THE EFFECTS OF USING PARTICLE DIAGRAMS ON THE CONCEPTUAL UNDERSTANDING OF STOICHIOMETRY OF STUDENTS AT ADVENTIST INTERNATIONAL MISSION SCHOOL, THAILAND

CONCEPTUAL UNDERSTANDING OF STOICHIOMETRY Asia-Pacific International University THE EFFECTS OF USING PARTICLE DIAGRAMS ON THE CONCEPTUAL UNDERSTANDING OF STOICHIOMETRY OF STUDENTS AT ADVENTIST INTERNATIONAL MISSION SCHOOL, THAILAND A Master thesis Presented in partial fulfillment of the requirements for the degree MASTER OF EDUCATION by Faridah Lausin May 2020

CONCEPTUAL UNDERSTANDING OF STOICHIOMETRY i THE EFFECTS OF USING PARTICLE DIAGRAMS ON THE CONCEPTUAL UNDERSTANDING OF STOICHIOMETRY OF STUDENTS AT ADVENTIST INTERNATIONAL MISSION SCHOOL, THAILAND A Master thesis Presented in partial fulfillment of the requirements for the degree MASTER OF EDUCATION By FARIDAH LAUSIN APPROVAL BY THE COMMITTEE Jimmy Kijai, PhD Josephine Esther Katenga, PhD Research Advisor Chair of Master Program Amanda Simon, PhD Naltan Lampadan Panelist Dean, Faculty of Education Damrong Sattayawaksakul, PhD External Examiner

CONCEPTUAL UNDERSTANDING OF STOICHIOMETRY ii ABSTRACT Master of Education Emphasis in Curriculum and Instruction Asia-Pacific International University Faculty of Education TITLE: THE EFFECTS OF USING PARTICLE DIAGRAMS ON THE CONCEPTUAL UNDERSTANDING OF STOICHIOMETRY OF STUDENTS AT ADVENTIST INTERNATIONAL MISSION SCHOOL, THAILAND Researcher: Faridah Lausin Research advisor: Dr Jimmy Kijai Date completed: May, 2020 The lack of conceptual understanding of stoichiometry among high school students generates interest in exploring instructional strategies that focus on conceptual learning. In this study, the effects of a visual-based pedagogical approach were investigated on the understanding of four concepts of stoichiometry among tenth-grade Chemistry students at the Adventist International Mission School in Saraburi, Thailand. The approach involved systematic and extensive use of particle diagrams in the instruction of stoichiometry in a real classroom setting. The study further examined the attitudes of the students towards the approach. Conducted using the one-group pre-test/posttest design, data for the study were collected using a conceptual stoichiometry test (CST) and an attitude questionnaire (ATPD). Analyses of data indicated that the

CONCEPTUAL UNDERSTANDING OF STOICHIOMETRY iii approach had significantly positive effects on the students’ conceptual understanding of stoichiometry, and that the students generally had a favorable attitude towards the use of the method. It is recommended that Chemistry teachers incorporate particle diagrams in stoichiometry lessons to support conceptual understanding.

CONCEPTUAL UNDERSTANDING OF STOICHIOMETRY iv ACKNOWLEDGEMENTS I would like to convey my gratitude and appreciation to the following individuals who assisted me in my thesis-writing journey. My principal supervisor, Dr Jimmy Kijai for his vital suggestions and assistance. My supervisor, Dr Josephine Katenga whose reminders and encouragement made it possible to complete this thesis. My dean, Mr. Naltan Lampadan for his words of motivation. My three sons, Haydn, Eldrian and Darien, who understood my busy days. My husband, Golden Gadoh, who keeps me going in the many journeys of my life including this one. My God, who began a good work in me and will carry it on to completion until the day He comes. Faridah Lausin

CONCEPTUAL UNDERSTANDING OF STOICHIOMETRY v TABLE OF CONTENTS ABSTRACT...................................................................................................................ii ACKNOWLEDGEMENTS..........................................................................................iv LIST OF TABLES......................................................................................................viii LIST OF FIGURES ......................................................................................................ix CHAPTER 1. INTRODUCTION .............................................................................................1 Background and Context of Study ................................................................1 Rationale .......................................................................................................4 Statement of Problem....................................................................................5 Purpose of the Study .....................................................................................5 Research Questions.......................................................................................6 Significance of the Study.....................................................................6 AIMS Science Teachers ......................................................................6 AIMS Chemistry Students...................................................................6 Limitations ....................................................................................................7 Delimitations.................................................................................................9 Definitions of Terms.....................................................................................9 Organization of the Study ...........................................................................10 2. LITERATURE REVIEW ................................................................................12 Introduction.................................................................................................12 Stoichiometry ....................................................................................12 Stoichiometry - A Problematic and Challenging Topic ....................14 The Mathematics of Stoichiometry.............................................................15 The Algorithmic Solution..................................................................16 Conceptual Stoichiometry...........................................................................18 The Conceptual Approach.................................................................21 The Particulate Nature of Matter ................................................................23 The Three Levels of Chemistry ..................................................................25 Particle Diagrams........................................................................................27 Summary .....................................................................................................28

CONCEPTUAL UNDERSTANDING OF STOICHIOMETRY vi 3. METHODOLOGY ..........................................................................................29 Introduction.................................................................................................29 Research Questions.....................................................................................29 Research Design..........................................................................................30 Treatment Conditions........................................................................32 Section 1: Topic - Types of Matter...................................................33 Section 2: Topic - Types of Chemical Reactions. .............................34 Section 3: Topic - Limiting Reagent .................................................36 Section 4: Topic – Theoretical Yield................................................38 Population and Sample................................................................................39 Instrumentation ...........................................................................................39 Conceptual Understanding of Stoichiometry Pretest Posttest ............................................................................................39 Attitudes Towards the Use of Particle Diagrams Questionaire ....................................................................................41 Procedure.....................................................................................................42 Piloting of Instruments......................................................................43 Data Collection..................................................................................43 Data Analysis..............................................................................................44 Summary .....................................................................................................45 4. RESULTS ........................................................................................................46 Introduction.................................................................................................46 Description of the Sample...........................................................................46 Participants’ Overall Performance in Chemistry...............................47 Analysis and Interpretation of CST Results....................................48 Analysis and Interpretation of CST Results....................................49 Results of paired-samples t-test.........................................................50 Analysis and Interpretation of ATPD Survey Results.......................53 Summary of Major Findings.......................................................................57 5. SUMMARY.....................................................................................................59 Introduction.................................................................................................59 Purpose of the Study ...................................................................................59 Review of the Literature..............................................................................60 Methods .....................................................................................................62

CONCEPTUAL UNDERSTANDING OF STOICHIOMETRY vii Results ................................................................................................... .........................................................................................................63 Discussion of the Findings..........................................................................63 Finding 1............................................................................................64 Explanation 1.....................................................................................64 Finding 2............................................................................................65 Explanation 2.....................................................................................65 Finding 3............................................................................................66 Explanation 3.....................................................................................67 Finding 4............................................................................................68 Explanation 4.....................................................................................68 Conclusions.................................................................................................69 Limitations ..................................................................................................70 Implications.................................................................................................71 Recommendations for Future Research ......................................................71 REFERENCES LIST...................................................................................................73 APPENDIX..................................................................................................................82

CONCEPTUAL UNDERSTANDING OF STOICHIOMETRY viii LIST OF TABLES 1. Pretest Posttest Questions and Related Concepts ............................................41 2. Demographic Profile of Sample.......................................................................48 3. Pretest Posttest Mean, Standard Deviation and Skewness (N=13)..................51 4. Mean Difference, Paired T-Test Results and Effect Size (N=13) ...................52 5. Attitude questionnaire reliability analysis (n=13) ...........................................54 6. Concept Attitude Descriptive Statistics, Skewness, and Reliability Estimates (N=13) .............................................................................................55 7. Descriptive Statistics for The Concept of Representative Particles (N=13)..............................................................................................................56 8. Descriptive Statistics for Mole Ratio (N=13)..................................................56 9. Descriptive Statistics on Limiting Agent (N=13)............................................57 10. Descriptive Statistics of Theoretical Yield (N=13) .........................................58

