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Keywords:

  • assumptions;
  • chemistry;
  • cognitive constraints;
  • college students;
  • heuristics;
  • reasoning

Abstract

  1. Top of page
  2. Abstract
  3. Introduction
  4. Assumptions and Heuristics
  5. Goals and Research Questions
  6. Methodology
  7. Targeted Reasoning
  8. Findings
  9. Discussion and Implications
  10. References

Diverse implicit cognitive elements seem to support but also constrain reasoning in different domains. Many of these cognitive constraints can be thought of as either implicit assumptions about the nature of things or reasoning heuristics for decision-making. In this study we applied this framework to investigate college students' understanding of structure–property relationships in the context of chemical reactivity. The ability to understand and apply structure–property relationships to explain the behavior of physical, chemical, and biological systems is a core competence that many science and engineering majors are expected to develop. Core findings were derived from semi-structured interviews based on a ranking task. Study participants relied on intuitive, spurious, and valid assumptions about the nature of chemical entities in building their responses. In particular, many of students appeared to conceive chemical reactions as macroscopic reassembling processes thought to be more favored the easier it seemed to break reactants apart or put products together. Students also expressed spurious chemical assumptions based on the misinterpretation and overgeneralization of chemical ideas. Reasoning heuristics for decision-making also played a significant role in the construction of answers to ranking questions. Specifically, interviewees demonstrated strong over-reliance on variable reduction strategies and recognition memory in their reasoning. Our findings reveal the need for educational approaches that more effectively affect the conceptual sophistication and depth of reasoning about structure–property relationships of college students. Our research framework provides a productive approach for the analysis of student reasoning in scientific domains. © 2013 Wiley Periodicals, Inc. J Res Sci Teach


Introduction

  1. Top of page
  2. Abstract
  3. Introduction
  4. Assumptions and Heuristics
  5. Goals and Research Questions
  6. Methodology
  7. Targeted Reasoning
  8. Findings
  9. Discussion and Implications
  10. References

Productive reasoning in science and engineering many times relies on the ability to understand and apply structure–property relationships to explain and predict the behavior of diverse chemical substances (NRC, 2003). Thus, it is not strange that past (AAAS, 1993; NRC, 1996) and recent (NRC, 2011) educational frameworks and standards for the teaching of science at different grade levels identify the understanding of the relationships between macroscopic properties and molecular composition and structure as a central learning goal. Unfortunately, results from research in science education suggest that a large proportion of students at all educational levels struggle to meaningfully understand structure–property relationships (Kind, 2004; Taber, 2001). The idea that most macroscopic properties of matter emerge from the random motion and interactions of the myriads of particles that comprise a sample of the material under investigation is difficult to comprehend (Chi, 2005; Penner, 2000; Talanquer, 2006). Instead, commonsense reasoning often leads students to assume that observable properties result from the weighted average of the properties of such submicroscopic components (Talanquer, 2008) and that macro and submicro entities share similar attributes (e.g., color, density, solidity, and boiling point; Ben-Zvi, Bat-Sheva, & Silberstein, 1986; Taber, 2001; Taber & García Franco, 2010).

Meaningful understanding of structure–property relationships is facilitated by recognizing and exploiting the predictive and explanatory power of both chemical representations and chemical classification systems. Chemists have developed a complex but rather powerful symbolic and iconic language that serves as a bridge between the macroscopic and the submicroscopic domains (Hoffmann & Laszlo, 1991). Chemical symbols and icons synthesize and convey implicit information that can be used to explain and predict the properties of the systems they are built to represent, from molecules to actual substances. However, many students struggle to extract and properly use such information. Several research studies in this area have elicited the many challenges students face in moving across the different levels of chemical knowledge (Gilbert & Treagust, 2009), as well as in giving meaning to chemical symbols (Cooper, Grove, Underwood, & Klymkowsky, 2010; Kozma & Russell, 1997).

Existing studies on student understanding of structure–property relationships have focused on problems involving the explanation or prediction of physical properties, such as melting points and solubility (Cooper et al., 2010; Maeyer & Talanquer, 2010). Fewer researchers have investigated student reasoning when chemical properties are involved. Within this latter set of studies, most efforts have been invested in characterizing students' ideas and reasoning strategies when making predictions about acid or base strength based on compositional and structural information (Bhattacharyya, 2006; McClary & Bretz, 2012; McClary & Talanquer, 2011a, 2011b). Thus, a central goal of the present qualitative research study was to explore student reasoning about structure–property relationships in tasks involving chemical processes. In particular, we wanted to characterize underlying assumptions and heuristic reasoning strategies used by students when making predictions about the relative thermodynamic likelihood of different chemical reactions. Our target population involved science and engineering majors who were about to complete their required first year of chemistry at the college level. It is in these chemistry courses that majors in the chemical, biological, chemical engineering, and materials engineering fields are expected to develop the ability to apply appropriate structure–property relationships. Acknowledging intrinsic limitations in terms of generalizability of our qualitative research approach, the results of our study shed light on major difficulties that instructors are likely to face in designing instructional strategies that better help students identify and apply relevant compositional and structural cues to predict the properties and behavior of chemical substances. Our findings also illustrate the application of a productive framework for the analysis of students' predictions and explanations in scientific domains that recognizes the central role that distinct cognitive constraints play in student thinking.

Assumptions and Heuristics

  1. Top of page
  2. Abstract
  3. Introduction
  4. Assumptions and Heuristics
  5. Goals and Research Questions
  6. Methodology
  7. Targeted Reasoning
  8. Findings
  9. Discussion and Implications
  10. References

Research findings in cognitive and developmental psychology indicate that when people interact with an object or event, prior knowledge together with perceptual and language cues are used to build mental representations that facilitate recognition, categorization, and decision-making (Gelman, 2009). These mental constructs, in conjunction with associative thinking, analogical reasoning, and metaphorical linking help us classify the entity or phenomenon as belonging to a certain category (Bowdle & Gentner, 2005; Vosniadou & Ortony, 1989). For example, we may identify an unknown object lying on the ground as a “solid entity” because it feels rigid or it looks like glass. Our categorizations of entities and phenomena have a crucial impact on how we reason with and about them (Chi, 2008). In general, we tend to assume that the properties of entities and phenomena are determined by the underlying properties that define the category to which they belong. Categories capture causal patterns and support, but also constrain our reasoning about what is possible.

To illustrate these ideas, let us imagine that we ask a young child to explain the presence of small droplets of water on the exterior of a glass jar full of water just taken out of the refrigerator. Based on prior experiences, it is likely that the child will think of the phenomenon as a “causal” process, that is, he or she will assume the existence of an active agent responsible for the event (Andersson, 1986). Depending on the context, existing prior knowledge, as well as perceptual and language cues, the child may decide that this is a “transfer” event and propose, for example, that someone with wet hands touched the glass. However, in the process of building the explanation, the child may remember seeing water filtering through paper or ceramic vases. Thus, he or she may choose to suddenly look at the phenomenon as a “passing through” event in which water from the inside filtered through the glass.

