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1 2 3 4 Chemistry Education Research and Practice 5 6 7 ARTICLE 8 9 10 11 Enhancing undergraduate chemistry learning by helping students 12 13 make connections among multiple graphical representations Manuscript 14 Received 00th January 20xx, a Accepted 00th January 20xx Martina A. Rau 15 16 DOI: 10.1039/x0xx00000x Multiple representations are ubiquitous in chemistry education. To benefit from multiple representations, students have to make connections between them. However, connection making is a difficult task for students. Prior research shows that 17 www.rsc.org/ 18 supporting connection making enhances students’ learning in math and science domains. Most prior research has focused 19 on supporting one type of connection-making process: conceptually making sense of connections among representations. 20 Yet, recent research suggests that a second type of connection-making process plays a role in students’ learning: 21 perceptual fluency in translating among representations. I hypothesized that combining support for both conceptual sense Accepted 22 making of connections and for perceptual fluency in connection making leads to higher learning gains in general chemistry 23 among undergraduate students. I tested this hypothesis in two experiments with altogether N = 158 undergraduate 24 students using an intelligent tutoring system for chemistry atomic structure and bonding. Results suggest that the combination of conceptual sense-making support and perceptual fluency-building support for connection making is 25 effective for students with low prior knowledge, whereas students with high prior knowledge benefit most from receiving 26 perceptual fluency-building support alone. This finding suggests that students’ learning in chemistry can be enhanced if 27 instruction provides support for connection making among multiple representations in a way that tailors to their specific 28 learning needs. Practice 29 30 et al. , 2000; Höst , et al. , 2012; Hinze , et al. , 2013). For exam- 31 Introduction ple, a student who is learning about bonding may be asked to 32 and In chemistry, students have to learn concepts that are inher- use the representations in Fig. 2 to predict how ethyne will re- 33 ently visuo-spatial. To make these concepts accessible to stu- act with other molecules. To do so, the student needs to con- 34 dents, chemistry instruction tends to heavily rely on the use of nect the triple bond shown in the Lewis structure and the ball- 35 graphical representations (Bodner and Domin, 2000; Taber, and-stick figure to the red region in the electrostatic potential 36 2009; De Jong and Taber, 2014). Graphical representations are map (EPM), and infer that this molecule is unstable. Airey and 37 instructional materials that use visuo-spatial elements to de- Lindner (2009) refer to this ability to make connections as 38 pict domain-relevant concepts (as opposed to text or symbols). “apresentation”–as the ability to “spontaneously infer the presence of further facets of a disciplinary way of knowing 39 Furthermore, graphical representations are important tools Research 40 that chemists use to think, to solve problems, and to com- over and above those made available through the mode a stu- 41 municate–in other words, graphical representations are an in- dent has been presented with” (p. 10). Hence, the ability to 42 tegral part of discourse within the chemistry make connections among multiple graphical representations 43 pline (Kozma , et al. , 2000; Schönborn and Anderson, 2006; enables students to participate in discourse and practices that 44 Airey and Linder, 2009). Therefore, representational compe- are common in scientific and professional practices that chem- 45 tences are key to students’ learning in chemistry (Wu , et al. , istry students aspire to join. Because graphical representations 46 2001; Kozma and Russell, 2005; Justi , et al. , 2009; Linenberger are the visual language through which instruction conveys 47 and Bretz, 2012). chemistry concepts, students learn domain knowledge by mak- 48 In particular, students’ learning success depends on their abil- ing connections among graphical representations (Schönborn Education and Anderson, 2006; Airey and Linder, 2009). 49 ity to make connections among graphical representations. Fig. 50 1 shows examples of graphical representations typically used 51 to depict atoms; Fig. 2 shows examples of representations 52 used to illustrate bonding in molecules (Bowen, 1990; Kozma , 53 54 55 Fig. 1. Representations of an oxygen atom: Lewis structure, Bohr model, energy

56 diagram, orbital diagram. Chemistry 57 58 59 60 This journal is © The Royal Society of Chemistry 20xx J. Name ., 2013, 00 , 1-3 | 1

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ARTICLE Journal Name 1 2 aspect of domain expertise because it frees “cognitive head 3 room” to engage in higher-order conceptual thinking about 4 domain-relevant concepts (Goldstone and Barsalou, 1998; 5 Gibson, 2000; Kellman and Garrigan, 2009). Cognitive theories 6 of learning suggest that perceptual fluency is the result of non- 7 Fig. 2. Representations of an ethyne molecule: Lewis structure, ball-and-stick figure, space-filling model, electrostatic potential map (EPM). verbal inductive learning processes (Richman , et al. , 1996; 8 Koedinger , et al. , 2012). Inductive processes are learning pro- 9 Yet, making such connections is a difficult and cognitively de- cesses that students engage in when they learn to discrimi- 10 manding task for students (Johnstone, 1991; Taber, 2013). In- nate, classify, categorize, and become more accurate and effi- 11 deed, undergraduate students’ frequent failure to make con- cient in doing so (Koedinger , et al. , 2012). Perceptual learning 12 nections among multiple representations has been found to processes are considered to be non-verbal because they do 13 jeopardize their learning of important chemistry con- not rely on explicit reasoning (Kellman and Garrigan, 2009; Manuscript 14 cepts (Dori and Barak, 2001; Talanquer, 2013). Even Ph.D. stu- Kellman and Massey, 2013). They are implicit because they 15 dents in chemistry lack crucial representational competences happen unintentionally and unconsciously (Shanks, 2005), 16 and focus on surface-level features of representations when through experience with many examples (Gibson, 1969; 17 asked to explain reactions (Strickland , et al. , 2010). Unfortu- Richman , et al. , 1996; Gibson, 2000; Airey and Linder, 2009; 18 nately, there is also evidence that instructors tend to oversti- Kellman and Garrigan, 2009). Recent research in educational 19 mate students’ ability to make connections among graphical psychology shows that providing perceptual trainings that 20 representations (Schönborn and Anderson, 2006; Uttal and support students’ acquisition of perceptual fluency in connec- 21 O’Doherty, 2008; Airey and Linder, 2009). Hence, supporting tion making enhances their learning in math and Accepted 22 students in learning to make connections among multiple ence (Kellman , et al. , 2009; Massey , et al. , 2011). 23 graphical representations is a major goal in chemistry educa- Thus, the educational psychology literature suggests that both 24 tion (Cheng and Gilbert, 2009; Talanquer, 2013). A number of conceptual sense making of connections and perceptual fluen- 25 studies in chemistry education indicate that students’ learning cy in connection making play a role in students’ learning. This 26 can be enhanced by providing students with connection- is in line with the chemistry education literature, which also 27 making activities (Davidowitz and Chittleborough, 2009; Lux- suggest that both conceptual sense making and perceptual ford , et al. , 2011; Linenberger and Bretz, 2012). fluency are important aspects of students’ learning (Wu , et al. ,

28 Practice Most prior research on connection making has focused on 29 2001; Kozma and Russell, 2005; Justi , et al. , 2009). Empirical supporting only one type of connection-making ability; name- 30 evidence for the notion that conceptual sense making and per- ly, conceptual sense making of connections (Kozma and Rus- ceptual fluency in connection making are distinguishable rep- 31 sell, 2005; Stieff, 2005; Bodemer and Faust, 2006; van der Meij resentational competences comes from a factor analysis on and 32 and de Jong, 2006; Michalchik , et al. , 2008). Conceptual sense- students’ responses to a test of connection making with multi- 33 making support targets explicit connection-making processes ple graphical representations of atoms and molecules (Rau , et 34 by helping students reason about how different representa- al. , 2015). This study also showed that conceptual sense mak- 35 tions show the same concepts and how the information shown ing and perceptual fluency in connection making are predictors 36 about the given concept differs between representations (e.g., of students’ knowledge about chemistry concepts. However, 37 in Fig. 1, relating the local negative charge that results from little empirical research has investigated whether instruction is 38 the triple bond shown in the Lewis structure to the region of most effective if it combines support for both conceptual

