Jon-Marc G. Rodriguez*^{a} and
Marcy H. Towns^{b}
^{a}Department of Chemistry, University of Iowa, Iowa City, Iowa 52242-1294, USA
^{b}Department of Chemistry, Purdue University, West Lafayette, Indiana 47907, USA

Received
10th February 2021
, Accepted 14th July 2021

First published on 16th July 2021

In this work, we discuss the importance of underlying theoretical assumptions in research, focusing on the conclusions reached when analyzing data from a misconceptions constructivist (stable, unitary) perspective in contrast to a fine-grained constructivist (resources, knowledge-in-pieces) perspective. Both frameworks are rooted in the idea that students construct knowledge based on experiences, but differ in terms of assumptions about the nature and structure of knowledge. Importantly, we argue that misconceptions constructivism and fine-grained constructivism represent different models that can be used to draw conclusions about student reasoning in order to modify instruction. To this end, we present the results of a qualitative study that focused on how students reasoned graphically, analyzing biochemistry student exam responses (n = 50) using both the misconceptions constructivist framework and the fine-grained constructivist framework. The prompts analyzed were two open-ended exam questions administered in a biochemistry course, with the questions requiring students to draw conclusions about rate and reason about how graphs (such as a typical Michaelis–Menten plot) are constructed. As part of this work, themes emerged related to (1) alternative conceptions for reaction rate, reaction order, and Michealis–Menten plots (misconceptions constructivist interpretation), as well as (2) perceptual cuing that lead students to attend to less relevant surface features (fine-grained constructivist interpretation).

The primary argument discussed in this work is elegantly presented in a paper by Elby (2000) that outlines a critical distinction between a misconceptions constructivist perspective and a fine-grained constructivist perspective. The misconceptions constructivist view frames students’ knowledge in terms of relatively large, stable concepts that are typically applied across contexts, with instruction involving identifying and replacing non-normative ideas. Thus, conceptual change involves guiding students in recognizing the inconsistencies related to their current conception and highlighting the plausibility and potential utility of an alternative conceptualization (Posner et al., 1982). Contrastingly, a fine-grained constructivist view frames students’ knowledge in terms of small cognitive units that are context-dependent, with instruction involving understanding the organization of students’ ideas, how they emerge, and how to productively leverage the knowledge students have (Hammer et al., 2005; diSessa et al., 2016). Within this model, conceptual change involves gradual modification of the overall knowledge structure by drawing connections between existing ideas and the incorporation of additional ideas into this knowledge structure. Additionally, a fine-grained constructivist perspective does not frame student use of ideas across contexts as an issue of transfer, because this implies a unitary view of knowledge acquisition and application; rather, an emphasis is placed on the emergent activation of resources as a result of focusing on salient features in a problem (Hammer et al., 2005).

Building on the discussion presented by Elby (2000), we posit different theoretical commitments associated with the use of different models related to student reasoning result in different interpretations and conclusions. It is within this context that we situate the current study, using chemical kinetics as the context to investigate students’ reasoning using different theoretical perspectives. To this end, we are interested in the guiding research question, How do students reason about graphs related to chemical kinetics and enzyme kinetics? This question is broad enough to lend itself to analysis involving misconceptions constructivism and fine-grained constructivism, with the presentation of the results emphasizing the ways in which the contrasting perspectives informed the conclusions reached.

In contrast, viewing the example provided in Fig. 1 within the assumptions of fine-grained constructivism, there would be an emphasis on trying to understand the knowledge elements (and the relationship between these elements) that contribute to the overall larger statement made by the student. When reasoning about rate, students may bring in a variety of intuitive resources (Fig. 1), such as general ideas with a phenomenological basis like fastness (Parnafes, 2007) and bouncing (diSessa, 1993; Rodriguez et al., 2020c), or other knowledge elements related to graphical reasoning such as recognizing that the relative steepness provides information about rate (steepness as rate) or that a linear plot is related to a constant value or rate (straight means constant) (Rodriguez et al., 2018). The activation and use of these knowledge elements are not inherently right or wrong, but in some instances, they may be more relevant or productive and students may need support deciding when to use them. Moreover, the activation of these resources is the result of perceptual cuing, in which students focus on salient and prominent features of the problem-solving task (Elby, 2000).

