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Education Research and Practice

’ always produces dioxide and ’: A Discussion of University Chemistry Student Use of Rules in Place of Principles

Journal: Chemistry Education Research and Practice

Manuscript ID: RP-ART-04-2014-000089.R2

Article Type:

Date Submitted by the Author: 31-Jul-2014

Complete List of Authors: Robertson, Amy; Seattle Pacific University, Physics Shaffer, Peter; University of Washington, Physics

Page 1 of 31 Chemistry Education Research and Practice

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 “Combustion always produces and water”: A discussion of university 20 21 chemistry student use of rules in place of principles 22 † 23 Amy D. Robertson* and Peter S. Shaffer 24 Department of Physics, University of Washington, Seattle, WA, 98195 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 This work was supported by the National Science Foundation under Grants DUE-0096511, 44 45 DUE-0618185, and DGE-0718124. 46 47 48 49 * Corresponding author; Mailing address: Seattle Pacific University Department of Physics, 50 3307 Third Ave W, Suite 307, Seattle, WA, 98119-1997; Telephone number: 206-386-7347; 51 52 Email: [email protected] 53 † 54 Mailing address: University of Washington Department of Physics, Box 351560, Seattle, 55 56 WA, 98195-1560; Telephone number: 206-543-6705; Email: [email protected] 57 58 59 60 1 Chemistry Education Research and Practice Page 2 of 31

1 2 3 Abstract. On the basis of responses to written questions administered to more than one 4 5 thousand introductory chemistry students, we claim that students often rotely apply 6 7 memorized combustion rules instead of reasoning based on explanatory models for what 8 9 happens at the molecular level during chemical reactions. In particular, many students argue 10 that combustion produces carbon dioxide and/or water, even when the reactants do not 11 12 contain or carbon, an answer that is inconsistent with the principle of 13 14 conservation. Our study also corroborates the finding that students frequently say that 15 16 is “necessary for” or “used in” combustion reactions without connecting this 17 reasoning to conservation principles, suggesting that this likewise may be a rotely applied, 18 19 memorized rule. 20 21 22 23 Keywords: chemical reactions, chemistry education, alternative conceptions 24 25 26 I. Introduction 27 28 The principle of conservation of and the concept of are two of 29 the most fundamental ideas to the study of science and, in particular, to chemistry. Most of 30 31 what is taught in university-level introductory chemistry courses – such as , 32 33 aqueous , , and bases, and the thermodynamics of 34 35 formation – relies on an understanding of both. In fact, macroscopic chemical change – in 36 which reactant substances are transformed into product substances – is often explained 37 38 using a molecular model in which the constituent are conserved and the new 39 40 substances contain the same (albeit rearranged) atoms as the old ones did. 41 42 The Physics Education Group at the University of Washington (UW) conducted a 43 multi-year investigation of university student reasoning about the of matter 44 45 that emphasized chemical change. On the basis of our research, conducted in large- 46 47 enrollment introductory chemistry courses at the UW, we claim that 48 49 Students often rotely apply memorized combustion rules, instead of reasoning based on explanatory 50 51 models for what happens at the molecular level during chemical reactions. 52 53 Prevalent patterns in student reasoning that emerge from students’ written responses to 54 questions about combustion serve as our evidence for this claim. Specifically, students argue 55 56 that ‘combustion always produces carbon dioxide and water’ and that ‘oxygen is necessary 57 58 59 60 2 Page 3 of 31 Chemistry Education Research and Practice

1 2 3 for or used in combustion,’ even in situations in which the former is inconsistent with the 4 5 principle of atom conservation. 6 7 Our research adds to existing literature on student understanding of combustion 8 9 reactions. 10 11 Literature on student understanding of combustion consistently reports that students 12 13 often rely on a descriptive – rather than an explanatory – characterization of burning. In 14 other words, many students describe burning prescriptively – stating what they think happens 15 16 and focusing on perceptible features of combustion, without articulating why . For example, 17 18 students often say that some substances ( e.g., , cardboard, and paper) and others 19 20 melt or evaporate ( e.g., metals, wax, and water) [1] (Boo, 1995; BouJaoude, 1991; Çalık & 21 Alipa şa, 2005; Johnson, 2000, 2002; Lofgren & Hellden, 2008; Meheut, Saltiel, & Tiberghien, 22 23 1985; Pfundt, 1982; R. Watson, Prieto, & Dillon, 1995). In addition, students often say that 24 25 oxygen is necessary for burning and that water and/or carbon dioxide is produced, but they 26 27 do not specifically connect either to the presence of carbon and/or hydrogen in the 28 reactants (BouJaoude, 1991; Driver, 1985; Lofgren & Hellden, 2009; Meheut et al., 1985; 29 30 Ross, 1991; Schollum & Happs, 1982; J. R. Watson, Prieto, & Dillon, 1997; R. Watson et al., 31 32 1995). 33 34 Other studies articulate students’ explanations for specific aspects of combustion. For 35 example, the literature offers three common (incorrect) student explanations for the 36 37 production of water during combustion: (1) the water condenses from the or 38 39 environment (Johnson, 2002; Ross, 1991); (2) the water comes from the flame (Meheut et al., 40 1985; Ross, 1991); and (3) the water is displaced from the wood (Driver, 1985; R. Watson et 41 42 al., 1995). 43 44 In addition, the literature repeatedly demonstrates that students answer questions in 45 46 ways that are inconsistent with the conservation of matter. (Many such studies specifically 47 focus on burning (Andersson, 1984, 1990; Barker & Millar, 1999; BouJaoude, 1991; Driver, 48 49 1985; Driver et al., 1984).) Research on conservation of matter at the molecular level 50 51 suggests that students often do not associate meanings with chemical symbols in 52 53 stoichiometric equations (Ben-Zvi, Eylon, & Silberstein, July 1987; Yarroch, 1985) and so do 54 not conserve numbers of atoms ( e.g., they interchange subscripts and coefficients) (Kruse & 55 56 Roehrig, 2005; Mulford & Robinson, 2002; Sanger, 2005). 57 58 59 60 3 Chemistry Education Research and Practice Page 4 of 31

