"><p>3.2</p></td><td align="left"><p>If the elemental mass fractions are the same and the M is the same, the molecular formulas may still be different</p></td></tr><tr><td align="left"><p>3.3</p></td><td align="left"><p>Constitutional isomers only apply to organic compounds, but the given question did not specify that the substances are definitely organic compounds</p></td></tr><tr><td align="left"><p>4.1</p></td><td align="left"><p>The compounds are not specified to be either organic or inorganic. If the compounds are inorganic, then they would not have constitutional isomers</p></td></tr><tr><td align="left"><p>4.2</p></td><td align="left"><p>The compounds may be the same substance</p></td></tr><tr><td align="left"><p>5.1</p></td><td align="left"><p>Neopentane has a stronger molecular symmetry and a higher melting and boiling point</p></td></tr><tr><td align="left"><p>5.2</p></td><td align="left"><p>The more stable the structure of neopentane, the higher its melting and boiling points</p></td></tr><tr><td align="left"><p>5.3</p></td><td align="left"><p>The more branched the structure of neopentane, the lower its melting and boiling points</p></td></tr><tr><td align="left"><p>5.4</p></td><td align="left"><p>The shorter the branched chains in neopentane, the higher its melting and boiling points</p></td></tr><tr><td align="left"><p>5.5</p></td><td align="left"><p>Neopentane has a main carbon chain of only three carbons, and therefore has the lowest melting and boiling points</p></td></tr><tr><td align="left"><p>5.6</p></td><td align="left"><p>Neopentane has stronger molecular symmetry, resulting in a higher boiling point; and it has fewer branched chains, resulting in a lower melting point</p></td></tr><tr><td align="left"><p>6.1</p></td><td align="left"><p>The two compounds have the same molecular formula. The latter has a carbon–carbon double bond, and the functional groups are different</p></td></tr><tr><td align="left"><p>6.2</p></td><td align="left"><p>The two compounds have the same molecular formula, but the positions of the functional groups are different</p></td></tr><tr><td align="left"><p>6.3</p></td><td align="left"><p>The first compound is cyclic, while the second compound is linear. The arrangement of the carbon atoms is different between the two</p></td></tr><tr><td align="left"><p>7.1</p></td><td align="left"><p>The two molecules have the same molecular formula, but the position of the Cl (chlorine) atom is different, resulting in different structures. This is a case of positional isomerism</p></td></tr><tr><td align="left"><p>7.2</p></td><td align="left"><p>The Cl (chlorine) atom is in the para position in one compound and the ortho position in the other. The rotation of the Cl atom cannot make them coincide, so they are structural isomers</p></td></tr><tr><td align="left"><p>7.3</p></td><td align="left"><p>The two molecules have asymmetric distributions of the Cl (chlorine) and H (hydrogen) atoms, resulting in different structures</p></td></tr><tr><td align="left"><p>7.4</p></td><td align="left"><p>The two molecules have different structures, but their molecular conformations are similar</p></td></tr><tr><td align="left"><p>7.5</p></td><td align="left"><p>The two molecules have asymmetric arrangements of their atoms, and they are geometric (cis–trans) isomers</p></td></tr><tr><td align="left"><p>7.6</p></td><td align="left"><p>The two molecules have the same molecular formula, and the equivalent hydrogen atoms are the same</p></td></tr><tr><td align="left"><p>7.7</p></td><td align="left"><p>The two molecules contain the same types and numbers of elements</p></td></tr><tr><td align="left"><p>8.1</p></td><td align="left"><p>The first molecule has no side chains, while the second molecule has an ethyl (CH<sub>3</sub>CH<sub>2</sub><sup>-</sup>) side chain</p></td></tr><tr><td align="left"><p>8.2</p></td><td align="left"><p>The first molecule has no side chains, while the second molecule has a methyl (CH<sub>3</sub>-) side chain</p></td></tr><tr><td align="left"><p>8.3</p></td><td align="left"><p>The two molecules have the same molecular formula, but the first molecule has a symmetric structure, while the second molecule has an asymmetric structure, and their structural frameworks are different</p></td></tr><tr><td align="left"><p>9.1</p></td><td align="left"><p>The two molecules have the same functional groups</p></td></tr><tr><td align="left"><p>9.2</p></td><td align="left"><p>One hydroxyl group is on the benzene ring, while the other is on a methyl group. The positions of the hydroxyl groups are different, and this represents positional isomerism of the hydroxyl groups</p></td></tr><tr><td align="left"><p>9.3</p></td><td align="left"><p>One molecule is CH<sub>3</sub>OH, while the other is CH<sub>2</sub>OH. The positions of the hydroxyl groups are different</p></td></tr><tr><td align="left"><p>9.4</p></td><td align="left"><p>The arrangement/structure of the carbon chain to which the hydroxyl group is attached is different between the two molecules</p></td></tr><tr><td align="left"><p>9.5</p></td><td align="left"><p>The functional group is a hydroxyl group, but the carbon