This perceptual cuing allows us to make predictions; for the example in Fig. 1, the linearity of the plot is the most prominent feature, and thus, we can predict that for this prompt (and other graphical prompts) students will likely use straight means constant to draw conclusions, even when this is less productive for the context (i.e., regardless of the axes). Empirically, we have found this to be the case; a growing body of literature indicates students consistently associate the same ideas with specific graphical shapes and characterizing their application (or misapplication) as misconceptions does not adequately represent the data and it does not capture the nuances in students’ reasoning in a way that affords targeted instructional scaffolding (Rodriguez et al., 2018, 2019b, 2019c, 2020a, 2020b). Thus, as a model, fine-grained constructivism provides an explanatory account in a way misconceptions constructivism does not. Fine-grained constructivism affords us insight into students’ reasoning that allows us to characterize the salient features students were attending to in the task and acknowledge students’ productive inferences, such as correctly recognizing that a straight linear plot has a constant rate. Rather than identifying the students’ reasoning simply as wrong, we assert the challenge is related more to combining mathematical inferences (constant rate) with chemistry principles (considering which reaction order has a constant rate) (Bain et al., 2019a).

As an implication, critics may call into question whether large units of analysis are appropriate within the fine-grained constructivist perspective. That is, how fine does a fine-grained constructivist analysis have to be? Stated differently, is there a point where units characterized as resources are large enough that a fine-grained constructivist analysis becomes a misconceptions constructivist analysis? In short, the answer is no—we posit that fine-grained constructivism and misconceptions constructivism do not exist along the same continuum; this is because they are separate models that involve different assumptions. Even in the scenario where a group of students’ resources are consistently activated together or the unit of analysis or resource of interest is relatively large, we can expect that analysis informed by fine-grained constructivism will yield different results than if it were approached from a misconceptions constructivist view, with the differences in interpretation due to the differences in assumptions of each model. This has been shown to be the case in the extant literature. For example, in the previously discussed work in physics education, Elby (2000) illustrated the differences in conclusions reached when analyzing data from both perspectives, with a similar approach applied to support these claims in the context of the life sciences (Southerland et al., 2001; Gouvea and Simon, 2018; Lira and Gardner, 2020). Therefore, we reemphasize some of the key features and assumptions of fine-grained constructivism emphasized in this body of literature: (1) leveraging knowledge—students’ knowledge, the structure of their knowledge, and how that changes over time plays a different role in learning within fine-grained constructivism, focusing more on what students currently know instead of what they still have to be taught; (2) context over content—specific contextual features and presentation of the content is more important in dictating student responses than the content itself; (3) explanatory and predictive power—the conclusions reached and the inferences that move beyond the current dataset are different than those afforded using misconceptions constructivism. These ideas will be explored in more detail in this study.

Fig. 4 Prompt used in a study by Madsen et al. (2012), which was adapted to a chemistry context for this study (see Fig. 3 for the prompt used in the current study). |

Fig. 5 Prompt 2 used in the study, focuses on enzyme kinetics, specifically, the construction of the Michaelis–Menten plot. |

Using the underlying theoretical assumptions of fine-grained constructivism, we can make predictions about student responses based on salient features of the graphs. For example, in Prompt 1, we can predict more responses that involve focusing on the intersection, which has been previously reported as a key feature students tend to focus on in graphs (Elby, 2000; Madsen et al., 2012). In addition, linearity has prominence as a feature students attend to, which could be a problem if students are not coordinating this with the axis labels (Rodriguez et al., 2018, 2019b, 2019c; Rodriguez et al., 2020a). Lastly, given the importance of contextual features and framing within fine-grained constructivism, we can predict that the use of V_{0} instead of rate for the y-axis of Michaelis–Menten graphs could activate different ideas. As an example, previous research has shown that students may associate V_{0} with physics, which may inform their reasoning processes (Rodriguez et al., 2019d). Importantly, as previously stated in relation to Fig. 1, we reiterate that characterizing the responses listed here as misconceptions does not adequately consider the role of context in eliciting these ideas and it does not acknowledge the potential role these ideas have in contributing to expertise and knowledge development (Elby, 2000).

