Analyzing Undergrads' Reasoning: Periodic Trends in Chemistry, Study notes of Reasoning

Download Analyzing Undergrads' Reasoning: Periodic Trends in Chemistry and more Study notes Reasoning in PDF only on Docsity! Student Reasoning Strategies Concerning Periodic Trends A Dissertation SUBMITTED TO THE FACULTY OF UNIVERSITY OF MINNESOTA BY Lynne M. Shenk IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF EDUCATION Gillian H. Roehrig, Adviser May, 2018 © Lynne M. Shenk, 2018 v Abstract The periodic table is recognized as one of the most powerful tools in science. While it is included in virtually all high school and undergraduate general chemistry curricula, it remains a mystery to many chemistry students who find it impossible to decode. Students are often able to predict periodic trends concerning atomic radius, ionization energy, and electronegativity, however they experience significant difficulty when trying to explain why these trends occur. One way to explore the cause of these difficulties is to focus on the reasoning strategies used by students as they attempt to explain periodic trends. This study investigated student reasoning strategies used to explain periodic trends in atomic and ionic radius, ionization energy, electronegativity, and reactivity. A theoretical framework of scientific reasoning, as it applied to qualitative problem solving, was utilized to identify how the problem solving constraints of domain specific knowledge (DSK) and heuristics were utilized by students as they attempted to explain the periodic trends. This phenomenographic study used semi-structured interviews to assess student reasoning strategies, as well as selected exam and assignment questions to determine the DSK for each student. The findings suggested that student understanding in the domain of electrostatic forces had the greatest influence on the type of reasoning strategies used. Those students with adequate understanding of electrostatic forces had more resources with which to construct explanations that integrated several scientifically appropriate force related factors. Those students without adequate understanding concerning electrostatic forces vi tended to limit themselves to the use of one factor that was not always adequately justified. They also tended to exhibit fixation by focusing on the same factor for multiple situations, even when that factor was no longer the most appropriate. When presented with an unfamiliar problem there was an increase in the number of one-factor strategies used, with a corresponding decrease in the number of force related explanations. This study suggested that an analysis of student explanations about difficult chemical topics might be helpful in diagnosing the underlying causes of student learning difficulties, and it also highlighted the need to help students learn how to formulate appropriate scientific explanations. vii Table of Contents Acknowledgements ............................................................................................................ iii Dedication .......................................................................................................................... iv Abstract ............................................................................................................................... v List of Tables ..................................................................................................................... xi List of Figures .................................................................................................................. xiii CHAPTER 1: INTRODUCTION ....................................................................................... 1 Rationale ......................................................................................................................... 1 Purpose and Potential Significance of Study .................................................................. 3 Framework and Research Questions ............................................................................... 4 Framework. ................................................................................................................. 4 Research questions ...................................................................................................... 9 Chapter Summary ........................................................................................................... 9 CHAPTER 2: LITERATURE REVIEW .......................................................................... 11 Domain Specific Knowledge ........................................................................................ 12 Atomic structure........................................................................................................ 13 Electrostatic forces within the atom. ......................................................................... 15 The ionization process. ............................................................................................. 17 x Conclusion .................................................................................................................. 152 CHAPTER 5: DISCUSSION .......................................................................................... 154 Research Question 1: Reasoning Strategies ................................................................ 155 Research Question 2: Domain Specific Knowledge ................................................... 161 Difficulty with electrostatic forces. ......................................................................... 162 Influence of inadequate DSK on Reasoning Strategies. ......................................... 163 Research Question 3: Unfamiliar Trends .................................................................... 166 Consistency of reasoning patterns .......................................................................... 167 Differences in reasoning patterns............................................................................ 168 Summary, Implications, and Suggestions for Further Research ................................. 173 Implications............................................................................................................. 174 Further research. ..................................................................................................... 176 Concluding Remarks ................................................................................................... 177 References ....................................................................................................................... 179 Appendices ...................................................................................................................... 192 Appendix A: Interview Protocol for Pilot Study ........................................................ 193 Appendix B: Figures and Tables used by Students during Interview ......................... 195 Appendix C: Exam Questions ..................................................................................... 