Blooming student difficulties in dealing with organic reaction mechanisms – an attempt at systemization†
Gyde
Asmussen
*a,
Marc
Rodemer
b and
Sascha
Bernholt
a
aLeibniz Institute for Science and Mathematics Education, Olshausenstraße 62, 24118 Kiel, Germany. E-mail: asmussen@leibniz-ipn.de
bUniversity of Duisburg-Essen, Schuetzenbahn 70, 45127 Essen, Germany
First published on 23rd May 2023
Abstract
Students are known to have various difficulties in dealing with organic reaction mechanisms. A systematic classification of these difficulties appears necessary to design appropriate support. This paper presents insights into whether and how Bloom's revised taxonomy can be used to classify student difficulties in dealing with organic reaction mechanisms. We conducted an interview study with 12 undergraduate chemistry students using problem-solving tasks on nucleophilic substitution and elimination reactions to provide examples to test the classification. In our attempt at systemization, student difficulties are perceived as unachieved learning objectives. The classification reveals that student difficulties pertain to different cognitive process and knowledge dimensions. Specific major difficulties occurred within each cell of Bloom's revised taxonomy and for individual students. Our analysis suggests that general support for dealing with reaction mechanisms might be less beneficial for some students and that more adapted support is needed. Our approach of using Bloom's revised taxonomy to classify student difficulties might also benefit other domains to better understand student difficulties and evaluate appropriate support.
Introduction
Problem-solving is one of the most important abilities students should acquire in their chemistry studies (Graulich, 2015), since success in chemistry at university level depends largely on this ability (Bodner and Herron, 2002). Several definitions of problem-solving exist, for example, “finding a way to cross the gap between where you are now and where you want to be” (Hayes, 1989) and “what you do when you do not know what to do” Wheatley (1984). In the domain of chemistry, Bodner (2015) described problem-solving as “what chemists do”. Particularly in organic chemistry, part of a chemist's tasks includes dealing with reaction mechanisms and, thus, this is also a central requirement for students, for example, in exams (Austin et al., 2015; Helix et al., 2022).Reaction mechanisms, however, seem to pose a major challenge for some students. On the one hand, students use various inadequate problem-solving strategies (Bhattacharyya and Bodner, 2005; Ferguson and Bodner, 2008; Kraft et al., 2010; McClary and Talanquer, 2010; Grove et al., 2012b; Bhattacharyya, 2014; Galloway et al., 2017). On the other hand, diverse gaps in students’ conceptual knowledge surfaced (Ferguson and Bodner, 2008; Cartrette and Mayo, 2011; Anzovino and Bretz, 2015; DeFever et al., 2015; Akkuzu and Uyulgan, 2016; Popova and Bretz, 2018b; Xue and Stains, 2020).
Many researchers made suggestions on how to support students (Grove et al., 2008; Fautch, 2015; Flynn and Ogilvie, 2015; Dood, et al., 2020). However, the diversity of difficulties makes assigning appropriate supporting strategies to students’ individual needs complex. It might be beneficial to further investigate student difficulties to support their dealing with reaction mechanisms. We surmise that a systematic classification of student difficulties might aid in grouping similar difficulties and identifying their underlying reasons. Ultimately, developing support and assigning already existing support based on the results of the classification could help address students’ individual difficulties. This paper provides an example of such a classification and its implications.
There are several taxonomies for classifying teaching and learning processes, for example, Bloom's taxonomy, Bloom's revised taxonomy or Biggs’ and Collis’ structure of the observed learning outcome (SOLO) taxonomy (Bloom et al., 1956; Biggs and Collis, 1982; Anderson and Krathwohl, 2001; Moseley et al., 2005). The application areas, purposes, and emphases of these taxonomies vary (Moseley et al., 2005). In general, however, they fall into the broad categories of frameworks that categorize desired learning objectives and frameworks that categorize achieved learning outcomes (Stone, 2021).
Bloom's revised taxonomy is an internationally known and widely implemented approach to classify learning objectives (Anderson and Krathwohl, 2001; Moseley et al., 2005; Elmas et al., 2020; Stone, 2021). Although not the primary purpose of this taxonomy, we argue that it can also serve to classify student difficulties when understood as indications of unachieved‡ learning objectives. We test this application of the taxonomy using student difficulties encountered in an interview study of typical problem-solving tasks on nucleophilic substitution and elimination reactions. This paper first focuses on the objective applicability of this classification approach. Second, the question is what conclusions can be drawn from such a classification about the nature of students’ difficulties and about ways to address these difficulties in the classroom.
Problem-solving in organic chemistry
Several investigations address students’ problem-solving in organic chemistry. They focus on different aspects of problem-solving, including dealing with representations (Cooper et al., 2010; Strickland et al., 2010), using the electron-pushing formalism (Bhattacharyya and Bodner, 2005; Ferguson and Bodner, 2008; Flynn and Featherstone, 2017), reasoning strategies (Kraft et al., 2010; McClary and Talanquer, 2010; Grove et al., 2012a; Bhattacharyya, 2014; Crandell et al., 2020; Watts et al., 2020; Watts et al., 2021), or conceptual knowledge (Cartrette and Mayo, 2011; Cruz-Ramírez de Arellano and Towns, 2014; Anzovino and Bretz, 2015; Akkuzu and Uyulgan, 2016; Popova and Bretz, 2018b; Xue and Stains, 2020; Brandfonbrener et al., 2021). Researchers have also proposed instructional interventions to address these aspects (Carle et al., 2020; Crandell et al., 2020; Dood et al., 2020). Despite their different emphases, most papers deal with reaction mechanisms. They report that students apply the rules learned in class and use different concepts to solve reaction mechanisms (Ferguson and Bodner, 2008). Students also form correct products when solving reaction mechanisms (Bhattacharyya and Bodner, 2005; Cruz-Ramírez de Arellano and Towns, 2014). Students have a good understanding of the starting and ending points of reaction mechanisms and how they are represented in reaction coordinate diagrams, and at least a partial understanding of the other points in reaction coordinate diagrams (Popova and Bretz, 2018a). When prompted, students are able to define and describe characteristics of different reactants that are involved in a mechanism, such as leaving groups, Brønsted–Lowry bases and acids, or nucleophiles (Cartrette and Mayo, 2011; Anzovino and Bretz, 2015; Popova and Bretz, 2018b). However, these studies all indicate that problem-solving and especially dealing with reaction mechanism is also very challenging for some students. On the one hand, this was evident in the approaches students used to solve problems. Students were shown to use heuristics or rely on rote memorization to solve reaction mechanisms. These approaches do not allow to develop a deep understanding of organic chemistry (Bhattacharyya and Bodner, 2005; McClary and Talanquer, 2010; Grove et al., 2012a, 2012b) and may be characterized by, for example, a lack of justification (McClary and Talanquer, 2010; Cruz-Ramírez de Arellano and Towns, 2014; Popova and Bretz, 2018b). Students also tend to refer to surface features of representations (Kraft et al., 2010; Galloway et al., 2017; Graulich and Bhattacharyya, 2017). Graulich and Bhattacharyya (2017) note that focusing on surface features leads students to include irrelevant aspects in their reasoning. Further studies have also shown that students integrate isolated variables into their problem-solving process (Kraft et al., 2010; Bhattacharyya, 2014; Watts et al., 2021), and use the electron-pushing formalism in an unproductive manner, leading to descriptions such as “decorating with arrows” or “connect the dots” (Bhattacharyya and Bodner, 2005; Ferguson and Bodner, 2008; Grove et al., 2012b).On the other hand, several studies have revealed student difficulties with specific chemical concepts. Popova and Bretz (2018b) investigated students’ understanding of leaving groups and indicated that students have fragmented knowledge structures. Similarly, Cartrette and Mayo (2011) reported that concepts poorly relate to each other in students’ mental models, resulting in a mixed use of concepts during problem-solving. Studies by Anzovino and Bretz (2015), Asmussen et al. (2022), and DeFever et al. (2015) support this finding, since they also showed that concepts poorly relate to each other. In particular, acid–base theory and its relationship to other concepts seems difficult, as mentioned in several papers. For example, students were found to have difficulties distinguishing between acid–base theory and the concepts of electrophilicity and nucleophilicity (Cartrette and Mayo, 2011; Anzovino and Bretz, 2015). Students also did not appear to understand the relationship to the quality of leaving groups (Popova and Bretz, 2018b). In addition, students appeared to have diverse difficulties with these chemical concepts, for example, they could only define them incorrectly or incompletely, or they could not decide when to use them in a task. Given examples included, among others, the nucleophile, Lewis base, and resonance (Ferguson and Bodner, 2008; Cartrette and Mayo, 2011; Anzovino and Bretz, 2015; Akkuzu and Uyulgan, 2016; Xue and Stains, 2020). Describing and connecting concepts correctly and choosing the proper concepts are crucial for successful problem-solving (Ferguson and Bodner, 2008; Cartrette and Mayo, 2011).