CONCEPTUAL UNDERSTANDING OF STOICHIOMETRY ix LIST OF FIGURES 1. Stoichiometry Flow Diagram...........................................................................17 2. Particle Diagrams of Water and Aluminum.....................................................24 3. Particle Diagrams Showing an Element, a Compound, and a Mixture and their Representative Particles....................................................................34 4. Particle Diagrams Showing a Synthesis Reaction Between Hydrogen Gas and Oxygen Gas to Produce Water...........................................................35 5. Particle Diagrams Illustrating the Concept of Limiting Reagents...................37 6. Particle Diagrams Showing the Theoretical Yield From a Reaction Between Magnesium and Oxygen Gas. ...........................................................39 7. Participants’ Chemistry Percent Grades for The First and Second Quarters of 2018-19. ........................................................................................49 8. Pre and Post Scores on CST by Participants....................................................50 9. Pre and Post Scores on CST by Concept .........................................................51

CONCEPTUAL UNDERSTANDING OF STOICHIOMETRY 1 CHAPTER 1 INTRODUCTION Background and Context of Study In my more-than-ten years of teaching high school Chemistry, I have observed a recurring trend. At the beginning of the first semester, students are elated and motivated to learn the language of Chemistry, which consists of complex-looking chemical formulas, formidable chemical names, and equations decipherable only (they think) by the likes of Einstein. Perhaps the students pride themselves a little on their ability to read a language as unfathomable as hieroglyphics to those who are not taking Chemistry. But alas, the excitement and sense of superiority do not last long. By the second half of the first semester, when I introduce a unit called Stoichiometry, the students become quite discouraged. Stoichiometry is a branch of chemistry that deals with the quantitative relationships that exist between the reactants and the products in chemical reactions. Reactants are the substances that participate in chemical reactions, while products are substances that are produced as a result of the chemical reactions (Wilbraham, et al., 2012). The students’ main task in this very mathematical part of Chemistry is solving stoichiometric problems in which they have to calculate the quantities of reactants and products in terms of mole, mass, volume, or number of representative particles. Some problems require students to identify which of the reactants is the limiting or excess reagent and calculate its quantity in terms of mole, mass, and volume.

CONCEPTUAL UNDERSTANDING OF STOICHIOMETRY 2 My students learn very quickly that they need more than mathematical problem-solving skills to solve stoichiometric problems. They soon realize that their success in stoichiometry problem solving depends heavily on their understanding of specific concepts such as the concepts of representative particles, the mole, chemical reactions, chemical equations, limiting reagent, and theoretical yield. Of primary importance is their understanding of the concept of representative particles. Representative particles are the infinitesimal particles that constitute all matter, including pure substances (chemical elements and compounds) that take part in chemical reactions. To solve stoichiometric problems that are based on chemical reactions, students need to be able to switch from thinking about the concrete aspects of matter to thinking that is more abstract and visualize the interactions among invisible particles as the chemical reactions occur. Unfortunately, many of my students prefer to dismiss the concept of representative particles because, as many of them confess, it is too intangible to make any sense. Yet, a good understanding of the concept of representative particles is essential to understanding other concepts of Stoichiometry. Many students resort to memorizing, simple reasoning strategies, and algorithm methods, which may be useful for answering simple stoichiometric questions but insufficient for solving complex problems that require an understanding of underlying concepts. I am somehow relieved to discover that this is not a problem unique to the students I have taught and the high school Chemistry students whom I am currently teaching at the Adventist International Mission School, Thailand. Dahsah and Coll (2007) reported that even after major national curriculum reforms, Thai grades 10 and 11 students who participated in a survey demonstrated less than the acceptable level of understanding of concepts related to stoichiometry. The Thai students’ responses

CONCEPTUAL UNDERSTANDING OF STOICHIOMETRY 3 also suggested that they resorted to the use of algorithms with little knowledge of the underlying concepts. Findings from a study involving eight hundred sixty-seven grade 12 Indonesian students showed that in general, Indonesian students were more successful in answering questions that are algorithmically based, and that there were no strong positive correlations between student performance on conceptual questions and algorithmic questions (Agung, 2007). These studies suggest that students, who have not sufficiently grasped the chemistry concepts behind a problem tend to use algorithmic methods by merely using a memorized formula, manipulate the equation and plug in numbers until they fit. Bridges (2015) suggests that teachers need to be “knowledgeable, creative, and resourceful” in helping their students to learn stoichiometry. In recent years many alternative approaches for teaching this unit of Chemistry have been developed. A study on 96 Indonesian students reported that macro–sub-micro–symbolic teaching, which employs multiple representations, could effectively enhance student mental models and understanding of chemical reaction, which is the basis for solving stoichiometric problems (Sunyono, Yuanita & Ibrahim, 2015). Inquiry-based lessons using particulate level models produce statistically significant improvement in grades 11 and 12 students’ conceptual understanding of stoichiometry even though there were variations in the intervention delivery (Kimberlin & Yezierski, 2016). An instructional model that incorporates definitions, computer-generated visuals at the submicroscopic level and physical samples of various substances at the macroscopic level seems to improve students’ conceptions of pure substances and mixtures (Sanger, 2000). These studies suggest that an understanding of the submicroscopic composition of chemical elements or/and compounds that make up the reacting and

CONCEPTUAL UNDERSTANDING OF STOICHIOMETRY 4 resulting substances in chemical reactions is an essential prerequisite to interpreting and solving stoichiometric problems. Rationale These studies cited above concluded and recommended that a more visual pedagogical approach to teaching Stoichiometry could effectively advance student conceptual understanding of Stoichiometry. Consequently, the AP Chemistry curriculum was redesigned to include learning objectives that contain references to particulate representations of chemical phenomena (College Board, 2013; Prilliman, 2014). However, the shift in emphasis toward conceptual understanding using particulate images presents a real challenge for many Chemistry teachers because most of them have had limited exposure to particulate ideas before teaching Chemistry, including during their high school years. Therefore, translating the recommendations for using particulate representations into teaching practices can be a daunting task. The scarcity of classroom-ready lessons or supplementary materials based primarily on particulate descriptions, further compounds the challenge (Kimberlin & Yezierski, 2016). From my own experience as a Chemistry teacher, I observe that in high school Chemistry textbooks, particle diagrams are used sparingly and sporadically as concept illustrations and as summative assessment items. Very few chemistry textbooks make extensive use of particle representations, and they are not easily accessible by teachers. In their action research, Kimberlin and Yezierski (2016) designed and provided evidence for the effectiveness of two particulate level inquiry-based lessons. Unfortunately, these lessons could not be accessed online. Without classroom-ready and easily accessible materials, recommendations to incorporate particulate ideas in Stoichiometry lessons create gaps in the literature.

CONCEPTUAL UNDERSTANDING OF STOICHIOMETRY 5 Statement of Problem Stoichiometry problem-solving poses challenges to Chemistry high school students at the Adventist International Mission School. From the analysis of student responses to a variety of stoichiometric questions, their Chemistry teacher has identified that the primary source of these challenges is students’ minimal or lack of conceptual understanding of Stoichiometry. AIMS students appear to have misconceptions regarding some Stoichiometry concepts, including the concept of mole, the concept of representative particles, stoichiometric ratio, and the concept of theoretical yield and limiting reagent. AIMS students’ inadequate understanding of these concepts impedes their ability to solve stoichiometry problems successfully. Although studies have shown that the use of particle diagrams can effectively improve students' conceptual understanding of stoichiometry, this visual tool has not been applied systematically and extensively in Chemistry classes at AIMS and its impact specifically on AIMS students’ conceptual understanding of Stoichiometry has not been explored. Purpose of the Study The purpose of this study is to investigate the effects of using particle diagrams (also called particulate diagrams), on AIMS high school students’ conceptual understanding of Stoichiometry, specifically on the concepts of representative particle, mole ratio, limiting reagent, and theoretical yield. In this study, a companion booklet entitled “Thinking the Particulate Way!” is designed and used as complementary material in lessons related to concepts of Stoichiometry. At the end of the series of lessons, its effect on students’ conceptual understanding of Stoichiometry, and the students’ attitudes towards its use in learning Stoichiometry is examined.