197 Appendix D: Atomic Structure Student Assessment Used in Pilot Study .................. 199 xi List of Tables Table 2.1 Heuristic Categories Used by Chemistry Students .......................................... 20 Table 3.1 Participant Demographic Information ............................................................. 37 Table 3.2 Data Collection Timetable ............................................................................... 38 Table 3.3 Interview Questions ......................................................................................... 40 Table 3.4 Atomic Structure Student Evaluation (ASSE) ................................................. 42 Table 3.5 Analysis Overview by Research Question....................................................... 43 Table 3.6 Development of Codes for Reasoning Strategies ............................................ 46 Table 3.7 Definitions for the Reasoning Strategy Codes ................................................. 47 Table 3.8 Criteria Used to Assess Students’ DSK ........................................................... 57 Table 4.1 Summary of Student DSK Related to Periodic Trends .................................... 85 Table 4.2 Students Giving an Accurate Explanation for IE Exception Trends ............... 90 Table 4.3 Issues Concerning Forces ................................................................................ 93 Table 4.4 Inadequate Force DSK: Use of Attraction/Repulsion in Periodic Trend Explanations .................................................................................................................... 102 Table 4.5 Student Equations Representing the First Ionization Process and Their Definition of Ionization Energy. ..................................................................................... 104 Table 4.6 Comparison of Students’ Use of Satisficing and Fixation as Reasoning Strategies ......................................................................................................................... 115 Table 4.7 Rhonda’s Use of Fixation .............................................................................. 116 Table 4.8 Examples of Similarity Reasoning Used to Explain Reactivity .................... 138 xii Table 4.9 Reasoning Strategies that Were Utilized for Both Familiar and Unfamiliar Trends ............................................................................................................................. 141 Table 4.10 Students Continuing to Utilize Fixation Factors for Reactivity Trend ........ 143 Table 4.11 Students who Showed a Decrease in the Use of Forces for Reactivity Trend ......................................................................................................................................... 146 Table 5.1 Summary of Reasoning Strategies by Periodic Trend .................................. 156 Table 5.2 Consistency of Student Reasoning When Crossing the Familiarity Threshold ......................................................................................................................................... 168 2 students (Franco-Mariscal, Oliva-Martínez, & Gil, 2015) found that 66% of the participants were able to appropriately explain the classification of elements using the periodic table, 37.9% could explain the existence of trends in properties using electronic configurations based on the periodic table, but only 7.5% could correctly explain the trend in atomic size. Similarly, in a study of 240 second semester General Chemistry students in a New York Community College, 80% did not understand the trends in atomic radius (Salame, Sarowar, Begum, & Krauss, 2011). This indicates that some students have difficulty understanding the reasons for periodic trends even when they can see that these trends exist. For this reason, a more in-depth exploration that investigates the type of reasoning strategies that students use when attempting to explain periodic patterns in the ‘king of all tables’ is warranted. After learning to recognize that patterns are present within the structure of the periodic table, the student is further challenged to predict and explain these patterns using their knowledge of atomic structure and electrostatic forces. One of the most basic trends that a student might be expected to explain is the trend in atomic size, which is traditionally expressed in terms of the radius of the atom. This trend is easily visualized, exhibiting only a few exceptions within the representative elements. The trends in atomic radii are directly related to the more abstract concepts of ionization energy (Eymur, Çetin, & Geban, 2013), electronegativity (Jensen, 2003; Leach, 2013), chemical bonding (Eymur et al., 2013; Nicoll, 2001; Wang & Barrow, 2013), and polarity (Wang & Barrow, 2013). Wang and Barrow (2013) state that an understanding of the above topics 3 is necessary if the student is to progress to more advanced ideas in both organic and inorganic chemistry. While there is certainly no lack of research about the periodic table and the difficulties that students encounter, there have been significantly fewer studies that focus on student reasoning strategies for explaining periodic trends and how this reasoning might be shaped by the student’s specific knowledge of atomic structure (the particles that make up an atom and their relative placement within the atom), electrostatic forces within the atom, and the ionization process. There have been studies concerning atomic size (Eymur et al., 2013; Salame et al., 2011), as well as ionization energy (Taber, 1998; Tan et al., 2008; Tan & Taber, 2009, 2009), which focus primarily on student misconceptions and how they affect the predictions that are given for periodic trends in either atomic size or ionization energy. The study that most closely approximates the goals of the present study focused on how the conceptual framework of high and low content knowledge students affected their ability to explain atomic radius, electronegativity, bonding, and polarity (Wang & Barrow, 2013). In contrast to previous research, an investigation which focuses primarily on the reasoning process, rather than specific explanations used by students as they predict periodic trends might help us to better understand some of the difficulties that students experience. Purpose and Potential Significance of Study The purpose of this study was to investigate the reasoning strategies used by students as they attempted to explain periodic trends and to see how their understanding 4 of atomic structure, the electrostatic forces within the atom, and the ionization process shaped the chemical explanations that they produced. Given the pivotal nature of the periodic table to the discipline of chemistry, a more complete understanding of the difficulties experienced by students as they strive to unlock the secrets of this organizational tool and apply it to chemical problems is worthwhile. With this knowledge, instructors might be enabled to design learning