39 high electron density shown in red in the EPM). sense-making of connections and perceptual fluency in con- Research 40 However, chemistry expertise also involves a second type of nection making among multiple representations. This paper 41 connection-making ability: perceptual fluency in translating presents two experiments that test this hypothesis in the con- 42 between representations (Kozma and Russell, 1997; Kozma text of undergraduate students learning about atomic struc- 43 and Russell, 2005; Airey and Linder, 2009) (e.g., in Fig. 1, rapid- ture and bonding. 44 ly “seeing” that the four representations likely show the same The experiments were carried out in the context of an educa- 45 molecule because they all have the same linear geometry). Re- tional technology designed to support students’ learning of 46 cent research in educational psychology draws attention to chemistry concepts through problem solving with multiple 47 novel ways to support students in acquiring perceptual fluency graphical representations: Chem Tutor. The use of an educa- 48 in translating between representations (Kellman and Massey, tional technology to support connection making in chemistry is Education 49 2013). Research on perceptual fluency in connection making appropriate for the following reasons. First, educational tech- 50 builds on research on expertise, which shows that experts can nologies can support interactive problem solving, which aligns 51 quickly and effortlessly make connections by “just seeing” with research on chemistry education that indicates that prob- 52 connections between representations, without cognitive ef- lem-solving activities can enhance conceptual learning (Bodner 53 fort (Chi , et al. , 1981; Kellman and Garrigan, 2009; and Domin, 2000), especially when they include graphical rep- 54 Gegenfurtner , et al. , 2011). For example, Airey and Lindner resentations (Bowen, 1990) and instructional support (Wu and 55 (2009) argue that this type of fluency is characterized by con- Shah, 2004). Second, educational technologies can ask stu- nection making becoming “unproblematic, almost second na- dents to manipulate dynamic, interactive representations. This 56 Chemistry ture” (p. 10). This type of perceptual fluency is an important 57 choice aligns with research showing that interactive represen- 58 59 60 2 | J. Name ., 2012, 00 , 1-3 This journal is © The Royal Society of Chemistry 20xx

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Journal Name ARTICLE 1 2 tations lead to better learning in chemistry than static repre- he/she does not understand VSEPR theory, an error feedback 3 sentations (Williamson, 2014). Finally, educational technolo- message would provide an explanation of the concept. This 4 gies play an increasingly important role in undergraduate edu- design ensures that Chem Tutor provides detailed content- 5 cation (Eichler and Peeples, 2013), thanks to the availability of level instruction only to students who need it. 6 course management systems such as Moodle. The push to- Chem Tutor covers two units: one focuses on atomic structure, 7 wards the use of educational technologies is also due to in- another focuses on bonding. Each unit uses a variety of graph- 8 creasing enrollments in undergraduate courses while financial ical representations that are commonly used in instructional 9 resources are decreasing. Therefore, situating this research in materials on these topics (Shusterman and Shusterman, 1997; 10 the context of educational technologies is both appropriate Furio , et al. , 2000; Matta and Gillespie, 2002; Cooper , et al. , 11 and timely. 2012; Höst , et al. , 2012; Bergqvist , et al. , 2013; Chung, 2013; 12 In the following, I first describe Chem Tutor. I then present re- Luxford, 2013). Specifically, the atomic structure unit incorpo- 13 sults from two experiments that test the effects of conceptual rates Lewis structures, Bohr models, energy diagrams, and or- Manuscript 14 sense-making support and perceptual fluency-building support bital diagrams (see Fig. 1). The bonding unit incorporates Lewis 15 for connection making on students’ learning of chemistry structures, ball-and-stick figures, space-filling models, and 16 knowledge. I conclude the paper by discussing implications EPMs (see Fig. 2). These representations were chosen based 17 from this research for our understanding of how students on a review of the chemistry education literature and based on 18 learn with multiple graphical representations in chemistry, as a review of a number of curricula used at the high school and 19 well as practical recommendations for chemistry education undergraduate levels (Rau, under review). Even though Chem 20 practice. Tutor is designed for introductory undergraduate courses, 21 high-school curricula were included in this review of curricula Accepted 22 because they likely yield insights into freshman students’ prior 23 Educational Technology for Undergraduate Chem- knowledge about representations and about chemistry. Chem 24 istry: Chem Tutor Tutor is available for free for anyone who would like to sign up at https://chem.tutorshop.web.cmu.edu/. It features a variety 25 Chem Tutor is an intelligent tutoring system for undergraduate of problem types, described in the following. 26 chemistry learning (Rau , et al. , 2015). Intelligent tutoring sys- 27 tems are a type of educational technology that is grounded in Introductory Units

28 cognitive theories of learning and artificial intelligence. They Practice Each unit of Chem Tutor provides a brief introduction into the 29 pose complex problem-solving activities and provide individu- topic covered and into the graphical representations used in 30 alized step-by-step guidance at any point during the problem- the unit. To introduce students to the given topic, the key con- 31 solving process (VanLehn, 2011). At the heart of intelligent tu- cepts that students need to know about in order to solve the and 32 toring systems lies a cognitive model of the students’ problem- tutor problems are reviewed (e.g., electronegativity in the in- 33 solving steps. This model allows to detect multiple strategies a troduction to the bonding unit). The introduction provides a 34 student might use to solve a problem (Aleven , et al. , 2009), review of these concepts with the expectation that students and to provide detailed feedback and hints on how to solve 35 have encountered these concepts in prior chemistry instruc- the next step (Corbett , et al. , 2001). Traditional intelligent tu- 36 tion, because Chem Tutor is designed to align with curricula toring systems use a rule-based cognitive model that is based 37 commonly used in introductory undergraduate courses (Rau , on production-rule theories of learning (Anderson , et al. , 38 et al. , 2015). To introduce students to the graphical represen- 1995; Corbett and Anderson, 2001; Ritter , et al. , 2007). Chem

39 tations, Chem Tutor reviews how each of them depict infor- Research Tutor is a newer type of intelligent tutoring systems, called ex- 40 mation about atoms and molecules. Specifically, the instruc- ample-tracing tutors (Aleven , et al. , 2009). Example-tracing tu- 41 tion for the atomic structure unit explains what information tors use a cognitive model that is not rule based, but instead 42 each of the graphical representations (see Fig. 1) show about relies on generalized examples of correct and incorrect solu- 43 atomic structure; in particular, which visual features denote tion paths. Chem Tutor was created using Cognitive Tutor Au- 44 relevant information, and what inferences they allow about thoring Tools (CTAT; Aleven et al., 2009), which allows for rap- 45 properties of the atom. The introduction for the bonding unit id iterations of prototyping and pilot-testing. The design of 46 explains what information each representation (see Fig. 2) Chem Tutor followed a learner-centered approach, which in- 47 shows about bonds, and what representational conventions

volved surveys of undergraduate chemistry students, inter- Education they use (e.g., CPK coloring in ball-and-stick figures and space- 48 views and eye-tracking studies with undergraduate and gradu- filling models). The introduction also briefly discusses how the 49 ate students, and extensive pilot testing (Rau , et al. , 2015; Rau, information that each representation provides about bonds re- 50 under review). As part of this learner-centered approach, ex- late to macroscopic phenomena that students are likely famil- 51 perienced chemistry instructors provided feedback on the de- iar with (e.g., ionic bonds result in crystalline structures that 52 sign of Chem Tutor’s activities. Findings from these learner- we know from table salt). The choice of topics covered in the 53 centered studies were used to design hint messages and error introduction was informed by the learner-centered studies al- 54 feedback messages so that they address misconceptions stu- ready mentioned: the introduction covered topics that stu- 55 dents might have about the content covered in the tutor prob- dents often struggle with and focused more on representa- 56 lems. For example, if a student makes a mistake that indicates Chemistry 57 tions that proved to be difficult for students (e.g., understand- 58 59 60 This journal is © The Royal Society of Chemistry 20xx J. Name ., 2013, 00 , 1-3 | 3

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ARTICLE Journal Name 1 2 ing orbital diagrams and electron density concepts) (Rau, tions has been shown to be effective in chemistry 3 under review). education (Wu , et al. , 2001; Wu and Shah, 2004). Fourth, stu- 4 dents are prompted to make inferences about the atom from 5 Individual-representation problems use the representation. Hints, error feedback messages, and 6 In individual-representations problems, students work with the wording of the prompts to help students make inferences 7 one graphical representation at a time to solve a given prob- are designed based on findings of interviews with Ph.D. stu- 8 lem. Fig. 3 shows an example of an individual-representation dents and undergraduate students that were conducted as 9 problem from Chem Tutor’s atomic structure unit, in which part of the learner-centered design approach (Rau , et al. , 10 students construct a Bohr model for oxygen. First, students are 2015; Rau, under review). The individual-representation prob- 11 asked to reflect on properties of the atom. They can use the lems were designed to correspond to typical problems in 12 periodic table to look up information about the atom (e.g., ox- chemistry textbooks (Wibraham, 2005; Loudon, 2009; Moore , 13 ygen has 8 electrons). Second, they plan how to construct the et al. , 2010; Brown , et al. , 2011), where students typically use Manuscript 14 Bohr model (e.g., the Bohr model should show 2 electrons on one graphical representation at a time to solve a problem. In 15 the inner shell and 6 on the outer shell). Third, they use an in- addition, the individual-representation problems were de- 16 teractive tool to construct the representation. They receive er- signed to help students gain some basic understanding of each 17 ror-specific feedback on their interactions (e.g., the Bohr mod- graphical representation, which is considered to be a prerequi- 18 el shows all electrons, not only the valence electrons). They site to making connections between different representa- 19 have to construct a correct representation before they can tions (Ainsworth, 2006; Eilam, 2013). 20 move on. Allowing students to construct graphical representa- 21 Accepted 22 23 24 25 26 27