Although there were ∼200 students enrolled in the course, it is not necessary to code every exam, rather, analysis should emphasize reaching saturation of themes and making sure these themes were well-represented among the dataset (Saunders et al., 2018). As part of the process for reaching saturation, each exam was assigned a number (a random-number generator was used to select exams for analysis) and for application of codes we used the student response to each question as the unit of analysis (Campbell et al., 2013). We determined thematic saturation and representation was reached after coding n = 30 student exams, based on the lack of emergence of new codes, with subsequent analysis only further populating the code categories. Following initial coding of this dataset, in order to build a case for reliability (Watts and Finkenstaedt-Quinn, 2021), an independent researcher used our established coding scheme to code 20% of the dataset, resulting in a Kappa value of 0.96. As a final step, based on requests from reviewers, we coded additional exams, making the final sample n = 50. Pseudonyms were assigned to the students for the purposes of presenting the data.

Misconceptions constructivist interpretation. Student responses for Item (a) are summarized in Fig. 6, with sample student quotes for commonly selected responses provided in Table 1. Overall, Point C was the most common point selected by students (42% of students selected Point C by itself or with another point); however, there was a large variation in terms of how students responded to the prompt, with 38% of students selecting Point E and 26% of the students selecting Point A. As an implication for instruction, students may benefit from directed instruction that illustrates why Point C best addresses the prompt by discussing the graphical determination of rate. For example, students can be prompted to recognize that although the concentration value and time value are the same for both reactions at Point E, what is relevant for rate is the ratio Δx/Δy, not the point (x, y).

Point selected | Percentage (%) | Student response |
---|---|---|

A | 26 | Audrey: “at time = 0, nothing has happened, therefore both rates are equal to 0.0 = 0” |

C | 42 | Helen: “The rate of a reaction can be determined by [product]/time, or in the case of the graph, it is the slope. At point C of Reaction 2 the slope is equal to the slope of reaction 2, therefore that is the point at which the reaction rates are equal.” |

E | 38 | Walter: “At point E, both reactions have made the same [Product] in the same amount of time.” |

Fine-grained constructivist interpretation. Focusing on the specific resources students used as they worked through the exam item, we can frame students’ responses as being the result of perceptual cuing of different graphical forms, with students that selected Point C focusing on relevant features in the prompt, and students that selected Point A and Point E focusing on less productive features of the graph. Among students that selected Point C, we can characterize this reasoning as steepness as rate, a graphical form that involves associating relative slope with rate, illustrated in Helen's response (Table 1). In the case of students such as Audrey that selected Point A (Table 1), this can be conceptualized as the graphical equivalent of the symbolic form identity, which is rooted in recognizing that values are equivalent (e.g., 0 = 0) (Sherin, 2001). Similarly, for students that selected Point E, we can frame this as the graphical form intersection means same, in which students attend to the intersection and assign equality. Although intersection means same has not yet been framed as a graphical form, further evidence that it reflects a generalizable cognitive resource can be found in Elby's (2000) analysis of physics students’ problem solving, noting students’ preferential focus on the intersection. Moreover, this can also be seen in work by Madsen et al. (2012), in which eye-tracking indicated the intersection was a salient feature attended to by the students when prompted with the physics question in Fig. 4. Given that students in physics and chemistry cued into the same surface feature when answering different prompts, we posit this further supports the case for making predictions within the fine-grained constructivist perspective that emphasize the role of salient contextual features. Importantly, the graphical forms framework provides the language to discuss and characterize the resources students used in response to the prompt, but simply categorizing students’ reasoning is not enough. The key is to use this information to provide insight regarding the ways in which the prompt (and instruction more broadly) can be modified to better support the activation of the desired resources. Among the resources discussed above, we posit these knowledge elements are productive and useful across a variety of contexts and can be leveraged, but students may need more support recognizing when to utilize them. Part of the problem is that the axes labels are less prominent for students than other features, a trend further discussed in the next section; thus, a productive direction forward could be to provide additional scaffolding added to the prompt that redirects students’ attention in order to activate existing productive resources (e.g., steepness as rate).