chain structures to which the hydroxyl groups are attached are different between the two molecules</p></td></tr><tr><td align="left"><p>9.6</p></td><td align="left"><p>The functional groups are the same, but the positions of the side chains are different</p></td></tr><tr><td align="left"><p>9.7</p></td><td align="left"><p>The positions of the carbon atom groups are different</p></td></tr><tr><td align="left"><p>10.1</p></td><td align="left"><p>For the first molecule, the group connected to the double bond is a C<sub>2</sub>H<sub>5</sub> group. For the second molecule, the groups connected to the double bond are two CH<sub>3</sub> groups</p></td></tr><tr><td align="left"><p>10.2</p></td><td align="left"><p>The functional groups in the two molecules are a methyl group and a carbon–carbon double bond, respectively</p></td></tr><tr><td align="left"><p>11.1</p></td><td align="left"><p>The branching substituents are different. The first molecule contains a CH<sub>3</sub> (methyl) group, while the second molecule contains a CH<sub>2</sub>OH (hydroxymethyl) group</p></td></tr><tr><td align="left"><p>11.2</p></td><td align="left"><p>Position isomerism refers to the different positions of the functional groups. The positions of the methyl groups are different between the two molecules</p></td></tr><tr><td align="left"><p>11.3</p></td><td align="left"><p>Position isomerism refers to the different positions of the substituent groups. The positions of the methyl (CH<sub>3</sub>) groups are different between the two molecules</p></td></tr><tr><td align="left"><p>11.4</p></td><td align="left"><p>Position isomerism refers to the different positions of the functional groups. In the first molecule, the hydroxyl group (-OH) is on the main carbon chain, while in the second molecule, the hydroxyl group is on the side chain</p></td></tr><tr><td align="left"><p>12.1</p></td><td align="left"><p>The two structures are similar, with a difference of 1 CH<sub>2</sub> group in their composition</p></td></tr><tr><td align="left"><p>12.2</p></td><td align="left"><p>The two molecules have the same functional groups, but they differ in their composition by n (where n ≥ 1) CH<sub>2</sub> (methylene) groups</p></td></tr><tr><td align="left"><p>12.3</p></td><td align="left"><p>The two structures are similar, but they have different carbon-to-hydrogen (C/H) ratios</p></td></tr><tr><td align="left"><p>12.4</p></td><td align="left"><p>Both compounds belong to the class of alcohols and have the same functional group, which is the hydroxyl (-OH) group</p></td></tr><tr><td align="left"><p>13.1</p></td><td align="left"><p>With 4 degrees of freedom, and the functional group being limited to only carboxyl/ester groups, the possible number of isomers is 4/6."</p></td></tr><tr><td align="left"><p>13.2</p></td><td align="left"><p>With 5 degrees of freedom, and the functional group being limited to only carboxyl/ester groups, the possible number of isomers is 4/6</p></td></tr><tr><td align="left"><p>13.3</p></td><td align="left"><p>The functional groups can be either carboxyl or ester groups. There are 3 isomers with the carboxyl group, and 3 isomers with the ester group, making a total of 6 isomers</p></td></tr><tr><td align="left"><p>13.4</p></td><td align="left"><p>The functional groups can be either carboxyl or ester groups. There are 4 isomers with the carboxyl group, and 5 isomers with the ester group, making a total of 9 isomers</p></td></tr></tbody></table> </ephtml> </p> <hd id="AN0183484467-39">Appendix 3 The Formal Four-tier test</hd> <p>Graph</p> <p>Graph</p> <p>Graph</p> <p>Graph</p> <p>See (Fig. 2)</p> <p>Graph: Fig. 2 The P-P plot of the normal distribution of students' formal test results</p> <hd id="AN0183484467-40">Data Availability</hd> <p>The data that support the findings of this study are available on request from the corresponding author. The data are not publicly available due to privacy or ethical restrictions.</p> <ref id="AN0183484467-41"> <title> References </title> <blist> <bibl id="bib1" idref="ref43" type="bt">1</bibl> <bibtext> Abimbola IO. 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  Data: Springer. Available from: Springer Nature. One New York Plaza, Suite 4600, New York, NY 10004. Tel: 800-777-4643; Tel: 212-460-1500; Fax: 212-460-1700; e-mail: customerservice@springernature.com; Web site: https://link.springer.com/
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  Label: Peer Reviewed
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  Data: Y
– Name: Pages
  Label: Page Count
  Group: Src
  Data: 41
– Name: DatePubCY
  Label: Publication Date
  Group: Date
  Data: 2025
– Name: TypeDocument
  Label: Document Type
  Group: TypDoc
  Data: Journal Articles<br />Reports - Research
– Name: Audience
  Label: Education Level
  Group: Audnce
  Data: <searchLink fieldCode="EL" term="%22Secondary+Education%22">Secondary Education</searchLink><br /><searchLink fieldCode="EL" term="%22High+Schools%22">High Schools</searchLink>
– Name: Subject
  Label: Descriptors