CONCEPTUAL UNDERSTANDING OF STOICHIOMETRY 6 Research Questions The following questions will guide the researcher in the study. Research Question 1. To what extent does the use of particle diagrams affect students’ conceptual understanding of representative particle, mole ratio, limiting reagent, and theoretical yield? Research Question 2. What are the students’ attitudes towards the use of particle diagrams? Significance of the Study AIMS and Other Schools This study will contribute to the development of science education at AIMS and other high schools. The researcher hopes that this research will encourage Science educators to explore and adapt research-based pedagogical recommendations to verify their effectiveness on the learning of their students in their school settings. AIMS Science Teachers The results of the study will help AIMS Science teachers evaluate the impact of using particle diagrams in developing students’ conceptual understanding of stoichiometry. The study will also help teachers establish the extent to which particulate ideas should be incorporated into instruction to maximize concept attainment while avoiding cognitive overloading. Therefore, this study can help teachers develop new and specific strategies for enhancing conceptual learning in Chemistry. AIMS Chemistry Students. This study encourages students to approach stoichiometric problems from the particulate perspective. Training students to think “in a particulate way” will build the

CONCEPTUAL UNDERSTANDING OF STOICHIOMETRY 7 conceptual foundation not only for stoichiometry but also for other high school Chemistry topics and will be beneficial for more advanced studies of the subject. This study can also help students rectify their misconceptions about some concepts of Stoichiometry, specifically the concepts of representative particles, mole ratio, limiting reagent, and theoretical yield. The researcher also hopes that this study will help students develop appreciation and preference for more in-depth, conceptual understanding rather than superficial learning. Limitations Limitations are potential weaknesses in the research that can affect the results (Creswell, 2012). They are a few limitations to the study. The first limitation is that the study focuses on a small population sample of only thirteen high school students enrolled in Chemistry class at only one international school, namely the Adventist International Mission School, in Thailand. The second limitation is that this study involves only one Chemistry teacher. Because of these limitations, the results of the study will have limited generalizability across students, teachers, and schools. However, the scope of the study is confined to the effects of using particle diagrams on the conceptual learning of AIMS high school Chemistry students only. Therefore, generalizability over general populations is both inconsequential and not an expected attribute of this study. Because of its small size, the study has a reduced statistical power to detect the actual difference between students’ conceptual understanding before and after the use of particle diagrams. Moreover, the use of a one-group pretest-posttest design in this study could compromise its internal validity. The researcher recognizes that the difference between the pretest and posttest data may not be representative of the

CONCEPTUAL UNDERSTANDING OF STOICHIOMETRY 8 actual effect of the use of particle diagrams and may be attributed to alternative factors such as history, maturation, and the testing itself (Joyner et al., 2013). Recognizing these limitations, the researcher is cautious about inferring causality from the data, nor does she intend to treat it as conclusive evidence for or against the use of particle diagrams in Stoichiometry lessons at AIMS. While the data can be useful for designing more extensive confirmatory studies or similar studies at AIMS in the future, the researcher planned the study to serve, more importantly, as a first - hand experience for both teacher and students at AIMS in using particle diagrams intentionally and systematically in the teaching-learning of Stoichiometry. The data will be analyzed to determine how using particle diagrams benefits AIMS students individually and to establish its overall impact on the class’ conceptual understanding as a whole. Another limitation is that the Chemistry teacher of the students involved in this study is also the researcher of this study. Because the teacher is both a familiar and an authority figure in their everyday lives, students might intentionally or unintentionally respond more favorably to the use of particle diagrams. However, this should not compromise the conclusions drawn from the study because all educators are expected to interact on familiar terms with their students and establish authority in the classroom. The researcher herself designed the particle diagrams used in the study. Their accuracy in representing different types and interactions of matter and their relevance to concepts of Stoichiometry is therefore limited to the researcher’s knowledge of Chemistry, resources available to her, and her teaching experience. To make sure that the particle diagrams were correct and consistent with Stoichiometry concepts, they were reviewed and revised by two high school Science teachers at AIMS.

CONCEPTUAL UNDERSTANDING OF STOICHIOMETRY 9 Delimitations Delimitations are purposeful limitations intended to confine the study within certain boundaries (Joyner et al., 2013). The study is delimited to grade ten students at the Adventist International Misson School, Thailand, who enrolled in General Chemistry class at the beginning of the academic year 2018-19. Grade ten students were chosen to be the participants of this study because at AIMS the topic Stoichiomtery is only introduced in their grade level. The reseacher did consider having a control group at another school to obtain results that more potentially reflect a cause and effect relationship. However such a plan would require a more elaborate planning and a close collaboration between two schools. It would also necessitate plans to ensure that variables such as delivery of lessons, learning environment, lesson plans, and test settings to be exactly the same for both the control group and the experimental group. Since such plan was not feasible during the time of the study, the researcher delimited the study to students at AIMS only. Definitions of Terms The following terms are used throughout this study and are defined as follows: Stoichiometry. The study of the quantitative relationships or ratios between two or more substances undergoing a physical change or chemical change. Stoichiometric ratio. A ratio that shows the molar relationship between all the substances involved in a chemical reaction. This ratio also represents the necessary quantities of the reactants for a chemical reaction to occur. Also known as molar ratio. Limiting reagent. The limiting reagent (or limiting reactant or limiting agent) in a chemical reaction is the substance that is totally consumed when the chemical

CONCEPTUAL UNDERSTANDING OF STOICHIOMETRY 10 reaction is complete. The amount of product formed is limited by this reagent, since the reaction cannot continue without it. Theoretical yield. The quantity of a product obtained from the complete conversion of the limiting reagent in a chemical reaction. Chemical equation. The symbolic representation of a chemical reaction in the form of symbols and formulae, wherein the reacting substances are given on the lefthand side and the products on the right-hand side. Chemical formula. A set of chemical symbols showing the elements present in a compound and their relative proportions. Chemical change/reaction. A chemical change/reaction is a process in which one or more substances, the reactants, are converted to one or more different substances, the products. Particulate diagram. A visual representation of the particles of a substance, with the particles typically represented as dots or circles. A particulate diagram is also known as particle diagram, particle-level diagram, or submicroscopic representation. Mole. The mole is the unit of amount in chemistry. A mole of a substance is defined as the mass of substance containing the same number of fundamental units as there are atoms in precisely 12.000 g of 12C. Fundamental units may be atoms, molecules, or formula units, depending on the substance concerned. Pure substances. A material that has a constant composition (is homogeneous) and has consistent properties throughout the sample. All elements and all compounds are pure substances. Organization of the Study This chapter has provided a synopsis of the research by highlighting the challenges that high school students face in their study of Stoichiometry and how this study would

CONCEPTUAL UNDERSTANDING OF STOICHIOMETRY 11 contribute to the learning experience of high school students at AIMS specifically on their understanding of Stoichiometry concepts. Chapter 2 discusses published works related to the research on which the study is based. Chapter 3 describes in detail how the study is conducted, the research design and the data collection techniques. Chapter 4 presents the results and findings of the study. Chapter 5 summarizes and discusses the findings and their implications. The last chapter concludes with the researcher's recommendations based on the results.

