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Mathematical Thinking through Simulations: Combustion Lab Stoichiometry

Author(s): 

Tanya Gupta, Department of Chemistry & Biochemistry, South Dakota State University, Brookings, SD

Abstract: 

Understanding of Stoichiometry is crucial for students pursuing various chemistry courses and aspiring for majors that require basic understanding of chemistry. It is important to provide several avenues to students in classroom, laboratory settings, and online through interactive visual tools to strengthen their understanding. Specifically new simulation models that are student centered need to be developed and explored. Through this paper the usefulness of an innovative simulation called Combustion Lab is explored.  The paper provides an introduction to a new-student centered model of Simulation Design that incorporates Learning Cycle Approach and knowledge evaluation throughout the simulation.

Introduction

The use of interactive simulations in chemistry instruction has seen a rapid surge in the past decade. A simulation is a dynamic, interactive, scaled down model of the real world phenomena, and complex natural or synthetic processes that are otherwise difficult to observe or manipulate (Plass, Homer & Hayward, 2009; Plass, Milne, Homer, Schwartz, Hayward, 2012). The key objective of simulations in chemistry instruction is to help students develop a coherent understanding and explanation of the concepts and theories underlying various chemical processes (Suits & Sanger, 2013).

Researchers involved in developing and implementing simulations for the chemistry instruction have found simulations to be effective in terms of helping students visualize relative motion of particles, and in improving problem-solving by supplementing sensory experiences of learners (Falvo, 2008; Gerjets & Hesse, 2004; Stieff & Wilensky, 2003; Tasker & Dalton, 2006). Simulations provide new affordances for learning science, particularly for abstract phenomena, and also promote interaction and thinking about complex scientific ideas (Webb, 2005). This is particularly important in chemistry- a solid grasp of chemistry depends on the understanding of interactions and the particulate nature of matter, which is otherwise hard to visualize. Further, simulations are cost effective, safe to use, and convenient to integrate with various instructional settings including lecture and laboratory (Millar & Osborne, 1998). 

Simulations and animations have been found effective in engaging students in classroom and improving student exam scores; their representational competence, and student understanding of specific concepts such as the particulate nature of matter and electrochemistry (Barak 2013; Barnea & Dori, 1999; Charistos; Tsipis, & Sigalas, 2005; Falvo, Urban, & Suits, 2011). Animations and simulations differ vastly. While animations are used to help students understand and explain abstract concepts, simulations allow students to explore phenomena and their representations while manipulating variables (Suits & Diack, 2002). Simulations thus provide a certain degree of control to learners through their interactive features such as play and pause buttons, adjusting variables such as mass, volume etc., using buttons and sliders, and stop, review, and exit functions.

Some researchers have focused on design features of animations and simulations. These researchers suggest that simulation developers should design simulations which are simple to use; display a balance of information, have audio and visual components in design; allow user control; reduce extraneous cognitive load on learners; and accurately portray the concepts and processes in chemistry (Landriscina, 2013; Plass, Homer, & Hayward, 2009; Jones, Honts, Tasker, Tversky, Suits, Falvo, D., et al., 2008). Simulation designers should also consider the prior knowledge of learners, which plays an important role in student use of simulations (Yang, Andre, Greenbowe, & Tibell, 2003). A simulation that enables leaner to explain the macroscopic observable chemical reaction at the molecular level is considered effective resource for conceptual connections and knowledge construction (Martin and Mahaffy, 2013; McKenzie, Versprille, Towns, Mahaffy, Martin, and Kirchhoff, 2013).

There have been numerous studies on the development and application simulations in chemistry. Researchers have in particular emphasized an intuitive and user-friendly simulation design to foster conceptual understanding. Simulations can also be used for promoting mathematical thinking particularly in chemistry where students struggle most with most fundamental ideas such as stoichiometry. There is a need of variety of such tools that are developed based on well-researched models of teaching and learning and provide a complete picture of a specific or a targeted concept and its relevance in everyday life. This paper highlights the development features of the a stoichiometry based simulation called Combustion Lab and its implementation in organic chemistry laboratory with students taking first semester of a two-semester sequence of organic chemistry laboratory course in a mid-western university.

 

Why a new simulation in Stoichiometry?