1 2 3 Whereas the majority of the existing studies on student understanding of 4 5 combustion/burning focus on children’s reasoning, our study examines adult reasoning. We 6 7 find that like the -aged pupils described in previous research, adults in our university 8 9 chemistry courses often state that oxygen is used by or necessary for combustion, 10 corroborating and extending the literature . We also find that university students use a 11 12 specific combustion rule – that combustion always produces carbon dioxide and/or water – 13 14 that, to our knowledge, is not reported elsewhere, adding to the extant literature. 15 16 Our research supplements existing literature on student use of heuristics and rules- 17 18 based reasoning in chemistry. 19 20 A trend in chemistry education research is to explain patterns of incorrect 21 reasoning (e.g., misconceptions) on the basis of more general models of student thinking. 22 23 For example, researchers have proposed heuristics (Christian & Talanquer, 2012; M. M. 24 25 Cooper, Corley, & Underwood, 2013; Maeyer & Talanquer, 2010; McClary & Talanquer, 26 27 2011; Talanquer, 2006) and rules-based reasoning (Christian & Talanquer, 2012; Kraft, 28 Strickland, & Bhattacharyya, 2010) as possible explanations for student use of rules (applied 29 30 appropriately and inappropriately) in chemistry. “Heuristics” are “simple reasoning 31 32 processes that reduce the effort associated with a task” (McClary & Talanquer, 2011). 33 Heuristics research is often motivated by cognitive models of the mind, in which the level or 34 35 amount of processing is constrained; in such a model, will often simplify or take 36 37 short cuts, especially in situations in which time or knowledge is limited (Christian & 38 39 Talanquer, 2012; M. M. Cooper et al., 2013; Maeyer & Talanquer, 2010; McClary & 40 Talanquer, 2011; Talanquer, 2006). Although heuristics have an appropriate range of 41 42 application, they sometimes “ students astray” (Maeyer & Talanquer, 2010). For 43 44 example, students may overgeneralize laws and principles that, in reality, have a limited range 45 46 of application, asserting that the “entropy in any process always increases” or that “like 47 dissolves like” (Talanquer, 2006). 48 49 Our research, although producing results consistent with the foci of research on 50 51 heuristics and rules-based reasoning, has a fundamentally different aim. Rather than seeking 52 53 to explain incorrect patterns in student reasoning, we seek to discern what those patterns are, 54 to inform the development of curricular materials that elicit, confront, and resolve specific 55 56 student difficulties. Our research group, in general, adopts the perspective of “instructor[s] 57 58 whose primary motivation for research is to better understand what students find difficult 59 60 4 Page 5 of 31 Chemistry Education Research and Practice

1 2 3 about physics [science] and to use this information to help make instruction more effective” 4 5 (L. McDermott, 1990). Our focus on student difficulties – or patterns in student reasoning 6 7 that do not align with the canon – reflects our “practical, instruction-oriented approach”: 8 9 identifying a difficulty “provides a target for instruction” (Heron, 2004a). In particular, we 10 focus on those incorrect reasoning patterns that are prevalent and/or fundamental to 11 12 conceptual understanding. We have found that many such patterns emerge consistently 13 14 across instructional contexts, regardless of other variables such as instructor or amount of 15 16 prior instruction, and so represent patterns in reasoning that are both common and persistent 17 (Heron, 2004b, 2013). We expect these incorrect reasoning patterns, in particular, to be 18 19 useful for instructors and curriculum developers, who can use our research to anticipate 20 21 where students might struggle and to plan instruction that seeks to address common 22 23 misunderstandings [2]. In particular, that these patterns are common – i.e., that they account 24 for the reasoning of an appreciable fraction of students in multiple different instructional 25 26 contexts – suggests some level of predictability; instructors of similar courses can plan 27 28 instruction that addresses or builds on these ideas and expect this instruction to be - 29 aimed. The specific (sometimes incorrect) rules that students use in the context of 30 31 combustion reported in this paper can serve as a guide to instructors and curriculum 32 33 developers. 34 35 II. Research Design and Methodology 36 This specific study was motivated by an initial, informal observation that a small 37 38 number of students used a specific combustion rule in response to the powder-on-a-balance 39 40 question (Figure 1), which required students to use the principle of conservation of [3]. 41 42 Although the reactant was not given (and thus could have been a non-), 5% of 43 the students who answered this question explicitly stated that the products were carbon 44 45 dioxide and/or water. For example: 46 47 [Insert Figure 1 about here.] 48 49 “[Equal to 100 g:] Combustion involves CO 2 [and] H 2O in the form of being released 50 from the substance being burned. Since these will be in the glass container which is on the 51 52 balance their mass will be accounted for so no mass is lost.” 53 “[Equal to 100 g:] When ignited the powder will be converted into CO and H O but all of 54 2 2 55 the new will still be on the scale, and matter is neither created nor destroyed so it will 56 weigh the same.” 57 58 59 60 5 Chemistry Education Research and Practice Page 6 of 31

1 2 3 “[Less than 100 g:] If the[re] is a reaction where things are ignited it indicates that the powder 4 5 must have released CO 2. This means the scale would register less than 100 g since some of the 6 substance is gas.” 7 8 In these cases, students seemed to be applying a rule that combustion always produces 9 carbon dioxide and/or water: they did not connect the production of CO and H O to 10 2 2 11 hydrocarbon combustion (i.e., a reactant that contains the requisite atoms of the products: 12 13 hydrogen, carbon, and oxygen). The use of such a rule in non-hydrocarbon contexts would 14 15 violate the fundamental principle of conservation of atoms, and we wondered whether 16 students would use similar rules in other contexts. This prompted the development of a 17 18 sequence of open-ended, written conceptual questions that ultimately framed this research 19 20 study. 21 Question design. Each question was designed to address a specific research question. 22 23 First, we developed the question [4] (Figure 2) to determine whether the original 24 25 ‘combustion rule’ that we discerned in a small number of student responses to the powder-on- 26 27 a-balance question was (a) prevalent and (b) used in a non-hydrocarbon combustion reaction 28 (i.e., do students use the rule when the specified reactants do not contain carbon or 29 30 hydrogen?). After administering the question and confirming that the use of the 31 32 combustion rule was prevalent and inappropriate, we developed three additional questions: 33 34 the symbolic beryllium oxide question, the unknown chemical question, and the burning candle question 35 (Figures 3, 4 [5], and 5, respectively) . The first two were developed to address research 36 37 questions about reproducibility: do students use the rule that ‘carbon dioxide and/or water 38 39 are always produced in combustion reactions’ (1) in symbolic contexts, where the 40 41 representation signifies the atoms themselves, and/or (2) when the question is asked in 42 reverse, such that the reactants are given to students rather than the products? In the 43 44 unknown chemical context, for example, we expected that students who reason that carbon 45 46 dioxide and water are the products of every combustion reaction may choose every reactant 47 burning candle question 48 given, regardless of its chemical makeup. The was developed to 49 investigate the extent to which students would use atom conservation to make sense of the 50 51 production of carbon dioxide and water during a hydrocarbon combustion (in which the 52 53 reactants do contain carbon, hydrogen, and oxygen atoms). Figure 6 summarizes our 54 research design. Note that although “combustion” is a general term that is used to describe 55 56 an exothermic between a and an oxidant, we chose to use the word 57 58 59 60 6 Page 7 of 31 Chemistry Education Research and Practice