In addition to the numerous findings about how students deal with reaction mechanisms and the difficulties they have in doing so, approaches exist to explain and summarize these findings. Some researchers identified reasons of student difficulties, such as inappropriate teaching strategies, rote memorization, or a lack of knowledge (Bhattacharyya and Bodner, 2005; Anderson and Bodner, 2008; Cruz-Ramírez de Arellano and Towns, 2014; Anzovino and Bretz, 2015; Akkuzu and Uyulgan, 2016; Popova and Bretz, 2018b). Approaches to classifications also exist. However, those classifications relate to students’ learning strategies rather than their difficulties. Grove and Bretz (2012) see the reason for student difficulties in their learning strategies. They classified learners into different groups using the strategies of rote memorization and meaningful learning. They noted that the most successful learners use the strategy of meaningful learning. Anderson and Bodner (2008) also emphasized that students have to make connections between different content aspects to solve problems. Simply applying rules does not suffice.
While many researchers have suggested how to support students, these suggestions are often general and do not address individual difficulties. For example, changes in instruction in form of group discussions, flipped classrooms or the implementation of video instruction (Cruz-Ramírez de Arellano and Towns, 2014; Fautch, 2015; Popova and Bretz, 2018b; Rodemer et al., 2021; Eckhard et al., 2022), changes in curriculum (Ferguson and Bodner, 2008; Grove et al., 2008; Flynn and Ogilvie, 2015), and more explicit connections (Anderson and Bodner, 2008; Anzovino and Bretz, 2015; Popova and Bretz, 2018b) offer promising potential to support students across the board. A more differentiated classification of specific types of student difficulties, however, could increase the benefits of these approaches by providing the opportunity to adapt these instructional strategies to individual student needs.
The underlying theoretical assumption is that prior knowledge is not a static construct that is permanently readily available to learners for problem-solving. Rather it consists of various knowledge pieces that need to be specifically activated by the problem-solving task at hand (Hammer et al., 2005; DiSessa, 2013). Thus, successful problem-solving fundamentally relies on the availability and activation of prior knowledge (Ausubel, 1968; Anderson, 1993; Hammer et al., 2005). Also, successful problem-solving implies that concepts are not memorized individually, but are integrated and connected with prior knowledge and, thus, stored in organized structures that support their goal-directed activation and application to solve the problem at hand (Bhattacharyya and Bodner, 2005; Galloway et al., 2018). In line with assumptions of a constructivist learning theory on the one hand (Cakir, 2008) and the resource-based framework proposed by Hammer et al. (2005) on the other hand, acquiring a specific concept depends on the activation of learners’ prior knowledge and the active and individual establishment of connections to this prior knowledge (Kendeou and O’Brien, 2015). In consequence, difficulties arising during problem-solving differ among students as a function of both the prior knowledge and the degree of interconnectedness in the students’ knowledge base (Asmussen et al., 2022), as well as the activation of the prior knowledge by the problem-solving task (DiSessa and Wagner, 2005; Hammer et al., 2005). A systematic classification of student difficulties might, thus, provide the basis for adaptively addressing these difficulties by specific support and scaffolds that aim at closing gaps, strengthening connections in students’ knowledge bases, or activating additional pieces of prior knowledge. In the present study, we aim to show how such a classification of student difficulties can be made using Bloom's revised taxonomy.
Bloom's revised taxonomy
Bloom's revised taxonomy builds on the taxonomy developed by Benjamin Bloom and colleagues (1956) and serves to systematically classify cognitive learning objectives. While the original taxonomy focused on examiners and thus aimed at operationalizing test materials, in their revised taxonomy Anderson and Krathwohl (2001) shifted the focus to teachers. Thus, the revised taxonomy is intended to classify teaching methods, learning processes, and test materials. This change in focus has brought new applications and target audiences. The taxonomy can serve for course planning, instruction, and assessment. In particular, the alignment of these three aspects is a major advantage of the taxonomy, as it provides an opportunity to check instruction for internal consistency (Anderson and Krathwohl, 2001; Moseley et al., 2005).Bloom's revised taxonomy is two-dimensional, with four knowledge dimensions and six cognitive process dimensions (Fig. 1). The knowledge dimensions are factual knowledge, conceptual knowledge, procedural knowledge, and metacognitive knowledge and form a continuum. While factual knowledge describes individual concrete knowledge pieces such as names or details, conceptual knowledge describes the interrelationships between these concrete knowledge pieces within a larger structure. Procedural knowledge describes the knowledge about subject-specific methods and criteria when to use them. Hence, factual knowledge and conceptual knowledge describe the ‘what’ while procedural knowledge describes the ‘how’, i.e., the procedures and algorithms necessary to carry out certain activities or the steps of a problem-solving process. Metacognitive knowledge describes knowledge about knowledge in general and one's own knowledge. Thus, the continuum goes from concrete (factual knowledge) to abstract (metacognitive knowledge).
 | ||
| Fig. 1 Design of Bloom's revised taxonomy based on Anderson and Krathwohl (2001). | ||
The six cognitive process dimensions are remember, understand, apply, analyze, evaluate, and create. The cognitive process dimension also forms a continuum. Whereas remember requires retrieving relevant knowledge from long-term memory, apply requires using knowledge productively, and create requires putting together knowledge to produce something new. These processes become increasingly cognitively demanding. Thus, the continuum describes cognitive complexity. Although the cognitive processes build on each other, they do not form a strict hierarchy. This is characterized by the fact that the individual cognitive process dimensions overlap and more complex cognitive process dimensions do not necessarily include lower cognitive process dimensions (see Anderson and Krathwohl (2001) for a detailed description of all knowledge dimensions and cognitive process dimensions).
To locate a learning objective in the taxonomy, it must be formulated, for example, as “The students will be able to/learn to [verb] [objective]”. The verb indicates the cognitive process dimension and the object the knowledge dimension. Based on the combination of verb and object, the learning objective is classified into the appropriate cell of the taxonomy. However, due to the abstract formulation of the taxonomy, which ensures that the taxonomy is applicable to many domains, a distinct classification becomes difficult sometimes. Bloom himself has suggested that each domain should adapt the taxonomy for itself. This would facilitate unambiguous classification based on domain-specific terminology. The terminology used to formulate the learning objectives also sometimes makes it difficult to classify them in the taxonomy. For example, different meanings of synonyms or vaguely defined terms must be identified and explicated to enable unambiguous classification. The classification of a learning objective might vary, depending on how much information is already available (Crowe et al., 2008). Finally, one must also consider that, despite the classification of learning objectives in the taxonomy, students may learn something different than intended, because their domain-specific prior knowledge, the activated pieces of this prior knowledge, and students’ learning strategies differ. Despite these possible challenges in using the taxonomy, it provides a useful tool for instructors to get an overview of what they want to teach, what they actually teach, and what they finally query in their classes (Anderson and Krathwohl, 2001). However, the question arises whether the taxonomy offers other applications in addition to its traditional use. For example, Christian and Talanquer (2012) demonstrated using Bloom's revised taxonomy to classify content-related conversations in learning groups leads to diagnostic information about students' cognitive processing levels. We assume that the taxonomy is also applicable to other student statements, e.g., to classify their difficulties, as shown below.
Using Bloom's revised taxonomy for problem-solving tasks in organic chemistry
“With respect to problem solving, for example, the particular rows, columns, and cells selected, and the order in which specific cognitive processes and knowledge subtypes would be expected to be used, would depend to a great extent on the particular type of problem being solved and/or the subject matter within which the problem was posed” (Anderson and Krathwohl, 2001, p. 270).With this quote, Anderson and Krathwohl describe how the requirements and learning objectives of problem-solving tasks can be classified into their revised taxonomy. The quote shows that problem-solving tasks involve multiple requirements and thus have not one, but multiple learning objectives, all of which must be achieved to successfully solve the problem. It also shows that the knowledge pieces to be used and the manner and order they should be incorporated depend on the problem-solving task.
The same applies to problem-solving tasks in organic chemistry. Problem-solving in organic chemistry can be understood as a multi-step problem-solving process in which the individual steps can be characterized by the use of specific knowledge pieces and by specific requirements. Flynn (2014) and Moloney (2015) illustrate this by presenting the individual steps that make up their problem-solving tasks on organic reaction mechanisms. The individual steps reflect separate learning objectives that, when taken together, enable problem-solving. According to Kraft et al. (2010), successful problem-solvers are able to break down the given task into individual steps. Their report supports the idea of a multi-step problem-solving process. These individual steps that make up a problem-solving task can in turn serve to scaffold students’ problem-solving (Caspari and Graulich, 2021).