Learning chemistry involves understanding submicroscopic processes through macroscopic observations and symbolic depiction of various chemical processes. Use of models and analogies makes it easy to grasp various concepts in chemistry that are otherwise too abstract or inexplicable (Gabel, 1999; Bou Jaoude & Barakat, 2003; Wolfer, 2000). Students often perceive chemistry to be a difficult subject. This can be attributed to the natural of chemical processes, which are physically observable or operate at macroscopic level. Such processes can be conceptually understood by examining the interactions taking place at the particle level. Students need to be able to draw connections between the three representational levels in chemistry – the macroscopic, submicroscopic or particulate level, and the symbolic level for developing a correct conceptual understanding. It is reported that a majority of students treat these three representational levels in a compartmentalized way and as operating independent of each other (Gulacar, Eilks, and Bowman, 2014; Marais and Combrinck, 2009).

Stoichiometry is a fundamental conceptual building block of for understanding chemistry. It is necessary to understand quantitative relationships between the various substances that chemically combine to form new substances either naturally or synthetically in a laboratory (Finley, Stewart, Yarroch, 1982). Chemists just don’t mix stuff and wait and watch to see what comes out. The experiments in a laboratory are carefully designed such that efficiency can be maximized. Though stoichiometry is fundamental for any chemical reaction, students struggle with the reaction stoichiometry and connecting the three representational levels to coherently understand and apply the law of conservation of mass for a given chemical reaction.

Despite their lack of understanding of stoichiometry, it has been reported that students can solve stoichiometry-based problems correctly. The problem-solving attempted by novice students is heavily focused on the surface features of the stoichiometric exercises and problems presented to them (Nurrenbern & Pickering, 1987; Gabel and Bunce, 1984; Yarroch, 1985).  Several persistent misconceptions have also been reported among students in this area. These misconceptions include incorrect use of subscripts and coefficients in the balanced chemical equation, errors in finding mole-ratios and using Avogadro’s number, limiting reagent and product yield, state of reactants in a reaction, and the reaction conditions (Huddle and Pillay, 1996; Johnstone, MacDonald, & Webb, 1977; Kesidou and Duit, 1993).

Understanding of Stoichiometry is crucial for students pursuing various chemistry courses and aspiring for majors that require basic understanding of chemistry. It is important to provide several avenues to students in classroom, laboratory settings, and online through interactive visual tools to strengthen their understanding. Specifically new simulation models that are student centered need to be developed and explored. Through this paper the usefulness of an innovative simulation called Combustion Lab is explored.  The paper provides an introduction to a new-student centered model of Simulation Design that incorporates Learning Cycle Approach and knowledge evaluation throughout the simulation.

 

A coherent mental model connecting three levels of representation and the Learning Cycle Approach

Expert problem-solvers often use various models and representations to arrive at the correct solution (Chi, Feltovich, and Glaser,1981; Kozma and Russell, 1997). The conceptual understanding of chemistry relies on acquisition and integration of various principles through representations at the macroscopic level, particulate level and the symbolic level. A coherent mental model of student will encompass all three levels as shown in figure 1 (Johnstone, 1993; Gupta, Ziolkowski, Albing, & Mehta, 2017).

 

Figure 1. Three representational levels that constitute a coherent mental model

 

Learning Cycle Approach to Inquiry Teaching

The goal of inquiry-based instruction is to establish the understanding of scientific concepts and processes and provide skills to students that are consistent with scientific practices of the experts in the discipline (Gupta, Burke, Mehta & Greenbowe, 2015). Learning cycle (LC) is a student-centered inquiry-based approach based on the constructivist paradigm of teaching and learning. The LC has three stages of a) concept exploration b) concept invention or concept introduction c) concept application, and concept evaluation that are conducted in a sequence (Abraham, 1998; Lawson, Abraham and Renner, 1989). In exploration stage learners engage in hands-on classroom, laboratory or online activities. The focus of this phase is data collection, observations, and seeking patterns.  

In the concept introduction stage students are introduced to the concept. This usually occurs by instructor facilitation and during discussion with peers based on the patterns observed. In this stage student engage in meaning making and develop explanations for the trends they see in data. Instructor helps students by asking appropriate questions to connect student prior knowledge to student experiences of the activity and introduces new concept and terminologies.

In the concept application stage of learning cycle students take their understanding further by applying it to a new problem. Students may also review, revise, and reinforce their understanding by working a similar problem in a different context. This could involve reading a research paper, solving problems, or designing the next stage of the activity or experiment. At this stage the focus is on the knowledge of students and how it can be applied further and reexamined. The final stage of concept evaluation is assessment based. In this student knowledge is evaluated. This could involve different activities such as further reading, group discussions, reflection, exams and quizzes.

The Combustion Lab Simulation incorporates all representations levels and the Learning Cycle Model. It takes the concept evaluation of the Learning Cycle Approach a step further by evaluating students at several points. The simulation design involves assessment of student prior knowledge and student understanding at each stage of the LC approach (knowledge evaluation component). Following section presents details of Combustion Lab Simulation.