28 Practice 29 30 31 32 and 33 34 35 36 Fig. 3. Example of an individual-representations problem from Chem Tutor’s atomic structure unit. Students are first asked to identify properties of the atom, using the periodic 37 table if they need to. Second, they plan the graphical representation. In the third step, they construct the graphical representation using an interactive tool. Finally, they are 38 prompted to make inferences about the atom based on the information depicted in the graphical representation

39 Conceptual sense-making problems for connection making students to actively make connections based on visual features Research 40 To support students in conceptually making sense of connec- that depict corresponding conceptual aspects of the chemistry 41 content, and they provide prompts and assistance for students 42 tions, Chem Tutor provides problems in which students have reason about differences and similarities among graphical rep- to make these connections (Seufert, 2003; Bodemer and Faust, 43 resentations by relating visual features to domain-relevant 2006; van der Meij and de Jong, 2006). The conceptual 44 concepts. Fig. 4 shows an example from Chem Tutor’s bonding prompts in these problems use a fill-in-the-gap format with 45 unit in which students have to reason about similarities be- menu-based selection to support self-explanation. Menu- 46 tween the Lewis structure and the EPM in terms of what in- based selection prompts have been shown to support self- 47 explanation in several empirical studies with intelligent tutor-

formation they show about polarity. Students are prompted to Education 48 self-explain how the two representations show where the ing systems (Aleven and Koedinger, 2002; Atkinson , et al. , 49 electrons are likely to be and how they depict local charges. To 2003), and have been shown to be more effective in enhancing 50 this end, students are prompted to connect the dipole mo- learning outcomes than open-ended prompts (Johnson and 51 ment vectors in the Lewis structure to the blue-to-red color Mayer, 2010; Van der Meij and de Jong, 2011; Gadgil, et al. , 52 gradient in the EPM because that is how the two representa- 2012). 53 tions depict the polar nature of the molecule that results from The content of the self-explanation prompts was designed 54 the electronegativity difference between carbon and oxygen. based on findings from learner-centered studies (Rau , et al. , 55 The design of conceptual sense-making problems aligns with 2015; Rau, under review) in which Ph.D. students in chemistry

56 findings from the educational psychology literature: they ask and undergraduate students enrolled in chemistry courses Chemistry 57 were interviewed about conceptual connections. The learner- 58 59 60 4 | J. Name ., 2012, 00 , 1-3 This journal is © The Royal Society of Chemistry 20xx

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Journal Name ARTICLE 1 2 centered studies showed that focusing solely on visual fea- The content of the self-explanation prompts was also informed 3 tures was associated with shallow reasoning about chemistry by the learner-centered studies of PhD. students and under- 4 concepts overall, whereas attending to information content graduate students. These studies identified concepts about 5 was associated with inferences about chemistry concepts that atomic structure and bonding that were mentioned significant- 6 extended beyond what was explicitly depicted in the visual ly more frequently by Ph.D. students mention than by under- 7 representations. This finding suggests that students' should graduate students. The self-explanation prompts focus on the- 8 learn to pay attention to the information the different repre- se concepts because they are important (Ph.D. students men- 9 sentations show about conceptual aspects of bonding, rather tion them frequently) but difficult for undergraduate students 10 than to surface features of the representations. Therefore, the to notice (undergraduate students often fail to mention them). 11 conceptual sense-making problems were designed to draw Finally, the wording of the prompts was based on actual stu- 12 students’ attention to information content of the graphical dent statements obtained from the learner-centered studies 13 representations, rather than to the visual features. when students were interviewed about conceptual connec- Manuscript 14 tions. 15 16 17 18 19 20 21 Accepted 22 23 24 25 26 27

28 Practice 29 30 Fig. 4. Example of a conceptual sense-making problem from Chem Tutor’s bonding unit. Students are comparing pairs of graphical representations that show the same molecule. 31 They are prompted to conceptually reason about similarities or differences between these graphical representations. 32 and than conceptual processes in the following ways. First, they 33 Perceptual fluency-building problems for connection making 34 provide repeated experience with a large variety of examples. 35 To support students in becoming perceptually fluent in trans- In Chem Tutor’s perceptual problems students are given one 36 lating among representations, Chem Tutor provides students representation (e.g., a Lewis structure) and have to identify 37 with many short classification problems. Consider the two ex- which of four alternative representations (e.g., an EPM) likely ample problems shown in Fig. 5. The design of these problems shows the same molecule. Each problem is short (i.e., it in- 38 aligns with Kellman and colleagues’ perceptual learning para- volves only one step). Students receive several of these prob-

39 Research digm (Kellman and Garrigan, 2009; Massey , et al. , 2011; lems in a row, and they receive immediate correctness feed- 40 Kellman and Massey, 2013) and encourage perceptual pro- back. 41 cesses (i.e., non-verbal inductive learning processes) rather 42 43 44 45 46 47 48 Education 49 50 51 52

53 54 Fig. 5. Example of a perceptual fluency-building problem from Chem Tutor’s bonding unit. Students receive many rapid classification tasks. They are prompted to 55 solve these tasks fast, based on perceptual strategies. The choice options use contrasting cases to emphasize relevant visual features. Students receive only correct- ness feedback.

56 Chemistry 57 58 59 60 This journal is © The Royal Society of Chemistry 20xx J. Name ., 2013, 00 , 1-3 | 5

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1 2 3 4 Chemistry Education Research and Practice 5 6 7 ARTICLE 8 9 10 Second, perceptual problems encourage students to rely on from conceptual sense-making support and from perceptual 11 perceptual problem-solving strategies, so as to foster implicit, fluency-building support. Experiment 1 was conducted in the 12 inductive learning . To this end, Chem Tutor provides a prompt context of Chem Tutor’s bonding unit. 13 to “solve this problem fast, without overthinking it”, before 14 each problem starts in order to encourage students to rely on Methods Manuscript 15 visual cues to solve the problem. Participants 16 Third, students receive immediate feedback . In Chem Tutor’s Students were recruited from an introductory general chemis- 17 perceptual problems, immediate feedback is given through try course for science majors at a large Midwestern university. 18 color highlighting: if the student gets the problem wrong, the Sixty-six students participated in the experiment. The institu- 19 choice is highlighted in red, if the student gets the problem tion’s internal review board (IRB) approved of the study. To 20 right, the choice is highlighted in green. protect students’ confidentiality, they were assigned an anon- 21 Fourth, the choice options use contrasting cases . In Chem Tu- ymous code for the duration of the study. The experimenters Accepted 22 tor, the four alternative representations vary irrelevant visual used this code to store the collected data. Informed consent was obtained from students after they were given the option 23 features of the representations and contrast visual features to ask questions about the experiment, and after they read 24 that provide relevant information (e.g., geometry). Contrasting over an IRB-approved document detailing in laymen's terms 25 cases were designed based on findings from the learner- centered studies already mentioned (Rau , et al. , 2015; Rau, that participation in the study is voluntary, that the student 26 under review): the alternative representations varied visual may withdraw participation at any time without consequenc- 27 features that students tend to confuse, fail to attend to, or are es, and that participation in the study is not associated with

28 Practice often distracted by. Thus, the four alternative representations foreseeable risks (they only worked with a computer, not with 29 emphasize visual features that students should learn to pay at- chemicals). To compensate students for their participation, 30 tention to. they received extra course credit towards their course grade. 31