One can expect different children confronted with the previous task to follow different explanatory paths, paying attention to different cues and settling on different event categorizations. However, although the final explanation that is produced may be sensitive to personal and contextual factors, research suggests that the range of possibilities will be constrained by the application of common reasoning strategies to search for relevant cues, make judgments, and map knowledge within and across domains. Reasoning will also be guided and constrained by underlying assumptions about the properties and behaviors of different categories of entities and phenomena in our world. For example, we can expect associative thinking to help children identify a likely cause for the event based on spatial (e.g., the water nearby) or temporal (e.g., the person who took the glass out of the refrigerator) proximity. Analogical reasoning or metaphorical linking will help them relate the event to particular past experiences (e.g., water filtering through paper) or events in different domains (e.g., human sweating). Categorization will trigger the deployment of prior implicit or explicit knowledge about the properties of general types of objects and processes (e.g., liquids stick to solids).

The assumptions that people make about the properties and behaviors of the members of a given category, together with the reasoning strategies used to identify relevant cues and make decisions act as cognitive constraints that support, but also restrict their thinking. These cognitive constraints help us make decisions about what behaviors are possible and what variables are most relevant in determining behavior. Reasoning about an entity or phenomenon seems to involve the automatic activation of a spectrum of cognitive constraints, from domain-general to domain-specific, from task-general to task-specific. These cognitive elements give rise to dynamic but constrained knowledge systems whose goal is not necessarily to achieve global conceptual coherence, but rather local explanatory coherence and efficient inference and decision-making as we work through a specific task in a determined context (Brown & Hammer, 2008; Gigerenzer & Gaissmaier, 2011; Sloman, 1996). These cognitive resources do not necessarily provide full mechanistic models of entities and phenomena, but help us recognize relevant properties and sense relational patterns. They allow us to make reasonable, adaptive inferences about the world given limited time or knowledge. They often generate acceptable answers with little effort, but sometimes lead to severe and systematic biases and errors (Hatano & Inagaki, 2000; Keil, 1990).

A variety of researchers in cognitive science, developmental psychology, and science education have identified diverse implicit cognitive elements that seem to support but also constrain reasoning in different domains. They have referred to them in different ways, such as core knowledge (Spelke & Kinzler, 2007), implicit presuppositions (Vosniadou, 1994), core hypothesis and ontological beliefs (Chi, 2008), phenomenological primitives (diSessa, 1993), intuitive rules (Stavy & Tirosh, 2000), fast and frugal heuristics (Gigerenzer & Gaissmaier, 2011), conceptual resources (Redish, 2004), and inductive constraints (Perfors, Tenenbaum, Griffiths, & Xu, 2011). Although many researchers invoke the existence of such cognitive elements, there is considerable debate on the extent to which they form coherent and integrated knowledge systems or more fragmented collections of cognitive tools (Brown & Hammer, 2008; Vosniadou, Vamvakoussi, & Skopeliti, 2008). It is likely that their level of integration varies depending on the nature of the knowledge domain and the prior knowledge and experiences of each individual.

Beyond issues of coherence, stability, and contextuality of students' ideas about the world, our own explorations of student reasoning in chemistry have focused on better characterizing the cognitive elements that guide and constrain novice student thinking in the domain. Our analysis of the research literature on students' thinking suggests that many relevant cognitive constraints seem to fall into two major groups (Talanquer, 2006): (a) presuppositions about the properties and behavior of the entities and phenomena in the domain (assumptions), and (b) reasoning strategies to make judgments and decisions under conditions of limited time and knowledge (heuristics). These types of cognitive elements are triggered when students face a task and they may be activated in automatic or deliberate ways. Their activation depends on personal factors, such as prior knowledge, experience, motivation, and affect, as well as on contextual issues, such as time available, and cue saliency and processing time (Giner-Sorolla & Chaiken, 1997).

We use the term “assumptions” to refer to beliefs or ideas students have about the properties and behavior of entities or processes in a given domain (e.g., assuming that matter is continuous). These assumptions may go from being intuitive presuppositions to learned principles or relationships. Their deployment will depend on categorization decisions about the nature of the objects and phenomena under analysis. These cognitive elements are likely to influence student reasoning via top-down mechanisms (Osman & Stavy, 2006). On the other hand, the term “heuristics” refers to fast and frugal reasoning rules used for judgment and decision-making (e.g., making choices based on familiarity with objects or events). These inferential devices facilitate reasoning by reducing the amount of information to be processed or by providing implicit rules of thumb for how and where to look for information, when to stop the search, and what to do with the results (Gigerenzer & Gaissmaier, 2011). Heuristics often influence reasoning via automatic bottom-up processes (Heckler, 2011) that exploit structures of information in the task environment (they are said to be ecologically rational). However, they may also be applied in deliberate ways. In general, both the nature of the task and an individual's memory will constrain the set of applicable rules, while an individual's processing capacity, motivation, and perceptions of the task environment will guide rule selection (Kruglanski & Gigerenzer, 2011).

Goals and Research Questions

  1. Top of page
  2. Abstract
  3. Introduction
  4. Assumptions and Heuristics
  5. Goals and Research Questions
  6. Methodology
  7. Targeted Reasoning
  8. Findings
  9. Discussion and Implications
  10. References

The central goal of this study was to explore student reasoning about structure–property relationships in the area of chemical reactivity. In particular, our investigation was guided by the following research question:

  • What assumptions and heuristic reasoning strategies do college students use when asked to rank sets of chemical reactions based on their thermodynamic likelihood or favorability?

We sought to characterize general and specific reasoning patterns in the analysis of chemical reactions representative of those commonly discussed in introductory college science courses. Our overarching goal was to introduce an approach to the analysis of student reasoning that pays attention to two major cognitive elements that seem to guide, but also constrain student thinking.

Methodology

  1. Top of page
  2. Abstract
  3. Introduction
  4. Assumptions and Heuristics
  5. Goals and Research Questions
  6. Methodology
  7. Targeted Reasoning
  8. Findings
  9. Discussion and Implications
  10. References

Setting and Participants

This study was conducted in a public research-intensive university in the southwestern United States. The student body, comprised of over 30,000 undergraduate students, is approximately 52% female and 48% male with close to 34% of them identifying as an underrepresented minority. The chemistry department at this institution offers a two-semester general chemistry course sequence for science and engineering majors. Most of these students are freshmen or sophomores with an ethnic and gender makeup similar to that of the entire university.