experiences that would allow students to develop ways of thinking that are more effective as they learn to use the periodic trends to predict chemical properties. Instructors might also see the importance of helping students to develop metacognitive awareness of the reasoning strategies they are using so that they can more accurately assess the limitations of less sophisticated strategies, and identify those situations in which more complex strategies are needed. Framework and Research Questions Framework. The present study is structured around the broad framework of scientific reasoning as it applies to qualitative problems in chemistry. Scientific reasoning is an important goal in science education (National Research Council, 1996). Dunbar and Klahr (2012) suggest that a central component of much scientific reasoning involves the development of causal explanations between variables of interest (such as atomic structure and atomic radius). This often involves the search for a causal mechanism which explains the way in which one variable acts to cause the other. This type of “causal/mechanical” explanation views events as being caused by the properties and interactions of the participants involved (Talanquer, 2010). 7 the cue, integrating the information gathered, and choosing the solution that promises the highest value. They then suggest that heuristics be classified by the way in which they reduce cognitive demands by either eliminating or simplifying the execution of these five tasks. Graulich, Hopf, and Schreiner (2010) contend that heuristics are an important tool used by professional chemists in order to structure the vast amount of chemical information that is needed to solve problems that they regularly encounter. The use of heuristics enables chemists to focus on essential information without becoming mired in the details. Unfortunately, heuristics as used by novices may sometimes introduce problems. A short-cut strategy might lead the student to a correct answer the majority of the time without the related content knowledge needed to make the answer meaningful. The lack of the requisite chemical knowledge may lead to difficulties with future knowledge construction (Graulich, 2015). When heuristics are used as a crutch to make up for a lack of knowledge, students may struggle to identify appropriate cues, misuse the cues they do identify, and overuse the heuristic in general (McClary & Talanquer, 2011). In the present study, students were asked to predict and/or explain several periodic trends. The reasoning strategies that they used to explain the various trends were categorized and compared in order to learn what type of reasoning was most prevalent, and to identify conditions that seemed to favor the use of heuristics rather than the more effortful type of causal/mechanical reasoning that recognizes the interaction of multiple factors, and weighs them appropriately. Once student reasoning is more 8 thoroughly investigated and understood, it might be possible to gain some insight into how these reasoning strategies might be developed into more effective ones. In the past, much of the research in chemical problem solving has focused on problems that involve mathematical reasoning (Bodner & Herron, 2006; Gabel & Bunce, 1994). Less research has been done on the ways that students reason with respect to qualitative problems (Christian & Talanquer, 2012). When qualitative problem solving has been addressed, the tendency has been to focus on misconceptions or alternative conceptions. These two terms will be used interchangeably in this study to mean the ideas students have regarding scientific concepts after being exposed to formal models or theories, that would not be deemed as scientifically acceptable (Boo, 1998). Over time a vast number of misconceptions have been inventoried by topic, which while helpful, can become overwhelming for any instructor attempting to address them all (Duit, 2009; Garnett, Garnett, & Hackling, 1995; Kind, 2004; Nakhleh, 1992; Talanquer, 2006). Due to the number and variety of misconceptions that are possible, Talanquer (2006) suggests that a more productive approach would be to look for the source of the problems, or patterns of reasoning that students exhibit. The use of heuristics as a major constraint in the problem solving of qualitative problems offers a powerful means to explore the differences in student reasoning. In the present study, the scientific reasoning/problem solving framework was useful to identify how the problem solving constraints of domain specific knowledge and reasoning strategies are utilized by students as they attempt to create explanations for periodic trends. The domain specific knowledge to be considered encompasses the areas 9 of atomic structure, electrostatic forces operating within the atom, and the ionization process. Student reasoning strategies involving both heuristic and causal/mechanical explanations that weigh multiple factors will be investigated. Research questions. The goal of this study is to examine the reasoning strategies used by undergraduate chemistry students to explain the periodic trends of atomic and ionic radii, ionization energy, electronegativity, and reactivity in light of the two constraints of domain specific knowledge and reasoning strategies. The research questions that will guide the study are as follows: 1. What are the types of reasoning strategies used by undergraduate general chemistry students in their explanations of periodic trends including atomic radii, ionic radii, ionization energy, electronegativity and reactivity? 2. How does domain specific knowledge concerning atomic structure, electrostatic forces operating within the atom, and the ionization process shape the reasoning strategies of undergraduate general chemistry students in regard to the above trends? 3. What effect will an unfamiliar periodic trend problem have on the reasoning strategies utilized by undergraduate general chemistry students? Chapter Summary This chapter presented the rationale, purpose, theoretical framework and research questions that will form the basis for the present study. The pivotal position of the periodic table to the study of chemistry has been illustrated, as well as the difficulty that students encounter when trying to explain the trends contained within it. This study 12 Domain Specific Knowledge The domain specific knowledge (DSK) referred to in the context of this study is knowledge which must have been previously learned in order for the problem solver to predict and explain periodic trends in a scientifically appropriate manner. Larkin (1980) asserts that problem solvers in every discipline require a significant amount of domain knowledge in order to become skillful. This knowledge is instrumental in guiding the problem solver to relevant information or factors that will assist in solving the problem (Morris et al., 2012). When a student has gaps in his/her knowledge of a topic, it leads to confusion and faulty reasoning (Nakiboglu, 2003; Taber, 2003b; Wang & Barrow, 