CONCEPTUAL UNDERSTANDING OF STOICHIOMETRY 12 CHAPTER 2 LITERATURE REVIEW Introduction AIMS high school students are required to take General Chemistry in grade 10 to graduate with a College Preparatory Diploma. The subject aims at giving students a foundational knowledge of Chemistry by introducing basic concepts and principles in topics such as atomic theories, chemical bonding, chemical periodicity, chemical nomenclature, chemical reactions, the mole, stoichiometry, thermochemistry, redox, nuclear chemistry, and organic chemistry. Stoichiometry is typically introduced halfway through the year and is built on the mastery of specific prerequisite concepts and skills. It is a primary focus of high school chemistry, but unfortunately, for many students, it represents what is hard about learning Chemistry (Sanger, 2005; Gulacor et al., 2013; Kimberlin & Yezierski, 2016). It is also one Chemistry topic among eight to be a significant predictor of college chemistry performance (Tai, 2006). The study of stoichiometry necessarily includes the application of mathematics, which also appears as a highly significant predictor of performance in college chemistry (Tai, 2006). It is, therefore, imperative that high school chemistry teachers equip their students with a strong background in stoichiometry to ensure their success in college chemistry courses. Stoichiometry Stoichiometry is a branch in Chemistry that deals with the calculations of the quantities of substances involved in chemical changes or chemical reactions

CONCEPTUAL UNDERSTANDING OF STOICHIOMETRY 13 (Wilbraham et al., 2017). The word stoichiometry is derived from Greek words: stoicheion, meaning “element” and metron, meaning “to measure” (Golberg, 2015). Though the translation from Greek to English seems to imply that only chemical elements are involved and measured, very often chemical compounds too are involved and measured in chemical reactions. Stoichiometry calculations deal with the quantities of the chemical elements/compounds present before undergoing a chemical change called the reactants, and the chemical elements/compounds produced after the chemical change called the products. These quantities are measured in terms of mass, volume, number of moles, and number of representative particles. The principles of stoichiometry are based upon the law of conservation of mass (Golberg, 2015). The law states that matter can neither be created nor destroyed, so the amount of matter present at the beginning and the end of a chemical reaction must be the same. Consequently, in any chemical reaction, the total mass of reactants is equal to the total mass of products. Balanced chemical equations, which are symbolic and numerical representations of chemical reactions, illustrates this law by showing that mass and the number of atoms of each element is conserved before and after a chemical reaction. A balanced chemical equation then must necessarily have fixed ratios of reactants and products. These ratios are called coefficient ratios and represent the quantitative or stoichiometric relationships among reactants and products and form the basis of constructing and solving a myriad of stoichiometric problems. For example, coefficient ratios are used to calculate the number of moles of any substances in a reaction from the number of moles of any one of the substances participating in the same chemical reaction or calculate the mass of any substance from the mass of another. More challenging problems involve calculating the quantities of other substances even if the amounts of reactants present are not in the

CONCEPTUAL UNDERSTANDING OF STOICHIOMETRY 14 mole ratio of the balanced equation or calculating the percentage yield of a product from the actual yield and theoretical yield, based on the amount(s) of reactant(s) (Goldberg, 2015; Wilbraham et al., 2017). In a nutshell, the goal of solving stoichiometry problems is to make predictions about the quantitative outcomes of chemical reactions and to determine the optimal ratio of reactants for a chemical reaction so that all reactants are fully consumed and thus preventing waste. Stoichiometry - A Problematic and Challenging Topic It has been almost two decades since literature brought to our attention the difficulties, discouragement, and anxiety that secondary students had with stoichiometry (Jaoude & Barakat, 2000; Schmidt & Jignéus, 2003). But even after alternative approaches for teaching stoichiometry were developed to help students succeed in stoichiometry, students and teachers still regarded the topic as being complicated and unmotivating (Fach, Boer & Parchman, 2007; Hand & Bruxvoot, 2006). Research authors who conducted studies related to stoichiometry also commented that stoichiometry concepts were challenging for students to grasp and therefore discouraging (Schmidt & Jignéus, 2003). Almost twenty years later, students and teachers still viewed stoichiometry as problematic and challenging. High school chemistry instructors reported that students' reactions toward learning about the concepts of stoichiometry were that of fear and apprehension, and admitted that they found it challenging to teach stoichiometry (Bridges, 2015). Both teachers and students still consider stoichiometry a problematic and abstract topic to teach and learn in chemistry (Gulacor et al., 2013). Recent literature confirms that stoichiometry problem solving presents recurrent difficulties to many students (Shadreck & Enunuwe, 2017; Taha et al., 2014). Childs and Sheehan (2009) concluded in their research that the persistence of stoichiometry being seen as difficult

CONCEPTUAL UNDERSTANDING OF STOICHIOMETRY 15 throughout both teachers and students’ experience of chemistry called for persistent efforts on the part of educators to address the problems associated with learning and teaching stoichiometry. Their conclusion applied then, and it appears to still apply now. The Mathematics of Stoichiometry The difficulty of learning and teaching stoichiometry arises from the fact that stoichiometry is highly mathematical and conceptual, which means solving stoichiometric problems requires both mathematical and conceptual applications. As mentioned earlier in this chapter, Stoichiometry deals with the calculations of the quantities of substances involved in chemical reactions (Wilbraham et al., 2017). These quantitative calculations require students to be proficient at specific mathematical skills, including the following. a) Calculate molecular mass and formula individual molecules and formula units, respectively. b) Calculate molar mass. c) Convert between units (grams, liters, moles). d) Apply the Avogadro’s number, NA = 6.022 × 1023 mol-1 e) Construct and apply conversion factors in dimensional analysis. f) Calculate mass percent composition from formula and elemental analysis. g) Determine the correct stoichiometric coefficients to balance chemical equations. h) Calculate the quantities of limiting reagents and excess reagents. i) Calculate the amount of theoretical yield and actual yield. j) Calculate the molarity and molality of a solution. (Goldberg, 2015; Wilbraham et al., 2017) Fortunately, students and teachers have found a solution to deal with the massive

CONCEPTUAL UNDERSTANDING OF STOICHIOMETRY 16 demand for mathematical adeptness in solving stoichiometric problems. The Algorithmic Solution Although all stoichiometric problems have a conceptual underpinning, many of them can appear to be purely mathematical and can be solved algorithmically, with little to no understanding of underlying concepts. In fact, many high school chemistry textbooks provide an algorithmic approach such as dimensional analysis (picket fence method), formulas, or maps (Figure 1) that can be memorized and applied to solve stoichiometric exercises (Goldberg, 2015; Wilbraham et al., 2017). Some students even create their own “non-mathematical” strategy (Schmidt & Jignéus, 2003), or use “inexplicable methods” for solving stoichiometric problems (Haider & Al Naqabi, 2008). Studies reveal that an overwhelming number of problem-solving strategies used by high school students were algorithmic (Saouma & Barakat, 2003; Tóth & Sebestyén, 2009; Kusi, 2013, Hanson & Oppong, 2014). Even high-achieving students tend to rely on the use of memorized formulae to deduce answers (Chandrasegaran et al., 2009). A reasonable proportion of novice and experienced chemistry teachers also use algorithms during problem-solving instruction (Okanlawon, 2010; Hanson, 2014). Hanson (2016) observed that teachers had persistent problems with conceptual interpretation and used unexplainable sets of rules for solving mathematical stoichiometric problems. The learning and teaching of stoichiometry in secondary schools are basically through the use of algorithms (Kusi, 2013; Hanson & Oppong, 2014). It is not surprising then that students become quickly adept at solving problems with algorithmic techniques, but have only limited understanding of the chemistry behind their algorithmic manipulations. The convenience of using algorithms cause overreliance on these “plug and chug” routines

CONCEPTUAL UNDERSTANDING OF STOICHIOMETRY 17 Figure 1 Stoichiometry Flow Diagram that students even use them to solve problems intended explicitly for a conceptual solution (Wolfer, 2000). While students seem to have found a “quick solution” to solve some of the mathematical parts of stoichiometry, they still lag in conceptual problem-solving ability. The algorithmic approach only or partially addresses the numerical aspect of stoichiometry problems, and being able to do the math of stoichiometry does not necessarily mean that the students understand the underlying concepts. Students' ability to solve algorithmic type problems increases as their school experience in chemistry increases, but their expertise in solving conceptual-type problems decreases (Salta & Tzougraki 2011). Students’ performance in solving algorithmic problems and conceptual questions are significantly different (Chiu, 2000). There is little connection between success in solving algorithmically based problems and understanding the chemical concept behind that problem (Boujaoude & Barakat 2003; Antwi, 2013). Presenting an algorithm and demonstrating dozens of problems that can be solved using that algorithm does not facilitate the learning of the underlying

