Zero-Order Chemical Kinetics as a Context To Investigate Student

Article Cite This: J. Chem. Educ. XXXX, XXX, XXX−XXX

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Zero-Order Chemical Kinetics as a Context To Investigate Student Understanding of Catalysts and Half-Life Kinsey Bain,† Jon-Marc G. Rodriguez,‡ and Marcy H. Towns‡,* †

Department of Chemistry, Michigan State University, East Lansing, Michigan 48832, United States Department of Chemistry, Purdue University, West Lafayette, Indiana 47907, United States

‡

ABSTRACT: Zero-order systems provide an interesting opportunity for students to think about the underlying mechanism behind the physical phenomena being modeled. The work reported here is part of a larger study that seeks to characterize how students integrate chemistry and mathematics in the context of chemical kinetics. Thirty-six general chemistry students, five physical chemistry students, and three chemical engineering students were asked to think aloud as they responded to an interview prompt about the half-life of a catalyst-driven zero-order reaction. Our findings revealed that students often described zero-order in mathematical terms (i.e., the zero-order rate law, integrated rate law, and graphical representation), but lacked a clear understanding of the particulate nature of zero-order systems. Results also indicated students have productive discipline-specific conceptions of catalysts but less productive ideas regarding half-life, expressing a limited view that seemed restricted to first-order decay reactions. Analysis of student problem solving further revealed patterns among this type of half-life reasoning. Our work suggests the need for instruction that varies context to promote a more holistic understanding of chemical kinetics concepts. KEYWORDS: First-Year Undergraduate/General, Upper-Division Undergraduate, Chemical Education Research, Kinetics, Interdisciplinary/Multidisciplinary FEATURE: Chemical Education Research

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need to explore research contexts that involve interdisciplinary content and participants from upper-level courses.14,15 In this article, we discuss trends noted among general chemistry and upper-level students as they worked through an interview prompt about the half-life for a zero-order reaction that occurred by way of catalysis. Analysis was guided by the following research questions: (1) How do students reason about zero-order systems? (2) How do students reason about catalysts and half-lives?

ero-order reactions have been described in the literature as “chemical kinetics curiosities.”1 Although instruction involving chemical kinetics often focuses on reaction orders that have integer values, such as first-order and second-order systems, discussion of more interesting reaction orders such as zero-order, negative-order, or fractional-order kinetics provides a unique opportunity for students to think about the chemistry modeled by the rate law.2,3 It is perhaps unsurprising that, with less attention given to zero-order reactions, prominent features of collision theory that are discussed in the context of unimoelcuar and biomolecular reactions are inappropriately applied by students when reasoning about zero-order systems. For example, although collision theory is limited to modeling the rate of concentration-dependent elementary reactions, students use ideas related to the collision model to reason that the rate of a zero-order reaction decreases over time as the reactants are consumed, or students reason there is a relationship between molecularity and the order in the rate law of a zero-order reaction.4,5 Chemical kinetics is an understudied context within Chemical Education Research (CER), with the subject of zero-order systems even less represented among the literature.6,7 Previous work involves an effort to provide analogies to help explain zeroorder reactions8,9 and the development of laboratory experiments that discuss zero-order reactions,10−13 but CER related to zero-order reactions plays a minor role in larger projects centered more generally on chemical kinetics.2−5 Furthermore, there is a © XXXX American Chemical Society and Division of Chemical Education, Inc.