2013). Talanquer (2015) expands on this idea with his use of “threshold concepts”. A threshold concept is one that opens the door to entirely new ways of thinking in the discipline. As such, it transforms a student’s thinking and allows them to integrate previously learned strands of knowledge. One characteristic of a threshold concept is that it is troublesome, often conceptually difficult or perhaps even alien in the sense of being counter-intuitive, functioning as a barrier to further progress in a subject (Park & Light, 2009). Two concepts will be explored as potential threshold concepts that open the door to understanding periodic trends as well as other fundamental ideas important to chemistry: atomic structure and electrostatic forces within the atom. Both atomic structure and forces have been identified as core ideas that make up the physical science standards (NGSS Lead States, 2013) for K-12 science education in the United States. Gillespie (1997), who worked on undergraduate chemistry curriculum reform on an American Chemical Society sponsored Task Force, included atomic structure and electrostatic 13 forces in his discussion of the ‘great ideas’ of chemistry. A third concept, the ionization process that occurs when a metal atom becomes a positive cation will also be briefly explored. An understanding of the ionization process is necessary to explain ionization energy trends, but would probably not be considered a threshold concept. Atomic structure. Atomic structure has been identified as a threshold concept in chemistry (Park & Light, 2009; Talanquer, 2015). Talanquer (2015) asserts that atomicity is a threshold concept necessary for “making sense, predicting, and controlling the properties of matter” (p. 4). A student attempting to explain periodic trends is attempting to make sense of, and predict the properties of atoms. Without a clear understanding of atomic structure, this will not be possible. Tabor (2003a) describes the topic of atomic structure as troublesome because learning about atomic structure is difficult, and many students continue to have problems with related topics that are more advanced. While the structure of an atom determines and includes the electrostatic forces within it, forces will be considered separately in this study. The atomic structure domain will include the identity of sub-atomic particles, along with their number, charge, and placement within the atom, while the electrostatic forces domain encompasses how the particles interact with each other. This differentiation has been chosen due to the distinct nature of the problems that students experience in each area, which will be elaborated upon in the following paragraphs. While atomic structure is emphasized in virtually all chemistry curricula, students continue to experience problems both in understanding and applying the concepts involved. Some students are unable to discern the difference between protons, neutrons, 14 electrons, and ions (Cokelez & Dumon, 2005). Often the terms ‘orbital’, ‘shell’, ‘orbits’, and ‘energy levels’ are used interchangeably (Nakiboglu, 2003; Nicoll, 2001) or the concept of energy level is missing entirely (Wang & Barrow, 2013). Students also have trouble distinguishing between atomic models and reality (Boo, 1998; Talanquer, 2015). An illustration of this confusion in the area of atomic structure is the misconception that orbitals are boxes that can be filled by electrons (Nakiboglu, 2003) a conception that probably originates in the orbital diagrams that are used to model how electrons are distributed among available orbitals. Students with lower conceptual understanding in the area of atomic structure often failed to grasp the meaning and limitations of the atomic models that they used, which then hindered their ability to visualize the atoms or use the models appropriately (Wang & Barrow, 2013). During the course of their education, students are taught about atomic structure by being exposed to atomic models with graduated levels of sophistication. This raises the question as to which model is necessary for students to master in order to explain periodic properties. The atomic model used most consistently by undergraduate students is the Bohr atom, with only a few progressing to the quantum model despite the prominent place that the quantum model has in the curriculum (Park & Light, 2009; Wang & Barrow, 2013). Taber (2003b) asserts that while a clear understanding of energy levels is absolutely necessary in order to understand periodic trends, the Bohr atom is sufficient to enable the student to explain basic trends in ionization energy. Since the trends in ionization energy are dependent on the trends in atomic radii, it can be inferred that the student must have attained an understanding of the Bohr model of the atom in 17 This last misconception has been named the “conservation of force” misconception and has been found to be particularly difficult to dislodge as it often leads to correct predictions of periodic trends (Taber, 1998). The ionization process. The third category of domain specific knowledge that students must understand if they are to explain periodic trends is the ionization process that occurs when a neutral atom loses an electron. Of the fourteen periodic trends included in this study, eight directly involved the ionization process. Trends in ionization energy cannot be explained if the ionization process itself is not understood. While the specific process of ionization is not mentioned as a core idea in the physical science standards (NGSS Lead States, 2013) for K-12 science education, it is one of the chemical processes addressed in the 9-12 standard PS1.B dealing with chemical processes and the ensuing energy changes. The literature in the area of ionization is limited to studies regarding student misconceptions concerning ionization energy. The primary misconceptions that students demonstrated dealt with problems using the octet rule, and misconceptions about forces (Taber, 1998, 1999, 2003b; Taber & Tan, 2011; Tan et al., 2008; Tan & Taber, 2009; Tan, Taber, Goh, & Chia, 2005). These topics will be covered in the section on student understanding and explanations of periodic trends. Reasoning Strategies Utilized by Students to Explain Chemical Ideas Even if a student has demonstrated mastery of domain specific knowledge pertinent to the problem context, they must still be able to identify relevant factors that are applicable to the specific situation, apply concepts in an appropriate manner, and find a way to weight the various concepts given the unique context of the problem and then 18 integrate the effect of all concepts in arriving at a solution. The process of explaining a periodic trend requires a fairly sophisticated level of reasoning. Using the weighted additive rule as outlined by Shah and Oppenheimer (2008) as an optimal approach to problem solving, an ideal explanation concerning a periodic trend in a group or period would identify all factors along with the effect they would have on the