Misconceptions constructivist interpretation. Across the sample, most of the students (76%) indicated the reaction was first order, with Drake's response being representative of a typical answer:

Drake: “Reaction 1 is a first order reaction. It has a non-zero linear slope which means it is constantly making product at the same rate.”

Notably, student responses such as Drake's were nearly correct; in most cases having the correct reasoning, but not the correct initial claim (simply replacing “first” with “zero” would reflect a target student response with scientifically normative reasoning). Based on previous research, students tend to have difficulty describing zero-order reactions, specifically, what is happening at the particulate-level (Bain et al., 2018). This could be due to students likely being provided more opportunities to reason about other reaction types (first order, second order) without being prompted to consider the underlying mechanism behind zero-order reactions. Nevertheless, as discussed by Bain and colleagues (2018), students should be provided a variety of contexts related to different reaction orders in order to develop a more holistic and sophisticated conception of reaction order. That said, instruction should involve working through examples involving zero-order processes and even fractional reaction orders to discuss their implications for the phenomena modeled and the empirical basis of reaction order represented in the rate law.

Fine-grained constructivist interpretation. As with the previous prompt, we can classify students’ reasoning using graphical forms, with students often using straight means constant (recognizing that something is constant because of the straight line); however, students subsequently attributed a constant rate to a first-order reaction. Arguably, the most prominent feature of the graph is the straight line, with students potentially not focusing on the axes. Evidence that the shapes associated with reaction order were more prominent and the axes were more of an afterthought is provided in our previous work involving interviews with students from a biochemistry course. In Rodriguez et al. (2019b) when students were asked to draw graphs related to reaction order the students tended to focus on drawing specific graphical shapes without labeling the axes, with some of the students labeling the axes after being prompted and others unsure what the axes should be. Revisiting the previously discussed study by Bain et al. (2018), students’ reasoning involving an over-emphasis on the simple linear shape may have been potentially guided by heuristic reasoning related to p-prims (diSessa, 1993; Cooper et al., 2013) or intuitive rules (Eshach, 2014), with students associating lower reaction-orders with a more basic or straightforward process. Over-emphasis on the shape was reflected in responses such as Steve's discussion:

Steve: “The reaction order of Reaction 1 is a first order. This can be concluded because the rate is constant and linear. A zero order reaction would have a horizontal line and second order has a exponential curve.”

Based on our collection of course artifacts and classroom observations from our previous study, students are likely thinking about a graph with different axes (Rodriguez et al., 2019b). Student responses such as Steve's were more explicit in terms of the reaction order the students assigned to specific shapes, which clarifies students were likely thinking about the shapes associated with rate vs. concentration graphs, as opposed to concentration vs. time graphs. As shown in Fig. 7, Steve's discussion (and other students that stated Reaction 1 was first order) makes sense if we consider an alternative way to model the data. That said, it is important to note that the students had productive resources for reasoning about reaction rate, including recognizing the constant rate. Indeed, there were only small differences when comparing the responses of students such as Drake and Steve with students that correctly identified the graph as zero order. As shown below, like Drake and Steve, Spencer noted that the rate was constant (graphical form straight means constant), but he made an explicit connection to the axes:

Fig. 7 Rate vs. concentration graphs, likely the graphs students were thinking about when responding to Prompt 1, Item (b); adapted from (Rodriguez et al., 2019b). |

Spencer: “Reaction one is zero order because the velocity would be at a consistent value due to the linear graph. [Product] increases the same amount per unit of time. Product/time would always be constant.”

One of the affordances of the fine-grained constructivist perspective is that we can see the ways in which students’ ideas are productive and can serve as a transition toward expert reasoning. As with the first item in Prompt 1, students such as Drake and Steve are bringing in useful ideas to reason about the prompt, with the problem being connecting these ideas to other relevant ideas and features in the graph. In both Prompt 1 items, the issue is focusing too much on salient features and not enough on the implications of the axes. In order to support students, instruction should draw attention to features such as the axes, helping students to view the axis as a key feature of the graph and how changing the axes changes the shape because of the relationship between the variables.