In sum, the perceptual fluency-building problems are designed The experiment was conducted in the middle of the semester. and 32 to help students become faster and more efficient at extract- According to the course instructor, the content and the graph- 33 ing relevant information from graphical representations. In ical representations in Chem Tutor’s bonding unit were aligned 34 contrast to the conceptual problems, the perceptual problems with the content covered in the chemistry course. 35 draw students’ attention to visual features, such as the geom- Experimental design 36 etry of the molecule. Note that the goal of the perceptual flu- Students were randomly assigned to one of four conditions 37 ency-building problems is to get students to the level at which that varied two experimental factors: (1) whether or not stu- 38 connection making no longer requires cognitive effort. Howev- dents received conceptual sense-making support for connec- tion making, and (2) whether or not they received perceptual

39 er, during the learning experience , before students achieve this Research 40 desired level of perceptual fluency, the perceptual fluency- fluency-building support for connection making. All students 41 building problems may require cognitive effort. worked through the introduction to Chem Tutor’s bonding 42 unit, and all students encountered all representations (see Fig. 43 2). Students in the control condition (no-sense-making / no- 44 Experiment 1 fluency-building) worked on individual-representation prob- lems only. Students in the sense-making / no-fluency-building 45 The goal of Experiment 1 was to test the hypothesis that in- condition received individual-representation problems and 46 struction is most effective if it combines support for both con- problems with conceptual sense-making support for connec- 47 ceptual sense making of connections and perceptual fluency in tion making. Students in the no-sense-making / fluency- Education 48 making connections among multiple graphical representations. building condition received individual-representation problems 49 To test this hypothesis, Experiment 1 contrasted the effects of and problems with perceptual fluency-building support for 50 providing students with conceptual sense-making problems connection making. Finally, students in the sense-making / flu- 51 (compared to not providing conceptual sense-making prob- ency-building condition received individual-representation 52 lems), and of providing students with perceptual fluency- problems, problems with conceptual sense-making support for building problems (compared to not providing perceptual flu- 53 connection making, and problems with perceptual fluency- ency-building problems) on students’ learning of chemistry 54 building support for connection making. knowledge. In addition, Experiment 1 explored whether stu- 55 To ensure that the amount of instruction students received dents’ prior knowledge about chemistry and their prior 56 was the same in all conditions, the number of problems per Chemistry 57 knowledge about connections affects whether they benefit 58 59 60 This journal is © The Royal Society of Chemistry 20xx J. Name ., 2013, 00 , 1-3 | 6

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Journal Name ARTICLE 1 2 condition was adjusted such that the number of steps was the were similar to the tutor problems, and transfer items that 3 same across conditions. Equating the number of steps (rather were different from the problems in Chem Tutor. For example, 4 than the number of problems) was necessary because the test items that were similar to the problems in Chem Tutor 5 problems had different number of steps: individual problems asked students to specify the local negative charge in a polar 6 had between seven and thirteen steps per problem, conceptu- covalent bond, or to provide a definition for covalent bonds. 7 al sense-making problems had between four and six steps per Test items that were dissimilar from the problems in Chem Tu- 8 problem, and perceptual fluency-building problems had only tor asked students to select a schematic drawing that best de- 9 one step per problem. Hence, students in the experimental scribes the relationship between electronegativity differences 10 conditions received fewer individual-representation problems and bond polarity, or to select a novel visualization of ionic 11 than students in the control condition. Likewise, students in bonding that best describes their mental model of ionic bond- 12 the sense-making / fluency-building condition received fewer ing, and to explain their reasoning. Thus, the chemistry 13 sense-making problems than students in the sense-making / knowledge test assessed both reproduction and transfer of Manuscript 14 no-fluency-building condition and fewer fluency-building prob- student’s knowledge about bonding. 15 lems than students in the no-sense-making / fluency-building Prior connections knowledge tests. To investigate whether stu- 16 condition. This adjustment yielded interventions that were dents’ prior knowledge about connections affects their benefit 17 equivalent in time. from connection-making support, students were given prior 18 The sequence of individual-representation problems, concep- knowledge tests that assessed their prior conceptual under- 19 tual sense-making problems and perceptual fluency-building standing of connections (prior conceptual-connections test), 20 problems was organized as follows. For each pair of represen- and their prior perceptual fluency in making connections (prior 21 tations, students first received individual-representation prob- perceptual-fluency test). The tests included the graphical rep- Accepted 22 lems (e.g., one problem with a Lewis structure, and one prob- resentations shown in Fig. 2. For example, the prior conceptu- 23 lem with a ball-and-stick model). Next, if they were in one of al-connections test asked students to answer a number of 24 the sense-making conditions, they received conceptual sense- true/false questions, such as “The EPM of formaldehyde uses 25 making problems for this pair of representations. Then, if they red to show a local negative charge, but the space-filling model 26 were in one of the fluency-building conditions, they received of formaldehyde uses red to denote the oxygen atom” (true), 27 perceptual fluency-building problems for this pair of represen- or “The Lewis structure shows that the Nitrogen atom in am- tations. This sequence proved to be more effective than other monia has an empty 2sp 3 orbital, but the orbital diagram does

28 Practice 29 sequences in prior research (Rau , et al. , 2014). not” (false). In the prior perceptual-fluency test students were Measures 30 given one graphical representation (e.g., a space-filling model The tests used in this experiment were developed as part of showing water), and a selection of six other graphical repre- 31 the learner-centered studies already mentioned (Rau , et al. , sentations (e.g., Lewis structure showing water, ball-and-stick and 32 2015; Rau, under review). Students took two tests, each de- figure showing carbon dioxide, EPM showing water, Lewis 33 scribed in turn. structure showing ammonia, ball-and-stick figure showing ni- 34 Chemistry knowledge tests. To investigate the effects of con- trogen dioxide, EPM showing carbon disulfide). Their task was 35 nection-making support on students’ learning of chemistry to select all graphical representations that show the same 36 knowledge, students took a pretest, an intermediate test, and molecule. So as to not force students to select any visual rep- 37 a final posttest that assessed their understanding of the bond- resentations, they had the option to select “none of the 38 ing concepts covered in Chem Tutor’s bonding unit. There above.”

39 were three equivalent versions of the chemistry knowledge Grading. Students’ performance on the tests was graded based Research 40 tests, such that the items on the test asked similar but not on a rubric that assigned one point to each test item if the stu- 41 identical questions (e.g., they contained different molecules). dent had answered the item correctly. Partial credit was given 42 Students were randomly assigned to receive the three differ- for items that involved more than one step. To compute the 43 ent versions of the chemistry knowledge test in different or- final test scores, the sum of points was divided by the number 44 ders for the pretest, the intermediate posttest, and the final of items on the test, so that the range of final scores was be- 45 posttest. The chemistry knowledge tests included reproduc- tween 0 and 1. 46 tion items with and without graphical representations that 47 Table 1. Means and standard deviations (in parentheses) on the prior conceptual-connections test, the prior perceptual-fluency test, and the chemistry knowledge tests, organized 48 by test time and condition for Experiment 1. Education Intermediate post- 49 Pretest Final posttest 50 test Conceptual- Perceptual-fluency Chemistry Chemistry Chemistry

51 connections test test knowledge test knowledge test knowledge test 52 No-sense-making / no-fluency-building .68 (.09) .66 (.26) .44 (.15) .56 (.15) .61 (.13) Sense-making / no-fluency-building .69 (.10) .73 (.26) .39 (.12) .56 (.11) .53 (.13) 53 No-sense-making / fluency-building .69 (.14) .68 (.29) .42 (.10) .67 (.16) .64 (.15) 54 Sense-making / fluency-building .64 (.11) .71 (.28) .41 (.11) .58 (.19) .56 (.14) 55 Overall .67 (.11) .72 (.27) .42 (.12) .58 (.14) .59 (.14)