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THEORETICAL FRAMEWORK From a theoretical perspective, the resource-based model of cognition framed and informed the analysis and discussion of results. The resources framework is rooted in constructivist ideas, in which students build mental models that account for their experiences,16,17 and it incorporates the “knowledge-in-pieces” notion regarding the disconnected nature of student ideas.18 Within the resources perspective, student knowledge is conceptualized as a dynamic network of interacting cognitive elements, which vary in complexity and are activated in specific contexts.19,20 These cognitive elements are generally described as resources that are characterized as productive or unproductive Received: December 19, 2017 Revised: February 28, 2018

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DOI: 10.1021/acs.jchemed.7b00974 J. Chem. Educ. XXXX, XXX, XXX−XXX

Journal of Chemical Education

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involving students working through a standard textbook-type problem (“chemistry prompt”) and the other prompt involving students talking about the zero-order integrated rate law (“math prompt”). To account for any priming effects associated with the order of the prompts, half of the students completed the math prompt before the chemistry prompt, and the other half of the students completed the chemistry prompt before the math prompt. The zero-order prompts used in this study, along with examples of probing questions, are provided in Boxes 1 and 2.

(depending on the context), and the goal of instruction should be to guide and help students to use resources that are useful for a given context. According to Hammer and Elby,20 the contextdependence of fine-grained resources accounts for inconsistency in student responses, but as students progress, appropriate connections are made between resources to create coordinated networks that can consistently be activated when appropriate, resulting in a more complete, expert-like understanding of a concept. Previous work in CER has discussed the utility of using a resources perspective for exploring student reasoning because it can help explain the fragmented and non-normative nature of student mental models.21 It also is a useful way to consider the practical application of research results in terms of how instructional support can aid students in the productive use of their knowledge.22 In the context of our study, the resources perspective affords a way to consider the variability in student responses. The interview prompt activated appropriate resources for some students, but for other students less productive resources were activated that were not useful for problem solving in this context. This provides a starting point to consider how to scaffold students in using their knowledge productively.

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METHODS

Student Participants

This analysis was part of a large project that analyzed how chemistry and mathematics knowledge interacted as students engaged in problem solving in the context of chemical kinetics.2 Here, we report on results that pertain to student understanding of zero-order systems. The participants, shown in Table 1, were Table 1. Study Participants Number of Students Interviewed

a

Course/Level

Fall 2015

Pilot Study (General Chemistry II) General Chemistry II Physical Chemistry for Life Sciencesa Chemical Reactions Engineeringa

4 17

Spring 2016 19 5 3

Upper-level courses.

sampled primarily from a second-semester general chemistry (GC) course (intended for engineering majors). The remaining participants were from two upper-level courses, a physical chemistry course for life science majors and a chemical reactions engineering course for chemical engineering majors. All aspects of this project were completed in accordance with our university’s Institutional Review Board. All participants were recruited prior to instruction on chemical kinetics content. Upon the completion of their interview, each student was given a $10 iTunes card for their participation and assigned a pseudonym to protect his/her identity. Data Collection and Analysis

Following instruction on chemical kinetics in their respective courses, students were interviewed using a think-aloud protocol, which involved probing questions to help make their reasoning explicit.23,24 During the interview, students worked through two zero-order prompts using a LiveScribe smartpen, which allowed us to collect real-time audio along with the students’ written work.25−27 The content of the prompts involved thinking about considerations of zero-order kinetics, with one of the prompts

Analysis of the data involved transcribing the interviews, restructuring the data to create “interpreted narratives”, opencoding, and constant comparison, as described in our recent publication.2,28,29 Most codes could be organized by mathematical understanding, conceptual understanding, or problemsolving strategies. For this analysis, codes such as “conceptual understanding of half-life” or “conceptual understanding of B



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Although the most frequent response was that students were unsure about the chemistry underpinning the zero-order system, some students attempted to provide an explanation. For example, students discussed the idea that zero-order reactions are simple or straightforward, often explicitly identifying them as decomposition reactions that involved a single reactant breaking apart into products, an idea based on the notion that a higher order indicates more complexity. This type of intuitive reasoning is reminiscent of a previously observed heuristic, more means more.31 Less frequently observed explanations involved discussions regarding how reactions were characterized as zeroorder based on the ratio of reactants to products or a discussion regarding how an excess of the reactants can make the rate independent of reactant concentration, resulting in a zero-order reaction. For examples of these types of reasoning see Table 2. Because of the conditions under which the reaction occurs, zero-order reactions have an observed rate that is constant and is independent of the concentration of the reactants.30 In the interview prompt, the reaction rate depends on the amount of platinum wire surface area available for nitrous oxide to bind (rather than the concentration of nitrous oxide), resulting in the observed constant rate and zero-order kinetics. Therefore, understanding the role of the catalyst is critical to understanding the physical mechanism behind the zero-order system. However, during the interviews, most participants indicated the order of the system was unaffected by the presence of the catalyst (Table 3). Additionally, less than half of the participants recognized that the catalyst physically interacted with the reactants and/or influenced the mechanism in any way. Further discussion of student understanding of catalysts is presented in the next section and in Table 3. Some students expressed multiple conceptions about catalysts in zero-order systems and, therefore, were sometimes counted in more than one row of Table 3. Catalysts