CONCEPTUAL UNDERSTANDING OF STOICHIOMETRY 18 concepts. A study showed that worked examples helped low prior knowledge learners to solve problems quickly and with limited mental resources, but high prior knowledge learners found them redundant and less useful for learning. Such instructional material did not differentially benefit learners of high and low prior knowledge levels. (Karabinos et al., 2014). While students become good algorithmic problem solvers, able to manipulate equations and able to achieve reasonably good grades in the topic, algorithmic calisthenics does not lead to conceptual understanding. Instruction, in general, emphasizes algorithmic problem-solving at the expense of conceptual understanding and meaningful problem-solving (Barakat, 2003). Conceptual Stoichiometry The conceptual part of stoichiometry is the foundation and justification for all stoichiometric problem-solving tasks and their solutions. The conceptual framework of stoichiometry is made up of many concepts that are interconnected and built upon previous knowledge. Developing a conceptual understanding necessitates the understanding and linking of these concepts as well as the different modes of the representations reflecting the changes that matter undergoes during a chemical change (Gulacar, 2007). The concepts referred to above include chemical formulas, types of chemical reactions, balanced chemical equations, the mole, representative particles, mole ratio, limiting reagent, actual yield, and theoretical yield. A study done on over 400 high school chemistry students identified the following difficulties encountered by high school chemistry students when solving stoichiometric problems; the lack of understanding of the mole concept, inability to balance chemical equations, inconsistent use of stoichiometric relationships, inability to identify the limiting reagent, determine the theoretical yields and identify the substance in excess

CONCEPTUAL UNDERSTANDING OF STOICHIOMETRY 19 (Chukunoye & Shadreck, 2017). Failure to understand and connect these concepts creates conceptual problems for students. For example, students who held some incorrect understanding and had weak links between the microscopic (the concept of representative particles) and macroscopic (observable chemical reactions) levels of chemistry experienced conceptual problems in their study of stoichiometry (Wolfer & Lederman, 2000). Dahsah & Coll (2008) reported that students with alternative conceptions found it challenging to solve conceptual problems, and their success in solving numerical problems seemed to be related to their conceptual understanding of stoichiometry. Taha, et al., 2014) concluded that students’ understanding of the concept of mole and their ability to make sense of chemical reactions are significant predictors in determining their success in solving stoichiometric problems. They further concluded that mathematical knowledge is not a substantial factor in determining students’ success in problem-solving. Sanger (2005) discovered that students who demonstrated confusion between subscripts and coefficients in writing chemical formulas performed worse on the stoichiometric calculations than students who did not confuse these concepts. Wolfer (2000) suggests that there appears to be a connection between students' conceptual structures of stoichiometry and their ability to solve computational problems. Nejla and others (2013), who reported that students’ conceptual understanding affects algorithmic problem-solving skills much more than mathematical processing skills, supported this observation. For example, students must be able to translate a worded stoichiometry problem into a balanced chemical equation and then apply the appropriate mathematical equation to solve the problem. (Taha et al., 2014). Furthermore, students’ misconception concerning chemical reaction is an

CONCEPTUAL UNDERSTANDING OF STOICHIOMETRY 20 impediment to their problem solving (Salta & Tzougraki, 2011). Lack of understanding of the mole concept also caused students to skip crucial steps relating to the stoichiometric ratio and mole concept in stoichiometry problems (Gulacar, Overton, and Bowman, 2013) and end up with incorrect answers. A study that surveyed introductory college chemistry students concluded that students reporting a focus on the development of a full understanding of concepts in their high school chemistry were more likely to earn higher college grades and those whose high school courses emphasized rote memorization typically earned lower grades (Tai, Sadler, Loehr, 2005). When performance, strategies, and mistakes in students problemsolving in stoichiometry were investigated, it was found that higher and lower achieving students differ significantly in their cognitive skills, especially in domainspecific (mole concept) skills and the ability to deal with complexity (Gulacar et al. 2013). These studies illustrate that successful problem-solving in stoichiometry requires both procedural knowledge (algorithms) and conceptual understanding. These studies also indicate that there is a need to develop learning strategies that support student conceptual understanding rather than just coaching them to solve numerical problems using formulae by rote. Therefore, it makes sense to suggest that teaching stoichiometry must take on a much more concept-based approach. Teachers must identify all concepts associated with stoichiometry at the start of the unit, and then they should move the emphasis away from teaching the use of simple and complex algorithms to strategies that require concept formation and higher cognitive skills, but in a step-wise manner (Hanson, 2016). Students should be guided to understand the underlying conceptual foundation of stoichiometry before introducing the algorithmic way of solving the

CONCEPTUAL UNDERSTANDING OF STOICHIOMETRY 21 problems (Taha et al., 2014). This study supports efforts to involve conceptualteaching pedagogies in the classrooms. The Conceptual Approach Several conceptual approaches to teach stoichiometry have been attempted over the years. Opara (2010) investigated the efficacy of mind-mapping subsumed in self-regulation on the achievement of students in Stoichiometry and concluded that students who practiced mind mapping on the mole concept scored higher than those who did not. She suggested that mind-mapping enhanced performance in Stoichiometry and teachers should employ self-regulated strategies in teaching sciences. In a study that was done by Niaz and Montes (2012), an experimental group was taught using a dialectic constructivist strategy that includes concept application, whereas the control group was instructed using the algorithmic approach. The experimental group performed better in both algorithmic and conceptual items. Another study used audience response systems during interactive lectures to promote active learning and conceptual understanding of stoichiometry. Most students reported that the strategy contributed to their understanding of stoichiometry (Cotes & Cotua, 2014). A study that researched the use of writing-to-learn strategies by Year 11 chemistry students concluded that the treatment students, whose task was to write a business letter to a younger audience, performed statistically better on conceptual questions compared to the control group. The treatment students also confirmed that the writing task promoted their understanding of stoichiometry concepts (Hand, Yang, & Bruxvoot, 2006). Another study used a productive inquiry method (PIM) as an intervention in the teaching of problem-solving in chemical stoichiometry. Although not all students endeared to the technique, it did produce superior outcomes on their problem-solving abilities (Sedumedi, 2014). In yet another study that used two

CONCEPTUAL UNDERSTANDING OF STOICHIOMETRY 22 inquiry-based activities to build accurate stoichiometric concepts, the students demonstrated improved conceptual understanding even though there were variations in the intervention delivery (Kimberlin & Yezierski, 2016). Using a mastery learning strategy was also found to improve students’ achievement in the mole concept (Lamidi, Oyelekan, Olorundare, 2015). Other attempts at conceptual approaches include the use of a submicroscopiclevel or particulate visualization of matter to illustrate the species involved in chemical reactions on which stoichiometric problems are based in the first place. One such approach aims at fostering a conceptual understanding as well as a relational understanding of the macro phenomena, sub micro, and symbolic representations that are relevant to the learning of stoichiometry. In this approach, the teaching sequence starts with a macro phenomenon, and then a sub micro representation of the corresponding macro phenomenon and finally deriving symbolic representation in the form of a chemical equation based on the sub micro description (Cheng & Gilbert, 2014). Since all stoichiometry problems are based on chemical reactions, macro–sub micro– symbolic teaching that uses multiple representation methods could be enhancing student mental models and understanding of chemical reactions (Khan & Slate 2015). In one study, students who were allowed to practice problems that emphasized the development of molecular-level conceptualization and visualization, as well as learning to recognize and relate different representations in chemistry through a Web-based instructional software program (McWeb) showed more improvement in their conceptual understanding of stoichiometry and limiting reagent (Weng 2014). Another study showed that knowledge of the particulate nature of matter was significantly correlated with writing and balancing chemical equations (Gulacar et al, 2013). It appears that conceptual approaches that focus on getting

CONCEPTUAL UNDERSTANDING OF STOICHIOMETRY 23 students to think in terms of submicroscopic particles are essential for conceptual understanding in stoichiometry. To be able to think in terms of submicroscopic particles, students must first become well-versed on the particulate nature of matter. The Particulate Nature of Matter The particulate nature of matter is foundational to almost every topic in chemistry and is encapsulated in the Particle Theory, which essentially states that matter is composed of discrete, submicroscopic, energetic particles that are separated by space (Harrison & Treagust, 2002). The particulate nature of matter can be illustrated using the particulate-nature-of-matter diagrams (PNOM) or in short particulate diagrams or particle diagrams. In particulate diagrams, colored circles are drawn to represent the particles that make up a particular substance, and space between the circles represents the empty space between particles. Figures 2 are particle diagrams that illustrate the particles (water molecules) that make up the compound water and the particles (aluminum atoms) that make up the element aluminum, respectively. The arrangement of the particles and the amount of space among them determine the substance’s state of matter. In Figure 2 the sparse arrangement of water molecules results in water being liquid, and the tightly packed arrangement of the aluminum atoms in Figure 2 results in aluminum being solid. During chemical reactions, the particles of reactants break into its constituent parts or break away from their tightly packed arrangement and rearrange to form products with different chemical and physical properties from the reactants (Wilbraham et al., 2017). A conceptual understanding of stoichiometry is, therefore, closely associated with the knowledge of the particulate nature of matter and how it relates to chemical reactions.