 

Stoichiometry through Combustion Lab

The author and her research team developed the Combustion Lab simulation. It is a 2-D activity that incorporates the LC approach. There are four buttons on the opening screen. These buttons (Figure-2) are designed according to the key components of the LC as a) Prior knowledge activation- PKA, b) Exploration Activity- EA c) Concept introduction – CI, and d) Post-Activity application - PAA. Knowledge evaluation is embedded within each component and also in the post-activity application component. The simulation is segmented to cover different examples of stoichiometry of combustion reactions. A user can begin by clicking on any of the four buttons. Author recommends that the users start from PKA and follow each sequence in order for an authentic learning cycle-based inquiry experience.

Figure 2. Combustion Lab Simulation

The goal of Combustion Lab simulation is to engage students in the process of inductive discovery of the stoichiometry of combustion reactions and a simultaneous evaluation of student knowledge through various problems embedded within the simulation. The simulation can currently run on different platforms (Windows, Mac, and Linux computers). Hardware requirements for these simulations are very low. Very few simulation objects are in use at any one time due to its segmented and focused design. Efforts are underway to develop versions for mobile devices.  

Prior Knowledge Activation:

The PKA segment of simulation is focused on assessing student prior knowledge through multiple-choice type question bank (Figure 3). The question bank in this component also includes questions adapted from Chemical Concept Inventory (CCI) by Robinson and Mulford (2002). A written consent was obtained for these questions to include them in PKA component. These questions are based on various topics such as dimensional analysis, physical and chemical changes, understanding of coefficients and subscripts in a reaction. The PKA component comes first prior to exploration phase. In the PKA segment, users are quizzed on 10 randomized questions. As a user answer these questions, he/she can see their score on the top right corner of the screen based on the correctness of their response. The maximum score for the PKA is 10 points for 10 questions.  

Figure 3. Sample Question from PKA segment of Combustion Lab

The Concept Exploration (CE) component of simulation is called Exploration Activity (EA) (Figure 4). On clicking the EA button one can see four individual combustions reactions for different fuels that are further segmented into series of macroscopic, submicroscopic, and symbolic representations. These include methane, propane, butane and octane. With the use of arrows one can explore a given reaction and navigate through four different fuels. The initial representation of the combustion reaction for any selected fuel is at the macroscopic level. After clicking the next arrow, one can see the symbolic representation of the equation and balance the equation for the combustion reaction. The objective is to allow the user to connect the macroscopic process with the symbolic representation. After clicking next button, the user experiences the molecular representation (space filling models). The representation is accompanied with the sliders for the user to see the relation between different amounts of reactants and products involved in the reaction in the units of moles, grams, kilograms, liters and gallons. This function of Combustion Lab is aimed at helping a learner connect the changes in number that correspond to the different units that are used. The learner can see the change in numbers as they use the slider. When the user picks a molecule (reactant or product) in the reaction and slides, the value for the amount of reactant and products accordingly (increases or decreases).  Figure 5 and 6 represent the symbolic representations and molecular representations of these reactions during the concept exploration.

 

Figure 4. Concept Exploration Component-Example of Reaction from Simulation

 

Figure 5. Symbolic Representation – determining coefficients to balance equation

 

Figure 6. A Space-filling molecular representation and showing relation between different units (quantities) for reactants and products

As mentioned, there are four combustion reactions in the Combustion Lab. For this paper only one component of the exploration-activity is presented as an example. When a student explores an activity that involves combustion of octane – the student is presented with sliders to adjust the ratio of air to fuel. In case of octane, once the student arrives arrives at the correct ratio (25:2) there is a flame observed in the simulation at the moving piston that indicates the ignition (Figure 7).

Figure 7. Combustion reaction stoichiometry of octane – sliders allow adjusting air (oxygen) and fuel ratio

Incorrect ratios will indicate dark fumes and some sparks. As the fuel ignites, a forward arrow appears on the bottom right corner of the screen. This allows the user to proceed to the next sub-segment, which is the blackboard (figure 5 for digital chalkboard with symbolic representation or reaction equation).

On the digital blackboard the user needs to balance the reaction equation for the reaction by entering coefficients for reactants and products. If the user enters the correct coefficients for the reaction, the number of atoms on both sides of the reaction equations match-up and turn green. Incorrect coefficients are displayed by a red color for the number of atoms and the user is asked to retry the coefficients.