Flynn (2014) demonstrated the feasibility of assigning the individual steps of a problem solution to specific learning objectives that can be classified into Bloom's revised taxonomy in the context of reaction mechanisms. Her findings also highlight that the individual steps of a problem-solving task often require different cognitive process dimensions. However, the results presented above on student difficulties dealing with reaction mechanisms show that these different requirements (individually or combined) are often not met. Based on the expected requirements, student difficulties in problem-solving could be understood as unachieved learning objectives characterized precisely by the cognitive processes and knowledge pieces that students were unable to perform fully or correctly at a given point in their problem-solving process. Although not the intended purpose of the taxonomy, Bloom's revised taxonomy proved suitable not only for classifying learning objectives, but also for classifying students’ statements (Christian and Talanquer, 2012). One could classify students’ difficulties in terms of failure to meet the learning objectives, for example, as “The student is not able/struggles to [verb] [objective]”. The classification would not only highlight those concepts that seem difficult for students due to a lack of prior knowledge or insufficient activation, but also which specific cognitive processes students struggle with when a task requires these concepts. Such a differentiated characterization of student difficulties could in turn provide a solid foundation for the systematic development of specific supports that could be adaptively offered to a student struggling with a particular step during problem-solving. To the best of our knowledge, no documentation presently exists regarding implementation of Bloom's revised taxonomy to classify student difficulties in organic chemistry.
Aim
Numerous papers have reported student difficulties in dealing with reaction mechanisms. Some of these papers focus on particular concepts, some on learning strategies or problem-solving approaches. In the present study, we are interested in classifying these difficulties as they occur in students’ problem-solving in detail. We aim to investigate whether the combined consideration of knowledge pieces and cognitive processes to characterize students’ difficulties during problem-solving leads to more differentiated conclusions about the nature of these difficulties. More specifically, we aim to exemplify how and whether student difficulties with typical organic chemistry tasks can be classified into Bloom's revised taxonomy. For this purpose, we conducted problem-centered interviews on purposefully developed problem-solving tasks and analyzed students’ difficulties. The results of this classification process are presented both at the level of all students in this sample and at the level of individual students to illustrate the nature and degree of differentiation of the findings obtained.Methods
Participants and setting
The data collection took place at a public German university during spring 2021. Participant recruitment was conducted online, due to the COVID-19 pandemic. Twelve undergraduate chemistry students volunteered to participate in semi-structured interviews. The participants included undergraduate students enrolled in the Organic Chemistry I and Organic Chemistry II courses, as well as students who had already passed both courses. Regardless of the course students enrolled in, all students had in common that they had already been taught nucleophilic substitution and elimination mechanisms and their influencing factors. Including students with varying levels of expertise in the field of nucleophilic substitution and elimination is intended to reveal a wide range of difficulties.The research complied with ethical guidelines and ensured that students could opt out at any time without disadvantage. All students received information about their rights and the handling of the data. Informed consent was obtained from all students prior to data collection, which included permission to use of their data for analysis and publication. Students received a financial compensation for their participation. The interviews were conducted in German, and quotes were translated verbatim for this publication. All students got pseudonyms to preserve their anonymity.
Interview task
For this study, typical problem-solving tasks on organic reaction mechanisms were developed. The tasks covered the topics of nucleophilic substitution and elimination reactions. Organic Chemistry I covered both of these reaction mechanisms. In total, four task sets exist, each consisting of two predict-the-product tasks that differed in one aspect and one case comparison task requiring comparison of the predict-the-product tasks (Fig. 2). Students often tend to use shortcuts during task processing and heuristics when solving predict-the-product tasks (Grove et al., 2012a, 2012b). Solving case comparisons by shortcuts is not possible, instead, it requires analyzing the representational features and applying conceptual knowledge (Graulich and Schween, 2018). In addition, case comparisons encourage deeper reasoning and the weighing of variables (Alfieri et al., 2013). In the predict-the-product tasks, students were prompted to (a) write down the products of the reaction and (b) explain and justify the process of the reaction. The task description provided the type of mechanism. In the case comparison tasks, students were prompted to (a) compare two reactions and look for differences and similarities and (b) decide which of the two reactions has a higher reaction rate and justify their decision. The explicit structural differences in the starting materials of the nucleophilic substitution tasks resulted in differences of electrophilicity and nucleophilicity of the respective molecules, while the structural differences in the elimination tasks pertained to double bond stabilization and leaving group ability. Identifying these concepts as relevant for the respective mechanisms is necessary especially for the case comparison. | ||
| Fig. 2 Task set of an elimination reaction used in this study. The cases differ in the position of the double bond. The two predict-the-product tasks are on the left and the case comparison task is on the right. | ||
Classification of the interview tasks into the revised Bloom taxonomy
The tasks were analyzed in relation to Bloom's revised taxonomy, to better understand which requirements the interview tasks used put on students. The focus was on the required knowledge and cognitive process dimensions. Therefore, the tasks were first divided into individual steps to be completed for problem-solving. These steps represent the learning objectives. Next, the steps were classified into Bloom's revised taxonomy (Table 1). For this purpose, a coding scheme was developed based on Anderson and Krathwohl's (2001) revised taxonomy on the one hand (Fig. 1) and similar classifications regarding organic chemistry from the literature on the other (Flynn, 2014).| Predict-the-product tasks | Case comparison task |
|---|---|
| The students should be able to… | The students should be able to… |
| • recall the E2 mechanism (remember conceptual knowledge) | • identify the similarities and differences between reaction A and B (understand conceptual knowledge) |
| • recognize Lewis acid, Lewis base, leaving group, and solvent in the representation (understand conceptual knowledge) | • recall properties that influence the difference between reaction A and B (remember conceptual knowledge) |
| • identify reactive sites of Lewis base and Lewis acid (analyze conceptual knowledge) | • derive properties that differ between reaction A and B from the representation (analyze conceptual knowledge) |
| • recall properties that influence the formation of the Hofmann and Saytzeff product (remember conceptual knowledge) | • explain how properties influence the reaction rate (apply conceptual knowledge) |
| • derive properties that influence the formation of the Hofmann and Saytzeff product from the representation (analyze conceptual knowledge) | • compare and weigh influencing properties to decide which reaction proceeds faster (evaluate conceptual knowledge) |
| • decide whether the reaction favors the Hofmann or Saytzeff product (evaluate conceptual knowledge) | |
| • use the E2 mechanism to predict the products (apply conceptual knowledge) | |
| • justify why the reaction proceeds like this (evaluate conceptual knowledge) |
Flynn (2014) provides a useful guide for adapting Bloom's revised taxonomy to learning objectives related to organic reaction mechanisms, as it lists exemplary learning objectives with associated cognitive process dimensions. Our coding scheme is provided in the ESI.†Table 1 shows which steps require completion to comprehensively solve the task set shown in Fig. 2. This analysis of the interview tasks was for illustration and allowed us to gain an impression of where difficulties may arise and where they are not to be expected. The combination of predict-the-product and case comparison tasks in different contexts provides a wide range of requirements. Our problem-solving tasks could thus stimulate a variety of cognitive processes, but also offer many steps at which difficulties could arise.
As the tasks and corresponding prompts used in the interviews focus on dealing with reaction mechanisms and require students to describe, explain, and compare different reaction mechanisms, we expect that the knowledge dimensions factual and conceptual knowledge will cover the majority of students’ difficulties. In a nutshell, the tasks focus on content-related aspects of reaction mechanisms and thus on the ‘what’ rather than the ‘how’. In addition, the cognitive process create is not expected to occur frequently as the corresponding learning objectives (e.g., deriving a synthetic route to form a specific product) are not required to solve the tasks. Only advanced courses deal with the independent planning of synthesis at the university where the study took place. Therefore, the tasks did not query this skill.