CONCEPTUAL UNDERSTANDING OF STOICHIOMETRY 24 Figure 2 Particle Diagrams of Water and Aluminum Scientists and teachers use the particle theory to explain the composition and properties of matter that make up substances that make up objects. Because particles that make up matter are invisible at the macro level, their types, arrangements, and behaviors are abstract concepts that are difficult for many students as well as teachers to grasp. Students also tend to conceptualize particles like bits of solid matter such as grains of sugar. This conception of particles often creates difficulties for students in understanding the intrinsic interactions of particles during chemical reactions (Riaz, 2004). This conception is inconsistent with the scientific view of particles of matter, which refers to particles as being represented by submicroscopic atoms and molecules. With some hesitation, many students do eventually accept the idea that matter is composed of submicroscopic particles. However, they do not seem to recognize it as something inherently powerful and useful in understanding and talking about everyday events (Gravel & Barbara, 2013), such as the chemical reactions that cause rusting of iron and photosynthesis. Most students cannot make connections between the interactions at the particulate level and the chemical processes at the macro level. A firm understanding of the particulate nature of matter makes it easier for students to Water Aluminum

CONCEPTUAL UNDERSTANDING OF STOICHIOMETRY 25 develop visual and conceptual reasoning at the atomic or molecular scale, thus enabling them to conceptualize, visualize and solve problems related to chemical reactions. If understood and applied correctly, the particle model will provide students with many benefits, such as a better comprehension of chemical concepts and more effective problem-solving skills (Williamson et al., 2004). These benefits are relevant to the study of stoichiometry. The Three Levels of Chemistry Chemical knowledge is acquired at three levels: (a) the macroscopic and tangible, (b) the sub-microscopic and, (c) the representational (Johnstone, 2000). To develop a conceptual understanding of stoichiometry, students must learn to interpret chemical reactions at (a) the macroscopic and tangible level (what is seen, heard, touched, smelt as a chemical reaction takes place); (b) the microscopic level (what and how atoms, molecules, and ions interact during a chemical reaction); and the symbolic level (chemical symbols, formulae, and equations used to describe the chemical reaction). In stoichiometry specifically, developing a conceptual understanding necessitates the linking of the macroscopic, microscopic, and symbolic representations of chemical reactions (Gulacar, 2007). The ability to relate the submicroscopic interactions to observable, macroscopic features (for example the formation of a precipitate or the change of color) during chemical reactions leads the students to be able to determine the quantities, in terms of moles, and the types of interacting particles involved in the chemical reactions. Only then can they recognize the connections between stoichiometric problems and the underlying submicroscopic processes, make sense of the stoichiometric relationships among the particles of the reactants and products, and consequently become more effective in problem-solving. However, because submicroscopic phenomena operate at a minuscule scale, students

CONCEPTUAL UNDERSTANDING OF STOICHIOMETRY 26 find visual reasoning at a molecular level to be challenging. Stoichiometric relationships among particles of reactants and products are still not understood well by students (Dori & Hameiri, 2003). Most students cannot make connections between the molecular, symbolic, and graphical representations of chemical phenomena, which results in them not being able to conceptualize, visualize and solve both complex numerical problems and conceptual problems. Developing an intuition for connecting macroscopic features with submicroscopic interactions is difficult for students (Yaron & Karabinos, 2004). Still, another learning challenge is mastering the skill of writing symbolic representations using chemical symbols and formulas to describe and explain these unseen submicroscopic actions that give rise to the macroscopic features. Although it is challenging for students to explain observable chemical changes in microscopic terms and translate these changes into symbols, the ability to do so makes problem-solving in stoichiometry more effective. Students who showed a high level of understanding of the interchange of the three means of representations were more successful in solving stoichiometry problems related to balancing chemical equations than those who showed average and low level of understanding (Sujak & Daniel, 2017). Students who were taught using the macro-micro-symbolic approach (IMMSA) developed more satisfactory translational skills than those who were exposed to the conventional lecture method (CLM) (Sanchez, 2018). The same method of teaching also enhanced students’ conceptual understanding and relational learning of chemical reactions (Jaber & Boujaoude, 2012). Chandrasegaran and others (2009) concluded in their study that emphasizing the triplet relationship of macroscopic, submicroscopic, and symbolic representations in chemistry help students achieve more meaningful learning in chemical representations.

CONCEPTUAL UNDERSTANDING OF STOICHIOMETRY 27 The conceptual approach of teaching stoichiometry then should focus on promoting students’ translational skills among the three representations of chemical reactions. Sanchez (2018) suggested that teachers should start their instruction from the microscopic aspect for a deeper understanding of the macroscopic and symbolic levels. Particle Diagrams Particle diagrams provide a way to start instruction from the microscopic aspect for a deeper understanding of chemical reactions between pure substances. Although chemical reactions can be described at three levels; macro, sub micro, and symbolic, explanations of chemical reactions are based on and focused at the submicro level (Davidowitz & Chittleborough; 2009). Particle diagrams provide a visual tool that illustrates the submicroscopic particles that make up reacting substances and how they interact at the sub-micro level in chemical reactions. To construct a particle diagram, one draws a square/box that represents a section of a particular substance and colored circles inside it to represent the atoms, molecules, or units of ions that constitute the substance. Multiple particle diagrams are drawn to represent the reactants and the products of a single chemical reaction. Particle diagrams may be easy to construct, but not as easy to understand without enough training to think in terms of particle interactions. Lack of understanding of the connections between the macro level and the particle diagrams and misinterpretations of the diagrams among students still occur and indicate a need for the particle diagrams to be used carefully and explicitly (Davidowitz & Chittleborough; 2009). Students are also having difficulty applying particle diagrams in problem-solving. Research has shown that students could perform algorithmic calculations but not explain those calculations using particulate representations

CONCEPTUAL UNDERSTANDING OF STOICHIOMETRY 28 (Prilliman, 2014). Despite the challenge, teaching students to interpret, and construct, sub microlevel diagrams that represent chemical reactions and relate them to chemical equations at the symbolic level provides a complete picture of the chemical reactions, leading to a deeper conceptual understanding of chemical equations and stoichiometry (Davidowitz et al., 2010). It is no coincidence that the use of particle diagrams is one of the ways the College Board has recommended shifting the AP Chemistry curriculum away from the algorithmic problem-solving and toward more meaningful conceptual understanding (College Board, 2014). To help students build the foundation for their conceptual understanding of stoichiometry, they need to be trained to switch from thinking about the visible aspects of chemical reactions to more abstract thinking of the submicroscopic events underlying all chemical phenomena. Summary This chapter reviews the literature pertinent to the study. First, the researcher elaborates on the particular difficulties of learning stoichiometry with an emphasis on solving conceptual problems. Second, a review of studies on tested and effective, research-informed chemistry instruction on stoichiometry is presented. Third, the literature on conceptual approaches that focus on the triplet relationship in chemistry to develop a strong conceptual base on stoichiometry is reviewed. Finally, the use of particle diagrams to complement students’ understanding of the three levels of chemistry is recommended.