Analyzing the student responses to the zero-order prompt, we also observed that in addition to discussing the catalyst’s role in zero-order systems (Table 3), our participants exhibited a range of responses that demonstrated variation in how they thought about catalysts in more general terms as shown in Tables 4 and 5. The predominant conceptions expressed by students were that catalysts increase the reaction rate and/or lower the activation energy as displayed in Table 4. However, these ideas often reflected a surface-level understanding of catalysts or were paired with less productive ideas. As previous literature suggests,6,32 students may be utilizing everyday knowledge and experience to inform their understanding of catalysts, stemming from use in colloquial language (just like the terms “heat” and “work”). For example, though many participants stated that catalysts lower the activation energy of a reaction, some were unable to convey an understanding of how or why this happened. Serena, a secondsemester general chemistry student, exemplified this perspective in her response. Interviewer: How do you think [the Pt wire catalyst] affects this reaction overall? Serena (GC): ...The catalyst would lower the activation energy, making it way easier for the reaction to take place... Interviewer: ...Do catalysts affect the mechanism of what goes on with all of the chemicals and how the reaction happens on the molecular [level]? Serena: I do not think so. From what I remember, equations that I’ve done, I do not think it really affects what’s happening here [circles chemical reaction].

catalysts” emerged from the data. Each of these codes had subcodes that represented a more fine-grained characterization of emergent themes (e.g., first-order half-life language or discipline-specific catalyst discussion). Coding was completed in tandem by two researchers requiring 100% agreement for assignment of codes.

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RESULTS AND DISCUSSION

Zero-Order Systems

Within our data set, we observed that students had a good working knowledge of zero-order systems (and order, in more general terms) in which they could reason mathematically, often conceptualizing order based on its rate law, integrated rate law, and its graphical representation (graph of concentration vs time). Additionally, students also often defined zero-order based on the rate being constant and independent of the concentration of reactants, but when prompted about the particulate-level chemistry that underlies zero-order systems students were often unable to provide an answer. The observed preference for algorithmic and mathematics-centric reasoning is consistent across the data set regardless of prompt order. This was not surprising, as our previous work reported that students frequently anchored their reasoning in mathematics and had difficulty reasoning about the phenomenon being modeled by the mathematical expressions.2 C



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Table 2. Student Reasoning about Zero-Order Systems

reaction (catalyst affects the rates of forward and reverse reactions differently). That is not to say that none of the participants held this idea; it simply may not have been activated in this interview context.

I think it just helps it get under way. I do not remember any situations where a catalyst really affects what’s happening in the reaction. It just makes it easier. Other ideas observed in our data set were analyzed and organized according to those reported previously in the literature and are displayed in Table 5.6 The most common of these was the idea that catalysts increase the average speed of molecules or increase the number of collisions. Some of these students used this idea to describe heat as a catalyst, like the following excerpt from Jenny’s (a second-semester general chemistry student) interview. Jenny (GC): Because in some cases heat is used as a catalyst to heat things up to make your reaction go faster. So, in that case, the heat itself is not really reacting with the reactants, but it is still a catalyst. These students are using the common result (increased reaction rate) to draw conclusions about the similarities between different entities and processes (catalysts and increased temperature conditions). As seen in Table 5, not all student conceptions reported in the literature were presented in this data. This does not mean that the participants in this study did not hold some of those ideas; rather, they were not activated by the prompt or probing questions. For example, none of the participants discussed the idea that a catalyst only speeds up the forward