Misconceptions constructivist interpretation. As summarized in Fig. 9, most of the graphs that students drew were linear for Experiment A (n = 38) and Experiment B (n = 46) in Item (a). In the case of Item (b), n = 26 students labeled the graph they drew as V_{0} and n = 8 students labeled V_{0} as a single point they drew on the graph, with the remainder of students not labelling their graph. Although the large number of linear plots was the primary trend observed, there was notable variation among the different types of linear plots drawn (positive vs. negative slope, zero vs. non-zero slope). More information would be needed to better understand students’ rationales for the specific shape they drew, but one way of interpreting these responses is that students drew a magnified view of the Michaelis–Menten plot, focusing on a literal subsection or region of the graph (Fig. 10). This could reflect a larger misconception related to the nature of graphs or how Michaelis–Menten graphs are constructed, which builds on students’ previous challenges with graphs and non-normative interpretations of graphical representations, such as conflating slope and height or viewing a graph as a picture that mirrors the process of interest (McDermott et al., 1987; Beichner, 1994). In terms of students’ responses to Item (b), for students to correctly label V_{0}, they first needed to have drawn a curve, thus, it serves to reason that few students would draw what was expected for V_{0}, since Item (a) and Item (b) build on one another.

Fig. 9 Summary of students’ responses to Prompt 2, Item (a). The values indicate how many students drew each general shape in response to the item. Note that not all students in this sample provided an answer for this item. See Fig. 8 for expected answer. |

Fine-grained constructivist interpretation. Drawing the expected graph for Item (a) requires two primary features students need to attend to: the general shape and the relative steepness of the graph. From a fine-grained constructivist perspective, it may not be that students were focusing on a subsection of the Michaelis–Menten graph, but rather that relative steepness was the most salient feature for the graph they drew. It is worth noting that some information is lost when we simply compare all the students’ responses for Experiment A or Experiment B. If we shift the focus to each student's drawing of Experiment A in comparison to how they drew Experiment B—ignoring that most graphs drawn by students were linear—we see that n = 11 students drew the line for Experiment B as having a steeper slope than the line drawn for Experiment A, which would be partially correct, especially if you only focus on the portion of graph that is relevant for determining V_{0}. Moreover, this is relevant because some of the students (n = 17) indicated in Item (b) that V_{0} was rate and, thus, V_{0} (slope for a [product] vs. time graph) describes the entire line. This is illustrated in Marissa's reasoning in Fig. 11, in which she operationalized rate as slope, another instance of students using the graphical form steepness as rate. This type of reasoning contrasts with other students (n = 8), such as Francine, that labeled V_{0} on the Experiment A or Experiment B graph as a single data point, in some cases this involved labelling the origin (the “initial” value). Notably, students conceptualizing “v-nought” as a point is correct in other contexts such as the study of motion in physics (kinematics), where “initial velocity” has a different meaning; v_{0} is the intitial velocity (y-intercept) in the equation used to describe motion v = v_{0} + at. Thus, based on the presentation of the content, students may be drawing on resources from other contexts to inform the inferences made. Recognizing that the current presentation of the content may be activating less productive resources is important, because it suggests directions for moving forward. For example, it may be useful to label the y-axis of a Michealis–Menten graph as rate instead of V_{0}.