Data collection
Semi-structured interviews were used for data collection. Due to the COVID-19 pandemic, the interviews were conducted online via a video conferencing tool in individual sessions. Tasks were presented via screen sharing and the interviews were recorded. Students’ solutions to the predict-the-product tasks were written on paper and then photographed. Students explained the reaction they expected to take place, after writing down their solution. Only verbal explanations were collected for the case comparison tasks.Data analysis
In addition to the requirements of the tasks, students’ statements from the interviews were also analyzed. Therefore, the interviews were first transcribed verbatim and then analyzed by qualitative content analysis using the coding software MAXQDA (VERBI GmbH, 2020). In a first coding phase, all text passages in which content-related difficulties during the problem-solving process occurred were identified. For this purpose, all interviews were coded deductively according to the main categories “content” and “accuracy”. Table 2 shows the corresponding coding scheme. For further analysis, all text passages were ordered according to content code and whether they contained difficulties. Text passages were excluded from further analysis when no difficulties occurred. In the second coding phase, the text passages from coding phase one, in which difficulties during the problem-solving process occurred, were analyzed using Bloom's revised taxonomy. Each text passage was assigned a learning objective that had not been achieved, and on this basis assignment was made to the appropriate cell regarding knowledge dimensions and cognitive process dimensions. For this purpose, the coding scheme based on Anderson and Krathwohl's (2001) revised taxonomy (Fig. 1) and Flynn (2014) was used (see ESI†). Students’ difficulties were analyzed to determine whether they involve factual knowledge, conceptual knowledge, procedural knowledge, or metacognitive knowledge for the knowledge dimension. For the cognitive process dimension, students’ difficulties were examined to determine whether they arose due to difficulties in remembering, understanding, applying, analyzing, evaluating or creating a specific knowledge piece. For classification into the revised Bloom taxonomy (coding phase 2), inter-rater reliability was again determined based on 20% of the data using two raters. A Cohen's kappa coefficient of 0.97 was calculated, indicating nearly perfect agreement. Hence, only one rater continued to code the remaining data. The number of difficulties encountered was determined for each knowledge and cognitive process dimension after coding. Difficulties that were identical and occurred more than once, e.g., for different students or multiple times for one student, were counted only once. Classification and counting of difficulties was performed for all students together as well as for each individual student.| Main category | Code | Exemplary sub codes | Description | Example |
|---|---|---|---|---|
| Content | Mechanism | • Nucleophilic substitution | Participant… | “Unlike E1 elimination, E2 elimination is synchronous.” |
| • Elimination | • describes a specific mechanism or its properties. | |||
| • … | • uses a specific mechanism or its properties for problem-solving. | |||
| • answers a question about a specific mechanism. | ||||
| Reactant | • Nucleophile | Participant… | “So generally you have a nucleophile, which is then also negatively charged.” | |
| • Electrophile | • identifies a specific reactant. | |||
| • Leaving group | • describes a specific reactant or its properties. | |||
| • … | • uses a specific reactant or its properties for problem-solving. | |||
| • answers a question about a specific reactant. | ||||
| Concept | • Basicity | Participant… | ||
| • Charge | • identifies a specific concept. | “Could you try to explain what resonance is?” | ||
| • Resonance | • describes a specific concept or its properties. | “Yes, I have the same number of atoms, but a different structure.” | ||
| • Steric hindrance | • uses a specific concept or its properties for problem-solving. | |||
| • … | • answers a question about a specific concept. | |||
| Accuracy | Correct | — | Participant… | “One explains bases and acids by saying that a base is an electron pair donor and an acid is an electron pair acceptor.” |
| • makes a correct statement about a specific content. | ||||
| Incorrect | — | Participant… | “Basicity is actually the ability to accept electrons.” | |
| • makes an incorrect statement about a specific content. | ||||
| Unclear | — | Participant… | “I'm not even sure which one is bigger now. Therefore, no, I can't.” | |
| • does not answer a question about a specific content. | ||||
| • makes a statement about a specific content which is neither correct nor incorrect. | ||||
Results and discussion
Results across all students
Content analysis of the interviews revealed that a total of 174 different difficulties, understood as unachieved learning objectives, emerged across tasks and students. According to Bloom's revised taxonomy, classification of these unachieved learning objectives showed that they are unevenly distributed throughout the taxonomy (Table 3). Conceptual knowledge is the most common knowledge dimension with 157 unachieved learning objectives, while remember is the most common cognitive process dimension with 58 unachieved learning objectives. As expected, no unachieved learning objectives occurred in the cognitive process dimension create, the knowledge dimensions procedural or metacognitive knowledge (see above). In the following, the individual dimensions and cells of the taxonomy are described separately. The results of this individual description of unachieved learning objectives are summarized in Table 4. While Table 4 lists first the major difficulties in each cell (left side) and second the impact of these major difficulties on students' success (right side) in bulleted form, the major difficulties and their impact on students' success are explained and discussed in detail in the text. For each cell, the text also provides examples of what difficulties looked like in the data.| Cognitive process dimension | ||||||
|---|---|---|---|---|---|---|
| Remember | Understand | Apply | Analyze | Evaluate | ||
| Knowledge dimension | Factual knowledge | 17 | — | — | — | — |
| Conceptual knowledge | 41 | 8 | 56 | 24 | 28 | |
| Cell in Bloom's revised taxonomy | Occurring difficulties | Impact on students’ success |
|---|---|---|
| The students are not able to… | ||
| Remember factual knowledge | • recall properties of chemical elements | • …which means that this information cannot be processed in higher cognitive process dimensions and that it cannot be used to make decisions and draw conclusions, which often stops problem-solving and leads to no or incorrect solutions. |
| • name mechanisms, reactants or concepts | • …and this lack of or incorrect use of terminology can lead to confusion and thus be an obstacle in learning and understanding organic chemistry, but it does not necessarily affect problem-solving or the solution itself, when limited to recall the appropriate name (and not also the to-be-named mechanism, reactant, or concept). | |
| Remember conceptual knowledge | • recall a mechanism, reactant or concept at all | • …which means that this information cannot be processed in higher cognitive process dimensions and that it cannot be used for deciding about relevant and irrelevant aspects and informing the next steps of the problem-solving process, which often stops problem-solving and leads to no or incorrect solutions. |
| • recall a mechanism, reactant or concept completely | • …and this lack of or incomplete information can make students feel uncertain about what they know, which can hinder problem-solving, but it does not necessarily affect problem-solving or the solution itself, depending on how relevant the missing aspects are for problem-solving. | |
| • recall a mechanism, reactant or concept correctly | • …which means that incorrect information is integrated into the problem-solving process, resulting in incorrect solutions. | |
| Understand conceptual knowledge | • recognize a reactant in the representation | • …and this lack of or incomplete information cannot be processed in other cognitive process dimensions and the incorrect identification of reactants can lead to the integration of incorrect information into the problem-solving process, which both often hinders or stops problem-solving and leads to no or incorrect solutions, but nevertheless students produced correct solutions because they did not use their classification for problem-solving. |
| Apply conceptual knowledge | • perform correct reaction steps | • …which means that incorrect information is integrated into the problem-solving process, resulting in incorrect solutions. |
| • let reactants behave correctly | ||
| • propose correct products | • …which is a result of an incorrect problem-solving process and an incorrect solution. | |
| • describe relationships between chemical concepts or reactants | • …and this lack of or incomplete information cannot be processed in other cognitive process dimensions and the description of incorrect relationships can lead to the integration of incorrect information into the problem-solving process, which both often hinders or stops problem-solving and leads to no or incorrect solutions. | |
| Analyze conceptual knowledge | • recognize reactive sites of molecules | • …and this lack of or incomplete information cannot be processed in other cognitive process dimensions and the identification of incorrect reactive sites can lead to incorrect reactant behavior and to the integration of incorrect information into the problem-solving process, which both often hinders or stops problem-solving and leads to no or incorrect solutions. |
| • derive chemical concepts from the representation | • …and this lack of or incomplete information cannot be processed in other cognitive process dimensions and the identification of incorrect concepts can lead to the integration of incorrect information into the problem-solving process, which both often hinders or stops problem-solving and leads to no or incorrect solutions. | |
| • differentiate between mechanisms, reactants or chemical concepts | • …which means that incorrect information is integrated into the problem-solving process, resulting in incorrect solutions. | |
| Evaluate conceptual knowledge | • compare reactants or reactions in terms of specific chemical concepts | • …and this lack of or incomplete information cannot be processed in other cognitive process dimensions and incorrect comparisons can lead to the integration of incorrect information into the problem-solving process, which both often hinders or stops problem-solving and leads to no or incorrect solutions |
| • justify a solution or explanation | • …but missing, insufficient, or incorrect justifications often do not affect the problem-solving process or the solution itself, while reasonable justifications enrich the argumentation. | |
#1 Ellie: “I don't know the electronegativity of chlorine off the top of my head right now, nor that of carbon.”
Since solving the task already failed in remembering basic element properties, it was consequently not possible to use the factual knowledge for other cognitive processes and to answer the other aspects of the interviewer's question, which also required higher cognitive process dimensions.
In Liam's case (#2), the interviewer asked to compare the atoms sulfur and oxygen. Since Liam had to recall the information to solve the task, a similar difficulty arose. Unlike Ellie (#1), however, Liam had an inkling and just was not sure about it.