trend in question. Factors to be considered include any change in the principle quantum number in which valence electrons reside (which helps to determine the relative size of the orbitals within the shell), the effective nuclear charge (which is generally simplified to be the number of protons, which attract valence electrons, minus the number of core electrons, which repel valence electrons), any additional repulsion caused by valence electrons, and the valence electron arrangement within the individual orbitals (since paired electrons repel each other). While there may be other factors, these are the ones that a general chemistry student might be expected to consider. The student would need to decide on the value of the factor (the number of protons, core electrons etc.), weigh the relative importance of each factor, and finally integrate the effect of all factors in order to choose a suitable solution. Because of the inherent complexity of this and other problem solving tasks in chemistry, students will often rely on particular reasoning strategies (heuristics) that simplify the process. These strategies are most probably influenced by the student’s limitations in cognitive processing ability and the environment in which the task is to be completed (Shah & Oppenheimer, 2008). Problems may arise because these simplified strategies (heuristics) are often used by novice problem solvers in ways that may not guarantee optimal results (Taber, 2009). 19 Much research has been done describing specific heuristics, with each group of researchers defining their own unique terms for particular heuristics that are often very similar in nature. This leads to a significant amount of redundancy resulting in confusion (Shah & Oppenheimer, 2008). In addition to the research that was not specific to any one domain or discipline, there has also been significant research identifying heuristics used by chemistry students, many of which are very similar to the heuristics used more generally. This study starts with those heuristics described by researchers in the chemistry discipline, and then adds heuristics that have more universal utility as needed. Heuristics used in chemistry. After an analysis of the literature pertaining to alternative conceptions as expressed by chemistry students, Talanquer (2006) reorganized his findings according to the patterns of reasoning used. His analysis of these patterns led him to describe several broad categories of heuristics frequently used by chemistry students, which included association, reduction, and fixation as shown in Table 2.1. 22 and recognizes an unfamiliar substance as being an acid, then predictions can more easily be made about its behavior. Additivity, also an association heuristic, occurs when effects are equally distributed among equivalent system portions (Talanquer, 2006). In the context of periodic trends, the additivity heuristic is sometimes used to express the idea that the nuclear force of attraction is equally divided among electrons, therefore if the number of electrons is reduced while the number of protons remains constant, each electron will feel more nuclear force. Reduction. Talanquer’s (2006) second heuristic category is reduction. This strategy is employed when the problem solver reduces the factors to be considered. Students using reduction style heuristics isolate particular features of the problem and do not see the problem as a whole (McClary & Talanquer, 2011). Within this category is the one-reason decision making heuristic in which a property in a system is seen as being caused by only one variable or factor. Tan et al. (2008) used the term relation-based thinking to describe any one-reason strategy. Relation-based thinking occurs when a problem-solver does not appreciate how a change in one factor might be cancelled by a change in another, such as increased nuclear charge being cancelled out by increased electron repulsion. Furió, Calatayud, Bárcenas, and Padilla (2000) had a similar idea in mind when they used the term functional reductionism. A problem solver engages in functional reductionism when they reduce the complexity of a problem by reducing the number of factors, or by equating two concepts that are very similar. An example might 23 be when a student describes a molecule as being polar because one of the bonds is polar, instead of looking at both bond polarity and the molecular shape. In some cases, the problem solver is aware of multiple factors, but in order to simplify the problem, a decision is made as soon as one factor differentiates between the options making it a sequential process of considering one factor at a time (Todd & Gigerenzer, 2000). This decision making behavior has been described using the term lexicographic (Fishburn, 1974; McClary & Talanquer, 2011; Todd & Gigerenzer, 2000). When using the lexicographic heuristic, the problem solver looks at factors one by one, comparing their values, (such as the number of electrons, or the number of protons) and stops as soon as there is a significant difference in the value of the factor being considered. Using the lexicographic heuristic, each factor is assessed until a factor is found that clearly differentiates the options. Another reduction heuristic introduced by Simon (1956) is called satisficing, which is meant to be a blend of sufficing and satisfying. When using this heuristic, a decision maker will choose the first solution that satisfies a minimal cut-off level and is perceived as being “good enough” (Shah & Oppenheimer, 2008; Todd & Gigerenzer, 2000). When using heuristics in which more than one factor might potentially be assessed, the problem solver still has the decision as to the order in which factors should be considered. This problem has been studied by Todd and Giberenzer (2000) who described several ways in which factors might be prioritized for consideration. The ‘take the best’ rule prioritizes a particular factor because of the proven validity of the factor for solving problems in the past. The ‘take the last’ rule starts with factors that were used in 24 the most recent problem solving event, whether they proved successful or not. The minimalist approach shows no specific strategy for the ordering of factors, but appears to consider them in a random manner. Both association and reduction type heuristics satisfy the effort-reduction criteria proposed by Shah and Oppenheimer (2008) by reducing the number of factors, often to only one, so that integration of less information is necessary. By reducing the number of factors, the difficulty of storing their values is reduced (Shah & Oppenheimer, 2008) and the need to compare the value of one factor to that of another is eliminated (Todd & Gigerenzer, 2000). Fixation. A third heuristic type as classified by Talanquer (2006) is fixation. This involves the tendency of the problem solver to repeatedly use the same strategy even when the nature of the problem changes and another strategy might be more effective. This strategy is reminiscent of the ‘take the last’ rule but