All of our study participants were about to finish the second semester of the general chemistry sequence (GCII) at the college level. In this course, at least 4 weeks of the academic semester are dedicated to the analysis of chemical reactivity from a thermodynamic perspective. At the end of the course, students are expected to recognize the major compositional and structural factors that affect and determine the thermodynamic likelihood of chemical reactions. Total enrollment in the GCII course was 1,229 students at the time of our study, distributed in five different sections. These course sections were taught by different instructors who followed the same conventional textbook and worked in large lecture halls with an average of 250 students each (a course structure that is similar to that present in many public universities across the US). Grade distributions in common midterm and final exams for different sections of GCII are very similar every semester, which suggests that they serve equivalent student populations. As a whole, students in GCII consistently perform at the average level in a standardized final exam (ACS exam) used by many chemistry departments in colleges and universities across the country.

Our core findings were derived from individual interviews conducted with 33 volunteers (15 female and 18 male) from two sections of the GCII course during a spring semester. All of the students in each course section were invited to participate via an open announcement during a class session, and contact information was collected from those who volunteered. Statistical analysis using Fisher's exact test revealed that the distribution of final grades among the interviewees was not significantly different (p = .35) from that of all of the students enrolled in the GCII course (which indicates similarity in represented levels of course performance). As part of our study, we also built a questionnaire based on the interview protocol, which was answered by students (N = 424) enrolled in three of the five sections of the same course. As described below, students answered this questionnaire under time constraints. Our goal was to collect data that could be indicative of the extent to which interview responses differed from those expected to be highly influenced by tacit assumptions and heuristic reasoning. Individual consent to participate in the study was obtained following procedures approved by the IRB at our university.

Research Instruments

The interview protocol (and associated questionnaire) included five questions that asked students to arrange three chemical reactions, represented in symbolic form, in order from least to most favored (see Table 1). Each set of three processes corresponded to a different reaction type: Acid–base, synthesis, oxidation–reduction (redox), combustion, and precipitation reactions. This arrangement by reaction types was chosen to ensure that relevant comparisons could be made based on a reduced set of common features within each set of reactions. Selected reactions were prototypical of those analyzed and discussed in general chemistry courses.

Table 1. Set of reactions used in the questionnaire and interviews
QuestionType of ReactionsReactionsa (1: Least Favored——3: Most Favored)
  1. In each case, students were asked to “Arrange the following chemical reactions from least favored to most favored (FAVORED = The reaction in which equilibrium lies furthest to the right is most favored, which may or may not be the fastest reaction)”.

  2. a

    Reactions are shown in order of least to most thermodynamically favored. They were shown in random order to study participants.

1Acid strength1. H2S(aq) + H2O(l) inline image H3O+(aq) + HS(aq)
2. HCl(aq) + H2O(l) inline image H3O+(aq) + Cl(aq)
3. HI(aq) + H2O(l) inline image H3O+(aq) + I(aq)
2Synthesis1. 8C(s) + 9H2(g) inline image C8H18(l)
2. 3C(s) + 4H2(g) inline image C3H8(g)
3. C(s) + 2H2(g) inline image CH4(g)
3Oxidation–reduction1. Na(s) + H2O(l) inline image NaOH(s) + 1/2H2(g)
2. Ca(s) + 2H2O(l) inline image Ca(OH)2(s) + H2(g)
3. Al(s) + 3H2O(l) inline image Al(OH)3(s) + 3/2H2(g)
4Combustion1. CH4(g) + 2O2(g) inline image CO2(g) + H2O(g)
2. C3H8(g) + 5O2(g) inline image 3CO2(g) + 4H2O(g)
3. C8H18(l) + 25/2O2(g) inline image 8CO2(g) + 9H2O(g)
5Precipitation1. Na+(aq) + Cl(aq) inline image NaCl(s)
2. Pb2+(aq) + 2Cl(aq) inline image PbCl2(s)
3. Ag+(aq) + Cl(aq) inline image AgCl(s)

Our selection of reactions in Table 1 was not arbitrary; we purposely included reactions that involved common or familiar reactants and products, such as NaCl, HCl, and CH4, mixed with less familiar compounds exhibiting both explicit and implicit similarities and differences. For example, AgCl and NaCl have Cl in their formulas (explicit) and are ionic compounds (implicit); the molecule of H2S has more hydrogen atoms than that of HCl (explicit), but both are covalent compounds (implicit). Our goal was to include cues that we hypothesized might trigger the application of heuristic reasoning based on our knowledge of common shortcut reasoning strategies in other areas and typical misconceptions in the field of chemistry (Maeyer & Talanquer, 2010; McClary & Talanquer, 2011a; Talanquer, 2006). All of the selected chemical equations included explicit or implicit information that could be used to make reasonable decisions about the relative thermodynamic likelihood of the chemical processes in each reaction set. All of the questions can be considered multivariable problems, as their answer requires analyzing the effect of more than one variable on chemical reactivity. The concepts, ideas, and type of reasoning needed to accomplish such tasks were discussed in the general chemistry courses taken by the study participants at our institution. The ranking tasks were reviewed by two different GCII instructors for content accuracy, and further revised based on results of pilot interviews with three GCII students.

Data Collection

All of the interviews and the questionnaire were completed near the end of the academic semester, when the concepts and ideas needed for successful completion of the ranking tasks had already been introduced. During the interviews, students were told that they were expected to individually answer five questions requiring them to arrange set of three chemical reactions from least to most favored. The common prompt for all of the questions (see Table 1) was presented on a PowerPoint slide and explained verbally to the participants. Students were instructed to think out loud as they answered each of the questions and asked to record their responses on an answer sheet. No explicit time limit was imposed on students' responses and probing questions were asked by the interviewer when needed to clarify an answer or better elicit student reasoning. Interviewees had access to a periodic table and recorded their actual rankings on an answer sheet. Individual interviews lasted between 10 and 25 min. Each of the interviews was audio-recorded and later transcribed. For reference and privacy purposes, an alphanumerical code was created to label each of the interviewees. This code has been used throughout the discussion of our results.

For the questionnaire, data were collected in the actual classrooms according to the following procedure: The different sets of reactions were presented one by one, in 60 s intervals, using individual slides that included the specific question prompt and the chemical equations of the processes to be arranged. Students were asked to record their responses on an answer sheet. All of the students had visual access to a large Periodic Table present in the classroom. Responses were collected from students in attendance who volunteered to turn them in; thus, different numbers of responses were gathered from different course sections. Research on people's cognitive biases and intuitive reasoning often relies on results from tasks completed under speeded conditions (Kelemen & Rosset, 2009); it is expected that time limits will constrain the action of control mechanisms associated with analytical reasoning. The 60-s limit used in our study was selected based on results from a similar previous study (Maeyer & Talanquer, 2010) in which pilot interviews indicated that most students generated first proposed rankings in 30–60 s. Thus, we chose 60 s as a reasonable time to capture students' initial responses expected to be constrained by tacit assumptions and heuristic reasoning.