Discipline-Specific Contexts

Catalysts and half-life concepts were often discussed in discipline-specific contexts. For example, we noted students often focused on the specific catalyst used in the interview prompt (a solid inorganic catalyst), causing them to make unproductive connections between topics presented in chemistry. Many students attended to the platinum wire catalyst, which activated ideas relating to electricity, current, conductivity, electrons, and metals. Some assumed current was running through the wire to provide energy to the reaction system, and one student inferred that the wire catalyst in the reaction was actually an electrochemical cell setup. Additionally, other students discussed the nature of metals and how they freely donated electrons to catalyze reactions. Other observed discipline-specific ideas were activated during participants’ catalyst discussions as well. For example, participants from the chemical reactions engineering course frequently discussed their understanding of catalysis in the context of plug flow reactors, packed bed reactors, or continuous stirred-tank reactor. In these discussions, the participants highlighted considerations such as mass transfer, selectivity, and efficiency. More commonly, discipline-specific discussions were seen among second-semester general chemistry and physical chemistry for life sciences students, where chemistry concepts were D



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Table 3. Student Reasoning about Catalysts in Zero-Order Systems

Table 4. General Student Reasoning about Catalysts

considered in biological settings. This included pharmacology (pharmacokinetics) contexts used by participants in relation to ideas about half-life. Other times, catalysts were considered in the context of or compared to enzyme−substrate systems. For example, using an enzyme−substrate backdrop, these students discussed ideas that were rarely noted among other participants.

Spatial considerations were often mentioned, stating that enzymes and substrates bind in a specific orientation to facilitate a reaction. A second-semester general chemistry student, Georgina, discussed this idea when attempting to explain what the platinum catalyst chemically did in the nitrous oxide reaction. E



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Table 5. Frequency of Student Conceptions About Catalysts Organized According to the General Chemistry Anchoring Concepts Content Map (ACCM) and Literature Findings (Bain and Towns, 2016)6

Penelope (GC): I know what half-life means. That is like how long it takes for a concentration to decrease by one-half... Okay, half-life, I do not think it would change [if you double the initial reactant concentration] because it is the same product or reactant, or thing that you are measuring, so it always has the same half-life. Interviewer: So the half-lives do not change,... if you have the same reactant? Penelope: Right. Interviewer: ...So, if a half-life does not depend on how much initial concentration you have, what does a half-life depend on? Penelope: The actual thing that you are measuring. Like dif ferent elements have dif ferent half-lives, I think. ... Like plutonium would be like way larger or something, I think. Interviewer: So it is more the identity of whatever it is, and its chemical makeup? Penelope: Right. In the above passage, Penelope, a second-semester general chemistry student, described half-life as the time it takes for a reaction to reach half the concentration of the initial reactant. However, she went on to describe her conception of half-life as always being a fixed quantity that depends on the chemical identity. Penelope’s definition of half-life in the above passage is appropriate only in the context of first-order reactions, often presented to students in the context of radioactive decay. Radioactive decay language appeared frequently in the student data, including the passage above, where Penelope cited plutonium as an example. Our analysis indicated this is more than students simply conflating reaction terminology; there is a clear pattern where they connected half-life exclusively to firstorder kinetics, with some explicitly mentioning concepts like radioactivity or carbon-dating. In the next two sections, we will discuss the implications of this limited understanding of half-life