#2 Liam: “Now you would have to know where sulfur is in the periodic table, right? So […] they definitely have a different atomic number. And I think that sulfur has a higher atomic number than oxygen. I think they both form two bonds. I think they're even in the same group, maybe? Sulfur is just below oxygen? But I don't know right now. I don't have the periodic table in my mind right now.”
The other major difficulty found here was that names of mechanisms, reactants, and concepts were confused or unknown. In Alexander's case (#3), the interviewer asked about the Hofmann and Saytzeff product when discussing the products of an elimination reaction. Alexander's quote shows that he knows the concept but struggles with the correct terminology.
#3 Alexander: “Saytzeff was the one that goes from the C that has the most Hs on it […]. And Hofmann was then the one that goes from the C, where there are the fewest.”
He correctly describes the location of the attack, but uses the terms Hofmann and Saytzeff in reverse. Although correct terminology does not necessarily indicate understanding of the concept and vice versa (Crandell et al., 2020), incorrect use of terminology can lead to confusion and can be an obstacle in learning and understanding organic chemistry. Since different researchers reported that the use of terminology affects students’ success in chemistry, students should receive support when difficulties arise such as those experienced by Alexander (Quílez, 2019; Rees et al., 2019).
For example, the first case occurred with Ellie. The interviewer asked if she could describe second-order nucleophilic substitution. Her answer was “No.”. She could not remember the mechanism at all. This resulted in an incorrect mechanism of nucleophilic substitution and incorrect products of the nucleophilic substitution reactions (Fig. 3). Ellie's case illustrates the self-evident point that remembering conceptual knowledge is necessary to use this knowledge for problem-solving. Ferguson and Bodner (2008) also reported that the inability to remember information is a barrier to success. In their study, the inability to remember information hindered students and resulted in no or incorrect solutions. Hence, remembering domain-specific conceptual knowledge plays a crucial role in the overall problem-solving process.
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| Fig. 3 Ellie's mechanism (left side) and products (right side) for task 4. | ||
The absence of some aspects in students’ answers was frequently noted in different contents. Students had a conception of a mechanism, a reactant, or a chemical concept, but missed relevant aspects. For example, in Alexander's case (#4), the interviewer asked him for a definition of nucleophiles. Alexander described that nucleophiles are negatively charged, which is correct, but he limited his definition to the surplus of electrons.
#4 Alexander: “So it's a negative molecule. I think in the lecture we had, the nucleophile was then quite often a base, and always negatively charged. So one electron pair too many that can attack.”
Incomplete explanations and definitions of various contents are also known from the literature. For example, Anzovino and Bretz (2015) reported that when defining nucleophiles and electrophiles, students mention correct characteristics such as the presence of full charges, but limit their definition to these, as also evident in Alexander's case. Xue and Stains (2020) found that students leave out important aspects of the explanation of resonance. When students could only provide incomplete answers they often expressed uncertainty because they themselves recognized their answer was incomplete. The case of Noah (#5) exemplifies this. Noah associates a correct aspect with the queried concept hyperconjugation, but is unable to embed this aspect meaningfully into an explanation. Overall, Noah is uncertain if his association is correct. Due to a lack of knowledge or an inability to retrieve additional information about the concept, he could not use it to proceed with the task.
#5 Interviewer: “Can you explain the concept of hyperconjugation to me?”
Noah: “I don't think so. I'll have to think about it. This is an orbital interaction in itself, but I'm not sure about that.”
Mistakes in defining and describing mechanisms, reactants, and chemical concepts occurred frequently. This is certainly true in the cases of Lukas (#6) and Jacob (#7). While Lukas’ answer contains both correct and incorrect aspects, Jacob's answer is completely wrong. The interviewer asked Lukas to explain what resonance is. He correctly answered that it is a change of the bonding ratios. However, it is incorrect that heteroatoms also move.
#6 Lukas: “Resonance is that a molecule does not change in its number of atoms, but only that the bonding ratios change within this molecule. That is, that a double bond, for example, moves or that some heteroatom such as oxygen, nitrogen or something else does not always bind to the same carbon, but that it can also sometimes bind to other ones.”
Jacob's quote differs from Lukas’ quote. When discussing leaving group ability, the interviewer asked Jacob to explain polarizability. His explanation of polarizability does not contain correct aspects, in contrast to Lukas’ answer. The comparison between Lukas’ and Jacob's quote shows a gradient between few and multiple mistakes. However, while Lukas can continue to use his idea of resonance to solve the tasks because of the correct aspects, Jacob's idea of polarizability means that he cannot use the concept to solve the task.
#7 Jacob: “Well, for me, polarizability just means that you can polarize something, that is, you throw in a positive charge and this positive charge is absorbed or processed. If you now put a proton in there, it somehow forms a bond.”
That students make mistakes in defining and describing resonance and polarizability was also evident in the work of Anzovino and Bretz (2015) and Xue and Stains (2020). However, incorrect definitions go beyond these two concepts. Overall, students seem to struggle when defining and describing various concepts (Bhattacharyya and Bodner, 2005; Cartrette and Mayo, 2011; Luxford and Bretz, 2013; Brandriet and Bretz, 2014; Akkuzu and Uyulgan, 2016).
In order to use conceptual knowledge in higher cognitive process dimensions, correct recall of this knowledge is necessary. Otherwise, there cannot be a meaningful integration into the problem-solving process (Ferguson and Bodner, 2008). The cases reported so far suggest that problem-solving often fails at the less complex cognitive process dimension remember, because tasks do not activate the required knowledge pieces or students have difficulties to recall different aspects of conceptual knowledge at all, completely, or correctly. Although the findings also show that it is not always the case that conceptual knowledge cannot be used for the problem-solving process due to mistakes or missing aspects, mistakes or missing aspects make it more difficult to solve a task. Therefore, providing or knowing the required conceptual knowledge is an important step.
#8 Emma: “So, it's an E2 elimination, tetrahydrofluoride is my base then.”
Interestingly, the misclassification did not lead to incorrect products or reaction processes. Even though Emma misclassified the solvent as a base, the attack still occurred by the free electron pair of the oxygen base. It seems like she performed the reaction process independently of this classification. This difficulty would not occur if she had meaningfully integrated the term base into the context of elimination. Bhattacharyya and Bodner (2005) showed that students can produce solutions without understanding the reaction process or the underlying concepts, as was also evident in the case of Emma. Apart from the base and solvent, misinterpretation of function also occurred with other reactants. Noah (#9), for example, misclassifies the electrophile in task 6. For him, the electrophile is the nitrogen molecule, which is actually the nucleophile. According to his description, the nitrogen molecule is attacked and does not attack itself, which would fit the properties of an electrophile. This shows that it is not a confusion of names, but an incorrect classification.
#9 Noah: “So the similarity is the position of the attack. The chlorine atom is split off and the whole molecule then attacks the nitrogen and not the methyl group. This creates a positive charge and the nitrogen is the electrophile and the chlorine atom is the nucleophile.”
However, correct products and reaction processes appeared here as well. First, because students, like Emma, formulated the reaction process independently of the classification, but also because students corrected their own classification after trying to perform the reaction with their classification and it did not result in meaningful reaction steps. Students should be supported with their difficulties in the dimension understand, even if an incorrect classification does not necessarily lead to failure in problem-solving. The reported case shows that providing necessary conceptual knowledge does not mean that students understand it. Here, it would be necessary to practice how to recognize mentioned properties so that the provided conceptual knowledge becomes meaningful for learners.
Sophie's quote (#10) illustrates both the incorrect reaction steps and the incorrect behavior of the reactants. Her description of the reaction process in task 7 is incorrect, as are the reaction steps performed by the sulfur nucleophile.
#10 Sophie: “So what I was thinking would be that the sulfur has a negative charge and accordingly can pass on that negative charge readily to the chloride. And that the chloride is a good leaving group.”
The sulfur nucleophile does not attack the leaving group chloride, but it attacks the alpha carbon atom. There is also no charge transfer. Despite the incorrect reaction steps, she has formed the correct products. Similar to Bhattacharyya's and Bodner's (2005) findings, Sophie's case shows that the formation of correct products is possible even without a correct mechanism. Such unexpected (and, from a learning perspective, possibly undesirable) solution successes are probably limited to comparatively simple tasks in which reaction products can be derived by recall or plausibility considerations. In more complex reaction conditions, failure is almost certain, which can lead to strong uncertainty from the learner's perspective. In another nucleophilic substitution task, Sophie again performs incorrect reaction steps (#11). This time, she forms incorrect products (Fig. 4). In her solution the nitrogen nucleophile attacks the negatively polarized chloride atom instead of the positively polarized alpha carbon atom. Due to the negative partial charge of the nitrogen nucleophile, this reaction step does not make sense. The incorrect reaction step results in the formation of incorrect products.