is broader than simply starting with the same factor most recently used in a similar problem. Fixation often results in overgeneralization of principles and laws to situations to which they do not apply, or to use the same strategy that worked in a previous situation regardless of any change in the nature of the problem. Furió et al. (2000) seem to be describing this same heuristic when referring to ‘functional fixedness’ which occurs when students over-generalize the use of a particular explanation. An example of this is shown by the overuse of Le Chatelier's Principle to explain every change in an equilibrium. Talanquer (2006) also refers to functional fixedness, but sees it as a sub-category under the general fixation category. He describes functional fixedness as the tendency of students to interpret models and 27 Student Understanding and Explanations of Periodic Trends This section focuses on a review of the literature specific to periodic trends. Studies directed towards periodic trends rarely focus on student reasoning strategies, but sometimes strategies did emerge as part of the findings. For example, Eymur et al. (2013) studied high school students and preservice science teachers in Turkey to determine the alternative conceptions that participants held about atomic size (radius). They used an eight-question, multiple-choice instrument that accessed the students’ conceptions concerning the relative size of the radius for various groups of atoms and ions, and found that many high school students and preservice teachers believed that the nuclear charge was the sole factor that determined the size of an atom. This seems to be an example of a very simple one-reason strategy where no additional factors were considered. While nuclear charge is important, it is not the only determinant of atomic or ionic radii. Other students expressed the idea that a higher positive charge made an ion larger, or that the size was determined by the period or group number itself. These are examples of students using an association type heuristic without any further justification. While the misconceptions generated by this study were very interesting, since the responses were suggested in the questionnaire rather than generated solely by the participants, it suggested a need for a more in-depth analysis to determine the actual thought processes that students were using to come up with their explanation choices. Another study (Salame et al., 2011) conducted in an urban four-year college in the United States, also addressed atomic radius. Through the combination of an open-ended question and interviews, the authors determined that most students relied on rote 28 memorization or simple guessing to determine atomic size. While the interview method was more effective in eliciting the reasoning used by students, it was limited in scope by the use of only one periodic trend. A series of studies on ionization energy (Taber, 1998; Tan et al., 2008, 2005; Tan & Taber, 2009) revealed several reasoning strategies that students commonly use to predict periodic trends. A multiple-choice ionization energy instrument developed by Taber (1999) was used in various settings to validate the representative nature of the research results. They found that the results were consistent in all of the settings where the instrument was used, and that the primary misconceptions expressed by students could be classified under the headings of octet rule, stability of full and half-filled shells, and conservation of force. The octet rule, which is found in most textbooks (Talanquer, 2007), states that atoms have a tendency to gain, lose, or share electrons until they have a total of eight in their valence shell. While the octet rule does not state that atoms ‘want’ or ‘need’ eight electrons, this is the idea that students quickly internalize and may never fully replace even after acquiring more scientifically appropriate explanations (Kelemen & Rosset, 2009). This is an example of teleological thinking in that it postulates that atoms have a natural state of eight valence electrons that they try to achieve. Kelemen (1999) asserts that teleological reasoning is a fundamental aspect of human thought and as such can be suppressed, but not completely erased. For this reason, the octet rule as well as the closely related ideas concerning the special stability of filled and half-filled shells, become firmly entrenched in the minds of many students even after being exposed to more scientifically appropriate reasoning involving particle and force interactions. 29 Unlike the octet rule that describes a general tendency concerning the behavior of atoms, the conservation of force concept actually distorts electrostatic principles in a subtle manner that appeals to students’ intuitive desire for simplicity. Rather than integrating the effect of nuclear attraction, electron repulsion (which varies between core and valence electrons) and the average distance of valence electrons from the nucleus, conservation of force thinking allows the student to simply compare the number of electrons and protons. If there are more protons, then each electron experiences a larger portion of a set amount of force. Conversely, if there are more electrons than protons, there will be less attractive force to share between the greater numbers of electrons. In a study of 450 high school and university students from five different countries including the United States, 38% chose the answer that “when an electron is removed from the sodium atom, the attraction of the nucleus for the ‘lost’ electron will be redistributed among the remaining electrons” (Tan et al., 2008, p. 270). The percentage of students from the United States affirming this answer was 54%. Conservation of force is classified as making use of the additivity heuristic that falls under the general association type heuristic as shown in Table 2.1. Taber (1998) speculates that the conservation of force idea may originate when the learner misinterprets what was read in textbooks, heard in the classroom, or from a misunderstanding of prerequisite topics. He also suggests that there might be some intuitive bias which leads to this particular misinterpretation. Taber noted that none of the students claimed to have been taught to reason using conservation of force. In a later study of graduate level preservice chemistry teachers in Singapore, Tan and Taber (2009) 32 Finally, student explanations in the area of periodic trends were reviewed. It was found that students seem to gravitate toward the reduction, or one-reason type heuristics when explaining trends in atomic radius. When explaining ionization energy, the teleological heuristic utilizing the octet rule and the additivity heuristic utilizing the concept of conservation of charge misconception predominated. None of the studies reviewed included the breadth of periodic trends included in the present study, nor did they specifically explore how the students would respond when asked to deal with an unfamiliar problem. The present study looks at undergraduate students with a range of ability levels to determine how they apply the domain specific understanding that they have about atomic structure, forces, and the ionization process to their explanations of the periodic trends of atomic radii, ionic radii, ionization energy, and reactivity. Their reasoning strategies will be identified and the consistency with which they use particular strategies will be considered. Finally, the present study compares the reasoning strategies used by students as they explain both familiar and unfamiliar periodic trends. In the next chapter, details regarding the study’s design, participants, data collection, and method of analysis is provided. 