Data Analysis

Interview tapes were fully transcribed and analyzed using an iterative, non-linear constant comparison method of analysis (Charmaz, 2006). During this procedure, we looked to identify (a) the underlying assumptions, and (b) the heuristic reasoning strategies used by students to make their ranking decisions. Coding for assumptions was guided by existing results on common sense reasoning (Talanquer, 2006) and students' alternative conceptions (Kind, 2004) in chemistry. We paid particular attention to students' justifications for the position of different chemical reactions in their rankings. Some of these justifications included ideas that reflected the application of intuitive knowledge about the properties and behavior of objects and processes in our world (e.g., the larger a molecule is, the more energy is needed to make it). We categorized these types of ideas as Intuitive Assumptions. Students also made references to well established and accepted chemical principles or models in justifying their decisions (e.g., the presence of reactants with weaker bonds facilitates the reaction). These ideas were classified as Valid Chemical Assumptions. Students' answers were also based on invalid ideas about the properties of chemical entities or reactions, often resulting from misinterpretations and overgeneralizations of chemical principles (e.g., the higher the electronegativity of the atoms in a molecule, the more reactive the molecule is). We categorized these ideas as Spurious Chemical Assumptions.

Coding for heuristic reasoning strategies was guided by existing research in the field of decision-making in both non-academic (Shah & Oppenheimer, 2008) and academic (Maeyer & Talanquer, 2010; McClary & Talanquer, 2011a) contexts. During this part of the analysis, we paid careful attention to the types, number, and sequence of cues used by students to make each ranking decision. For example, many students made ranking decisions based on the analysis and comparison of a single feature (e.g., number of reactants involved). This reasoning strategy was identified as the One-Reason Decision Making heuristic. They also often selected the top or bottom elements in their rankings based on the mere recognition of an entity (e.g., a reactant or product) from past experiences. This heuristic was coded as Recognition. Other examples included: More AMore B (i.e., building arbitrary positive correlations between two variables); Representativeness (i.e., making decisions based on explicit similarity between two systems).

To ensure inter-rater reliability, the two authors independently coded all of the interviewees' responses, looking to identify the specific assumptions and heuristics used by the study participants in ranking the five different sets of chemical substances. The individual codes were then compared, discussed, and, if necessary, reassigned until reaching over 90% overall agreement. Coding reassignments were based on individual reanalysis of the data, followed by evaluation of different claims to try to reach consensus. A total of 336 codes were assigned in the analysis of 33 transcripts, with an average of two different codes per student response to a given task. Of these, 46.7% referred to assumptions made by students in generating answers, 51.8% of the codes referred to heuristics, and 1.5% were marked as “guesses”. Once final code assignations were made, further analysis was completed to identify general trends in students' responses.

Questionnaire answers from the larger GCII student sample were analyzed to quantify the frequency of different rankings for the thermodynamic favorability of the three reactions included in each reaction set shown in Table 1. This allowed us to determine the percentage of correct responses and the most preferred rankings for each set of reactions.

Targeted Reasoning

  1. Top of page
  2. Abstract
  3. Introduction
  4. Assumptions and Heuristics
  5. Goals and Research Questions
  6. Methodology
  7. Targeted Reasoning
  8. Findings
  9. Discussion and Implications
  10. References

To facilitate the interpretation and discussion of our findings, in this section we present the type of reasoning that college students who finish the GCII course are expected to apply when faced with the task of evaluating the relative thermodynamic likelihood of the different sets of processes presented in Table 1. This “targeted” reasoning was developed based on the analysis of the conventional general chemistry textbook used in the course (Tro, 2010), the common class notes used by all of the instructors teaching GCII, and our own experience teaching the class. This way of reasoning defines an ideal learning outcome in general chemistry courses and is thus a useful reference in assessing the extent to which student thinking deviates from the target.

In general, the thermodynamic favorability of a chemical reaction is determined by energetic and entropic factors. Favored processes that occur under conditions of constant temperature and pressure are characterized by final states that have a lower enthalpy or/and a higher entropy than the initial states. It can also be said that favored chemical reactions at constant temperature and pressure lead to products with an overall Gibbs free energy that is lower than that of the reactants. In the absence of numerical experimental data to make quantitative predictions about expected changes in enthalpy, entropy, or Gibbs free energy, one can use composition and structural cues to make judgments about the relative internal potential energy of reactants and products (which determines enthalpy values) and the relative number of possible submicroscopic configurations (which determines entropy values).

Qualitative judgments of the internal potential energy of different chemical substances can be made by comparing the strength of the bonds between the atoms or ions that make up each system. Individual molecules, ionic networks, or any other systems of interacting particles held together by strong chemical bonds or intermolecular forces are expected to have lower internal potential energies than those involving weaker interactions. Informed guesses about relative bond strength in molecular systems can be made by paying attention to the nature of the bonded atoms; in general, the smaller the atoms and the larger the difference in electronegativities between them, the stronger the bonds. In the case of ionic systems, the smaller the ions and the larger their electrical charges, the stronger the forces that they may exert on other particles. Thus, for example, the formation of Al(OH)3(s) from Al(s) to H2O(l) is likely to be more energetically favored than that of NaOH(s) from Na(s) to H2O(l), given the much stronger interactions between OH ions and Al3+ ions in Al(OH)3(s) than between OH ions and Na+ ions in NaOH(s). Similarly, the formation of a larger number of strong C[DOUBLE BOND]O bonds (in CO2 molecules) and O[BOND]H bonds (in H2O molecules) during the combustion of longer hydrocarbons should increase the likelihood of such reactions over the combustion of molecules with shorter carbon chains.

Inferences about the relative entropy of reactants and products in chemical reactions can be generated by considering factors such as the state of matter of the substances involved, the number of different species formed, their molar masses, and their molecular complexity. Strength of interactions between the particles that make up each substance is also a relevant cue, as weaker interactions generally increase the number of configurations that particles may adopt (thus, increasing the entropy of the system). Compounds made up of molecules with a larger number and more diverse types of atoms can be expected to have larger entropies than other substances in a similar state of matter. Using these ideas one may predict that the combustion of liquid octane C8H18(l) should be more entropically favored than that of CH4(g) as the former process leads to the formation of larger amounts of gaseous substances. Meanwhile, the dissociation of HI(aq) in water should be more entropically favored than that of H2S(aq) as the large I ions interact more weakly with water molecules than the smaller and more negatively charged S2− ions, thus imposing fewer restrictions on the configurations that water molecules may adopt.