On the other hand, if we assume a context-specific and manifold perspective of knowledge, subsequent analysis naturally raises questions regarding understanding how context influences emergence of ideas as well as the organization of ideas within a manifold structure. To this end, we focused on the features students attended to as they drew inferences about graphs related to reaction rate. Analysis indicated students utilized intuitive mathematical resources to interpret the [product] vs. time graph provided in Prompt 1 including: steepness as rate, intersection means same, and identity. Moreover, students also used steepness as rate when reasoning about Prompt 2. We argue that these cognitive resources are broadly useful for reasoning across contexts; however, issues arise when perceptual cuing results in the activation of less productive resources for a specific context (e.g., intersection means same). Prior research related to undergraduate mathematics education indicates students may view graphs as objects, to which ideas are assigned (Moore and Thompson, 2015). Although viewing the graph as an object and assigning ideas may sound analogous to graphical forms, the distinction is related to the nature of ideas assigned. Graphical forms involve assigning mathematical ideas to patterns in a graph, whereas viewing the graph as an object may involve assigning non-mathematical ideas, such as viewing a sigmoidal shape as an indicator that a titration occurred (even though the axes are concentration vs. time) (Rodriguez et al., 2019c). In the current dataset we noted instances in which students simply associated ideas with objects, such as when students tended to associate linearity with first order, reflecting an over-emphasis on surface features of the graphical representation. These results provide evidence in support of the generalizability of the results from our previously published small-scale study involving interviews with students, which indicated students tended to focus on the surface features of enzyme kinetics graphs and need more support unpacking how the Michaelis–Menten plot is constructed (Rodriguez and Towns, 2020). Based on these results, we suggest changes to instruction that consider students’ reasoning by focusing on the potential role the prompt plays in activating specific resources. This is discussed in more detail in the next section.

In contrast, the focus is shifted from the students’ conceptualization to the instructor's framing of the task within fine-grained constructivism as we focus on the role of perceptual cuing due to presentation of content. As discussed previously, changes to the prompt to help students focus on the importance of the axes would be useful for both items in Prompt 1 to activate relevant resources. Thus, instructors should leverage this information and provide opportunities for students to utilize productive resources with scaffolding. As an example, taking into account the features students focused on, we suggest specific changes to the prompt, such as adding a new initial item (before students select a point) that prompts them to begin thinking about the graphical determination of rate. This could be done by including a question that focuses on the definition of rate or relevant units to activate more productive resources such as steepness as rate. We have previously documented students’ tendency to use the graphical form steepness as rate across student samples and contexts—including two universities in the United States and one university in Sweden (Rodriguez et al., 2018, 2019b, 2019c, 2020a, 2020b)—suggesting a phenomenological basis and relatively high saliency. Thus, we posit that reminding students about rate within the prompt could support students in activating relevant resources. As another example, we noted students may inappropriately apply ideas such as intersection means same but recognizing this type of non-normative reasoning in a large-lecture classroom may be challenging. That said, one approach would be to employ collaborative student-centered learning, which provides opportunities for students to make their reasoning explicit (Becker and Towns, 2012), in addition to improving student learning outcomes across multiple dimensions (Freeman et al., 2014; Theobald et al., 2020). Additionally, one modification to subsequent versions of the prompt could be to use more precise language that specifies students should select a single point. We previously mentioned that Prompt 1 was adapted from a physics study, which is worth mentioning because in its original form the prompt was presented as a multiple-choice item, thus, students were forced to select a single response (Madsen et al., 2012). That said, given our version of the prompt was a free-response question, variation could be reduced by modifying the language for clarity.

Lastly, for Prompt 2, we noted students framing V_{0} as a single point, which may be the result of students incorporating ideas from other science courses. Interestingly, in our previous interviews related to enzyme kinetics, one of the students stated the y-axis of the Michaelis–Menten plot had the units of meters per second (an explicit reference to physics) and subsequently used this as part of her reasoning in interpreting the graph (Rodriguez et al., 2019d). This highlights the previously discussed importance of context and presentation, where the use of V_{0} may result in students potentially thinking about physics ideas. Consequently, we could predict students would be less likely to conceptualize V_{0} as a point and more likely to recognize it is related to slope if the y-axis were labled as rate instead of V_{0} (this is a claim we are particularly comfortable making given students’ demonstrated ability with regard to framing relative steepness as rate).