33 CHAPTER 3: METHODS This chapter details the methodological approach used in the present study. Following a description of the methodology will be a description of the context in which this study took place, followed by details concerning data collection and the analysis techniques that were utilized. Methodological Approach The following research questions, which guided the data collection and analysis phase of this study, are listed below. 1. What are the types of reasoning strategies used by undergraduate general chemistry students in their explanations of periodic trends including atomic radii, ionic radii, ionization energy, electronegativity and reactivity? 2. How does domain specific knowledge concerning atomic structure, electrostatic forces operating within the atom, and the ionization process shape the reasoning strategies of undergraduate general chemistry students in regard to the above trends? 3. What effect will an unfamiliar periodic trend problem have on the reasoning strategies utilized by undergraduate general chemistry students? The use of a qualitative approach, utilizing rich description of student thought processes, was seen as most suitable to obtain the answers to these questions. The strength of qualitative methods lie in their inductive approach and emphasis on descriptions rather than numbers (Maxwell, 2013). While qualitative research methods do not provide information that can be used to predict and control behavior, they do provide 34 understanding of the way people make sense of the world around them, which can be especially valuable to educators (Sjöström & Dahlgren, 2002). The qualitative framework to be used is a modified form of phenomenography which is defined by Marton (1986) as “mapping the qualitatively different ways in which people experience, conceptualize, perceive, and understand various aspects of, and phenomena in, the world around them” (1986, p. 31). The present study looked at the ways in which undergraduate students perceived and understood the implications of the periodic organization of elements, as embodied in the periodic table, on various periodic trends. The focus, however, was not on students’ perceptions of the content related to the periodic trends, but in the explanations that they supplied. By focusing on reasoning strategies rather than the content, this study departs from the normal phenomenography focus. However, by focusing on reasoning strategies, especially in relationship to domain specific knowledge, much can be learned about why students construct the specific conceptions that they do. The primary outcome of phenomenographic research is a categorization of the various ways in which a phenomena may be conceived and the structural framework within which the categories exist (Marton, 1986; Sjöström & Dahlgren, 2002). The present study categorized the various reasoning strategies used when explaining periodic trends, and the circumstances that seemed to favor the use of those strategies. The focus of a phenomenographic study is not the individual participant, but, according to Marton (1986), it is the “pool of meanings” (p. 43) that are embedded within the quotes that are being examined. The individual utterances are grouped according to similarities and then each category is clearly differentiated from all others. Marton (1986) goes on to say that 37 interviews were collected primarily to supply more examples if needed, however only one was used as they did not seem to add anything unique to those that had already been transcribed and it was felt that the sampling criterion of redundancy as described by Lincoln and Guba (1985) had been achieved. Background on the Periodic Trends Unit The chemistry course in which this study was conducted, covered the topic of periodic trends about four weeks before the end of the semester. Data was collected after completion of the unit in the two weeks following the unit exam. Prior to the unit on periodic trends, the students had been exposed to a unit on atomic structure, quantum numbers, and electron configuration. About seven class sessions were devoted to the topic of periodic trends. This included information about the trends in atomic and ionic radii, effective nuclear charge, ionization energy, electron affinity, and general trends Table 3.1 Participant Demographic Information Pseudonym Declared Major Semester Grade Corban Exercise Science B- Karla Nursing A Katie Exercise Science A- Krissy Nursing A Loni Nursing A Macy Nursing C+ Monica Psychology C Nathan Elementary Education A- Rhonda Nursing C Robert Nursing C+ Sandy Nursing B- Sonya Nursing B Tina Nursing B 38 among metals and nonmetals. Individual group trends were not covered. The unit was taught using several group activities that utilized inquiry worksheets to enable students to construct conceptions concerning the topic, interspersed with short lectures, and quick- response assessments. The phrase ‘octet rule’ was never used by the instructor, nor the idea of a special stability of full and half-filled shells. Instead, electrostatic forces, as governed by Coulomb’s Law and energy principles, were emphasized. Data Collection Several data sources were used in this study including the Atomic Structure Student Evaluation (ASSE), audio recordings of semi-structured interviews, and students’ unit exam results for the course. These were collected over the last four weeks of each semester in which the study was conducted. Table 3.2 gives the dates on which this data was collected. Interviews. The focus of all three research questions involved the identification of the reasoning strategies used by students. This was addressed through the use of semi- structured interviews, the preferred method of data collection in phenomenographic Table 3.2 Data Collection Timetable Date Range Data Collected 11/17/2016 ASSE 11/18/2016 Unit Exam 11/22/2016 – 12/13/2016 Interviews 04/18/2017 ASSE 04/21/2017 Unit Exam 04/26/2017 – 05/04/2017 Interviews 39 studies (Marton, 1986; Ornek, 2008; Sjöström & Dahlgren, 2002), using a “think-aloud” protocol (Bowen, 1994). The interviews ranged from 25-50 minutes depending on the students’ willingness to talk and the number of follow-up questions used to clarify answers. The interviews were audio-recorded and then transcribed verbatim. Pseudonyms were assigned to each participant in an effort to maintain confidentiality. Interview questions were first developed after consulting two pre-existing instruments: the Atomic Size Diagnostic Instrument (Eymur et al., 2013) and the Ionization Energy Diagnostic Instrument (Tan et al., 2005). Since both of these instruments were constructed as multiple choice instruments with a limited scope, they were used only used as guides to stimulate thinking. Open-ended questions were developed that included questions concerning atomic structure, forces, the ionization process, periodic radius trends and ionization energy trends. This protocol was used in the pilot study conducted in April 2016 and can be found in Appendix A. After conducting the pilot study, the following changes were made in the ASSE and interview protocol:  Four questions concerning high school chemistry background were added to better understand what may have affected the students’ understanding beyond the current course.  