56 Chemistry 57 58 59 60 This journal is © The Royal Society of Chemistry 20xx J. Name ., 2013, 00 , 1-3 | 7

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ARTICLE Journal Name 1 2 Procedure knowledge affects the effectiveness of these two types of con- 3 The experiment took place in a laboratory and involved two nection-making support. To investigate main effects of the ex- 4 sessions of 90 minutes each. Sessions were scheduled no more perimental conditions on students’ learning outcomes, I used a 5 than three days apart from one another. At the beginning of repeated-measures ANCOVA with posttest time (i.e., interme- 6 the first session, informed consent was obtained. Then, stu- diate, and final posttest) as the repeated within-subjects fac- 7 dents received the chemistry knowledge pretest, the prior tor, and conceptual sense-making support and perceptual flu- 8 conceptual-connections test, and the prior perceptual- ency-building support as between-subjects factors, and per- 9 connections test. They then received an introduction into us- formance on the chemistry knowledge pretest as the covari- 10 ing the tutoring system. Next, students worked with the ver- ate. The ANCOVA model also tested for interactions of sense- 11 sion of Chem Tutor’s bonding unit that corresponded to their making support and of perceptual fluency-building support 12 experimental condition. In the first session, students worked with students’ performance on the chemistry knowledge pre- 13 through about half of the tutor problems. At the end of the test, on the prior conceptual-connections test, and on the pri- Manuscript 14 first session, they took the intermediate chemistry knowledge or perceptual-connections test. Performance on the interme- 15 posttest. When they returned for the second session, students diate and final chemistry knowledge posttests was used as the 16 worked through the remainder of the tutor problems. Then, dependent measure. Further, there was a marginally signifi- 17 they took a final chemistry knowledge posttest. cant negative main effect of conceptual sense-making support, 18 F(1,61) = 3.32, p < .10, partial η² = .05. There was a marginally 19 Results significant positive main effect of perceptual fluency-building 20 The final sample contained N = 66 students, n = 21 in the no- support, F(1,61) = 3.10, p < .10, partial η² = .05. There was no 21 sense-making / no-fluency-building condition, n = 13 in the significant interaction between conceptual sense-making sup- Accepted 22 sense-making / no-fluency-building condition, n = 15 in the no- port and perceptual fluency-building support, F(1,61) = 1.02, p 23 sense-making / fluency-building condition, and n = 17 in the > .10. Fig. 6 provides a summary of these results. 24 sense-making / fluency-building condition. There were no dif- There were no significant interactions of perceptual fluency- 25 ferences between conditions at the pretest (F < 1). Table 1 building support with students’ performance on the chemistry 26 shows means and standard deviations for students’ scores on knowledge pretest, F(1,61) = 1.52, p > .10, with students’ per- 27 the chemistry knowledge tests, the prior conceptual- formance on the prior conceptual-connections test (F < 1), or connections test, and the prior perceptual-fluency test, orga- on the prior perceptual-connections test ( F < 1). There were no

28 Practice 29 nized by test time and condition. In the analyses reported in significant interactions of conceptual sense-making support 30 the following, all p-values for post-hoc comparisons were ad- with students’ performance on the prior conceptual- justed using the Bonferroni correction. I report partial η2 for connections test ( F < 1), or on the prior perceptual- 31 effect sizes on effects including more than two conditions, and connections test ( F < 1). However, there was a marginally sig- and 32 Cohen’s d for effect sizes of pairwise comparisons. According nificant interaction of conceptual sense-making support with 33 2 to (Cohen, 1988), an effect size partial η of .01 corresponds students’ performance on the chemistry knowledge pretest, 34 to a small effect, .06 to a medium effect, and .14 to a large ef- F(1,61) = 3.40, p < .10, partial η² = .06, such that conceptual 35 fect. An effect size d of .20 corresponds to a small effect, .50 to sense-making support had a stronger negative effect on stu- 36 a medium effect, and .80 to a large effect. dents with high prior chemistry knowledge than for students 37 Learning gains with low prior chemistry knowledge. 38 First, I investigated whether working with Chem Tutor resulted

39 in learning of chemistry knowledge. To do so, I used a repeat- Research 40 ed-measures ANOVA with test time (i.e., pretest, intermediate, 41 and final posttest) as the repeated within-subjects factor, and 42 performance on the chemistry knowledge tests as dependent 43 measures. There was a significant effect of test time, F(2,130) 44 = 57.20, p < .01, partial η² = .47. Post-hoc comparisons showed 45 that students performed significantly better at the intermedi- 46 ate posttest than at the pretest, t(65) = 8.56, p < .01, d = 1.30, 47 and that they performed significantly better at the final post- 48 test than at the pretest, t(65) = 9.05, p < .01, d = 1.32. These Education 49 results show that working with Chem Tutor’s bonding unit re- 50 sulted in significant learning gains on a test that assessed re- 51 production and transfer of students’ conceptual understanding

52 of bonding. 53 Effects of connection-making support Fig. 6. Effects of conceptual sense-making support and perceptual fluency-building 54 Next, I investigated whether providing conceptual sense- support on students’ learning outcomes on the intermediate and final posttests in Ex- making support and perceptual fluency-building support for periment 1. Bars show estimated marginal means from the ANCOVA model. Error bars 55 connection making is effective in enhancing students’ learning show standard errors of the mean. 56 Chemistry of chemistry knowledge, and whether students’ prior 57 58 59 60 8 | J. Name ., 2012, 00 , 1-3 This journal is © The Royal Society of Chemistry 20xx

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Journal Name ARTICLE 1 2 Discussion whether choosing a different population of students, who 3 have less prior knowledge about chemistry and less experience 4 Experiment 1 tested the hypothesis that a combination of con- ceptual sense-making support for connection making and per- with the graphical representations, would yield similar results. 5 Experiment 2 was conducted to address this question. 6 ceptual fluency-building support for connection making would 7 enhance students’ learning of chemistry knowledge. With re- 8 spect to conceptual sense-making support, the results do not Experiment 2 9 support this hypothesis. To the contrary: conceptual sense- The goal of Experiment 2 was to investigate whether the find- 10 making support had a small, marginally significant negative ef- ings from Experiment 1 generalize to students who encounter 11 fect on students’ learning outcomes. This finding is surprising because it stands in contrast to prior research on learning with representations they are unfamiliar with. To this end, students 12 multiple representations in educational psychology (Seufert, were recruited from a chemistry course for non-science ma- 13

2003; Bodemer and Faust, 2006) and chemistry jors. Experiment 2 was conducted in the context of Chem Tu- Manuscript 14 tion (Stieff, 2005; Luxford , et al. , 2011; Linenberger and Bretz, tor’s atomic structure unit, because the course instructor felt 15 2012), which showed that interventions that help students in that this unit was appropriate for the course. 16 conceptually making sense of connections among multiple rep- A further change in Experiment 2 was that it investigated the 17 resentations can enhance their learning outcomes. It is possi- role of an additional prior competence: mental rotation ability. 18 ble that the students who participated in Experiment 1 already Mental rotation ability has been found to significantly predict 19 had considerable experience in making sense of among be- students’ learning outcomes in chemistry (Stieff, 2007; Stieff , 20 tween the graphical representations that Chem Tutor provid- et al. , 2011; Stieff, 2013) and in other STEM domains that 21 ed. The fact that the negative effect of conceptual sense- heavily rely on the use of graphical representations (Wai , et Accepted 22 making support was more pronounced for students with high al. , 2009). Mental rotation ability has also been associated 23 prior chemistry knowledge lends credibility to this interpreta- with students’ pursuit of careers in STEM domains (Uttal , et 24 tion. Indeed, the instructor for the chemistry course from al. , 2013). Hence, including a test of mental rotation ability 25 which these students were recruited confirmed that they had may yield additional insights into how non-science majors 26 encountered the graphical representations in their course pri- learn with graphical representations. 27 or to the experiment. Table 1 (column 2, labeled “conceptual- Methods

28 connections test”; M = .67, SD = .11) indicates that the stu- Practice 29 dents in Experiment 1 had some prior conceptual understand- Participants 30 ing of connections, although the average score of .67 is cer- A total of ninety-two students from an introductory general 31 tainly not perfect. The results from Experiment 1 indicate that chemistry course for non-science majors participated in the 32 students with at least a moderate level of prior conceptual un- experiment. For most of the students enrolled in this course, and 33 derstanding of connections do not benefit from conceptual this course is the only required chemistry course for their un- 34 sense-making support, but instead should practice to solve dergraduate degree. The same IRB process was used as in Ex- periment 1. Students received course credit for participating in 35 problems with the graphical representations, as they do in the study. According to the instructor, students had not en- 36 Chem Tutor’s individual-representations problems. Given that countered the representations used in this unit, except for the 37 the individual-representations problems were designed to re- Lewis structure. Students worked with Chem Tutor’s unit on 38 semble regular textbook problems, this finding is promising because it indicates that regular educational practice is effec- atomic structure.