1 2 3 “burned” in each of our questions to avoid confusion between our contexts and 4 5 hydrocarbon combustion. Chemistry faculty at the University of Washington reviewed each 6 7 question and deemed it appropriate for use on written surveys given in their courses – which 8 9 covered the topics of stoichiometery, chemical reactions, and basic conservation principles – 10 establishing the face validity of the questions. 11 12 [Insert Figures 2-6 about here.] 13 14 Correct answers to all four questions rely on appropriate use of the principle of 15 16 conservation of atoms, which requires that the products in each case be comprised of the 17 atoms of the reactants . The correct answer to the beryllium oxide question is (c), beryllium 18 19 oxide, which contains the atoms of the reactant powder and the oxidizing agent – oxygen – 20 21 from the air, and the correct answer to the symbolic beryllium oxide question is also (c), the 22 → 23 balanced chemical equation 2Be + O 2 2BeO. The correct answers to the unknown chemical 24 question are and wood: since the products of the reaction are carbon dioxide and 25 26 water (made up of carbon, hydrogen, and oxygen atoms), the reactants must also contain 27 28 carbon, hydrogen, and oxygen. Since oxygen is present in the air, the unknown chemical 29 30 must contain carbon and hydrogen. This is true only of butane and wood. When a candle 31 burns, as in the burning candle question , bonds between the carbon and the hydrogen in the 32 33 paraffin wax break, and bonds form between carbon and oxygen (to make carbon dioxide) 34 35 and between hydrogen and oxygen (to make water). Thus, the correct answer to this 36 37 question is that the amount of oxygen in the container decreases, while the amounts of 38 carbon dioxide and water increase. 39 40 Sample. Participants in this study were students in large (1) introductory and (2) 41 42 advanced introductory chemistry sequences for physical and science majors at the UW, a 43 44 large, public university in the Pacific Northwest. Students in the advanced introductory 45 chemistry course at the UW are required to have completed at least one quarter of calculus 46 47 and the equivalent of a one-year high school chemistry course. The Chemistry Department 48 49 at the UW estimates that these students constitute the top 10% of all students taking 50 introductory chemistry. Both courses are three-quarter sequences that typically cover topics 51 52 such as: atomic structure, stoichiometry, solutions and molarity, , equilibrium, acids and 53 54 bases, chemical thermodynamics, , bonding, kinetics, and periodic trends. 55 56 57 58 59 60 7 Chemistry Education Research and Practice Page 8 of 31

1 2 3 Course demographics were not made available to us, so we cannot claim that our 4 5 sample was representative. However, the questions in this study were included on course 6 7 assignments and quizzes, and nearly all students in each course responded. 8 9 Data collection. Together, the four questions described above were administered to 1173 10 students in five introductory and advanced introductory chemistry courses (Courses A-E) at 11 12 the University of Washington. (See Table I.) In some cases, the questions were administered 13 14 as online surveys; students were given a survey link and responded to questions outside of 15 16 class. Other questions were given on written quizzes in mandatory recitation sections staffed 17 by teaching assistants. The types of reasoning given by students in response to the written 18 19 and online questions were similar and thus are not distinguished in the text. Each question 20 21 was given after all relevant lecture and textbook instruction on stoichiometry and chemical 22 23 change. 24 [Insert Table I about here.] 25 26 This study was part of an investigation with Institutional Review Board exempt status. 27 28 The questions were administered in the natural course of classroom activity. Students were 29 informed of the purposes of the study when asked to complete online surveys or written 30 31 quizzes. Their responses were stored on a secure server. Results reported in presentations 32 33 or publications are never associated with an individual’s name or identity. 34 35 Data analysis. We developed an emergent coding scheme (Krippendorff, 2013) on the 36 basis of students’ written responses to the beryllium oxide question described above. Categories 37 38 in the scheme described students’ reasons for giving a particular response, e.g., the products 39 40 of a reaction in which beryllium is burned in air are carbon dioxide and water, because 41 42 combustion always produces carbon dioxide and water. We corroborated our original categories by 43 asking the symbolic beryllium oxide, unknown chemical, and burning candle questions and discerning 44 45 whether the same categories accounted for patterns in student responses to those questions. 46 47 We modified and added to our original coding scheme on the basis of this additional data, 48 49 and returned to the initial data to see whether new codes bore out. Individual student 50 responses were coded (or re-coded) by the first author using our final scheme. A single 51 52 response received more than one code in cases where student reasoning instantiated more 53 54 than one category. 55 56 As in many other contexts, student reasoning in response to the questions we posed 57 tended to fall into a small number of interpretive categories (Brown & Hammer, 2008; 58 59 60 8 Page 9 of 31 Chemistry Education Research and Practice

1 2 3 Heron, 2004a). The consistent recurrence of these categories (Cook, 2002) suggests to us 4 5 that they represent common misunderstandings about combustion. We report the prevalent, 6 7 cross-contextual patterns in student reasoning in the section entitled, “Student Use of 8 9 Combustion Rules.” 10 Overview of results. Tables II through V summarize student on the four 11 12 questions. We list the percentages of students who answered each question correctly and 13 14 incorrectly as well as those who offered explicit conservation reasoning to accompany their 15 16 responses. We interpreted a student response as “with explicit conservation reasoning” when 17 they explicitly articulated (1) that the products must be comprised of the atoms of the 18 19 reactants (or vice versa) or (2) that the equation must be balanced. Examples of student 20 21 responses coded in this way are given in Appendix A. 22 23 [Insert Tables II-V about here.] 24 III. Student Use of Combustion Rules 25 26 In general, the resounding answer to our research design questions was yes: student use 27 28 of combustion rules was prevalent, reproducible across contexts, and inappropriate ( i.e., used 29 to explain non-hydrocarbon combustion). The two most common rules in use were 30 31 “combustion produces carbon dioxide and/or water” and “oxygen is used by/necessary 32 33 for/released during combustion.” In this section, we report, illustrate, and begin to explain 34 35 student use of these rules. 36 Between 4% and 7% of student responses to the beryllium oxide question (5% in Course 37 38 A, 7% in Course B, and 4% in Course C) , 4% of student responses to the unknown chemical 39 40 question, and 39% of student responses to the burning candle question represent the use of the 41 42 rule that oxygen is “used by” or “necessary for” combustion and thus corroborate extensive 43 previous research (Andersson, 1990; BouJaoude, 1991; Driver, 1985; Lofgren & Hellden, 44 45 2009; Meheut et al., 1985; Ross, 1991; Schollum & Happs, 1982; J. R. Watson et al., 1997; R. 46 47 Watson et al., 1995). Because this result has been so widely reported in the literature, we 48 49 limit detailed discussion in this paper to the use of the rule “combustion always produces 50 carbon dioxide and/or water.” 51 52 a. Use of rule, “Combustion always produces carbon dioxide and/or 53 54 water.” 55 56 Between 9% and 44% of the students in Courses A through E answered that carbon 57 dioxide and/or water were the products of the burning reaction in question and justified 58 59 60 9 Chemistry Education Research and Practice Page 10 of 31

1 2 3 their answers using statements like, “Combustion produces carbon dioxide and/or water” 4 5 (see Table VI). That these statements represent the application of a rule – rather than a 6 7 principle – is particularly evident in answers that violate atom conservation (between 2 and 8 9 10% of student responses; see Table VI). For example, in the beryllium oxide and symbolic 10 beryllium oxide questions, students often excluded beryllium from the products or chemical 11 12 equations they chose: 13 14 15 “[Carbon dioxide and water:] In all combustion problems H 2O and CO 2 are produced.” (original 16 beryllium oxide question) 17 18 “[Carbon dioxide and :] When anything combusts it gives off carbon dioxide and water 19 vapor.” (original beryllium oxide question) 20 → 21 “[Be + 2O 2 CO 2 + H 2O:] combustion equation.” (symbolic beryllium oxide question) 22 → 23 “[Be + 2O 2 CO 2 + H 2O:] combustion equation; always yields CO 2 [and] H 2O.” (symbolic 24 beryllium oxide question) 25 26 Other students used a combustion rule but also included beryllium oxide as a product (see 27 “partially consistent with conservation of atoms” in Table VI for exact percentages). These 28 29 responses are particularly puzzling in their simultaneous conservation and non-conservation 30 31 of atoms. In fact, some of these students explicitly justified their choice of beryllium oxide as 32 33 a possible product by noting the presence of beryllium at the beginning of the experiment. 34 For example: 35 36 37 “[Carbon dioxide, water, and beryllium oxide:] combustion produces carbon dioxide and water, but 38 [I] also assume that beryllium oxide has to be formed because the beryllium can not just go away.” 39 (original beryllium oxide question) 40 41 “[Carbon dioxide and beryllium oxide:]…Since it is Beryllium powder, the product must give off 42 something [with] beryllium, so Beryllium oxide makes sense. Also, since Beryllium powder is 43 burning, it should produce CO 2.” (original beryllium oxide question) 44