Georgina (GC): Whatever [the platinum catalyst is] doing, I’m not sure specif ically for this [N2O reaction]. But I know as far as enzymes go. I’m a science major so this is easier for me [to discuss]. As far as enzymes go, I know that they have specif ic shapes... You have these two [reactants] that you want to react together, and you want them to come together, but they have to f it together a certain way. Enzymes will have these little pockets where these [reactants] can rest so they can come together in the exact way that they need to come together so that they can form one molecule. In nature opened freely without this enzyme catalyst, [the reaction] would happen at a much lower rate. As seen in Georgina’s quote above, many of these students stated that they were more comfortable thinking about biological catalysts (enzymes) and were unsure how to relate their knowledge to chemistry catalysts (Pt wire catalyst). Georgina continued her enzyme discussion trying to relate her knowledge to the catalyst system in the zero-order chemistry prompt. Georgina: As far as enzymes, that is what happens. I’m not sure what the platinum wire physically has to do with this [reaction], but it would have something to do with making it easier for this reaction to proceed in the forward direction. I’m not sure of the actual [mechanism], looking at it at a molecular level. I know somehow it would assist it, it would make it easier. I kind of went off topic [referring to enzyme discussion], but that is what I’m more comfortable with, the biology side of it. First-Order Kinetics Reasoning

Most of the students in our sample correctly answered the zeroorder chemistry prompt, indicating that doubling the initial concentration of the reactant in the zero-order system would result in a half-life that is twice as large. However, analysis of the student responses revealed that students often defined and described half-life using language that was reminiscent of radioactive decay reactions. F



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and how conceptualizing half-life as tied to a single context is not productive for problem solving.

Resolving Cognitive Dissonance among Students That Exhibited First-Order Reasoning

Problem-Solving Trends

The tendency for students to engage in reasoning and perform calculations related to first-order kinetics was a trend that was noted across the introductory- and upper-level students. This type of reasoning was well-represented among students regardless of whether they answered the prompt correctly or if they were unable to solve the prompt (Figure 2). What seemed to differentiate these three groups of students was how they responded to resolving the lack of agreement between competing ideas. For each group of students, the competing ideas included first-order kinetics reasoning (which suggested half-lives have a fixed value) and reasoning that stemmed from doing calculations and manipulating the data provided (which indicated half-life depends on concentration). Students often experienced cognitive dissonance as they responded to the prompt with one type of reasoning (e.g., first-order reasoning) and then realized how it was inconsistent with other methods of approaching the problem (e.g., solving the problem graphically). In the sections that follow we describe trends noted among the different groups of students that exhibited first-order reasoning. Students That Solved the Prompt Incorrectly. We found that the students who incorrectly answered the chemistry prompt (Box 1) often followed the problem-solving route outlined below (see also Figure 2). • They initially answered conceptually using the first-order kinetics reasoning described previously. • This was followed by one of two approaches: • They felt they had satisfactorily answered the prompt and did not feel they needed to do any calculations. • They performed calculations that they interpreted within the context of first-order reasoning, believing it supported their claim. It was also common among these students to persist with their (incorrect) claim even after not being able to perform calculations that supported their claim. This suggests that this group of students felt confident in their reasoning, resolving the lack of agreement between the competing ideas by trusting in their initial conceptual claim. Students That Were Unable To Solve the Prompt. For this group of students, their inability to solve the prompt was a result of them not being able to resolve the lack of agreement between competing ideas. They essentially gave up, indicating they were unsure what the answer was. Among these students, it seemed they were unable to entertain the plausibility of a concentration-dependent half-life for a system that has a concentration-independent rate, yet they were dissatisfied with their initial conception that was rooted in first-order fixed half-life quantity. Since they were uncomfortable with their initial idea and did not understand how the new conception addressed the inconsistencies in their previous conception, they simply did not provide a final answer. Students That Solved the Prompt Correctly. Among the students that answered the prompt correctly, we noted that firstorder kinetics reasoning still influenced their understanding of half-life, just as it did the other groups. These students often initially answered conceptually (incorrectly using first-order reasoning), but seemed more willing to change their initial conceptual claims after performing some calculations and using the data to reason about the zero-order system. These students exhibited clear dissatisfaction with their initial ideas regarding a