39 Experimental design Research 40 tive for students who have a good conceptual grasp of how dif- ferent graphical representations depict similar and different The experimental design was the same as in Experiment 1: 41 aspects of chemistry concepts. Students were randomly assigned to one of four conditions 42 With respect to perceptual fluency-building support, the re- (i.e., the no-sense-making / no-fluency-building condition, the 43 sults provide qualified support for the hypothesis: perceptual sense-making / no-fluency-building condition, the no-sense- 44 fluency-building support had a marginally significant positive making / fluency-building condition, or the sense-making / flu- 45 effect on students’ learning outcomes. This finding suggests ency-building condition). The difference to Experiment 1 was 46 that students’ learning of chemistry knowledge can be en- that students worked through the atomic structure unit of 47 hanced by supporting them in becoming perceptually fluent in Chem Tutor (instead of the bonding unit), and that the tests Education 48 making these connections. However, in light of the marginally were adjusted accordingly. 49 significant effects, further research is warranted to support Procedure 50 this claim. The experiment took place in a laboratory and involved two 51 A limitation of this experiment is that the majority of the stu- sessions of 90 minutes each. Sessions were scheduled no more 52 dents who participated in Experiment 1 were science majors than three days apart. At the beginning of the first session, in- 53 who had a considerable amount of prior knowledge about the formed consent was obtained. Next, students first received the 54 content covered in Chem Tutor’s bonding unit, and (perhaps chemistry knowledge pretest, the prior conceptual- 55 more importantly) who had encountered the graphical repre- connections test, the prior perceptual-connections test, and the mental rotation ability test. They then received an intro- 56 sentations used in Chem Tutor. This raises the question Chemistry 57 duction into atomic structure. Next, students worked with the 58 59 60 This journal is © The Royal Society of Chemistry 20xx J. Name ., 2013, 00 , 1-3 | 9

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ARTICLE Journal Name 1 2 version of Chem Tutor’s atomic structure unit that corre- .01, d = 1.02. These results show that working with Chem Tu- 3 sponded to their experimental condition. In the first session, tor’s atomic structure unit resulted in significant learning gains 4 students worked through about half of the tutor problems. At on tests that assess reproduction and transfer of students’ 5 the end of the first session, they took the intermediate chem- conceptual understanding of atomic structure. 6 istry knowledge posttest. When they returned for the second 7 session, students worked through the remainder of the tutor Effects of connection-making support 8 problems. Then, they took the final chemistry knowledge post- 9 test. 10 Measures 11 The measures were identical to those used in Experiment 1, 12 with the following two exceptions. First, the chemistry 13 knowledge tests focused on concepts of atomic structure (to Manuscript 14 align with the Chem Tutor unit on atomic structure). Second, 15 students received an additional test that assessed their mental 16 rotation ability. Specifically, they were given the Vandenberg & 17 Kuse mental rotation ability test (Peters , et al. , 1995). This test 18 presents students with a drawing of an object and asks them 19 to identify which of four other drawings show the same object. 20 This task requires students to mentally rotate the given object 21 to align it with the comparison objects. I chose this test for the Accepted 22 experiment because it has been used in prior research on the impact of students’ mental rotation ability on STEM 23 Fig. 7. Effects of conceptual sense-making support and perceptual fluency-building ing (Stieff, 2007; Wai , et al. , 2009; Stieff , et al. , 2011; Stieff, 24 support on students’ learning outcomes on the intermediate and final posttests in Ex- 25 2013; Uttal , et al. , 2013). periment 2. Bars show estimated marginal means from the ANCOVA model. Error bars show standard errors of the mean. 26 Results 27 The final sample contained N = 92 students, n = 18 in the no- Like in Experiment 1, I investigated the effects of connection-

28 Practice sense-making / no-fluency-building condition, n = 24 in the making support using a repeated-measures ANCOVA with 29 sense-making / no-fluency-building condition, n = 23 in the no- posttest time (i.e., intermediate, and final posttest) as the re- 30 sense-making / fluency-building condition, and n = 27 in the peated within-subjects factor, and conceptual sense-making 31 sense-making / fluency-building condition. There were no dif- support and perceptual fluency-building support as between- and 32 ferences between conditions at the pretest, F(1,94) = 1.22, p > subjects factors, and performance on the chemistry knowledge 33 .10. Table 2 shows means and standard deviations for stu- pretest as the covariate. The ANCOVA model tested for inter- 34 dents’ scores on the chemistry knowledge test, the prior con- actions of conceptual sense-making support with pretest per- 35 ceptual-connections test, the prior perceptual-fluency test, formance, with students’ performance on the mental rotation 36 and the mental rotation ability test organized by test time and ability test, on the prior conceptual-connections test, and on 37 condition. the prior perceptual-connections test, as well as of perceptual 38 Learning gains fluency-building support with pretest performance, with stu- dents’ performance on the mental rotation ability test, on the 39 First, I investigated whether working with Chem Tutor resulted Research 40 in learning of chemistry knowledge. Like in Experiment 1, I prior conceptual-connections test, and on the prior perceptu- 41 used a repeated-measures ANOVA with test time (i.e., pretest, al-connections test. Performance on the chemistry knowledge 42 intermediate, and final posttest) as the repeated within- posttests was used as the dependent measure. 43 subjects factor, and performance on the chemistry knowledge There was no significant main effect of conceptual sense- 44 tests as dependent measures. There was a significant effect of making support, F(1,84) = 1.50, p > .10. There was a significant 45 test time, F(2,182) = 32.28, p < .01, partial η² = .26. Post-hoc positive main effect of perceptual fluency-building support, 46 comparisons showed that students performed significantly F(1,84) = 4.27, p < .05, partial η² = .05. There was a marginally 47 better at the intermediate posttest than at the pretest, t(91) = 48 6.14, p < .01, d = .73, and that they performed significantly Education 49 better at the final posttest than at the pretest, t(91) = 7.41, p < 50 Table 2. Means and standard deviations (in parentheses) on the prior conceptual-connections test, the prior perceptual-fluency test, the mental rotation ability test, and the chemistry knowledge tests, organized by test time and condition for Experiment 2. 51 52 Pretest Intermediate posttest Final posttest Conceptual- Perceptual- Mental rotation Chemistry Chemistry Chemistry 53 connections test fluency test ability test knowledge test knowledge test knowledge test 54 No-sense-making / no-fluency-building .45 (.21) .29 (.16) .50 (.20) .42 (.17) .52 (.21) .56 (.16) 55 Sense -making / no -fluency -building .32 (.22) .25 (.16) .48 (.20) .33 (.16) .49 (.18) .51 (.15) No-sense-making / fluency-building .31 (.14) .34 (.21) .60 (.17) .40 (.16) .50 (.21) .57 (.18) 56 Sense -making / fluency -building .43 (.24) .34 (.16) .53 (.20) .40 (.18) .56 (.18) .59 (.18) Chemistry 57 Overall .37 (.21) .31 (.17) .51 (.20) .38 (.17) .52 (.19) .56 (.17) 58 59 60 10 | J. Name ., 2012, 00 , 1-3 This journal is © The Royal Society of Chemistry 20xx

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1 2 3 4 Chemistry Education Research and Practice 5 6 7 ARTICLE 8 9 10 significant interaction between conceptual sense-making sup- which students were recruited, they only had experience with 11 port and perceptual fluency-building support, F(1,84) = 2.89, p the Lewis structure, not with the other representations. Com- 12 < .10, partial η² = .03. Fig. 7 illustrates the nature of this effect: paring Tables 1 and 2 (column 2, labeled “conceptual- 13 perceptual fluency-building support was effective only if it was connections test”) confirms that students in Experiment 2 had 14 provided in combination with conceptual sense-making sup- lower average scores on the prior conceptual-connections test Manuscript 15 port. For students who did not receive conceptual sense- (M = .37, SD = .23) than students in Experiment 1 (M = .67, SD 16 making support, perceptual fluency-building support was not = .11). It is important to note that a comparison between Ex- 17 effective; these students learned better with individual- periments 1 and 2 is difficult because the participating stu- 18 representations problems only. dents differed on many factors (e.g., the experiments took 19 There were no significant interactions of conceptual sense- place in different semesters, the students were enrolled in dif- 20 making support or perceptual fluency-building support with ferent courses with different instructors, and they worked on 21 students’ performance on the chemistry knowledge pretest, different units of Chem Tutor). Yet, the conclusion seems rea- Accepted 22 on the prior conceptual-connections test, or on the prior per- sonable that students who already have a relatively good con- 23 ceptual-connections test ( ps > .10). There was no significant in- ceptual understanding of how to make sense of connections 24 teraction of conceptual sense-making support with students’ (Experiment 1) do not benefit from conceptual sense-making 25 mental rotation ability ( F < 1), but there was a significant in- support, whereas students who do not know how to make teraction of perceptual fluency-building support with students’ sense of connections (Experiment 2) benefit from conceptual 26 mental rotation ability, F(1,84) = 5.21, p < .05, partial η² = .06, sense-making support. 27 such that students with high mental rotation ability benefited This difference between Experiments 1 and 2 may also explain