CONCEPTUAL UNDERSTANDING OF STOICHIOMETRY 29 CHAPTER 3 METHODOLOGY Introduction The study attempted to investigate the effects of a visual-based pedagogical approach on the conceptual understanding of stoichiometry among 10th -grade students attending the Adventist International Mission School (AIMS), in Muak Lek, Thailand. A conceptual understanding enables students to solve stoichiometric problems from the conceptual point of view rather than by the algorithmic method alone. The study also explored the students’ attitudes towards the pedagogical approach. The approach (from now on referred to as treatment or intervention) involved systematic and extensive use of particle diagrams in the teaching and learning of concepts underlying stoichiometry. In this chapter, the following are listed, described, and explained: research questions, research design, sampling technique, instrumentation, procedure, and data analysis. Research Questions The following research questions guided the study. 1. To what extent does the use of particle diagrams affect students’ conceptual understanding of representative particles, mole ratio, theoretical yield, and limiting reagent? 2. What are the students’ attitudes towards the use of particle diagrams?

CONCEPTUAL UNDERSTANDING OF STOICHIOMETRY 30 Research Design The study employed, pre-experimental one-group pre-test post-test design (or paired-sample design). In this design, the same dependent variable was measured on one group of participants once before treatment was implemented (pretest) and once after it was implemented (posttest) (Price, Jhangiani, & Chiang 2015). Conclusions about the effects of the treatment were formulated based on the difference between the pretest and posttest data. By using this design for this study, the researcher was able to determine the effects of a particular treatment (using particle diagrams) on a specific variable (conceptual understanding of Stoichiometry) in a specific group of subjects (10th -grade students at AIMS). This design afforded a few advantages. The first advantage was that, since it necessarily implied within-subject design, the researcher could compare pretest and posttest scores on the same variable (conceptual understanding) in the same students. Since each student served as her or his own baseline, errors associated with individual differences were reduced. (Fatade et al., 2013). The second advantage was since all students were given the same treatment, any merit that the treatment had would benefit all students; thus, ethical questions did not arise (Price et al., 2017). The third advantage was that this design was easier to set up than true experimental designs because it eliminated the need to assign participants to a treatment randomly. (Fatade et al., 2013). In this study, the researcher did not have to assign students for a treatment randomly but applied the treatment to a single group of students who already met all her sampling criteria. While this could be an advantage, it was also a limitation. Since students were not randomly assigned to the treatment, this meant that any other factors related to the conceptual understanding of Stoichiometry, such as getting help from tutorials and learning styles, were beyond the control of the

CONCEPTUAL UNDERSTANDING OF STOICHIOMETRY 31 researcher and could have also influenced the results. The design was susceptible to threats to internal validity. Since it lacked a control or comparison group, the results might not demonstrate a cause-and-effect relationship or the absence of it. Even if the average posttest score turned out to be higher than the average pretest score, the researcher could not conclude with a high degree of certainty that the treatment was responsible for the improvement. Other explanations, such as history, maturation, testing, instrumentation, and regression to the mean could also account for the change (Price et al., 2017). To minimize threats to internal validity, the researcher undertook the following control procedures. (1) Maintained consistency to reduce instrumentation threat (Price et al., 2017). The Stochiometry pretest and posttest questions were precisely the same; the method of test administration, the test administrator, and data collection were the same during the pretest and posttest. (2) Limited the time to five weeks between the pretest and posttest to minimize history and maturation threats. The researcher also identified external events such as the formation of after-school study groups or a significant school event that might affect the results (Price et al., 2017). (3) After taking the pretest, allowed enough time (four weeks) for the participants to “unfamiliarize” themselves with the test content before taking the posttest. Testing effects are less of a threat to internal validity when there is a long interval between tests (Price et al., 2017). (4) Minimized regression threat by ensuring that the sample did not include individuals who were likely to score extremely low or high in the pretest (Price et al., 2017). The 10th -grade Chemistry students who were the participants of this study were equally competent academically as reflected in their regular quiz and test scores, and were more likely to score around a norm. Recognizing the threats mentioned above, the researcher knew that she must

CONCEPTUAL UNDERSTANDING OF STOICHIOMETRY 32 carefully consider the extent to which these threats were a problem to her study and generally be very cautious about inferring causality from the results. Moreover, the researcher’s primary objective in conducting this study was not to generalize a population but to explore the functionality and usefulness of a particular pedagogical tool for the current AIMS Chemistry students. Despite the threats mentioned above, the researcher adopted this design for several important reasons. First and foremost, this was the research design that was recommended by the panel when the researcher defended her research proposal. Second, this design allowed the study to be done in a real classroom setting, within a single class without having to separate students, and during school hours without disrupting the smooth running of any classes or school programs. Third, the treatment itself could be easily embedded in the Chemistry lessons without compromising real learning time for the students. The fourth reason was that the researcher had no control over the number of students who enrolled in General Chemistry class, and since the number was small (thirteen students), it was more feasible to adopt a onegroup design. Treatment Conditions The treatment engaged students in simple, non-intrusive activities compiled in a booklet entitled Thinking the Particulate Way (TPW). The booklet contains 54 particle diagrams (also called particulate diagrams or submicroscopic diagrams) related to topics and concepts of Stoichiometry. The method of instruction for the unit of stoichiometry traditionally included the interactive lecture method, modeling problem-solving, peer coaching, laboratory activities, and very minimal use of particulate diagrams drawn on the whiteboard and shown on power points. In this treatment-added approach, the same strategies were used but with the integration of

CONCEPTUAL UNDERSTANDING OF STOICHIOMETRY 33 the information and exercises contained in the TPW booklet wherever and whenever they were relevant in the lessons. The booklet served as supplementary materials that allow students ample opportunities to examine the submicroscopic basis of concepts related to stoichiometry, specifically the concepts of representative particles, mole ratio, limiting reagent, and theoretical yield. The researcher hoped that by “thinking the particulate way,” that is interpreting chemical phenomena in terms of submicroscopic particles and processes, students would develop an accurate and longlasting understanding of some of the fundamental ideas that constitute a conceptual understanding of stoichiometry. The TPW booklet is divided into four sections. Each section includes a topic and one Stoichiometry concept that is related to the study. Section 1: Topic - Types of Matter Concept related to Stoichiometry: Representative particles. The first section connects students’ prior understanding of matter to the concept of representative particles. Students should already know the three types of matter - element, compound, and mixture, but may not be able to describe their chemical or physical composition. In this section, particle diagrams (see examples in Figure 3 are used to illustrate the three types of matter, from which students should observe that each type of matter is composed of representative particles which can be atoms, molecules, formula units (ions) or a combination of these. Figure 3 shows an element composed of individual atoms, a compound composed of molecules, and a mixture composed of an element and a compound. All stoichiometry problems are based on chemical reactions involving the pure substances (element and compound), and understanding the kind of particles represented in each substance is the first step

CONCEPTUAL UNDERSTANDING OF STOICHIOMETRY 34 in solving them. This section also aims to usher students into thinking at the submicroscopic or particulate level. Figure 3. Particle Diagrams Showing an Element, a Compound, and a Mixture and their Representative Particles. Reinforcement exercises at the end of this section are the following: 1. Students identify the representative particles and the types of matter represented in four particle diagrams. 2. Students draw particle diagrams to show the representative particles that make up two elements and two compounds. Section 2: Topic - Types of Chemical Reactions. Concept related to Stoichiometry: Mole ratio. In this section, particle diagrams are used to illustrate and explain five types of chemical reactions – synthesis, decomposition, combustion, single-replacement, and double-replacement. While these diagrams help students visualize the rearrangement of particles in different types of chemical reactions, they also serve as pictorial representations of the quantities of substances involved in chemical reactions as well as the quantitative relationships among reactants and products. For example, the particle diagrams in Figure 4 shows that in a synthesis reaction between hydrogen gas (a) Element (b) Compound (c) Mixture