Decisions about the relative thermodynamic favorability of the set of chemical processes depicted in Table 1 are not necessarily straightforward, as the effects of several factors need to be considered simultaneously. Moreover, in various cases some of these effects compete with each other and additional cues have to be considered to decide which of them will be dominant. For example, the synthesis of liquid octane C8H18(l) is more energetically favored than that of CH4(g) due to the formation of a large number of strong C[BOND]H bonds, but more entropically disfavored because it involves the transformation of a larger amount of gaseous reactants into a liquid substance. Entropic effects dominate in this case, but knowledge about the actual cost of breaking H[BOND]H bonds may be needed to make the right prediction. Our research instrument was designed to include problems with different levels of complexity in their analysis. Our goal was not to investigate whether students could generate the right answers, but to explore the assumptions and reasoning strategies that they applied to generate what they judged as plausible responses.

Findings

  1. Top of page
  2. Abstract
  3. Introduction
  4. Assumptions and Heuristics
  5. Goals and Research Questions
  6. Methodology
  7. Targeted Reasoning
  8. Findings
  9. Discussion and Implications
  10. References

The major findings of our study are summarized in the following subsections. We focus on the description of results derived from the analysis of individual interviews, using data from questionnaire responses only to highlight differences and similarities in response trends. In general, most of our interviewees were rather unsuccessful in generating correct rankings for the thermodynamic likelihood of the different sets of reactions shown in Table 1. Similar or lower levels of performance were observed in the analysis of all but one (Question 1) of the questionnaire answers as can be seen in Table 2; this table includes the rankings proposed by over 15% of our study participants (in either the interviews or the questionnaires) together with the main types of assumptions and heuristics identified in the corresponding interview responses. Lower performance by the larger student sample may be expected given the time constraints imposed in generating questionnaire responses. However, statistical analysis using Fisher's exact test revealed no significant difference in the distribution of rankings proposed by the two sets of students in a given task, except for Question 2 (p = 0.0075). This was the only question in which the most common proposed ranking was not the same for the two sets of students. Similarities in response patterns may be indicative of commonalities in reasoning strategies, despite differences in conditions and time allotted to answer the ranking tasks.

Table 2. Percentage of responses corresponding to most common rankings for the thermodynamic favorability (from least to most favored) of the different set of reactions in Table 1
 Top Rankingsa% Responses (Interviews)% Responses (Questionnaire)Main Assumptionsb (Interviews)Main Heuristicsb (Interviews)
  1. The table includes the most common assumptions and heuristics made by the interviewees who selected those rankings.

  2. a

    Only distinctive reactants or products are shown. Correct rankings are in bold.

  3. b

    Assumptions are labeled as Intuitive (I); Spurious (S); Valid (V). Numbers in parentheses indicate the percentage of the interviewees who relied on the associated assumption or heuristic to generate their rankings (we include only assumptions and heuristics used by over 30% of the students).

Question 1 (acid–base)H2S, HI, HCl39.434.8S: periodicity (31)Recognition (77); representativeness (46)
H2S, HCl, HI18.230.2V: weaker bonds (33)Recognition (33)
HI, H2S, HCl18.213.6S: electronega-tivity (33)Recognition (83); ORDM (33)
Question 2 (synthesis)C8H18, C3H8, CH463.635.2I: easiness (86)ORDM (71)
CH4, C3H8, C8H1821.243.7 ORDM (100)
Question 3 (redox)Al, Ca, Na48.533.7I: easiness (38)Recognition (56); ORDM (44)
Na, Ca, Al33.325.0 ORDM (73)
Question 4 (combustion)CH4, C3H8, C8H1854.653.4V: entropy (33)ORDM (78)
C8H18, C3H8, CH442.426.5I: easiness (86)ORDM (86)
Question 5 (precipitation)Na+, Ag+, Pb2+36.438.6 Recognition (92); ORDM (33)
Pb2+, Ag+, Na+30.326.0S: periodicity (40)Recognition (70); ORDM (40)

Assumptions

Analysis of interview transcripts allowed us to identify 21 different assumptions, 13 of which were made by 10% or more of the interviewees when building and justifying their selected rankings (see Table 3). Some of these assumptions were more prevalent in students' responses than others. In many cases, they represented beliefs about relationships between properties and behaviors. We categorized the different assumptions into three groups: Intuitive, Spurious, and Valid. This classification highlights the role of three major types of constraints in student reasoning: (a) intuitive beliefs about the properties and behaviors of chemical entities, (b) spurious ideas reflecting misinterpretation and overgeneralization of chemical concepts and ideas, and (c) valid chemical principles and rules.

Table 3. Different assumptions and heuristics identified in over 10% of the interview transcripts
DescriptionNumber of Students% of Total
  1. We indicate the number of interviewees (N = 33) who used them and the percentage of the total number of codes for assumptions (NA = 157) or heuristics (NH = 174) that they represent.

Intuitive assumptions
The easier the process (less effort or complexity), the more favored it is2835
The more products generated, the more favored the process88
The more naturally abundant or common a substance is, the more likely to form44
The stronger the attraction between reactants, the more favored the process43
The more energy a substance has (contains), the more reactive it is33
Heavier/bigger particles separate faster32
Spurious chemical assumptions
Relative location in the periodic table can be used to infer a sought trend that determines which process is most favored1211
The higher the electronegativity χ (or Δχ) of the reactants, the more favored the process108
The more (fewer) hydrogen atoms in a molecule, the more (less) acidic43
Valid chemical assumptions
Entropy differences between reactant and products influence reaction extent78
Reactions are more favored when reactants have weaker chemical bonds53
Amount of energy released can be indicative of reaction extent53
Reactions are more favored when products have stronger chemical bonds44
Heuristics
ORDM3150
Recognition2937
More A–More B128
Representativeness64
Intuitive Assumptions

These types of assumptions were the most common, representing 55% of the total assumptions identified in the analysis of the interview transcripts. All but three of the interviewees used at least one intuitive assumption in guiding their ranking decisions. As shown in Table 3, the most prevalent intuitive assumption in this category refers to the idea that the most favored process is the one perceived as easier to occur based on judgments of required effort or complexity of the process. Specific factors that influenced students' perceptions of “easiness” were various. For example, many students paid attention to the number of atoms present in the molecules of the products, assuming that the smaller or less complex the molecules of the product, the more likely the process would be:

“methane would be the easiest to be formed because it is the least complicated of the molecules. Propane would be next because it is slightly more complicated and octane would be the hardest because it is the most complicated. … There are more atoms, it is bigger chain.” (S2 answering Question 2 in Table 1)