28 Practice more from perceptual fluency-building support than students why Experiment 2 revealed a significant interaction between 29 with low mental rotation ability. conceptual sense-making support and perceptual fluency- 30 building support, whereas Experiment 1 did not. It seems that, 31 Discussion

in order to benefit from perceptual fluency-building support, and 32 Experiment 2 tested the hypothesis that a combination of con- students need to have some level of conceptual understanding 33 ceptual sense-making support for connection making and per- of the connections among graphical representations. Because 34 ceptual fluency-building support for connection making would students in Experiment 1 had this conceptual understanding 35 enhance students’ learning of chemistry knowledge. The re- prior to the experiment, they benefited from perceptual fluen- 36 sults are somewhat surprising: only the combination of con- cy-building support. Because students in Experiment 2 did not 37 ceptual sense-making support and perceptual fluency-building have this prior conceptual understanding of connections, they 38 support for connection making were effective. Providing only needed conceptual sense-making support in order to benefit

39 perceptual fluency-building support (i.e., without conceptual from perceptual fluency-building support. This result suggests Research 40 sense-making support) resulted in lower learning gains on a that learning perceptual mappings based on visual features is 41 chemistry knowledge test than providing no connection- only beneficial if students understand what concepts the map- 42 making support at all. Likewise, conceptual sense-making sup- pings between visual features stand for. If students only learn 43 port was effective only when combined with perceptual con- mappings based on visual features (i.e., if they do not have 44 nection-making support. This finding provides support for the prior knowledge about conceptual connections and receive on- 45 overall hypothesis that both aspects of connection making, the ly perceptual fluency-building problems), students learn mean- 46 ability to conceptually make sense of connections and the abil- ingless mappings, and these do not help them learn chemistry. 47 ity to fluently translate among them based on perceptual cues, Put differently, it seems that acquiring conceptual understand- 48 are important aspects of students’ learning. By supporting stu- ing of connections is an intermediate step that students have Education 49 dents in making connections, we can enhance their learning of to engage in to become perceptually fluent in making connec- 50 chemistry knowledge. tions, if the goal is to enhance their learning of chemistry 51 In contrast to Experiment 1, Experiment 2 shows that students knowledge. Thus, the results from Experiments 1 and 2 pro- 52 benefit from conceptual sense-making support (when com- vide some support for the notion that the ability to conceptu- 53 bined with perceptual fluency-building support). It is possible ally make sense of connections is a prerequisite for students’ 54 that the fact that students in Experiment 2 had lower prior benefit from support that helps them to become perceptually knowledge and less experience with the graphical representa- fluent in translating between multiple graphical representa- 55 tions accounts for this difference between Experiments 1 and tions. 56 Chemistry 2. According to the instructor of the chemistry course from 57 58 59 60 This journal is © The Royal Society of Chemistry 20xx J. Name ., 2013, 00 , 1-3 | 11

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ARTICLE Journal Name 1 2 Another interesting finding is that the positive effect of per- chemistry problems using only one graphical representation at 3 ceptual fluency-building support is more pronounced for stu- a time. Hence, the results presented in this paper suggest that 4 dents with high mental rotation ability than for students with regular practice is effective for students who have a good con- 5 low mental rotation ability. The perceptual fluency-building ceptual understanding of connections. For chemistry educa- 6 problems ask students to map visual features that are not al- tors, this finding suggest that they might want to test their 7 ways spatially aligned. Hence, students may have to mentally students’ conceptual-connections knowledge before they de- 8 rotate the graphical representations when solving the percep- cide whether to provide instructional support that aims at 9 tual fluency-building problems. This task is arguably harder for helping them conceptually make sense of connections among 10 students with low mental rotation ability than for students multiple graphical representations, or to have them work on 11 with high mental rotation ability. As a consequence, students regular chemistry problems. Specifically, chemistry educators 12 with low mental rotation ability may fail at this task, which could test whether their students have understood how differ- 13 might jeopardize their benefit from perceptual fluency- ent graphical representations (e.g., a Lewis structure, an EPM) Manuscript 14 building support. It is possible that students with low mental provide complementary information about the given topic 15 rotation ability may benefit more from a version of perceptual (e.g., bonding). For example, a chemistry educator could ask 16 fluency-building support that provides spatially aligned exam- students to explain that the lines in Lewis structures that de- 17 ples. Future research should investigate how best to tailor per- note bonds do not indicate the polarity of the bond (i.e., how 18 ceptual fluency-building support to the needs of students with the electrons are likely to be distributed across the molecule), 19 low mental rotation ability. whereas EPMs use color to indicate electron density do not 20 It would also be interesting to investigate how students’ famil- show which atoms form the bonds. If students have not yet 21 iarity with the different representations may have affected understood these conceptual connections, they should work Accepted 22 their benefit from particular connection-making problems. For on conceptual sense-making problems. If they already do un- 23 example, it is possible that students benefit more from con- derstand how the different representations about the given 24 ceptual sense-making problems and perceptual fluency- topic, they should rather work on problem-solving tasks with- 25 building problems in which they connect a familiar representa- out conceptual sense-making support. 26 tion (e.g., the Lewis structure) to an unfamiliar representation The results from both experiments reported provide empirical 27 (e.g., the orbital diagram), than from problems in which they evidence for the hypothesis that helping students become per- connect two unfamiliar representations (e.g., energy diagram ceptually fluent (i.e., by helping them become more efficient

28 Practice 29 and orbital diagram). Experiment 2 was not set up to investi- at attending to visual features that depict relevant infor- 30 gate this question, but it would be interesting to explore this mation) promotes their learning of chemistry knowledge. question in future research. However, the results from the two experiments also cautions 31 that perceptual fluency-building support is only effective if and 32 students either already have at least a moderate level of prior 33 Conclusions conceptual understanding of connections (Experiment 1) or if 34 they also receive conceptual sense-making support for connec- 35 This paper presented two experiments that investigated how best to enhance students’ learning of chemistry by helping tion making (Experiment 2). This finding extends our theoreti- 36 cal understanding of how students learn with multiple graph- 37 them acquire critical representational competences: the ability to make connections among multiple graphical representa- ical representations. It seems that perceptual fluency in con- 38 tions. The hypothesis tested in this paper was that two aspects nection making builds on a prerequisite ability to conceptually

39 Research of connection making are important: (1) students’ ability to make sense of connections. This finding also extends prior ob- 40 conceptually make sense of connections and (2) perceptual servational studies showing that fluency can facilitate stu- 41 fluency in making connections. By testing this hypothesis, this dents’ learning of domain knowledge (Airey and Linder, 2009): 42 paper extends prior research on connection making that has the present experiments indicate that fluency enhances learn- 43 focused on conceptual sense making of connections (Stieff, ing of domain knowledge only if it is built on a solid foundation 44 2005; Bodemer and Faust, 2006; van der Meij and de Jong, of students’ ability to conceptually make sense of connections. 45 2006; Michalchik , et al. , 2008) and integrates this research This finding also provides practical suggestions for chemistry 46 with positions arguing that perceptual fluency plays a critical educators: they should be aware of their students’ conceptual- 47 role in students’ becoming part of community practices be- connections knowledge when deciding whether and when to Education 48 cause it allows them to participate in discipline provide perceptual fluency-building support designed to help 49 course (Kozma and Russell, 2005; Airey and Linder, 2009). students become efficient at translating between multiple 50 This paper provides a somewhat surprising result: support for graphical representations based on perceptual cues. Specifical- 51 conceptual sense-making of connections may not always be ly, educators should make sure that their students have a 52 beneficial. For students who already have a relatively good sound conceptual understanding of what the relations be- 53 conceptual understanding of connections, this type of support tween different graphical representations mean in terms of 54 is not effective. These students benefited more from individu- conceptual aspects they show about the topic, before they 55 al-representation problems alone. Recall that the individual- provide students with perceptual fluency-building problems. The finding that perceptual fluency-building support is effec- 56 representation problems in Chem Tutor were designed to re- Chemistry 57 semble typical textbook problems, in which students solve tive is also interesting against the background of recent devel- 58 59 60 12 | J. Name ., 2012, 00 , 1-3 This journal is © The Royal Society of Chemistry 20xx