Associating half-life only with decay reactions was problematic because students often tried to use first-order kinetics reasoning and equations to solve the zero-order chemistry prompt. For example, in the chemistry prompt the students were supposed to determine how changing the initial concentration of the reactant affected the half-life, to which Georgina responded: Georgina (GC): I would assume that [the half-lives are] equal. I know, specif ically, carbon-14 has a set half-life, no matter how much of it there is. You can go online [to] look it up. I’m not sure exactly what the number is now, but it is always “this” amount of time for the half of it to be gone. In this example, we saw that Georgina’s understanding of halflife was rooted to a specific context, exhibiting a clear connection between half-life and radioactive decay, which influenced how she thought about half-life in other contexts. We saw similar reasoning when Rufus, another general chemistry student, made the following statement at the beginning of his discussion of the chemistry prompt: Rufus (GC): A half-life is based of f of the molecular structure. So, like the compound, so I mean, if you double the concentration, the half-life is not going to change because you still have the same compound. You have more of it. The time for half that to go away, it does not change. Here Rufus initially answered the question incorrectly (conceptually), due to his understanding of half-life as being a constant value for a specific compound. Once again, this understanding of half-life is appropriate, but only in the context of first-order reaction kinetics. In his interview, Rufus then went on to solve the problem algorithmically, as shown in Figure 1.

Figure 1. Rufus’ (GC) problem-solving approach for the zero-order chemistry prompt.

Although Rufus did not provide the correct equation, it is clear the equation he provided was an attempt to write the first-order integrated rate law. Looking at the rest of Rufus’ interview, his understanding of half-life and its associations with first-order kinetics affected his problem-solving approaches. He ultimately persisted with his initial claim, arguing the half-life would be unaffected by changing the initial concentration in the zero-order system. G



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Figure 2. Problem-solving approaches for different groups of students that utilized first-order reasoning in the zero-order chemistry prompt.

conceptualizations of half-life and catalysts. We found that student ideas regarding zero-order emphasized the mathematical representation, with a limited understanding of the particulatelevel mechanism that underlies this type of system. Students also expressed a limited understanding of half-life, framing it almost exclusively in terms of first-order reasoning, which greatly influenced their problem solving. These results suggest students would benefit from exposure to additional varied examples of both reaction order and half-life. According to Bussey, Orgill, and Crippen,45,46 students develop a more robust understanding when they are presented with varied contexts that have multiple examples of an idea. More specifically, for students to understand a concept, they must experience variation within the presentation of the concept, where critical features differ in each example so that students attend to important aspects and develop a comprehensive understanding. Within the context of our study, students’ ideas regarding what gives rise to a zero-order reaction suggest they are not thinking enough about the particulate-level phenomenon modeled by the mathematical expressions they use in class. However, exposure to a variety of reaction orders (such as zero-order), coupled with intentional prompting by instructors, could help students to consider the mechanism implied by the reaction order. Similarly, students considered half-life using almost exclusively first-order reasoning, likely because they only discussed half-life in the context of radioactive decay reactions. We suggest students should be exposed to half-life systems of different reaction orders to expand their understanding and move their conceptualization of half-life beyond radioactive decay reactions. When problem solving, participants who used first-order reasoning followed three main patterns that had striking commonalities with the conceptual change model, which describes the conditions necessary for the accommodation of new ideas.47 According to this model, students must recognize a problem or inconsistency with their current idea (dissatisfaction), understand the new idea and how it addresses the problem with their current understanding (intelligibility/plausibility), and acknowledge the greater explanatory power and transferability of the new idea for other contexts (future potential). While it was not part of the interview design or intent, some students (those that solved the prompt correctly) exhibited the conditions necessary for conceptual change, where they modified their understanding of half-life as a constant value to encompass the order-specific nuances of half-life that reflect a more expert-like understanding. Other students, like those that solved the import incorrectly, did not allow their conception to be challenged, which prevented them from becoming dissatisfied. The way students moved (or did not move) through the conceptual

constant-half-life after performing calculations that contradicted this claim, which led the students to consider how a concentration-dependent half-life was a reasonable and plausible solution to the problem. Influence of Prompt Order