Moving forward, we would like to direct readers to one of the key assumptions that informed this work: depending on the theoretical commitments, frameworks influence the narrative of a research study (Abraham, 2008). As stated previously, misconceptions constructivism and fine-grained constructivism can be conceptualized as different models used to describe the same phenomena related to knowledge, reasoning, and learning. As chemists, we can appreciate both the use of models to describe phenomena that is not readily observable as well as the presence of multiple models to describe the same process (Taber, 2010). Arguably, evaluation of the utility of models related to students’ reasoning is subject to the same criteria used for scientific models (Passmore et al., 2016), that is, the model must be consistent with data and provide explanatory and predictive power. Stated differently, Elby (2000) emphasized that the distinction between the two frameworks moves beyond word choice (e.g., resources vs. concepts; unproductive resource vs. misconception, etc.):

“… the different cognitive structures posited by the two flavors of constructivism are not empty theoretical baggage; they lead to empirical differences … misconceptions constructivism and fine-grained constructivism, when taken seriously, do not disagree only about word choice, or about attitudes toward students, or about cognitive structures. They make different sets of predictions about students’ interpretations of representations,” (emphasis added, p. 500).

The fine-grained constructivist view allows us draw conclusions and make predictions about how cognitive units may be activated based on perceptual features—which was illustrated using our data. Based on the work reported herein and elsewhere, we emphasize the strong phenomenological basis of mathematical resources such as symbolic and graphical forms (Sherin, 2001; Rodriguez et al., 2019a). Outside of chemistry, in contexts such as physics and mathematics students learn fine-grained mathematical ideas such as the idea that the relative steepness of a graph provides information about rate, and it is likely these ideas are reinforced throughout their education. Thus, we can predict and expect that students will utilize these ideas across contexts based on the presence of specific graphical patterns. In contrast, part of the challenge with cataloging misconceptions is that they may be idiosyncratic, but even if a case can be built for their generalizability in a population, there is still little explanation as to why students may hold these ideas which makes it challenging to predict how students may use these ideas in different contexts.

Given chemistry education research is inherently an interdisciplinary field that has historically borrowed from other fields and traditions, our central claims build on the rich discussions across education research communities (diSessa, 1993; Elby, 2000; Southerland et al., 2001; Hammer et al., 2005; Gouvea and Simon, 2018; Lira and Gardner, 2020). As an implication for this work, we hope to continue a dialogue across the education community about the critical role of theoretical frameworks in discipline-based education research and the ways in which theoretical commitments influence the nature of the findings and implications.

Code | Description |
---|---|

Item (a) | |

Point A selected | Student selected Point A |

Point B selected | Student selected Point B |

Point C selected | Student selected Point C |

Point E selected | Student selected Point E |

Steepness as rate | Student describes relative steepness/slope as providing information about rate |

Intersection means same | Student describes that values are equal or the same because they intersect; does not include student discussions of the origin (see “Identity”) |

Identity | Student states that values are zero and are, thus, the same; often coded as a result of student selecting Point A for Item (a); may be coded with “Steepness as Rate” if students’ reasoning references slope/steepness |

Item (b) | |

Reaction 1 is first order | Student states Reaction 1 is a first-order reaction |

Reaction 1 is zero order | Student states Reaction 1 is a zero-order reaction |

Incomplete student response | Student did not state an order for Reaction 1 in Item (b) |

Straight means constant | Student associates a straight line with something being constant; students must recognize that something (e.g., rate, slope, product formation, etc.) is constant or “steady”, it is not enough to simply state that the graph is linear |

Code | Description |
---|---|

Item (a) | |

Point A or Point B Graph is Linear, Positive Slope | Student drew a straight line with a positive slope (increasing over time) |

Point A or Point B Graph is Linear, Negative Slope | Student drew a straight line with a positive slope (decreasing over time) |

Point A or Point B Graph is Linear, Horizontal | Student drew a horizontal straight line |

Point A or Point B Graph is Non-Linear | Student drew a curved graph |

Item (b) | |

V-naught is the Initial Data Point | Student labels the initial value (point) as V_{0} |

V-naught is a Data Point (Not Initial) | Student labels a data point (not initial value) as V_{0} |

V-naught is the Graph | Student labels the graph drawn as V_{0}; in some cases, it is clear students recognized that V_{0} is supposed to be the slope of the plot, but if they drew a linear graph than V_{0} is essentially the whole graph |

No V-naught Label | Student did not label V_{0} |

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