45 “Combustion requires O 2 and produces CO 2 and H 2O and Be cannot be unaccounted for. Therefore 46 [2Be + 3O → CO + 2H O + 2BeO] is the right answer.” (symbolic beryllium oxide 47 2 2 2 48 question) 49 Similarly, in the unknown chemical question, several students (6%) chose both hydrocarbon and 50 51 non-hydrocarbon reactants, arguing that all of the reactants were possible since carbon 52 53 dioxide and water are always products of combustion reactions. For example: 54 55 “[, , wood, and butane:] Everything that burns in air produces CO2 and 56 H2O[.]” 57 58 59 60 10 Page 11 of 31 Chemistry Education Research and Practice

1 2 3 “[Magnesium, copper, and butane:] These could be the chemical. Since the known is that it produces 4 5 CO2 and H2O[,] which is the product of combustion. So I’m thinking if any of these chemicals 6 underwent combustion the results would be the two compounds [carbon dioxide and water].” 7 8 Students also applied the combustion rule in the context of hydrocarbon combustion 9 (e.g., in response to the burning candle and unknown chemical questions) . For example, 44% of 10 11 those students answering the burning candle question and 17% of those answering the unknown 12 13 chemical question justified their answers on the basis of a generally-stated rule without explicit 14 15 indication of its consistency with atom conservation. For example: 16 17 “[The amount of O 2 will:] Decrease. As the candle burns, it will consume oxygen from the 18 environment around it. [The amount of CO 2 will:] Increase. This reaction is a combustion reaction, 19 and CO 2 is always a product of a combustion reaction. [The amount of H 2O will:] Increase. This is 20 a combustion reaction, and H O is always a product of a combustion reaction.” (burning candle 21 2 22 context) 23 “[Butane:] Butane when reacted with air is a combustion reaction which forms carbon dioxide and 24 25 water.” (unknown chemical context) 26 “[Butane and wood:] In any combustion situation the products are carbon dioxide, these [two] will 27 28 burn so they will produce carbon dioxide and water[.]” (unknown chemical context) 29 These responses are analogous to those that argue that ‘oxygen is used during combustion’: 30 31 although true, this response offers no indication of the reason this is the case and may in fact 32 33 mask a misunderstanding of why hydrocarbon combustion produces carbon dioxide and 34 35 water. 36 In addition, many students who answered the burning candle question (15% of the total) 37 38 used the rule only in the context of carbon dioxide. That is, they claimed that the amount of 39 40 carbon dioxide in the container increases because it is a product of combustion, and at the 41 42 same time they argued that the amount of water vapor decreases or remains the same. This 43 suggests that some students were not simply neglecting to mention the underlying 44 45 conservation principles (if so, they should have also conserved the hydrogen atoms in the 46 47 wax) but instead were applying a memorized rule that included CO 2 but not H 2O. For 48 49 example: 50 51 “[The amount of oxygen will:] decrease – combustion requires oxygen, and therefore the amount of

52 oxygen will decrease…during the reaction. [The amount of carbon dioxide will:] Increase – CO 2 is 53 usually the product of combustion and will therefore increase as the combustion reaction goes on. [The 54 amount of water vapor will have:] No change – No water was in the container at first to be 55 56 evaporated into vapor.” 57 58 59 60 11 Chemistry Education Research and Practice Page 12 of 31

1 2 3 “The oxygen will decrease; oxygen is used up by the reaction…The CO will increase; reaction 4 2 5 produced more CO 2 by burning…The water vapor remains the same. Water in form is 6 converted to vapor.” 7 8 Table VI provides the percentages of students in each context whose responses 9 demonstrate use of this combustion rule. Note that our purpose in tabulating percentages is 10 11 not to suggest that the numbers themselves are representative or reproducible but to 12 13 demonstrate the relative prevalence of rule use across the contexts we examined. To 14 15 establish the intuitive plausibility of this coding scheme – and the assignment of particular 16 codes to specific student responses by the first author – Appendix A presents additional 17 18 examples of student responses that correspond to the categories (rows) in Table VI. 19 20 [Insert Table VI about here.] 21 b. Proposed sources of combustion rule 22 23 A few recent articles (M. M. Cooper et al., 2013; Melanie M. Cooper, Grove, 24 25 Underwood, & Klymkowsky, 2010) separate students’ chemistry heuristics into 26 27 “instructional” and “personal”. In particular, Cooper, et al., (2010) describe students’ 28 misapplication of the “,” arguing that such “confusions” may be didaskalogenic, or 29 30 instruction-induced, arising from or reinforced by instruction. We hypothesize that the 31 32 combustion rules applied by students in this study may be similarly didaskalogenic, 33 34 particularly in the case of ‘carbon dioxide and/or water are always products of combustion.’ 35 This rule does not seem to be the kind of thing that one develops on the basis of intuition 36 37 and everyday experiences; it makes more sense to us that it is the product of 38 39 overgeneralizations about hydrocarbon combustion, which often serves as the sole example 40 41 of burning reactions in chemistry courses. 42 In addition, a limited number of student responses suggest hypotheses about 43 44 observations or ways of conceptualizing combustion that may support use of combustion 45 46 rules. In particular, between 0 and 4% of the students in Courses A through E did not 47 completely burned 48 choose beryllium oxide as a product and reasoned that the beryllium was . For 49 example: 50 51 52 “[Carbon dioxide and water:] Carbon dioxide and water are both common products of a 53 combustion reaction. It is unlik[e]ly that Beryllium oxide forms as it is stated all the powder 54 completely burns…” (original beryllium oxide question) 55 56 57 58 59 60 12 Page 13 of 31 Chemistry Education Research and Practice