As described in the Methods section, the students completed two prompts, a chemistry prompt and a math prompt. To consider priming effects, these prompts were alternated so that half of the students did the chemistry prompt first and half of the students did the math prompt first. The students that completed the math prompt first were more likely to correctly answer the chemistry prompt. That is, 74% of the participants that had the math prompt first solved for a correct answer, compared to only 56% of the participants that had the chemistry prompt first. For the general chemistry students, the percentages were 74% and 62%, respectively, whereas the upper-level students were 75% and 25%.

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LIMITATIONS The small size of the upper-level participants sample limits any claims that can be made about comparisons with the introductory-level participants, which led us to discuss trends among the groups. Additionally, the main purpose of the larger study was to investigate how students understand and solve kinetics problems. During the interviews and analysis, we noted rich student data about their conceptions of catalysts, half-life, order, etc. One limitation of this approach is that the findings regarding student understanding are not necessarily exhaustive, as the primary purpose of the interviews originally was not to map students’ conceptions about these ideas. Further work is needed to expand upon these findings.

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CONCLUSION AND IMPLICATIONS Findings from this study suggest that chemistry students have prior knowledge relating to catalysts and half-life. Instructors should be aware of and explicitly assess these ideas. Some intuitive ideas may stem from colloquial language and experience, which can lead to incorrect patterns of reasoning or a surface-level understanding of the phenomena. However, other student ideas that are activated could serve as productive contexts for student learning. For example, many students aptly discussed enzyme−substrate systems when discussing catalysts. Instructors could utilize this type of student understanding to foster learning about other types of catalysts, like solid-state inorganic catalysts. In the interviews, two prompts were used to elicit student understanding of zero-order systems, as well as student H