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Journal Name ARTICLE 1 2 opments in chemistry education to incorporate connection- longer experiment with a longer intervention would be needed 3 making games that ask students to rapidly translate among to investigate how students’ benefit from conceptual and per- 4 graphical representations (Eastwood, 2013; Moreira, 2013). ceptual support differs, depending on how much conceptual 5 These connection-making games are similar to the perceptual understanding of connections they have at any point in time. 6 fluency-building problems tested in this paper with respect to In other words, the experiments reported in this paper yield a 7 some aspects: they ask students to rapidly translate among new hypothesis that can be evaluated empirically; namely, 8 graphical representations, in order to promote efficiency in that students’ learning of chemistry knowledge can be en- 9 connection making. Thus, these connection-making games hanced by providing different types of connection-making 10 provide experience with many examples and they provide im- support as they learn to conceptually make sense of connec- 11 mediate feedback. However, these games do not incorporate tions throughout a longer learning experience. 12 other aspects of perceptual fluency-building problems: the ex- A third limitation of this research is that it was situated in a 13 amples are not designed based on considerations of visual fea- highly interactive educational technology. As mentioned, edu- Manuscript 14 tures that depict relevant information (i.e., contrasting cases), cational technologies are becoming more prevalent in under- 15 and they do not explicitly ask students to employ perceptual graduate education in chemistry, because they offer several 16 problem-solving strategies, as opposed to conceptual strate- features that provide advantages over more traditional learn- 17 gies. Although it remains an open question whether these ing environments, such as textbooks and lectures: they can 18 games indeed foster perceptual fluency in connection making, support problem solving with interactive representations, and 19 it might be advisable to consider students’ levels of conceptu- they can provide detailed, individualized feedback in real time. 20 al-connections knowledge before providing them with connec- While it seems reasonable to assume that findings from the 21 tion-making games. experiments reported in this paper may generalize to other Accepted 22 The finding that mental rotation ability affects students’ bene- educational technologies, it is possible that the interactive na- 23 fit from perceptual fluency-building support is also interesting ture of Chem Tutor restricts the generalizability of the findings 24 in the light of the discussion about connection-making games. to educational technologies. Therefore, further research would 25 It is possible that students with low mental rotation ability be needed to address the question whether the combination 26 benefit less from playing connection-making games, or that of conceptual and perceptual support for connection making is 27 they may need additional support when playing these games. most effective when these types of support are implemented Future research should investigate this question to ensure that in more traditional, less interactive types of materials, such as

28 Practice 29 novel interventions that target representational competences textbooks and lectures. 30 do not put students with low mental rotation ability at a disad- Finally, a potential limitation of the experiments reported here vantage. is that they did not investigate whether the specific pairing of 31 Several limitations of the two experiments need to be dis- graphical representations that were presented in the connec- and 32 cussed. First, both experiments were conducted in a lab set- tion-making problems had an impact on students’ benefit from 33 ting. Chem Tutor is designed to be used as a homework system the connection-making problems. The representation pairs 34 within undergraduate chemistry courses. In future research, I (e.g., Bohr model and Lewis structure vs. Bohr model and en- 35 will investigate whether a more natural setting will yield simi- ergy diagram) differed with respect to their “information over- 36 lar results as the experiments reported in this paper. A second lap”: that is, to what extent they provide the same information 37 limitation is that Experiment 1 did not include a mental rota- about the given concept. The information overlap may how 38 tion ability test. Therefore, it is unclear whether the mental ro- cognitively demanding the connection-making problems were,

39 tation ability of the students who were enrolled in a course for which may in turn affect how much students' benefited from Research 40 chemistry majors affected their benefit from perceptual fluen- these problems. Further, it is possible that the effect of infor- 41 cy-building support. Thus, more research is needed to explore mation overlap on students’ benefit from connection-making 42 how mental rotation ability affects students’ benefit from dif- problems depends on the individual student’s prior experience 43 ferent types of support for connection making among multiple with the given graphical representations. Future research 44 graphical representations. should investigate these questions, so as to provide further in- 45 Another limitation is that, as already mentioned, comparing sights into how best to design conceptual sense-making prob- 46 students from two different experiments based on their prior lems and perceptual fluency-building problems with the opti- 47 conceptual understanding of connections is difficult because mal representation pairs. 48 many other factors may have contributed to the differences To conclude, the experiments presented in this paper extend Education 49 between Experiments 1 and 2. Future research should there- our understanding of how students learn with multiple graph- 50 fore investigate whether, indeed, students’ prior conceptual ical representations. Specifically, both studies provide empiri- 51 understanding of connections as it develops over the course of cal evidence that we can enhance undergraduate students’ 52 a longer learning experience (e.g., during a chemistry course) learning of chemistry knowledge by supporting them in making 53 affects their benefit from conceptual and perceptual support connections among multiple graphical representations. They 54 for connection making. The experiments reported here cannot also provide evidence that both conceptual sense-making of 55 test this hypothesis because they were cross-sectional (i.e., connections and perceptual fluency in connection making are they investigated the effects of students’ prior competences as important aspects of students’ learning of chemistry content. 56 Chemistry 57 they happened to be at the beginning of the intervention). A The overall finding across Experiments 1 and 2 seems to be 58 59 60 This journal is © The Royal Society of Chemistry 20xx J. Name ., 2013, 00 , 1-3 | 13

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ARTICLE Journal Name 1 2 that perceptual fluency-building builds on conceptual sense- Bodner G. M. and Domin D. S., (2000), Mental models: The role of 3 making of connections. These findings yield practical recom- representations in problem solving in chemistry, 4 mendations for how best to combine conceptual and percep- University Chemistry Education , 4, 24-30. 5 tual support for connection making. If students have low prior Bowen C. W., (1990), Representational systems used by graduate students while problem solving in organic synthesis, 6 conceptual understanding of connections, they should receive Journal of Research in Science Teaching , 27 , 351-370. 7 both conceptual sense-making support and perceptual fluen- Brown T. L., LeMay H. E., Bursten B. E., Murphy C. J. and Woodward 8 cy-building support. If they have high prior conceptual under- 9 P. M., (2011), Chemistry - The central science Prentice Hall. standing of connections, they should receive only perceptual Cheng M. and Gilbert J. K., (2009), in Multiple Representations in 10 fluency-building support for connection making. Given the Chemical Education , eds. Gilbert J. K. and Treagust D. F., 11 pervasiveness of multiple graphical representations in chemis- Berlin / Heidelberg: Springer, pp. 191-208. 12 try education, these findings have the potential to generalize Chi M. T. H., Feltovitch P. J. and Glaser R., (1981), Categorization 13 to other topics than atomic structure and bonding. and Representation of Physics Problems by Experts and 14 Novices, Cognitive Science , 5, 121-152. Manuscript 15 Chung W. C., (2013), Three-dimensional atomic orbital plots in the 16 Acknowledgements classroom using Winplot, Journal of Chemical Education , 17 90 , 1090-1092. The University of Wisconsin—Madison Graduate School and Cohen J., (1988), Statistical Power Analysis for the Behavioral 18 the Wisconsin Center for Education Research supported this Sciences , Hillsdale, NJ: Lawrence Erlbaum Associates. 19 research. We thank John Moore for his advice. I thank John Cooper M. M., Underwood S. M. and Hilley C. Z., (2012), 20 Moore, Oana Martin, Teri Larson, Ned Siebert, and and Ste- Development and validation of the implicit information 21 from Lewis structures instrument (IILSI): do students

phen Block for their help in recruiting students. I thank Aman- Accepted 22 da Evenstone, Joe Michaelis, Sally Wu, Greyson Bahr, Youn Ku connect structures with properties?, Chemistry Education 23 Choi, Brady Cleveland, Natalie Fay, Taryn Gordon, Ashley Research and Practice , 13 , 195-200. 24 Hong, Will Keesler, Amber Kim, Ashley Lee, Marguerite Lee, Corbett A. and Anderson J., (2001), in Proceedings of CHI 2001 , vol. ACM Press. 25 Aditi Renganathan, Jamie Schuberth, Mike Schwanke, Peter Corbett A. T., Koedinger K. and Hadley W. S., (2001), in Technology Van Sandt, Theresa Shim, and Philip Zimring for their help in 26 enhanced learning: Opportunities for change. , ed. 27 conducting the experiments. Goodman P. S., Mahwah, NJ, US: Lawrence Erlbaum

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