1 2 3 → 4 “[Be + O 2 CO 2:] this is because when the powder has burned off, carbon dioxide is released 5 and the Be substance will be completely cancelled out too since it’s ‘burned off,’ in the reaction, you 6 can also note that the oxygen is balanced.” (symbolic beryllium oxide question) 7 8 In addition, approximately 1% of the students in each of Courses A through E did include 9 beryllium oxide, but indicated that it is present only because the reaction did not go to 10 11 completion. This implies that students might have been thinking that beryllium oxide was 12 13 the ‘left over’ beryllium, and that, had the reaction continued, it, too, would have 14 15 ‘disappeared.’ For example: 16 17 “[Carbon dioxide, water, and beryllium oxide:] because the combustion always result[s in] carbon 18 dioxide and water. In addit[i]on, uncomplete combustion also produce beryllium oxide.” (original 19 beryllium oxide question) 20 21 “[2Be + 3O → CO + 2H O + 2BeO:] The burning of the beryllium is a combustion reaction, 22 2 2 2 23 which means the products will be CO 2 (g) and H 2O (g). Since not all the beryllium will be 24 vaporized, some of it will remain as blackened soot.” (symbolic beryllium oxide question) 25 26 Andersson (1990) describes several models that middle-school-aged pupils use to explain 27 chemical reactions that are consistent with these responses. Two such models are 28 29 ‘disappearance,’ where matter is treated as though it can come into and out of existence in 30 31 chemical reactions, and ‘transmutation,’ where students respond as though one substance is 32 33 (inexplicably) transformed into another. University students in our study likewise apply these 34 models to combustion: burning is a mechanism by which reactants disappear or turn into 35 36 products. 37 38 Some students explicitly attributed the production of carbon dioxide to the flames or 39 . This was especially true in the burning candle context, representing 7% of the students in 40 41 Course B. For example: 42 43 44 “Carbon dioxide will increase because fire produced it. No change [in the amount of water], the 45 candle will neither consume nor produce H 2O.” (burning candle context) 46 47 “There would be an increase in CO 2 because CO 2 is a product of the flame. There would be no 48 change [in the amount of water] because nothing is reacting to form H 2O.” (burning candle 49 context) 50 51 These students may be thinking of the flame or the fire as a reactant (Haidar & Abraham, 52 1991; Hesse III & Anderson, 1992; Lee, Eichinger, Anderson, Berkheimer, & Blakeslee, 53 54 1993), rather than as a combination of heat and (released in the exothermic reaction) 55 56 and gaseous products. 57 58 c. Discussion 59 60 13 Chemistry Education Research and Practice Page 14 of 31

1 2 3 The response patterns described in this section often reflect the inappropriate use of 4 5 rules about what takes place during combustion reactions. An expert might expect these rules 6 7 to flow out of or connect to an understanding of conservation principles: the production of 8 9 CO 2 and H 2O in many combustion reactions is tied to the presence of carbon, hydrogen, 10 and oxygen atoms in the reactant substances. However, it appears instead that these rules in 11 12 some cases displace and in other cases inappropriately supplement the application of the 13 14 principle of conservation of atoms. 15 16 IV. Limitations of Our Study 17 The patterns we report in the previous section arose in multiple contexts and represent 18 19 our interpretations of large percentages of students’ responses – between 9 and 44%, 20 21 depending on the course. For this reason, we believe that the patterns are not solely artifacts 22 23 of individual questions. Rather, we believe that they tell us something more fundamental 24 about the difficulties that students encounter when learning about combustion. 25 26 However, we acknowledge that there are a number of limitations to our analysis. The 27 28 generalizability of our study is limited by our inability to determine the representativeness of 29 our sample. However, this limitation is mitigated by: (1) the recurrence of our results across 30 31 courses and question contexts and (2) our sampling method (including our questions on 32 33 course assignments and quizzes) which meant that large fractions of each course responded 34 35 to our questions. 36 In addition, our data are insufficient to determine on what basis these rules are 37 38 formulated ( e.g., do they emerge from students’ interpretations of lecture instruction in 39 40 chemistry?) or why students might apply them when responding to our questions. We 41 42 speculate that the use of such rules might be plausibly connected both to students’ 43 epistemological stance toward learning science as well as to overgeneralizations of 44 45 demonstrations or examples used in instruction. The former speculation is informed by a 46 47 significant body of research that suggests that students often think of science as a collection 48 49 of facts and formulae and therefore approach the learning of science as the memorization 50 and application of such (Hammer, 1994; May & Etkina, 2002; Redish, Saul, & Steinberg, 51 52 1998; Songer & Linn, 1991). The latter is based on (1) our understanding that the most 53 54 commonly-cited examples and demonstrations of burning in introductory chemistry courses 55 56 involve the combustion of , and on (2) research on student use of heuristics 57 (M. M. Cooper et al., 2013; Maeyer & Talanquer, 2010; McClary & Talanquer, 2011; 58 59 60 14 Page 15 of 31 Chemistry Education Research and Practice

1 2 3 Talanquer, 2006). Together, one might posit that students see the production of carbon 4 5 dioxide and water in combustion as a rule to be memorized and applied in other contexts, 6 7 without seeking to understand the underlying mechanism for their production ( i.e., the 8 9 rearrangement of constituent atoms). This remains an open question worth exploring 10 further. 11 12 The purpose of this study was to report prevalent, cross-contextual student difficulties 13 14 with combustion. However, others might wonder what variables affect student performance 15 16 on the questions we have posed. We noted in the Introduction that we have generally found 17 that variables such as amount of instruction, course instructor, and time of day do not seem 18 19 to affect student performance on the kinds of conceptual questions we often pose (Heron, 20 21 2004b, 2013). However, we did notice in this study that students who received paired 22 23 questions ( e.g., both the beryllium oxide question and the burning candle question ) performed better 24 on the beryllium oxide question than did students who received this question alone. Although a 25 26 detailed statistical calculation of the variance attributable to the presence or absence of both 27 28 questions is beyond the scope of this paper, we note that the presence of both questions 29 may have enhanced student performance. If this is the case, it may artificially diminish the 30 31 prevalence of some of the response patterns reported in Table VI. More data – and a more 32 33 detailed analysis – is necessary to separate this effect from that of other possibly 34 35 confounding variables. 36 V. Conclusions and Implications for Instruction and Curriculum Development 37 38 Introductory chemistry student responses to questions about combustion reflect a 39 40 tendency to reason on the basis of rules, rather than on the basis of principles. Specifically, 41 42 rather than reasoning on the basis of the principle of conservation of atoms, they reason that 43 combustion always produces carbon dioxide and/or water and that oxygen is used by or 44 45 necessary for combustion. In fact, many of their answers are inconsistent with conservation 46 47 principles, suggesting that in some cases the rule is more salient than the principle. 48 49 Our research adds to the existing literature in two significant ways. First, we found that 50 adults in our population often argue that oxygen is used by or required for combustion, a 51 52 commonly-cited result in the literature on children’s ideas about burning (BouJaoude, 1991; 53 54 Driver, 1985; Lofgren & Hellden, 2009; Meheut et al., 1985; Ross, 1991; Schollum & Happs, 55 56 1982; J. R. Watson et al., 1997; R. Watson et al., 1995). , to our knowledge, our 57 finding that large percentages of introductory and advanced introductory chemistry students 58 59 60 15 Chemistry Education Research and Practice Page 16 of 31