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(9) Arnáiz, F. J. Mice in the Box for Zero-Order Kinetics. J. Chem. Educ. 1999, 76 (10), 1458. (10) Sanger, M. J.; Wiley, R. A.; Richter, E. W.; Phelps, A. J. Rate Law Determination of Everyday Processes. J. Chem. Educ. 2002, 79 (8), 989− 991. (11) Kustin, K.; Ross, E. W. Reduction of Iodine by Phosphorus(I): Integration of the Rate Equation. J. Chem. Educ. 2005, 82 (9), 1413− 1417. (12) Mucientes, A. E.; de la Peña, M. A. Ruthenium(VI)-Catalyzed Oxidation of Alcohols by Hexacyanoferrate(III): An Example of Mixed Order. J. Chem. Educ. 2006, 83 (11), 1643−1644. (13) Pryce-Jones, T. Heterogeneous Kinetics in the Laboratory. J. Chem. Educ. 1972, 49 (12), 848−849. (14) Singer, S. R.; Nielson, N. R.; Schweingruber, H. A. Discipline-Based Education Research: Uuderstanding and Improving Learning in Undergradute Science and Engineering; National Academies Press: Washington, DC, 2012. (15) Pienta, N. J. What We Do and Don’t Know about Teaching and Learning Science: The National Research Council Weighs in on Discipline-Based Education Research. J. Chem. Educ. 2012, 89 (8), 963− 964. (16) Bodner, G.; Klobuchar, M.; Geelan, D. The Many Forms of Constructivism. J. Chem. Educ. 2001, 78 (8), 1107. (17) Bodner, G. M. Constructivism: A Theory of Knowledge. J. Chem. Educ. 1986, 63 (10), 873−878. (18) diSessa, A. A. Toward an Epistemology of Physics. Cogn. Instr. 1993, 10 (2−3), 105−225. (19) Hammer, D.; Elby, A. Tapping Epistemological Resources for Learning Physics. J. Learn. Sci. 2003, 12 (1), 53−90. (20) Hammer, D.; Elby, A. On the Form of a Personal Epistemology. In Personal Epistemology: The Psychology of Beliefs about Knowledge and Knowing; Hofer, B. K., Pintrich, P. R., Eds.; Erlbaum: Mahwah, NJ, 2002; pp 169−190. (21) Heisterkamp, K.; Talanquer, V. Interpreting Data: The Hybrid Mind. J. Chem. Educ. 2015, 92 (12), 1988−1995. (22) Becker, N. M.; Rupp, C. A.; Brandriet, A. Engaging Students in Analyzing and Interpreting Data to Construct Mathematical Models: An Analysis of Students’ Reasoning in a Method of Initial Rates Task. Chem. Educ. Res. Pract. 2017, 18, 798−810. (23) Becker, N.; Towns, M. Students’ Understanding of Mathematical Expressions in Physical Chemistry Contexts: An Analysis Using Sherin’s Symbolic Forms. Chem. Educ. Res. Pract. 2012, 13, 209−220. (24) King, N.; Horrocks, C. Interviews in Qualitative Research; SAGE Publications Ltd.: Thousand Oaks, CA, 2010. (25) Cruz-Ramirez de Arellano, D.; Towns, M. H. Students’ Understanding of Alkyl Halide Reactions in Undergraduate Organic Chemistry. Chem. Educ. Res. Pract. 2014, 15, 501−515. (26) Linenberger, K. J.; Lowery Bretz, S. A Novel Technology to Investigate Students’ Understandings. J. Coll. Sci. Teach. 2012, 42 (1), 45−49. (27) Harle, M.; Towns, M. H. Students’ Understanding of Primary and Secondary Protein Structure: Drawing Secondary Protein Structure Reveals Student Understanding Better Than Simple Recognition of Structures. Biochem. Mol. Biol. Educ. 2013, 41 (6), 369−376. (28) Page, J. M. Childcare Choices and Voices: Using Interpreted Narratives and Thematic Meaning-Making to Analyze Mothers’ Life Histories. Int. J. Qual. Stud. Educ. 2014, 27 (7), 850−876. (29) Strauss, A.; Corbin, J. Basics of Qualitative Research: Grounded Theory Procedures and Techniques; SAGE Publications Ltd.: Newbury Park, CA, 1990. (30) House, J. E. Principles of Chemical Kinetics, 2nd ed.; Elsevier Science, 2007. (31) Cooper, M. M.; Corley, L. M.; Underwood, S. M. An Investigation of College Chemistry Students’ Understanding of Structure-Property Relationships. J. Res. Sci. Teach. 2013, 50 (6), 699−721. (32) Bain, K.; Moon, A.; Mack, M. R.; Towns, M. H. A Review of Research on the Teaching and Learning of Thermodynamics and the University Level. Chem. Educ. Res. Pract. 2014, 15, 320−335.

change model has implications for teaching. Instructors could mirror this process in their teaching, providing the space for students to become dissatisfied with their current conceptions and guiding them to consider plausible alternatives that are more consistent with the data provided. This process reflects the nature of scientific knowledge and how it changes as scientists gain more evidence and engage in inquiry. Finally, our analysis and interpretation emphasizes the importance of asking for student reasoning during assessments. Recent work by Underwood et al.,48 which is an ACS Editors’ Choice article, provides excellent guidance in developing assessment items that request that students explain their reasoning and support their answers using particulate models, experimental data, mathematical models, etc. These items require students to integrate three “strands”: chemistry core ideas, crosscutting concepts, and scientific practices. The design and implementation of assessments is crucial, because it is a driving factor in student learning.49

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Kinsey Bain: 0000-0003-0898-1862 Marcy H. Towns: 0000-0002-8422-4874 Notes

Any opinions, conclusions, or recommendations expressed in this article are those of the authors and do not necessarily reflect the views of the National Science Foundation. The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The National Science Foundation under Grant DUE-1504371 supported this work. We wish to thank Tom Holme, Ryan Bain, and the Towns research group for their support and helpful comments on the manuscript.

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REFERENCES

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Zero-Order Chemical Kinetics as a Context To Investigate Student

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