Other students considered the number of particles that would have to react with each other to form the products,

“… so maybe Na might be next most favored because it only requires one mole of water to reduce. And then Ca would be the least favored because it would need two moles.” (S20 answering Question 3 in Table 1)

A few students also referred to factors such as (a) how easy would be to break molecules apart based on the number of atoms present, assuming that the fewer atoms to separate, the more likely the process would be:

“I figured methane would be the easiest to break apart and combust the most. … It has less carbon and hydrogens, it's a smaller molecule.” (S4 answering Question 4 in Table 1)

(b) how easy it would be to lose or gain electrons, assuming that the fewer electron, the more likely the process to occur:

“Maybe because Na only loses one electron it will be more favored. I just want to say that the one that loses the least electrons… well? yeah. I will say that one, because … it uses less energy to lose one electron as opposed to two or three.” (S8 answering Question 3 in Table 1).

or (c) how easy would be to form a substance in a different state of matter, assuming that forming liquids or solids would be more difficult (e.g., require more energy):

“Octane is a liquid, propane is a gas, um… I know it requires more, um… like energy to go to a more solid state.” (S14 answering Question 2 in Table 1).

Judgments based on the perceived easiness of the process were more common in those tasks in which differences in the number of atoms present in molecules of reactants and products were rather explicit, such as Questions 2 and 4 in Table 1. These types of assumptions led close to 60% of our interviewees to select the synthesis of methane as most favored and that of octane as least favored in Question 2. This is actually the correct answer although very few students based their ranking on valid chemical assumptions. As shown in Table 2, only 35% of the questionnaire respondents proposed this particular ranking, which suggests that one must be cautious in the generalization of our interview results to the larger sample. In the case of Question 4, this intuitive assumption misled almost 40% of our interviewees in choosing the combustion of methane as the most favored process and that of octane as the least favored reaction. Again, a smaller percentage of the questionnaire answers (27%) matched this ranking.

The second most common intuitive assumption identified in our study refers to the belief that the most favored chemical reactions are those that generate the largest amounts of products. The following excerpt illustrates this type of reasoning:

“So now, I am just go to look at limiting reactants and mole ratios again. Which is going to produce more? The one that will produce more is probably going to be more favored. If it's not going to produce more, then it's not favored as much.” (S33 answering Question 3 in Table 1)

In these types of cases, students seemed to confound the thermodynamically likelihood of a process with the perceived theoretical yield based on the stoichiometry of the reaction. This type of assumption was mainly observed in answers to Questions 3 and 4 which included chemical equations with explicit differences in the stochiometric coefficients of one or more products. For these two particular tasks, the intuitive assumption directed students towards the right answers.

Analysis of students' answers revealed that a few students paid attention to attributes of reactants and products that, based on experiences with entities in our surroundings, one may intuitively assume affect the reactivity (or agency) of chemical substances. For example, the strength of the attractive force between interacting agents, the energy that these agents are perceived to have or bring to the process, and their size or weight. Additionally, a few students also considered the natural abundance or common presence of certain substances in our environment as indications of likelihood of formation (see Table 3).

Spurious Chemical Assumptions

Two thirds of the interviewees (22 out of 33) relied on at least one spurious chemical idea to generate their rankings. These types of ideas constituted 22% of all coded assumptions. As shown in Table 3, we identified two main assumptions in this group, which can be seen as invalid misinterpretations and overgeneralizations of two important chemical concepts: periodicity and electronegativity.

Over a third of the interviewees assumed that the relative location of different chemical elements in the periodic table could be used to infer a sought property trend, without much rationale for the suggested pattern. Consider, for example, the following interview excerpt:

“Ok, so Na, Pb, and Ag is right there. I think it has something to do with a periodic trend. … Uh, just the way they are set out. Ag and Pg are both… well I guess Pb is not a transition metal. Both are metals, Na is a…, well they are all metals, Na is alkali. But they are in different sections… pause. Well, I think NaCl is the most favored… And that is my thinking because we see it a lot, and they're relatively close to each other on the board. Using that thought process, then AgCl would be next favored, and then PbCl2.” (S6 answering Question 5 in Table 1)

This excerpt illustrates how the combination of an intuitive assumption about natural abundance (the formation of NaCl is the most favored because we see this salt a lot), with the spurious assumption about the existence of a periodic trend guided a student in generating an answer. Decisions based on the existence of a spurious periodic pattern were associated with responses to Questions 1, 3, and 5 in which the most explicit difference between set of reactions was the presence of different chemical elements in one of the reactants or products.

As illustrated by the following excerpt, another common spurious idea was to assume that the higher the electronegativity of the atoms present in a chemical species (or the larger the difference in electronegativities between atoms in the reacting species), the more favored the reaction would be:

“Um, I guess I'd use electronegativity again. I guess in that case, it's Na… Yeah, least favored. Followed by silver. I guess an electronegative atom is gonna want to form into a product easier.” (S23 answering Question 5 in Table 1)

Electronegativity in many of these cases was conceived as a measure of the drive to react with other substances. Similarly to the “periodicity” assumption, students invoked these types of arguments in answers related to Questions 1, 3, and 5.

Valid Chemical Assumptions

Over half of the interviewees (18 out of 33) used at least one valid chemical principle to guide their reasoning during the different ranking tasks. However, not all of them applied them correctly. These types of ideas accounted for 22% of all coded assumptions. As shown in Table 3, students considered changes in entropy during the reaction, mainly based on differences in the amounts of gaseous substances between reactants and products (Questions 2, 3, and 4), differences in bond strength between reactants and products (Questions 1 and 5), and amount of energy released during a process (Question 4).

Heuristics

All of the interviewees used at least one heuristic reasoning strategy to generate answers to the different ranking tasks. These heuristics facilitated the generation of responses by reducing the amount of information to be processed and by providing short-cuts for the identification of a chemical process likely to be the most or the least favored in a set of reactions. The type of heuristic applied depended on the nature of the information represented in the different chemical equations in Table 1. As shown in Table 3, four major types of heuristics were used by over 10% of the study participants: One-reason decision-making, Recognition, More A–More B, and Representativeness.

One-Reason Decision Making (ORDM)

This was the heuristic most commonly used by our interviewees. Thirty-one out of 33 study participants used it at least once when solving the five ranking tasks, and 21 of them applied it in generating answers for three or more such tasks. Fifty percent of all coded heuristics were of this kind. When applying ORDM, individuals may consider more than one differentiating cue in making decisions, but they tend to consider them sequentially and base their decisions on only one of them (Gigerenzer & Gaissmaier, 2011). In particular, the heuristic used by our interviewees could be summarized by these basic rules: (a) search for cues one at a time to differentiate between options, (b) look for the corresponding cue values for each alternative, (c) compare the options on their values for that cue dimension, and (d) stop the search when a cue is found that enables a choice between options. In many cases, final cue selection was guided by students' assumptions about factors that affected the likelihood of chemical processes.