1 2 3 justify their answers with a combustion rule that is often inconsistent with conservation 4 5 principles has not been reported elsewhere. However, it is consistent with recent research 6 7 (Christian & Talanquer, 2012; M. M. Cooper et al., 2013; Melanie M. Cooper et al., 2010; 8 9 Kraft et al., 2010; Maeyer & Talanquer, 2010; McClary & Talanquer, 2011; Taber, 2009; 10 Taber & Bricheno, 2009; Talanquer, 2006) in which students treat complex chemical 11 12 principles as rules to be memorized and is more generally consistent with research about 13 14 students’ epistemological stances toward science learning (Hammer, 1994; May & Etkina, 15 16 2002; Redish et al., 1998; Songer & Linn, 1991). 17 The research described in this paper has a number of implications for instruction and 18 19 curriculum development. In particular, instructors and curriculum developers can use the 20 21 patterns in student reasoning we describe to anticipate where students might struggle as they 22 23 learn about combustion and to design instructional materials that seek to specifically address 24 student difficulties. For example, on the basis of our research, we recommend that 25 26 instruction on combustion should both: (1) focus on why carbon dioxide and water are 27 28 produced during the combustion of hydrocarbons ( i.e., because there are carbon and 29 hydrogen atoms available in the hydrocarbon reactant and oxygen atoms available from the 30 31 air); and (2) provide salient examples of combustion reactions that do not result in the 32 33 production of carbon dioxide and water ( e.g., burning magnesium or beryllium). It is 34 35 important to note that the incorrect reasoning patterns we identified persist beyond 36 instruction and arose in multiple contexts. The experience of the Physics Education Group 37 38 at the UW has been that standard lecture instruction is often insufficient to address these 39 40 types of difficulties and that instead students must go through the reasoning required to 41 42 develop and apply the ideas themselves. (This approach is consistent with the constructivist 43 theory of learning (Driver, Asoko, Leach, Mortimer, & Scott, 1994; Driver & Bell, 1986; 44 45 Fosnot, 1996; von Glasersfeld, 1983).) Thus, we do not suggest that instruction simply 46 47 incorporate the emphases above into a standard lecture; rather, we suggest the development 48 49 of instructional activities that offer students an opportunity to actively participate in the 50 construction of an explanatory model for combustion. 51 52 In addition, we suspect that students’ tendency to use inappropriate rules is not limited 53 54 to the context of combustion. Instead, we speculate that this is representative of a broader 55 56 phenomenon in which students treat chemistry learning as the memorization and rote 57 application of facts and rather than as seeking to understand and explain chemical 58 59 60 16 Page 17 of 31 Chemistry Education Research and Practice

1 2 3 phenomena. This has implications for all of chemistry learning. Not only does it suggest that 4 5 we should pay attention to and seek to address the incorrect formulation and application of 6 7 specific rules; we should also seek to foster an epistemologically and metacognitively robust 8 9 stance toward learning chemistry, as making sense of chemical phenomena using general 10 models and principles. 11 12 Finally, the results of this investigation have implications for inquiry into student 13 14 understanding. The application of the specific combustion rules reported here is only 15 16 problematic in the context of non-hydrocarbon combustion; in all situations in which 17 hydrocarbons are burned in the presence of oxygen, carbon dioxide and water vapor are 18 19 produced. Thus, students’ misunderstandings may be masked by exam or other research 20 21 questions (such as the burning candle question ) posed in the context of hydrocarbon 22 23 combustion. Instructors and researchers may need to ask questions in multiple contexts in 24 order to understand student thinking. 25 26 VI. Acknowledgments 27 28 The authors wish to thank members of the Physics Education Group at the University 29 of Washington, particularly Lillian C. McDermott, Paula R. L. Heron, and Isaac Leinwber, 30 31 who contributed to this research, and to acknowledge the thoughtful feedback from Carolina 32 33 Alvarado, Abigail R. Daane, Natasha Holmes, Mary Bridget Kustusch, Sarah B. McKagan, 34 35 Thomas M. Scaife, and two anonymous reviewers. The authors would also like to thank the 36 faculty of the University of Washington Chemistry Department without whose support this 37 38 research would not have been possible. In particular, we wish to recognize Andrea Carroll, 39 40 Marianne Cavelti, D. Michael Heinekey, Josephus Norman, and William Zoller. Finally, the 41 42 authors gratefully acknowledge the support of the National Science Foundation through 43 Grant Nos. DUE-0096511, DUE-0618185, and DGE-0718124. The authors declare no 44 45 competing personal or institutional interests. 46 47 48 49 Appendix A: Examples of coded data 50 Context 51 52 Beryllium oxide Symbolic beryllium Burning candle Unknown chemical 53 question oxide question question question 54 Examples of “Beryllium burning “Can’t be a, b, d, e “[The amount of “This product 55 “with explicit means Be and O because products oxygen will:] Dec- could either be 56 conservation are the reactants. side contains rease – some of the wood or Butane. The products can elements that O2 in the air is This is because 57 reasoning” 58 only have whatever weren’t added on bonding [with] the water and carbon 59 60 17 Chemistry Education Research and Practice Page 18 of 31

1 2 3 is in the reactant so the reactant side. C and H in the wax dioxide are made 4 Beryllium oxide Burning something to form CO 2 and up of carbon[,] 5 would be the only involves adding H2O. Therefore, hydrogen[,] and 6 possible product oxygen so c is best less O 2 will be in oxygen. The Oxy- 7 from the list.” fit, and it’s also the air over time.” gen comes from the 8 balanced.” air as O2. How- 9 “None of the other “[The amount of ever, the Carbon 10 products have Ber- “I chose (c) be- carbon dioxide and the Hydrogen 11 yllium, which is still cause in reactions will:] Increase – as must come from 12 an element (e.g., (a), (b), (d), and (e) the wax is burning, one of the re- 13 contains only Ber- there are atoms in the are actants. Both wood 14 yllium) and is only the product mol- joining with the O 2 and butane have 15 reactant said to ecules that are not to create CO 2 carbon and hydro- 16 burn. You cannot present in the re- product. [The a- gen in them so they 17 burn filings actant side. It is mount of water va- could have been 18 and get copper not possible to gen- por will:] Increase – burned.” 19 oxide.” erate, in the case of as the wax is bur- 20 reaction (b), CO 2 ning, the hydrogen “Butane is the only 21 molecules without atoms will combine possible identity of 22 the presence of with the O 2 present the chemical be- 23 carbon atoms in the in the container.” cause it[‘]s the only 24 first place. If one one containing Hy- argues that carbon drogen and Carbon; 25 is present in the air we can’t magically 26 and is utilized in create the hydrogen 27 the reaction, then it needed for H2O 28 must be included in and the carbon 29 the reactant side to needed for CO2, it 30 make the equation has to come from 31 valid.” the reactants and 32 Butane is the only 33 [one] with H and 34 C.” 35 Examples of “combustion always produces carbon dioxide and water”: 36 “[Carbon dioxide “[Be + 2O → CO 37 “in no way 2 2 and water:] In + 2H O:] When 38 consistent 2 combustion reac- something com- 39 with tions, the products busts, O 2 is always 40 conservation are carbon dioxide a reactant [and] 41 of atoms” and water!!” CO 2 + H 2O is a 42 product.” 43 “[Carbon dioxide 44 ------and water:] Com- “[Be + 2O 2 → CO 2 45 bustion forms car- + 2H2O:] It[‘]s a 46 bon dioxide and combustion reac- 47 water, and this is a tion O 2 is always a 48 combustion reac- reactant [and] CO 2 49 tion since the ber- [and] H 2O are 50 yllium powder is always products.” 51 being burned.” 52 “partially “[Carbon dioxide “[2Be + 3O2 → “[Magnesium, 53 consistent and beryllium ox- CO 2 + 2H2O + copper, and wood:] 54 with ide:] Carbon di- 2BeO:] A Carbon dioxide and oxide and beryllium combustion [reac- --- water are products 55 conservation 56 oxide are possible tion] produces CO 2 of combustion.” 57 of atoms” products after ber- [and] H 2O and 58 yllium is burned be- since the Be has to “[Magnesium, cop- 59 60 18 Page 19 of 31 Chemistry Education Research and Practice