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| Fig. 4 Sophie's mechanism and products for task 4. | ||
#11 Sophie: “And so I think that a CH3group will split off. And then, afterwards you have the nitrogen with chloride again.”
The cases reported so far indicate that incorrect reaction steps, incorrect reactant behavior and incorrect products can but do not have to occur together. The common occurrence of these difficulties was found in another study. In this context, incorrect reaction steps in the context of nucleophilic substitution and elimination also led to incorrect products (Cruz-Ramírez de Arellano and Towns, 2014). Mia's (#12) and Charlotte's (#13) quotes show examples of cases where chemical concepts were incorrectly related to other chemical concepts. The interviewer asked Mia to explain the position of the newly formed double bond in the products of task 1. She used inductive effects to do this. Even though Mia has defined positive inductive effects correctly before, she implements them incorrectly in her explanation. The effects she describes are just the opposite.
#12 Mia: “Because contrary to the positive charge, the negative charge is less destabilized by the +I-effect of the carbon, because no further electron density is pushed into the already negative charge. Therefore, the negative charge is more stable there than at the other location.”
Likewise, Charlotte also describes an effect that is just the opposite. The interviewer asked her how the electronegativity of the central atom influences the nucleophilicity of the molecule.
#13 Charlotte: “Yes, so I was relating electronegativity to nucleophilicity. And probably the greater electronegativity is the higher nucleophilicity.”
The relationship between electronegativity and nucleophilicity was also incorrectly explained by many other students. Emma's quote (#14) illustrates this. In the case comparison of task 9, she argues that the higher reactivity of the nucleophile is a result of its higher electronegativity.
(#14) Emma: “My oxygen atom is more electronegative than my sulfur atom, so I can conclude that B proceeds faster because my nucleophile is more reactive, since my electrophile is the same, it can only depend on the nucleophile.”
Incorrect correlations between chemical concepts also occurred several times by other students and chemical concepts. Overall, it appears that the application of mechanisms, reactants, and chemical concepts is challenging for students. This finding is consistent with the literature. Using electrophiles and nucleophiles as examples, Cartrette and Mayo (2011) showed that students have difficulties moving from definition to application. McClary and Talanquer (2010) found that students do not know when and how to use specific concepts. Similarly, Anzovino and Bretz (2015) reported that students rarely use the concept of polarizability in their problem-solving process, and when they do, they use it incorrectly. Other researchers argued that a key to successful problem-solving processes lies in proper application (Ferguson and Bodner, 2008; Cruz-Ramírez de Arellano and Towns, 2014).
The difficulties in the cognitive process dimension apply differ from those in the previous cognitive process dimensions. In contrast to the difficulties in remember and understand, the difficulties in apply are less likely to result in a failure to solve the task at all or to have little effect on the solution. It is more likely that students present incorrect solutions. Additionally, the findings show the difficulties in apply are often related and students incorrectly relate chemical concepts to each other in many different ways. It may thus not be surprising that many difficulties identified in students‘ problem-solving in this study were assigned to the cognitive process dimension apply. Numerous studies have reported similar difficulties before. These findings support the idea that it is not enough to only learn the conceptual knowledge by heart, but that deliberate practice is necessary. Hence, teaching might need to provide more opportunities to apply specific concepts to different reaction contexts, but also to provide students with the overview about how different concepts relate to each other.
An interview excerpt from Ellie (#15) illustrates the first difficulty. In task 4, she misrecognizes the part of the nucleophile that attacks the carbon. It is actually the nitrogen atom that has a free electron pair. However, she identifies the methyl group as reactive, a part of the nucleophile that does not have a free electron pair. Exactly the same problem occurred with Liam. In his case (#16), the methyl group also attacked the electrophile. Therefore, both cannot differentiate between relevant and irrelevant parts of the representation.
#15 Interviewer: “Okay. And can you tell me what this attacks with, what is used to form the bond that is newly formed?”
Ellie: “The C at the end.”
(#16) Liam: “And I just took a methyl group and added it because the nitrogen atom seemed a little bit nonsensical to me that it now forms a quadruple bond and becomes positively charged.”
This finding is consistent with those of several other reports. Students struggle to identify relevant features from given representations. Therefore, it challenges students to identify electron-deficient and electron-rich areas as well as to predict reactive sites of the molecule (McClary and Talanquer, 2010; Cartrette and Mayo, 2011; Cruz-Ramírez de Arellano and Towns, 2014; DeFever et al., 2015).
Difficulties with deriving chemical concepts manifested themselves in two different forms. Paul's (#17) and Mila's (#18) quotes illustrate these. Whereas Paul recognizes a concept within a representation although it is not present, Mila does not recognize a concept although it is present. In task 8, Paul recognizes resonance in the oxygen nucleophile. He explains the delocalization of oxygen's free electron pairs by forming contributing structures. However, the electrons cannot move to the tertiary carbon because it does not have a p-orbital and thus cannot form contributing structures. Thus, there is no resonance in the oxygen nucleophile.
#17 Paul: “We have three free electron pairs on the oxygen. One of them could move to the tertiary carbon and then we would have for example a negative charge there.”
This matches with Carle's and Flynn's (2020) findings that chemistry textbooks rarely explicitly practice recognizing resonance. Furthermore, it does not seem surprising, as Brandfonbrener and colleagues (2021) reported, that students tend not to discuss the structural requirements for resonance. On the other hand, based on the study of Xue and Stains (2020), one might have expected that recognizing resonance would not be difficult for students, since they reported that students’ explanations of resonance focus on how to draw and recognize resonance.
Mila's case shows the opposite, she does not recognize a chemical concept in the representation, even though it is present. In task 9, she was asked about the positive inductive effect. Although there is an alkyl group that has a positive inductive effect, she does not recognize the effect, even after the interviewer specifically asked about it.
#18 Mila: “So inductive effect is just the tendency to pull or push electrons, like plus- and minus-effect. […]”
I: “And can you locate +I-effects somewhere here?”
Mila: “I can't locate the +I effect directly. No.”
Jacob's statement is an example of not being able to differentiate between mechanisms or chemical concepts (#19). Although the task description stated in advance that both reactions are second-order nucleophilic substitutions, he stated that one reaction was a first-order nucleophilic substitution. He admitted, however, that he wasn't sure why he believed that. In this way he shows not only that he does not know what criteria to use to distinguish between the two types of mechanisms, but also more generally, that he cannot derive a mechanism from a representation.
#19 Jacob: “I am not sure. I don't really know either. I can't explain exactly why I think this either, but I think B is an SN2 and A is an SN1. […] I don't really know. I can't explain exactly why. I kind of think that.”
While it is surprising that distinguishing the mechanism occurred as a difficulty, since the mechanism was given in the tasks, it also illustrates that deriving the mechanism is a major challenge for students (Crandell et al., 2020). Moreover, this type of difficulty is also evident in other content areas, both in the material we collected and in the literature. Here, distinguishing between nucleophiles and electrophiles and distinguishing between nucleophiles and bases has proven to be particularly difficult (Bhattacharyya and Bodner, 2005; Cartrette and Mayo, 2011; Bhattacharyya, 2014; Akkuzu and Uyulgan, 2016).
Difficulties in analyze lead to incorrect or no solutions at all. If chemical concepts cannot be derived from the representation, they cannot be integrated into the problem-solving process. Deriving concepts that are not actually relevant and difficulties in differentiating between concepts lead to the inclusion of incorrect aspects in the problem-solving process. This hinders the correct solution of the task. Thus, support is necessary for a successful problem-solving process. Here, similar to understand, deliberate practice and task-related feedback seem crucial for recognizing the relevant features in a representation that guide students to derive the properties and concepts relevant for the task at hand.
#20 Noah: “I would now guess sulfur, but I cannot exactly justify why. […] But yes, I'm not exactly sure how to explain which one reacts faster now.”
On the contrary, Paul (#21) gives a justification that is insufficient. It is not a chemical justification and thus shows no more expertise than if he had made no statement at all. After writing down the products of task 1, he claims that his products are correct. The interviewer asks him to explain why he thinks so.
#21 Paul: “Looks good that way. Also a gut feeling.”
Both Noah's and Paul's decision are correct, but come without a satisfying explanation. In contrast, Luke's statement (#22) is incorrect. To decide whether bromide or chloride is the better leaving group in task 12, he compares them according to a number of aspects. In doing so, he compares the basicity of bromide and chloride incorrectly. Bromide is the stronger acid. Similar to Noah, he also does not provide a justification.