A forward arrow at the bottom right of simulation window leads users to the next screen of the Combustion Lab wherein the conversion factors for various amounts of reactants and products are provided along with the space-filled models of each reactant and product (see Figure 6 for molecular level representation with various units). In this component of exploration students can use sliders and set the amount of reactants and products in various units moles, grams, kilograms, liters and gallons. As students change the amount on the slider the amount of reactants and products displayed underneath molecular representation also changes. This enables students to view the quantity of reactants and products in various units (conversion factors). Students can click on the unit buttons to see various amounts of reactants and products for each of the five units presented in this simulation. These can be done for each of the four combustion reaction activities. The EA involves inbuilt trials and errors for students, which is consistent with the LC approach. Students can play with various ratios for each reaction and try different coefficients and explore conversions for different amounts of reactants and products.

The next button is Concept Introduction (CI). In the CI section students are presented very brief information on coefficients, law of conservation of mass, combustion reactions and the impact of the use of fossil fuels on global warming.

Figure 8. The Concept Introduction Component of Combustion Lab

 

There are two buttons in this component of Combustion Lab (Figure 8). The Go Back button allows user to revisit any of the four combustion activities. Visit EPA website (Environmental Protection Agency) button allows the user to access the EPA website from within the Combustion Lab. This inbuilt feature provides users an opportunity to understand the relevance of the stoichiometry of combustion reactions in light of the effects of these fuels on global warming leading to climate change.

The last component of the Combustion Lab is Concept Application and Evaluation Phase of the Learning Cycle Model and is titled Post Activity Application (PAA). PAA involves stoichiometry based problems, problems on limiting reagent involving particulate or submicroscopic representations, and real world problems for example: calculating the gas mileage and cost for a round-trip to Disneyland, and the resultant quantity of a greenhouse gas (carbon-dioxide) emitted by car (Figure 9: PAA problem)

 

Figure 9. Concept Application and Knowledge Evaluation through Post Activity Application

PAA problems cover basic to advanced understanding of the stoichiometry of combustion reactions, and also aim at providing students an opportunity to reflect on the impact of using fossil fuels on a daily basis in terms of the greenhouse gas released into the environment by a simple act of round-trip for leisure. Students receive an immediate feedback for the responses entered in this section. If the student response is incorrect, they are asked to try again or see a red flash based in the check answer button. The next section describes implementation of the Combustion-Lab to study its effectiveness.

 

Implementation and the study of the effectiveness of Combustion Lab Simulation

After developing the simulation on Combustion Lab incorporating the Learning Cycle and Prior Knowledge Activation, it was important to study the impact of the Simulation on student learning. To achieve this objective, the combustion Lab was implemented at an undergraduate level organic chemistry course to answer the research question on the impact of Combustion Lab Simulation on student performance on stoichiometry-based problems. The theoretical framework of constructivism, symbolic interactionism and model-based learning and teaching informed this study.

From a constructivist perspective, the construction of scientific knowledge among learners needs to be coherent, viable, and consistent with the established principles of the discipline (Duckworth, 1964; Herron, 1975; Kretchmar, 2016). Learners should have sufficient opportunities through carefully designed activities to develop correct understanding of scientific processes. Symbolic interactionism is a based on the need for symbols and their importance in knowledge construction. This is especially relevant for chemistry (stoichiometry) as the development of the knowledge in this discipline to a large extent relies on the use of symbols as a language (formulas and equations), and microscopic and macroscopic representation of phenomena.

Models are important for scientific reasoning and comprehensions. Scientists often construct and use models to explore and explain phenomena, to arrive at correct explanations and to build evidence and scientific argumentation (Campbell & Oh 2015; Clement, 2000). Model-based teaching and learning can improve student’s ability to make sense of scientific phenomena by enabling students to construct causal explanations. A target qualitative model, which is the simplified analogous model of specific phenomena or a concept such as stoichiometry can be very helpful for students to develop scientifically coherent conceptual models. Various models of chemical processes when presented to students in the form of representations, animations and/simulations can positively impact student conceptual understanding of chemistry (Tasker & Dalton, 2006).

Research Method

A sequential explanatory mixed-methods approach was used for this study. A sequential explanatory study is characterized by collection of both quantitative and qualitative data. Quantitative data is collected and analyzed first followed by qualitative data to support or explain quantitative findings (Creswell and Plano Clark, 2011). The qualitative data in the form of student written laboratory reports was integral in explaining and interpreting the results of the quantitative data of the tests. For this Confchem paper, the author will present and discuss only a small part of the quantitative component of this study on the effectiveness of the Combustion Lab Simulation.