The following interview excerpt for student S3 while answering Question 3 (redox reaction) in Table 1 illustrates how ORDM, in combination with assumptions about chemical processes, was commonly used by interviewees to generate their rankings:

“I: Have you seen reactions like this?

S3: Yeah, I have. So… I don't know as far as the spontaneity of it, but you can see… knowing that in the products the OH is minus on, and since they are all like neutral, then you know the Na is plus one, and Ca is plus two, and Al is plus three. I don't know if it has anything to do with the hydrogen that are produced, but… redox… um… I am going to say the ones with the lower charges are going to be more spontaneous. So, Na, Ca, Al…

I: Why would you pick the lower one to be more favored rather than the higher one?

S3: I just think it is easier to make something if you only have like… plus one going with minus one instead of plus three going with three different things.”

In this example, the student first noticed explicit differences between the products of the reactions, such as the number of OH ions present in the chemical formulas of the hydroxides and the number of hydrogen molecules produced (this second cue was dismissed). The number of OH was used to infer the electric charge of the corresponding cations (Na+, Ca2+, and Al3+) which then became the only determining cue for the proposed rankings. The selection of this cue was guided by the recognition of the nature of the reactions (i.e., redox processes, which may have made ion charge a more salient cue) and the intuitive assumption that it is easier to combine two things (“plus one going with minus one”) than four things (“plus three going with three different things”). This general pattern of reasoning, based on the selection of a single differentiating cue guided by implicit or explicit assumptions, was used by close to two thirds of the interviewees to generate answers to Questions 2–4 in Table 1.

Recognition

Another common heuristic applied at least once by 31 of our study participants relied on recognition memory. Thirty-seven percent of all coded heuristics belonged to this group. The rule behind the recognition heuristic may be expressed in the following manner: If one of several objects is recognized and the others are not, then infer that the recognized object has the higher value with respect to the criterion (Gigerenzer & Gaissmaier, 2011). This heuristic uses recognition of an entity as the single decision cue, particularly when there is a perceived strong correlation between recognizing an object (e.g., HCl) and having higher values on a given criterion (e.g., being an strong acid). In our study, the application of the recognition heuristic was triggered by the presence of a substance that students recognized, such as HCl in Question 1, NaOH in Question 3, or NaCl in Question 5, which prompted them to select the associated chemical reaction as the most or the least favored in the set. Consider, for example, the following interview excerpt:

“NaOH, because we talk about that in class all of the time… yeah, I would probably put NaOH as the most favored because I have seen that one the most.” (S12 answering Question 3 in Table 1)

In these types of cases, recognition of a substance in the reactants or products led students to choose such reaction as the most favored process. The use of this heuristic may explain the large percentage of answers to Questions 1, 3, and 5, both in the interviews and the questionnaire, in which processes involving familiar substances were placed either at the top or bottom of the rankings (see Table 2). Close to half of the interviewees used this heuristic in ranking acid–base (18/33) and redox (15/33) reactions, and three quarters of them (25/33) applied it in the analysis of precipitation reactions. Recognition was often used by these interviewees as the first step in generating their rankings. It was used to identify the most or the least favored process, which created an anchor for subsequent decisions.

More A–More B

This heuristic was applied by 12 of the interviewees (8% of all heuristic codes). The strategy was used across all questions and it was based on establishing a non-justified, somewhat intuitive positive correlation between two quantities (Stavy & Tirosh, 2000). For example:

“I think I will have to just put Al, Ca, and Na, just because it goes from Al is three plus and Ca is 2 plus, and Na is 1 plus. … Al would be most favored, I think… Because it had the greatest oxidation number change.” (S14 answering Question 3 in Table 1)

In this case, the likelihood of the reaction was associated with the change in oxidation state of the metallic atoms. Other students established unexplained correlations between the favorability of the reactions and factors such as the mass, charge, or number of atoms in reactants or products.

Representativeness

Another reasoning strategy used by our study participants can be identified as the representativeness heuristic. This strategy is based on assuming commonalities between objects of similar appearance (Gilovich, Griffin, & Kahneman, 2002). The heuristic was applied by six interviewees in answering Question 1. Consider, for example, the following interview excerpt in which a student used similarities in ion charges to propose a ranking:

“Ok, well I know HCl is a strong acid so I would guess that one would be one of the…

more favored ones…. um… HI… so I think I would be in the middle because they have the same charge… And then S … it has like the charges different.” (S11 answering Question 1 in Table 1)

This example also illustrates how the representativeness heuristic was applied in conjunction with other reasoning strategies, recognition in this case, that allowed students to first rank one of the reactions and then use it as an anchor from which to base other decisions.

Discussion and Implications

  1. Top of page
  2. Abstract
  3. Introduction
  4. Assumptions and Heuristics
  5. Goals and Research Questions
  6. Methodology
  7. Targeted Reasoning
  8. Findings
  9. Discussion and Implications
  10. References

Our results indicate that students' reasoning about structure–property relationships was highly constrained by both: (1) implicit assumptions about the nature and behavior of chemical substances and processes, and (2) reasoning heuristics for cue selection and decision-making. In particular, intuitive, spurious, and valid assumptions guided our interviewees in the identification and selection of relevant features to make their rankings decisions. Students' responses were also determined by the application of reasoning heuristics that helped reduce cognitive effort during the ranking tasks by minimizing the number of cues to be evaluated, facilitating the recall of cue values, or simplifying the evaluation of cue effects. Given the similarities in ranking patterns generated from the interviews and questionnaires, we suspect that our study revealed patterns of reasoning about structure–property relationships that may be common among the targeted population of college students, particularly under conditions of limited knowledge, time constraints, or low motivation. Nevertheless, given the intrinsic limitations of our qualitative research approach, further studies would be needed to confirm such generalization. Although assumptions and heuristics are interconnected cognitive constraints, their distinction is useful for educational purposes not only in chemistry, but in other science domains.

Intuitive assumptions about chemical entities and processes played a central role in the ranking decisions made by our interviewees. Although the intuitive assumptions summarized in Table 3 may seem rather diverse and idiosyncratic, they reveal three major commonsense ideas about the favorability of chemical reactions. For many students, favored chemical processes are those that: (a) are easy to carry out, (b) produce the most products, or (c) involve reactants with perceived high agency. These intuitive ideas suggest that many of our interviewees thought of chemical reactions as macroscopic “reassembling” processes, in which parts of a system have to be pulled apart and then recombined to form new products. This would explain why a large number of study participants seemed to believe that the less effort that was required to complete a chemical process, the more favored it would be. More favored processes would have, for example, fewer parts to be taken apart, fewer pieces to be put together, fewer components to be transferred from one place to another, or more components with intrinsic properties that facilitated their assembling or disassembling. The specific factors students selected were influenced by the most salient features of the tasks (e.g., presence of familiar compounds, explicit differences in molecular size), introducing variability in response patterns.