#22 Luke: “I think that chlorine is more acidic and has a lower basicity than bromine.”
Charlotte's quote (#23) exemplifies another incorrect justification. She claims that chloride is a good leaving group. The interviewer queries her to explain why she thinks so. Her justification is incorrect.
#23 Charlotte: “Well, two chlorine ions could actually react with each other, giving up one electron and forming chlorine gas.”
The finding that justification is a major challenge for students is also evident in many other studies (Kraft et al., 2010; McClary and Talanquer, 2010; Strickland et al., 2010; Cartrette and Mayo, 2011; Watts et al., 2020). Especially the comparison with the results of Popova's and Bretz’ (2018b) study on leaving groups shows similarities. Here as well, the students’ justifications why a leaving group can be considered a good leaving group were often inadequate or incorrect. Some students did not provide any justification. The comparison or estimation of acid or base strength in particular has also been well investigated. Here, contradictory results were found: while McClary and Talanquer (2010) and Strickland et al. (2010) reported that students are able to correctly estimate the strength of an acid or base, Cartrette and Mayo (2011) showed the opposite. Consistent with our results, however, all reported that the students were unable to justify their statements. The difficulty in providing justifications occurred not only with the examples presented, but also with many other concepts.
Contrary to our expectations, difficulties with weighing or comparing influencing factors, which was required in the case comparison tasks, did not occur as a difficulty. This could be because students often only used isolated chemical concepts for decision-making, one-reason decision making is an approach often used by students (Kraft et al., 2010; Bhattacharyya, 2014; Watts et al., 2021). In these cases, the interviewer queried further relevant chemical concepts. Regarding these concepts, students’ answers usually already showed difficulties on the lower cognitive process dimensions and hence were not integrated into the subsequent problem-solving process. For example, if concepts were not known (remember) or could not be derived from the representation (analyze), the step of weighing or comparing multiple concepts or influencing factors did not take place. This is the case, for example, with Jacob (#7) and Mila (#18). In both cases, the interviewer asked for chemical concepts so that they could be considered for the subsequent problem-solving process. However, both could not use the queried concepts for problem-solving and comparing their influence with that of other concepts, because in Jacob's case the concept was remembered incorrectly and in Mila's case the concept was not recognized within the representation.
Difficulties that concerned evaluate in the dimension of conceptual knowledge did not necessarily hinder the problem-solving process. In particular, when students provided no, insufficient, or incorrect justifications, the solution and problem-solving process were often not affected. Some students could present their arguments while solving the task, but when asked again for a justification afterwards, they were unable to pick it up again. However, a missing and incorrect comparison of chemical concepts hinders the problem-solving process and reasonable justifications enrich the problem-solving process. For example, it has been shown that students who can provide proper justifications are more likely to be able to connect chemical concepts (DeGlopper et al., 2022). Hence, difficulties in evaluate should be supported.
Individual student results
In addition to the unachieved learning objectives of all students and their distribution in Bloom's revised taxonomy, the unachieved learning objectives of individual students and their distribution were also examined. A minimum of 23 and a maximum of 46 unachieved learning objectives were found per student. Paul was the student with the least and Ellie was the student with the most unachieved learning objectives. To illustrate the range, the distribution of Paul's and Ellie's unachieved learning objectives is shown in Table 5 as examples.| Cognitive process dimension | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Remember | Understand | Apply | Analyze | Evaluate | |||||||
| Paul | Ellie | Paul | Ellie | Paul | Ellie | Paul | Ellie | Paul | Ellie | ||
| Knowledge dimension | Factual knowledge | 2 | 6 | — | — | — | — | — | — | — | — |
| Conceptual knowledge | 5 | 16 | — | 5 | 6 | 9 | 6 | 2 | 4 | 8 | |
These results suggest that students' difficulties are individual and no general statements can be made regarding the cell in which a student's difficulty will occur. Rather, the occurrence of difficulties and their cell in the taxonomy depends on the student and the concept.
The distribution of difficulties for individual students shows a similar result as the distribution across all students. The difficulties are distributed across the individual cells of the taxonomy. There are definitely differences in the distribution between the individual students, but there is no clustering of difficulties within a cell. For Paul, for example, no difficulties occurred in the cell understand conceptual knowledge, but there was an even distribution of difficulties in the other cells. For Ellie, on the other hand, difficulties occurred in all cells of the taxonomy, but most difficulties occurred in remember conceptual knowledge and the fewest in analyze conceptual knowledge. Students not presented here had similar results. The difficulties encountered are distributed rather evenly across the cells of the taxonomy. This examination of the individual results shows that in the overall results, the difficulties in the individual cells do not come from specific students, but from all students together. At the individual level, the cells of the taxonomy show that the difficulties that occurred vary among students. Only certain difficulties occurred per student. The concepts related to these difficulties also differ among students. For example, in the case of Paul and Ellie, Ellie encountered the difficulty of not being able to estimate properties of the elements in the cell remember factual knowledge. This difficulty did not occur with Paul. However, both struggled with the correct terminology. With Ellie, this involved the solvent and the Hofmann and Saytzeff product as well as the terms resonance and polarizability. Paul struggled with the name of the first- and second-order nucleophilic substitution and the concept of hyperconjugation. These differences in difficulties and concepts related to those difficulties were also found in the other cells of the taxonomy. The comparison with the students not shown reveals that there are both the same difficulties within a cell and different ones. A similar result is seen with the concepts that relate to these difficulties. For some students the same difficulty with the same concept occurred in one cell; for other students the same difficulty occurred but it concerned another concept.
Limitations
The actual purpose of Bloom's revised taxonomy is to classify learning objectives. In our approach, however, we have exemplified how to use the taxonomy for student difficulties. Because our sample is rather small, we cannot assume that all student difficulties with concepts related to nucleophilic substitution and elimination also occurred. For example, students with different experiences or lower or higher levels of expertise might have different difficulties than the students in our sample, resulting in a different distribution of difficulties in Bloom's revised taxonomy. Furthermore, other topics in organic chemistry are not covered by nucleophilic substitution or elimination. Because the tasks focus on reaction mechanisms, no conclusions can be drawn on whether the taxonomy is also applicable to difficulties in other settings, such as laboratory work. Thus, there could be difficulties in the field of organic chemistry that cannot be classified into a cell of the taxonomy. To rule this out, a study with a larger sample, different tasks, or a classification of all difficulties reported in the literature so far would be conceivable. Even though the classification worked very well according to inter-rater agreement, it is important to note that difficulties can only be classified into the taxonomy as students express them. Conclusions regarding their mental models can only be drawn to a limited extent from the classification. For example, difficulties might exist that students did not express, or there might be difficulties with a concept in other cells of Bloom's revised taxonomy. How or whether a difficulty is expressed also depends on the context. Thus, different tasks may result in different difficulties and a different distribution within the taxonomy for the same group of students. Since prior knowledge is not a static construct but depends on the knowledge pieces activated by the problem context, the expressed difficulties might not have been present in other contexts where the required prior knowledge could have been activated by the task at hand. We attempted to address this context dependence by selecting reaction mechanism tasks that have typical requirements for students.Applicability of Bloom's revised taxonomy in classifying student difficulties in problem-solving
The purpose of this study was to illustrate whether and how Bloom's revised taxonomy can be used to systematically classify student difficulties in a complex domain such as organic chemistry. For this purpose, problem-solving tasks on nucleophilic substitution and elimination reactions with different requirements for students were investigated. Given the high inter-rater reliability, our results suggest that, at a purely technical level, difficulties that occur in problem-centered interviews can be classified into the taxonomy. The similarity of the difficulties presented in our study to those reported in the literature also suggests that the taxonomy could be used to classify the results of other studies as well. It should be noted, however, that the comparisons we made with the literature are only exemplary.In addition to the result that the classification into the revised Bloom taxonomy is technically possible, the classification also provides systematic insight into students’ problem-solving process. The results of the classification show a wide distribution of unachieved learning objectives across the taxonomy. This indicates that there is not one specific difficulty for all students during problem-solving. Instead, a variety of difficulties occur and the reason for failure differs. Nevertheless, certain major difficulties have emerged in each cell of the taxonomy. The major difficulties occurred with several students and with different content. In addition, individual students' difficulties were also distributed throughout the taxonomy rather than clustered in specific cells. At the individual student level, only some of the major difficulties occurred in each cell. When a major difficulty occurred, it only concerned specific content, which varied from student to student. These observations suggest that the problem-solving process is hindered by several major difficulties, the occurrence of which depends on both the individual student and the specific content. A more differentiated analysis of the individual contents per student, as Yik et al. (2023) did using the example of nucleophiles, could possibly be a meaningful addition to further investigate the reasons for the occurrence of the difficulties.