1 2 3 cause this is a com - go somewhere it per, butane, and 4 bustion reaction. must be on both wood:] Any com- 5 Whenever there is sides of the [reac- bustion reaction, 6 combustion invol- tion] in a different involves Carbon 7 ved, it will produce form.” Dioxide and water 8 CO2. Beryllium as some of the 9 can’t be completely “[2Be + 3O2 → products. Since it 10 gone so Beryllium CO 2 + 2H2O + did not say that 11 oxide could result 2BeO:] The burn- carbon dioxide and 12 since there is gas ing of the beryllium water are the 13 involved and is is a combustion ONLY products of 14 released.” reaction, which the reaction, it is 15 means the products possible that any 16 “[Carbon dioxide will be CO 2 (g) and one of the 4 17 and beryllium ox- H2O (g). Since not choices could have 18 ide:]…Since it is all the beryllium been what was 19 Beryllium powder, will be vaporized, burned.” 20 the product must some of it will re- 21 give off something main as blackened 22 [with] beryllium, so soot.” 23 Beryllium oxide 24 makes sense. Also, since Beryllium 25 powder is burning, 26 it should produce 27 CO .” 28 2 “[C + Be +4O + “[The amount of “[Butane:] Butane 29 “consistent 2 H → CO + H O oxygen will:] when reacted with 30 with 2 2 2 + BeO:] The only Decrease – the air is a combustion 31 conservation balanced equation candle needs oxy- reaction which 32 of atoms but is c, but when gen to burn. [The forms carbon diox- 33 interpreted as things burn, CO 2 amount of carbon ide and water.” 34 rote and water are dioxide will:] In- 35 typically products, crease – oxygen is “[Butane and 36 application of rule” which means that converted to CO 2 wood:] This is a 37 their components as the candle burns. combustion reac- 38 must also be [The amount of tion, therefore Bu- 39 reactants. There is water vapor will:] tane is a valid an- 40 hydrogen in the air, Increase – water va- swer since CO2 and 41 so we know it is a por is a by-product H2O are always 42 --- reactant.” of combustion.” products of a com- 43 bustion process, 44 “[The amount of and a hydrocarbon 45 oxygen will] de- is always a reactant. 46 crease; combustion Wood is also an 47 consumes the oxy- applicable answer 48 gen. [The amount because it gives off 49 of carbon dioxide and carbon 50 will] increase; CO 2 dioxide, it may not 51 is a byproduct of be a hydrocarbon 52 combustion. [The though as far as my 53 sensor for water knowledge goes.” vapor will detect] 54 no change; doesn’t 55 affect water vapor.” 56 57 58 59 60 19 Chemistry Education Research and Practice Page 20 of 31

1 2 3 Authors 4 5 • Amy D. Robertson is a Research Assistant Professor in the Department of Physics 6 7 at Seattle Pacific University. Her research interests include research paradigms and 8 methodologies in physics education research, responsive teaching, the development 9 10 of curricular knowledge among novice teachers, and issues of identity and 11 empowerment. 12 13 • Peter S. Shaffer is a Professor in the Department of Physics at the University of 14 15 Washington. His research focuses on the learning and teaching of physics and 16 physical science among populations that range from preservice and inservice 17 18 teachers to beginning and advanced undergraduates in university physics courses. 19 20 21 Endnotes 22 23 1. Although it is true that only certain materials can burn, the classification schemes used by these 24 students did not reflect this sophisticated view. Rather, students used visual cues to characterize 25 26 a reaction as burning (e.g., the appearance of a flame) or (e.g., a decrease in the level of 27 28 liquid). 29 2. Our research group has a long history of success in the design and dissemination of research- 30 31 validated, effective instructional materials that include strategies for specifically addressing 32 student difficulties (L. C. McDermott, Shaffer, & Washington, 2011; & 33 L. C. McDermott 34 Washington , 1995 , 1996 ). 35 36 3. Early in our study, we gave students enrolled in an advanced introductory chemistry course (a 37 population described more fully below) a quiz that included the powder-on-a-balance question 38 39 (reproduced in Figure 1), a modified version of an end-of-chapter question from their course 40 41 textbook, Chemical Principles (Zumdahl , 2009 ) and similar to questions reported elsewhere (e.g., 42 Andersson (1990)). The correct answer to this question is (c): since the system is closed, the mass 43 44 of the system will remain the same, regardless of the that occurs. A majority of 45 46 the students (75% of the 257 who answered the question) gave the correct answer. 47 4. There were rare cases in which students either stated (or questioned) that beryllium is a 48 49 compound or that the combustion reaction involves other elements from the air ( i.e., there were 50 rare cases in which students created a situation that conserves atoms and produces carbon 51 52 dioxide and water vapor when beryllium burns). In such cases, we categorized the student’s 53 54 response as incorrect but “with explicit conservation reasoning.” 55 5. The unknown chemical question did not state explicitly that carbon dioxide and water are the only 56 57 products of the reaction. The reader may wonder whether any of the students who chose 58 59 60 20 Page 21 of 31 Chemistry Education Research and Practice

1 2 3 magnesium or copper imagined a reaction that produced carbon dioxide, water, and copper or 4 5 magnesium. Only three students (of the 235) chose Mg or Cu and supported their answer with 6 7 such reasoning. 8 6. Table IV shows that 31% answered correctly that both butane and wood could have been the 9 10 ‘unknown chemical.’ Many students chose butane as a possible reactant but not wood. We can 11 think of several reasons that this may be the case: (1) Students may have missed our request that 12 13 they select all possible reactants. (2) Students may not consider wood a ‘chemical.’ This was 14 indicated explicitly by only 4 of the 235 student responses, but it may have implicitly affected a 15 16 greater number. For example, a study with university chemistry students (Nicoll , 1997 ) 17 18 indicated that students often have alternative interpretations of the word “chemical” ( e.g., 19 chemicals are unhealthy substances). (3) Students may not know that wood is a hydrocarbon. 20 21 For these reasons, we regard the 89% figure for those who chose butane and/or wood as 22 23 correct. 24 7. 34% of the introductory chemistry students and 57% of the advanced introductory students who 25 26 answered the symbolic beryllium oxide question did not provide reasoning for their responses. Many 27 students who chose answer choices (a), (b), and (d) – all consistent with the use of a combustion 28 29 rule – gave no reasoning. Thus, we hypothesize that the percentages of students using a 30 31 combustion rule, as well as the percentages of students who provided explicit conservation 32 reasoning, are underestimates. 33 34 35 36 References 37 Andersson, B. (1984). Chemical Reactions. Gothenburg, : EKNA Group, 38 39 University of Gothenburg. 40 Andersson, B. (1990). Pupils' conceptions of matter and its transformations (age 12- 41 16). In P. L. Lijnse, W. de Vos & A. J. Waarlo (Eds.), Relating Macroscopic 42 Phenomena to Microscopic . A Central Problem in Secondary Science 43 Education . University of Utrecht, . 44 45 Barker, V., & Millar, R. (1999). Students' reasoning about chemical reactions: what 46 changes occur in a context-based post-16 chemistry course? International 47 Journal of Science Education, 21 (6), 645-655. 48 Ben-Zvi, R., Eylon, B.-S., & Silberstein, J. (July 1987). Students' visualization of a 49 chemical reaction. Education in Chemistry , 117-120. 50 51 Boo, H. K. (1995). A burning issue for chemistry teachers. Teaching and Learning, 52 15 (2), 52-60. 53 BouJaoude, S. B. (1991). A study of the nature of students' understandings about the 54 concept of burning. Journal of Research in Science Teaching, 28 (8), 689-704. 55 56 57 58 59 60 21 Chemistry Education Research and Practice Page 22 of 31