Data Collection and Analysis

The participants in this study were enrolled in the first semester of a two-semester sequence of an organic chemistry laboratory course. The simulation was implemented as an alternate online laboratory activity. All students enrolled in this course had been introduced to Stoichiometry during the two-semester sequence of general chemistry, which is a perquisite for the organic chemistry course. It was anticipated that students have sufficient prior knowledge to engage in a stoichiometry based online lab with a minimal directions on downloading and doing the laboratory activity. The activity was assigned to students during the second week before students engaged in any wet laboratory on organic synthesis that require stoichiometry based calculations from the students (mole ratios and limiting reagents).

The learning management system folders were timed and organized in a way that students would first do the randomized pre-quiz, then download and run the Combustion Lab during the laboratory section meeting for the same amount of time (2 hours and fifty minutes) as their regular in laboratory session meeting. Students were required to write and submit a laboratory report in the D2L dropbox at the conclusion of the activity. After students submitted their laboratory report, the randomized post-quiz opened on D2L for 30 minutes. After completing the post-quiz the survey link opened for students to complete the online survey related to the Combustion Lab Simulation experience. Students were electronically graded for pre- and post quiz. The laboratory reports were graded by the course instructor and followed the same rubric for all participating students. Toward the end of semester, students were given the laboratory practical exam, which contained multiple-choice questions that were based on questions from PKA, EA, CI and PAA questions from the Combustion Lab. The exam was conducted in the laboratory during the final exams week.

About 215 students (82.4%) consented to participate in this study.  The students taking this chemistry laboratory course are mainly pre-med, pre-pharmacy, pre-dental or allied health science majors. About 43% participants were males and 57% were females. Students enrolled in the laboratory were also enrolled in the co-requisite organic lecture course. It is important to note that the implementation of combustion lab simulation was done in the laboratory and the data is collected only from the laboratory component of the course. The data for student performance on the pre- and post quiz was downloaded from the D2L as Microsoft Excel files. The files were then cleaned and organized - students who did not consent to participation in the research study were omitted from data analysis. Students with incomplete data (missing a quiz or laboratory report) were also eliminated which led to a sample size of 193 students.

The backend user data generated from the simulation use by students was downloaded as Microsoft Excel spreadsheets.  These files were then organized into the different sections of the simulation - Prior Knowledge Activation (PKA), post-activity application (PAA), and Concept-Introduction (CI) for generating response frequencies and studying simulation user behavior. A two-tailed matched pairs t-test was performed (Howell, 2007) to compare student performance on pre- and post-quiz and for PKA and PAA combustion lab questions. Only results from pre- and post quiz and laboratory practical exams are presented and discussed in this paper.

 

Results & Discussion Student performance on stoichiometry problems

Table 1 provides a summary of the pre- and post quiz mean scores and paired samples t-test. The results of two-tailed t-test for pre- and post-quiz indicate a statistically significant difference (p=0.008; α=0.05, DF, 192) between student scores from pre to post-quiz. It is important to note that the quiz was based on stoichiometry and the randomized questions were similar in levels of difficulty from pre-to post-quiz but essentially not the same (wording or numbers in questions could have differed due to random assignment). Students also performed significantly better on stoichiometry questions in laboratory final exams (two-tailed t-test; p=0.0001; α=0.05, DF, 192).

Table 1: Comparison of student performance on stoichiometry problems in pre- and post-quiz; PKA and PAA problems within simulation final laboratory practical examination

(N=193)

Mean
(Out of 10)

Standard
Deviation

Paired t-test

Pre-Quiz

6.90

2.14

p=0.0008*

Significant at α=0.05)

DF=192; 95% confidence

Post-Quiz

7.60

2.25

Lab practical exam questions (stoichiometry questions)

6.39

1.65

p=0.001*

Significant at α=0.05)

DF=192; 95% confidence

The quantitative results indicate that students showed an improvement in student understanding of stoichiometry from pre- to post quiz on use of Combustion Lab Simulation. It seems that the simulation-helped students understand that stoichiometry involved in combustion reactions and they were able to translate their understanding to solving post-quiz and laboratory exam problems correctly.

 

Conclusions, limitations and further research

The study helps in establishing that the simulation on combustion lab was helpful in furthering student understanding based on the assessment of student performance on pre- and post quiz and final lab exams. The study was limited in its implementation being online as a laboratory activity. It will be worthwhile to implement this activity in a classroom setting or in a face-to-face laboratory structure. The study has important implications for the use of simulations tools for exploration and knowledge evaluation for online and in class instruction. Instructors can use this simulation in multiple ways depending on their need. One important use for instructors would be to exactly pinpoint and address gaps in student understanding. Instead of waiting for final assessment, the student data can be used to provide remedial instruction targeted to individual students in real time based on the back end user data.

 

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Date: 
04/23/18 to 04/25/18

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