Although intuitive assumptions played a major role in the reasoning of our interviewees, their answers also revealed the application of richer cognitive resources, including spurious and valid chemical understandings. We characterized spurious assumptions as ideas that result from the misinterpretation and overgeneralization of central concepts in chemistry. Main assumptions in this category included the belief that any chemical behavior follows a periodic trend that can be revealed by looking at the position of elemental components in the periodic table, and the assumption that the electronegativity of such elemental components determines the chemical reactivity of chemical compounds. These two ideas guided the generation of a significant number of responses to questions that included sets of reactions with salient differences in the elemental composition of reactants or products. Students' tendency to overgeneralize, which reveals the difficulties they have in identifying the conditions in which scientific principles apply, have been highlighted in prior studies (Claesgens, Scalise, Wilson, & Stacy, 2009; Maeyer & Talanquer, 2010; Stains & Talanquer, 2007). Although over half of the interviewees also relied on valid assumptions to propose their rankings, application of this type of assumptions was sporadic.

The use of reasoning heuristics for decision-making was prevalent among participants in our study. In particular, one-reason decision making (ORDM) and recognition were widely applied across different tasks, although the use of the recognition heuristic was tightly linked to the presence of familiar chemical compounds (e.g., HCl, NaOH, and NaCl) acting as reactants or products in the selected chemical reactions. Reliance on the effects of a single variable in building explanations or making decisions seems to be characteristic of learners in the earlier stages of their conceptual development in various domains (Brown, Nagashima, Fu, Timms, & Wilson, 2010; Claesgens et al., 2009). Our results suggest that many science and engineering majors may be at such a stage when completing their first year of college chemistry, demonstrating strong over-reliance on variable reduction strategies and recognition memory in their reasoning.

The generalization of our findings may be limited by different factors that are important to point out. Our interview protocol included only one set of reactions per each reaction type. It is possible that the assumptions and heuristics that were elicited may be closely tied to the specific nature of such reactions. However, the reasoning patterns that we observed seemed less related to the chemical nature of the processes, but tied more to general features of the reactants and products involved (e.g., molecular size, number of moles required or produced, common use in the lab). We did not observe patterns of reasoning that were solely associated with a specific chemical process or reaction type. Thus, we believe that the assumptions and heuristics revealed in our study are broadly applied when evaluating the favorability of diverse chemical processes.

We also recognize that the low-stake nature of our interview tasks may have negatively affected students' motivation to invest time and cognitive effort in answering the questions. This may explain, in part, the overall low performance and the lack of sophisticated chemical thinking that we observed during the interviews. Although our results may not be indicative of the actual level of understanding of students completing their first year of college chemistry, our findings reveal reasoning patterns that are likely to constrain the development of meaningful understandings as students engage with chemistry concepts and ideas.

The identification of the implicit assumptions and heuristics that guide, but also constrain student reasoning enriches our understanding of the challenges that educators face in helping students progress towards targeted ways of thinking in a domain. Assumptions influence what we believe is possible in the systems being studied and the factors that we judge to be relevant, while heuristics affect how we weight the effects of different cues. These two types of cognitive elements are often differentiated in models of inductive reasoning (Perfors et al., 2011). These cognitive constraints highlight the need to work with students in two interconnected, but distinct dimensions. On the one hand, we need to help them progress in their conceptual sophistication about targeted ideas, which characterizes the ability to use relevant cues and models to build explanations and make predictions and decisions. On the other hand, we should support the development of their depth of reasoning, which relates to the ability to identify and evaluate the effect of multiple variables, consider the interactions between various properties, components, or processes, and recognize relevant constraints and boundary conditions (von Aufschnaiter & von Aufschnaiter, 2003).

Our results suggest that the educational approaches used in the general chemistry courses completed by our interviewees were ineffective in helping students develop the targeted reasoning. College instruction may thus benefit from the recognition of cognitive constraints, both assumptions and heuristics, that may direct students' attention and efforts to less productive ideas and practices. Identifying these constraints is helpful in devising instructional sequences that take advantage of student reasoning. For example, our findings indicate that many college students may conceptualize chemical reactions as effortful assembling processes rather than as random collision events constrained by structural and energetic factors. This “miscategorization” of chemical processes shares similarities with that highlighted by Chi and colleagues in their analysis of students' causal explanations of emergent processes (Chi, 2005; Chi, Roscoe, Slotta, Roy, & Chase, 2011). In both cases, the activation of inappropriate schemas results in misconceptions that may appear incoherent or piecemeal, but reveal underlying common assumptions about the nature of the process of interest. Helping students understand structure–property relationships thus may demand the type of ontological training devised by these authors (Chi et al., 2011). Following this approach, students could be engaged in comparing and contrasting attributes and interaction patterns of different types of processes (e.g., a direct reassembling versus constrained random collision), and asked to analyze how explanations and predictions of properties and behaviors are built within each process schema. This type of instructional intervention has been shown to increase students' metacognitive awareness of their intuitive assumptions and facilitate their understanding of alternative constructs.

Reducing students' over-reliance on heuristic reasoning strategies for decision making may demand educational interventions focused on explicit training in metacognitive intercession, monitoring, and control (Klaczynski, 2004). Expertise in a discipline often does not imply the absence of heuristic reasoning in making judgments and decisions, but rather a more deliberate, controlled, and effective use of heuristics in proper contexts (Kruglanski & Gigerenzer, 2011). From this perspective, instruction directed at improving students' abilities to extract relevant information may be beneficial. Studies on perceptual learning indicate that tasks that require learners to distinguish, classify or contrast key features and relations that carry important information in a domain improve students' pattern recognition, structure extraction, and fluency (Kellman, Massey, & Son, 2010). Additionally, educational improvement in this area would benefit from studies that explore how practitioners in a discipline approach the types of tasks that students are commonly asked to complete in academic settings, and how this reasoning differs from the targeted reasoning defined by textbooks or experienced instructors. This would allow us to better judge how far student reasoning is from that of experienced professionals and how to best support progression towards actual expert ways of reasoning in a given field, which may differ from prescribed academic thinking.

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  2. Abstract
  3. Introduction
  4. Assumptions and Heuristics
  5. Goals and Research Questions
  6. Methodology
  7. Targeted Reasoning
  8. Findings
  9. Discussion and Implications
  10. References
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