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1 2 3 Tables 4 5 Table I. Populations that received each written question 6 7 Populations 8 9 10 Beryllium oxide question Courses A, B, and C: Introductory chemistry students 11 (N = 831) 12 13 Symbolic beryllium oxide question Course D: Introductory chemistry students ( N = 250) 14 Course E: Advanced introductory chemistry students 15 (N = 92) 16 17 Unknown chemical question Course B: Introductory chemistry students ( N = 229) 18 19 20 Burning candle question Course C: Introductory chemistry students ( N = 235) 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 25 Chemistry Education Research and Practice Page 26 of 31

1 2 3 Table II. Percentages of students who chose each product in response to the beryllium oxide 4 5 question 6 Introductory chemistry students 7 8 (N = 831) 9 10 Introductory Introductory Introductory 11 chemistry chemistry chemistry 12 students, students, students, 13 Course A 14 Course B Course C 15 (N = 367) (N = 229) (N = 229) 16 17 Only beryllium oxide (correct) 44% 58% 69% 18 With explicit conservation 22% 21% 34% 19 reasoning 20 21 Only products other than 17% 7% 7% 22 beryllium oxide (total) 23 24 Only carbon dioxide 7% 3% 2% 25 26 Both carbon dioxide and water 7% 3% 3% 27 Beryllium oxide plus other 35% 34% 20% 28 products (total) 29 30 Beryllium oxide and carbon 12% 13% 5% 31 dioxide 32 33 Beryllium oxide and water 3% 6% 1% 34 Beryllium oxide, carbon dioxide, 35 7% 13% 6% 36 and water 37 None of the above. 4% 2% 5% 38 39 a In all tables, percentages reported in regular (non-bold) text are percentages of the 40 total, not percentages of bolded text. 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 26 Page 27 of 31 Chemistry Education Research and Practice

1 2 3 Table III. Percentages of students who selected each chemical equation in response to the 4 5 symbolic beryllium oxide question 6 Advanced 7 Introductory introductory 8 chemistry students, 9 chemistry students, Course D 10 Course E (N = 250) 11 (N = 92) 12 13 →→→ 2Be + O 2 2BeO (correct) 49% 71% 14 15 With explicit conservation reasoning 23% 16% 16 Only products other than beryllium oxide 17 13% 5% 18 (total) 19 Be + O → CO 6% --- 20 2 2 21 Be + 2O → CO + 2H O 8% 5% 22 2 2 2 23 Beryllium oxide plus other products (total) 30% 13% 24 → 25 2Be + 3O 2 CO 2 + 2H 2O + 2BeO 21% 11% 26 2Be + 4O → 2BeO + NO + 2H O + 27 2 2 2 6% 2% 28 CO 2 29 Other. (Students chose to write their own 30 4% 7% 31 chemical equation.) 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 27 Chemistry Education Research and Practice Page 28 of 31

1 2 3 4 5 Table IV. Percentages of students who chose each reactant in response to the unknown 6 chemical question 7 8 Introductory chemistry 9 students, 10 11 Course C 12 (N = 235) 13 Only hydrocarbons (total, correct) 89% [6] 14 15 Butane and wood 31% 16 17 Butane only 55% 18 Wood only 3% 19 20 With explicit conservation reasoning 50% 21 Only non-hydrocarbons ( e.g., only 22 3% 23 copper) 24 Combination of hydrocarbons and non- 25 8% 26 hydrocarbons 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 28 Page 29 of 31 Chemistry Education Research and Practice

1 2 3 4 Table V. Percentages of students who indicated changes in amounts of oxygen, carbon 5 dioxide, and water vapor in response to the burning candle question 6 7 Introductory chemistry 8 students,

9 Course B 10 11 (N = 229) 12 Oxygen 13 14 Decreases (correct) 95% 15 Increases 2% 16 Remains the same 3% 17 Carbon dioxide 18 19 Increases (correct) 95% 20 Decreases 3% 21 Remains the same 2% 22 23 Water vapor 24 Increases (correct) 79% 25 Decreases 5% 26 Remains the same 13% 27 28 Correct on all three 73% 29 With explicit conservation reasoning 34% 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 29 Chemistry Education Research and Practice Page 30 of 31

1 2 3 4 Table VI. Percentages of students who used each rule in the beryllium oxide, symbolic beryllium 5 oxide, unknown chemical, and burning candle contexts 6 7 Beryllium oxide question Symbolic beryllium oxide Burning Unknown 8 question candle chemical Intro chem students 9 question question 10 (N = 831) Intro chem Intro chem 11 Advanced Intro chem students, students , 12 intro chem Course A Course B Course C students, Course B Course C 13 students, Course D (N = 229) (N = 235) 14 (N = 367) (N = 229) (N = 229) Course E (N = 250) 15 (N = 92) 16 Correct answer with 17 explicit conservation 22% 21% 34% 23% 16% 34% 50% 18 reasoning 19 20 “Combustion always 21 produces carbon 25% 27% 12% 22% [7] 9% 44% 23-25% 22 dioxide and/or 23 water.” 24 In no way 25 consistent with 26 conservation of 27 atoms ( e.g., 28 students chose 10% 5% 5% 7% 2% ------29 only CO 2 and/or 30 H2O as products 31 of beryllium 32 combustion) 33 34 Partially consistent 35 with conservation 36 of atoms ( e.g., students chose 37 15% 22% 8% 13% 4% --- 6% BeO, CO , and 38 2 H O as products 39 2 of beryllium 40 combustion) 41 42 Consistent with 43 conservation of 44 atoms but 45 interpreted as rote 46 application of rule (e.g., students 47 ------2% 44% 17% 48 answered that 49 burning candle 50 produces CO 2 51 because combustion always 52 produces CO ) 53 2 54 55 56 57 58 59 60 30 Page 31 of 31 Chemistry Education Research and Practice

1 2 3 Figure captions 4 5 Figure 1. Powder-on-a-balance question, adapted from CHEMICAL PRINCIPLES, Sixth Edition, 6 Student Edition. Copyright © 2009 by Houghton Mifflin Company. All rights reserved. 7 Reproduced by permission of the publisher, Houghton Mifflin Harcourt Publishing 8 9 Company. 10 11 Figure 2. Beryllium oxide question 12 13 Figure 3. Symbolic beryllium oxide question. The specific answer choices in this question were 14 based on the most common student responses to the original beryllium oxide 15 question (Fig. 2). 16 17 Figure 4. Unknown chemical question 18 19 Figure 5. Burning chemical question 20 21 Figure 6. Design of written questions 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 31