CONCEPTUAL UNDERSTANDING OF STOICHIOMETRY 35 and oxygen gas, every two molecules of hydrogen gas react completely with one molecule of oxygen gas to produce two molecules of water vapor. Since this quantitative relationship is fixed, the chemical equation can also be interpreted in terms of moles. That is, in a chemical reaction between hydrogen gas and oxygen gas, every 2 moles of hydrogen gas react completely with 1 mole of oxygen gas to produce 2 moles of water vapor. The mole ratios that can be generated from this quantitative relationship are hydrogen to oxygen 2:1, hydrogen to water 1:1, and oxygen to water 1:2. Therefore particle diagrams can help students make sense of the numbers (also called coefficients) written in front of chemical formulas in balanced chemical equations, extrapolate them to moles, and understand how mole ratios are derived from balanced chemical equations. Mole ratios are used as conversion factors in simple and complex stoichiometric problems. Figure 4. Particle Diagrams Showing a Synthesis Reaction Between Hydrogen Gas and Oxygen Gas to Produce Water. Reinforcement exercises at the end of this section are the following: 1. Students identify the types of chemical reactions represented by five sets of particle diagrams. 2. Students generate mole ratios from each of the chemical reactions in question 2H2 0 (g) O2 (g) 2H2 0 (1) Reactant Reactant Product

CONCEPTUAL UNDERSTANDING OF STOICHIOMETRY 36 3. Students translate particle diagrams to symbolic representations with the correct coefficients. Section 3: Topic - Limiting Reagent Concept related to stoichiometry: Limiting reagent Students tend to develop the notion that for a chemical reaction to occur, the reactants must be present in the mole ratio as represented by its balanced chemical equation. This notion naturally leads to the assumption that all reactants are entirely used up in a chemical reaction. Then once the students learn that the limiting reagent is the reactant that is used up first and that it limits the quantities of products formed, they assume that the least reactant must be the limiting reagent. This section aims to dispel these misconceptions and to help students construct a mental picture of the concept of limiting reagent. Figure 5, which is an example of the particle diagrams found in this section, represents the chemical reaction between hydrogen gas and nitrogen gas to form the gas ammonia. The symbolic representation of this chemical reaction is 3H2 + N2 2NH3. The reactants, however, do not have to be present in a 3:1 ratio, as shown in the balanced chemical equation. The chemical reaction can start with any amounts of reactants. Figure 3 shows that the chemical reaction can begin with six molecules of hydrogen gas and four molecules of nitrogen gas, and as they react in a 3:1 ratio, one reactant is completely used up while another is in excess. Students are taught to cross out reactant particles and product particles on the particle diagrams until all the product particles are accounted for, which means the reaction can no longer proceed. As a result, all six molecules of hydrogen react with only two molecules of nitrogen gas to form 3 molecules of ammonia. Students should see from the particle diagrams that the hydrogen molecules are completely used up. Therefore hydrogen is the limiting reagent. Since nitrogen molecules are not all used

CONCEPTUAL UNDERSTANDING OF STOICHIOMETRY 37 up, it has to be the excess reagent. The leftmost particle diagram clearly shows that the hydrogen gas is no longer present, but two leftover nitrogen molecules in their unchanged form are still present upon completion of the reaction. Figure 5 also shows that the least reactant (four nitrogen molecules) is not necessarily the limiting reagent, thus dispelling the assumption that the least reactant is most likely the limiting reagent. Particle diagrams provide the students with a way of visualizing the concept of limiting reagent hence developing a mental model that leads to an accurate understanding of what limiting reagent is and its role in chemical reactions. Figure 5 Particle Diagrams Illustrating the Concept of Limiting Reagents. Reinforcement exercises at the end of this section are the following: 1. Students identify the limiting reagents in three chemical reactions represented by particle diagrams. 2. Students (a) complete three sets of particle diagrams that represent three different chemical reactions by crossing out reacting particles and drawing product particles, (b) identify the limiting reagent in each. Section 4: Topic – Theoretical Yield Concept-related to stoichiometry: Theoretical Yield Most students know how to use a balanced chemical equation to calculate the amount of product that will form during a reaction. The calculated value represents H2 N2 NH3 and excess N2

CONCEPTUAL UNDERSTANDING OF STOICHIOMETRY 38 the theoretical yield, which is the maximum amount of product that a chemical reaction can create from the given amounts of reactants. However, stoichiometric questions in which students need to compute the theoretical yield do not come in the form of neatly balanced chemical equations. These questions are often loaded with subquestions that require students first to work through multiple steps and apply concepts, especially the concept of limiting reagent before arriving at the answer for theoretical yield. In the process, students “forget” what theoretical yield is and simply apply algorithmic procedures to solve the problems as quickly as possible. Understanding what represents theoretical yield in a reaction becomes more relevant when students perform laboratory experiments in which they have to compute both theoretical yield and actual yield. In their laboratory reports, students often make the mistake of using these two terms interchangeably. Particle diagrams similar to the ones in Figure 6 help students to visualize where the theoretical yield comes from and why it is the maximum amount of product that the reaction can generate. Figure 4 illustrates the reaction between magnesium metal and oxygen gas to form magnesium oxide. The balanced chemical equation for this reaction is 2Mg + O2 2MgO. According to this equation, every two atoms of magnesium react with one molecule of oxygen to form two formula units of magnesium oxide. Students should observe that the yield of 4 formula units of MgO in Figure 6 represents the maximum yield that the chemical reaction can create from six atoms of magnesium and two molecules of oxygen gas and that the limiting reagent oxygen determines the yield. The reinforcement exercises for this section are in Section 3. Students revisit the particle diagrams they have completed in Section 3 exercise 2 and identify and quantify the theoretical yield in each reaction. Population and Sample

CONCEPTUAL UNDERSTANDING OF STOICHIOMETRY 39 The sample for this study was thirteen 10th grade students who were enrolled in the General Chemistry class for the academic year 2018-19 at AIMS. Thus, no sampling was necessary. By this sampling technique, it was not possible to specify the target population from which this sample was drawn. However, generalizability was not a concern for the researcher because her interest was only in discovering the effects of a pedagogical approach on a specific group of individuals at AIMS only to whom the results were relevant. Figure 6 Particle Particle Diagrams Showing the Theoretical Yield From a Reaction Between Magnesium and Oxygen Gas. Instrumentation Conceptual Understanding of Stoichiometry Pretest Posttest To determine the effects of the use of particle diagrams on students’ conceptual understanding of Stoichiometry, an improved version of a published instrument called Conceptual Stoichiometry Test (CST) designed by Wood and Breyfogle (2006) was used as the pretest and posttest in this study. Kimberly and Yezierski (2015) later improved the test by correcting one conceptually inaccurate term and reducing the number of distractors from five to four for the multipleresponse items. The test contained ten problems, of which six were four-option Mg O2 MgO and excess Mg

CONCEPTUAL UNDERSTANDING OF STOICHIOMETRY 40 response items and four free-response items. Each correct response for the four-option response items earns 2 points. An incorrect response earns no point. Student responses for the free-response items were checked against a rubric scaled from 0 – No understanding, 1 – Specific Misconception, 2 – Partial Understanding with Misconception, 3 – Partial Understanding, to 4 – Complete Understanding. Each of the ten problems requires knowledge of two or more of the four concepts of stoichiometry mentioned in the first research question. Consequently, the stoichiometric concepts addressed and measured by the test were: a) Representative Particles, b) Mole Ratio, c) Limiting Reagent, and d) Theoretical Yield. Table 1 shows the underlying stoichiometric concepts related to each question. The problems were listed in an increasing degree of complexity, with the more complex problems requiring greater conceptual understanding. The researcher herself, one high school Physical Science teacher from AIMS and one Chemistry professor from Asia Pacific International University, reviewed the test and confirmed its appropriateness for grade 10 General Chemistry students. The test was piloted with nine grade 10 students who were not participants of the study but were enrolled in Physical Science class at AIMS. The pilot study was essential to determine the approximate time needed to complete the test and find out if the wording and difficulty level of the test items were appropriate for their grade level. Students in the pilot study completed the test in approximately one class period (40 minutes) and had no problems with the wording. Also, the students reported that the questions were not difficult to understand, but they lacked the knowledge to answer some of them. This feedback was not unexpected since, like the participants in the study, they had not learned the related concepts in their class. A few students were confused about the manner questions 9 and 10 were listed. Apart from question