Further, our results show that the difficulties varied in impact on the problem-solving process. While some difficulties hardly affected students’ problem-solving process, most difficulties led to incorrect solutions or to an early terminated problem-solving process. However, conclusions about the importance of supporting students with these difficulties should not be drawn from the varying impact on the problem-solving process. Difficulties that strongly affect the problem-solving process must be overcome by students to reach a correct result, or a result at all. Difficulties that lead to the correct solution despite incorrect approaches to solve the problem seem less important at first glance but should not be neglected. These can lead to problems in the long run because incorrect approaches do not lead to correct solutions in every context (Graulich, 2015). An identification of all difficulties, therefore, seems reasonable regardless of their impact on the problem-solving process. By identifying all difficulties it becomes clear where difficulties might also occur in other contexts and where support is needed. Support could lead to students overcoming their difficulties and possibly completing their problem-solving process successfully after all.
Supporting students in their problem-solving process is complex, since first, the major difficulties encountered differ between cells, and second, not every student seems to need support in the same steps of the problem-solving process, so a one-fits-all approach seems inappropriate. The first aspect could be addressed by selecting and developing differentiated support for each cell of the revised Bloom taxonomy. Difficulties in remember factual knowledge, for example, could be addressed by providing a periodic table. Overall, it could be useful to make a periodic table permanently available for all problem-solving processes in chemistry, because problem-solving is not about memorizing the periodic table, but about using the information in the periodic table. That way, difficulties like Ellie's (#1) and Liam's (#2) might not have occurred. Difficulties in remember conceptual knowledge could be countered by providing a glossary with definitions of important chemical concepts or encouraging students to create a glossary or flashcards themselves for concepts they have difficulties recalling. While providing information can be used for difficulties in the cognitive process dimension remember, difficulties in other cells require other approaches. Deliberate practice is necessary, if the reason lies in higher cognitive process dimensions, since achieving more complex cognitive process dimensions requires strategies that go beyond memorization (Newton and Martin, 2014). Here, one could use exercises that practice identifying reactants or concepts or that practice connecting concepts to others. Therefore, criteria could be provided that explain how to recognize relevant properties or worked examples could be conceived that exemplify how to solve the exercises (Renkl, 2014). Teaching could also focus more on explicitly connecting concepts (Anderson and Bodner, 2008; Anzovino and Bretz, 2015; Popova and Bretz, 2018b). Criteria for comparison or justification could be used for difficulties in evaluate conceptual knowledge (Caspari and Graulich, 2021). In addition, students should be prompted to justify their decisions and definitions (DeGlopper et al., 2022). Many other formats for exercises or support are conceivable. When designing support formats, it should always be considered that students' difficulties may not necessarily be based on a lack of prior knowledge, but also on a nonactivation of knowledge pieces (DiSessa and Wagner, 2005; Hammer et al., 2005). Therefore, when designing support formats, prompts should also be included that explicitly ask about relevant knowledge pieces and that can thus activate these. Fig. 5 shows two examples of how the support formats could be implemented. These support formats relate to Sophie's (#12) (apply conceptual knowledge) and Mila's (#18) (analyze conceptual knowledge) difficulties. The first support aims to facilitate the use of a mechanism for students by breaking it down into smaller steps and thus less complex tasks. The second support provides students with the opportunity to specifically practice recognizing relevant features in representations in terms of specific chemical concepts. This is intended to facilitate the recognition of implicit relevant features through experience. In addition, explicitly asking for the required knowledge pieces can activate prior knowledge that may not have been activated by the original problem-solving task. For both formats, there could also be additional supports explaining the individual small steps or presenting solutions to the recognition exercises. In a similar vein, further support formats could be derived that address specific problems in students’ problem-solving process and whose design and objectives are guided by the classification of the specific difficulties in Bloom's revised taxonomy.
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| Fig. 5 Possible implementations of the support formats for apply conceptual knowledge using the example of nucleophilic substitution (left) and analyze conceptual knowledge using the example of the positive inductive effect (right). | ||
The aspect that students need support in different steps of the problem-solving process could be addressed by adaptive support. In this case, support would be provided only when a difficulty occurs, and then only with specific supporting material that addresses a specific difficulty. This approach combines aspects of two support strategies already proposed by other researchers (Hermanns and Schmidt, 2018; Dood et al., 2020). For example, Sophie (#12) and Mila (#18) would not receive both supports presented, but only the one that fits their particular difficulty. While Sophie had no difficulty recognizing the positive inductive effect, performing a nucleophilic substitution was not challenging for Mila. So Sophie does not need further practice in recognizing the positive inductive effect, and Mila does not require smaller steps to use the mechanism.
Another approach to support students that can be derived from our results is changing the tasks used in class. Mechanism tasks are often used, which are characteristic for organic chemistry and must ultimately be solvable by students, but they also require many individual steps to solve the task. The mechanism tasks could be effectively supplemented by small-step tasks that specifically train these individual steps and support students in building up the necessary skills individually, before requiring them in combination. The results show that students do not fail the problem-solving process as a whole, but particular steps are challenging. Therefore, it is not effective to repeatedly set the same type of mechanism tasks that require many steps at the same time because the problematic aspects are not specifically trained. Additional small-step tasks could thus better prepare students to solve complex mechanism tasks, provided that students are made aware that these small-step tasks are part of mechanism tasks and that the learning objectives of tasks used in instruction and the learning objectives of complex mechanism tasks match (Pungente and Badger, 2003; Stoyanovich et al., 2015). For this purpose, the individual steps required to solve different mechanisms could be thought through in advance and appropriate tasks could be developed to train the competencies of these steps.
Outlook
In the future, researchers could apply the classification of student difficulties using Bloom's revised taxonomy to other domains, such as inorganic chemistry, physical chemistry, or even disciplines outside chemistry. This would allow them to determine whether students in their domains have difficulties with the entire problem-solving process or, as in our case, only with specific steps, which steps are challenging, and whether this is the same for all students.In particular, conducting the classification with a large sample could be valuable, as the classification would thus allow to draw conclusions about the entire domain. This would also be a valuable addition to the domain of organic reaction mechanisms. From the results, researchers could derive implications for instruction or directly select and develop appropriate support formats. These implications and support formats could be provided to educators to support their students in problem-solving. However, to address the needs of their own students more specifically, educators could also classify their own student difficulties themselves. Based on these conclusions, educators could develop systematic support themselves or assign existing support adapted to the needs of their students.
Educators could select appropriate support on different levels. On the one hand, the difficulties of an individual student could be classified using Bloom's revised taxonomy and support could be adapted to this classification. On the other hand, the difficulties of a group could be classified in order to select support for the most frequently occurring major difficulties.
It should be noted, however, that classifying student difficulties in complex problem-solving tasks is very time-consuming and therefore not necessarily practical in the day-to-day practices of educators. Therefore, there would also be the alternative for educators to investigate their students' difficulties by getting back to the original function of Bloom's taxonomy. Instead of classifying student difficulties that occur when solving complex problem-solving tasks into the taxonomy, smaller-step tasks that query specific learning objectives could be used. The need for support could be derived from the completion or failure of these small-step tasks (Bloom et al., 1956).
One could also implement the selected support in different ways, for example, directly in instruction. By using the selected support in instruction, content can be learned and practiced that may not have been addressed or not sufficiently addressed in the learning process, e.g., because of not conveyed relevance or insufficient practice. At the same time, the selected exercises and support could also be used directly while working on a task. Compared to the demands that problem-solving tasks in organic chemistry place on students, these exercises and support could help students in their problem-solving process via adaptive feedback or stepped support by enabling them to master the individual steps to solve the task. The use could help students complete the tasks more successfully, especially when students only have difficulties with individual steps and not with the problem-solving process as a whole. Thus, unachieved learning objectives could become achieved learning objectives. Empirical investigation can determine whether the use of support adapted to the presumed reasons for unachieved learning objectives in problem-solving have an added value for students.
All in all, systematizing student difficulties using Bloom's revised taxonomy enables researchers and educators of a variety of domains to understand the nature of student difficulties and thus enables inferences about their problem-solving process and appropriate support formats for students in a whole domain, a class, or for individual students.
Conflicts of interest
There are no conflicts to declare.Acknowledgements
We would like to thank Nicole Graulich for her support and feedback during the preparation of this manuscript. We also thank Tim Stamp for his support in data analysis.Notes and references
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Footnotes |
| † Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d2rp00204c |
| ‡ The term “unachieved” is deliberate and does not assume that a learning objective has never been met, but rather that it was not achieved at a particular moment. |
| This journal is © The Royal Society of Chemistry 2023 |