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Secondary+School+Science%22">Secondary School Science</searchLink><br /><searchLink fieldCode="DE" term="%22High+School+Students%22">High School Students</searchLink><br /><searchLink fieldCode="DE" term="%22Scientific+Concepts%22">Scientific Concepts</searchLink><br /><searchLink fieldCode="DE" term="%22Science+Tests%22">Science Tests</searchLink><br /><searchLink fieldCode="DE" term="%22Student+Evaluation%22">Student Evaluation</searchLink><br /><searchLink fieldCode="DE" term="%22Misconceptions%22">Misconceptions</searchLink><br /><searchLink fieldCode="DE" term="%22Mastery+Learning%22">Mastery Learning</searchLink><br /><searchLink fieldCode="DE" term="%22Scores%22">Scores</searchLink><br /><searchLink fieldCode="DE" term="%22Chemistry%22">Chemistry</searchLink>
– Name: DOI
  Label: DOI
  Group: ID
  Data: 10.1007/s10763-024-10494-y
– Name: ISSN
  Label: ISSN
  Group: ISSN
  Data: 1571-0068<br />1573-1774
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: This study aimed to develop a comprehensive diagnostic tool for assessing upper-secondary school students' understanding of isomers, expanding upon existing two- and three-tier conceptual diagnostic methods. By incorporating 'Confidence Rating Factor' tiers within the answer and reason sections, a four-tier test was designed and developed. This test was utilized to evaluate students' comprehension of the isomeric conceptual framework and to identify prevalent misconceptions in terms of quantity, complexity, and typicality. The initial phase involved evaluating the reliability and content validity of the developed test before its distribution, resulting in a total of 385 effective test returned for analysis. Data analysis focused on descriptive statistics of students' scores across each tier and dimension, supplemented by unstructured interviews to gain deeper insights. Results indicated a general suboptimal mastery of isomer conceptual understanding among upper secondary school students. Notably, students exhibited higher scores and confidence ratings in the answer tier compared to the reason tier. At both tiers, there was a significant positive correlation between scores and their confidence ratings. Further examination revealed varying levels of proficiency across different content dimensions, with students demonstrating the strongest grasp on the concept of isomers but facing challenges, particularly in 'number judgment and writing'. The study identified eight misconceptions, classified as moderate, serious, and typical across four dimensions, offering valuable insights for teachers. These insights enable teacher to address students' specific learning challenges related to isomers promptly and effectively, ultimately enhancing their understanding and mastery of the subject.
– Name: AbstractInfo
  Label: Abstractor
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  Data: As Provided
– Name: DateEntry
  Label: Entry Date
  Group: Date
  Data: 2025
– Name: AN
  Label: Accession Number
  Group: ID
  Data: EJ1461684
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=eric&AN=EJ1461684
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      – Type: doi
        Value: 10.1007/s10763-024-10494-y
    Languages:
      – Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 41
        StartPage: 907
    Subjects:
      – SubjectFull: Secondary School Science
        Type: general
      – SubjectFull: High School Students
        Type: general
      – SubjectFull: Scientific Concepts
        Type: general
      – SubjectFull: Science Tests
        Type: general
      – SubjectFull: Student Evaluation
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      – SubjectFull: Misconceptions
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      – SubjectFull: Mastery Learning
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      – SubjectFull: Scores
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      – SubjectFull: Chemistry
        Type: general
    Titles:
      – TitleFull: Evaluating Students' Conceptual Understanding of Isomers Based on a Four-Tier Diagnostic Tool in Upper Secondary Schools
        Type: main
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            NameFull: Min Wu
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            NameFull: Peiyao Tian
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            NameFull: Daner Sun
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            NameFull: Dan Feng
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            NameFull: Ma Luo
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            – D: 01
              M: 04
              Type: published
              Y: 2025
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            – Type: issn-print
              Value: 1571-0068
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              Value: 1573-1774
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              Value: 23
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              Value: 4
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            – TitleFull: International Journal of Science and Mathematics Education
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