Questions regarding domain specific knowledge (DSK) were separated from questions about trends. The DSK questions were primarily in the ASSE while the questions asking about periodic trends were all placed within the interview. This was done to be able to ask more detailed questions in the 42 the unit exam (Appendix C), and the interview data. The ASSE used in this study was an open-ended instrument consisting of seven questions used to elicit both explanations as well as student-drawn representations. Questions about atom structure and orbitals, intra- atomic forces, as well as ion formation were included in the instrument. The instrument that was used in the pilot study can be seen in Appendix D. The instrument was changed after the pilot study, as previously described, and the final version is shown in Table 3.4 (without spaces left for answers). This instrument, in conjunction with the exam questions, was intended to help ascertain whether a participant had an adequate DSK to predict the various periodic trends. Table 3.4 Atomic Structure Student Evaluation (ASSE) ASSE Questions 1. Draw a representation (picture) of a sodium atom.  Show all subatomic particles in their correct locations relative to each other, and name them (you may use a key to identify particles).  Identify the charge if there is one on all subatomic particles. 2. Use your picture to identify “valence electrons” and describe what a valence electron is. 3. Use your picture to identify “core electrons” and describe what a core electron is. 4. a. Describe or define an atomic orbital. b. How many orbitals would be needed for all of the electrons in the sodium atom? c. Show a labeled orbital diagram for sodium (using boxes for each orbital with arrows to illustrate the electrons). d. Could an electron in a 3s-orbital of sodium ever be closer to the nucleus than an electron in a 2s-orbital? Explain. 5. Describe the attractive and repulsive forces within an atom. 43 6. a. The term ionization energy is the amount of energy needed to take away one electron from an atom. Write a chemical equation that shows this process for sodium. b. If this occurred for sodium, how would your atomic picture change? 7. Imagine a picture of a fluorine atom. How would the picture change when the fluorine (F) becomes a fluoride ion (F-)? Data Analysis This section describes the data analysis procedures used to answer each of the research questions. Table 3.5 serves as a summary of the overall plan for the analysis of the data with alignment to the research questions. Table 3.5 Analysis Overview by Research Question Research Question Data Sources* Analysis What are the types of reasoning strategies used by undergraduate general chemistry students in their explanations of periodic trends including atomic radii, ionic radii, ionization energy, electronegativity and reactivity? Interviews  Determine frequency of each reasoning code How does domain specific knowledge concerning atomic structure, electrostatic forces operating within the atom, and the ionization process shape the reasoning strategies of undergraduate general chemistry students in regard to the above trends? ASSE Exam Interviews  Assess DSK in each of the DSK domains  Determine distribution of codes by adequate/inadequate DSK What effect will an unfamiliar periodic trend problem have on the reasoning strategies utilized by undergraduate general chemistry students? Interviews  Compare coding for reactivity with overall frequency determined by question one  Determine consistency of reasoning between reactivity and all other trends *ASSE = Atomic Structure Student Evaluation 44 Analysis of reasoning strategies. The answers to all three research questions hinged on the identification of student research strategies. The identification of these strategies made use of the student interview data. The coding unit selected for the analysis of reasoning strategies was the entire explanation that a student gave for a specific periodic trend in either a group or a period. It was possible for several codes to be assigned to one periodic trend explanation if there were several different aspects of a student’s explanation that each demonstrated a different reasoning type. Because the students were asked to think aloud, at times their thinking changed directions as they tried out various ideas or they combined strategies to form their complete explanation. In the coding process, individual interviews were coded one at a time rather than going through all of the interviews and coding one trend at a time. This decision was made because sometimes the students’ thinking would continue into the following trend, and important aspects would be missed by looking at only one trend in isolation. Analysis of the interviews began by first reviewing the transcripts holistically, to become familiar with the data, correcting any transcription errors, and recording overall impressions concerning student understanding and general reasoning strategies. Once an overview of the transcripts was complete, coding could commence. In phenomenography, codes are usually determined by identifying the most significant elements in each coding unit (Ornek, 2008; Sjöström & Dahlgren, 2002), grouping these elements and allowing the codes to emerge. This practice was observed in the pilot study with the result that five codes were identified. On the basis of the holistic review of the interviews as well as the results from the first three students coded, the original five codes 47 These codes were provisionally defined using the definitions from the literature (see Table 3.7) and all previous coding was reviewed. As coding continued, some coding definitions were refined to fit the unique context of the study. The coding rules underwent a final revision at the end of the first round of coding and before the second round began. Table 3.7 provides a summary of all codes, the literature definition, and the final coding rules that were used in the study. Table 3.7 Definitions for the Reasoning Strategy Codes Reasoning strategy code Definition followed by rules for use Additivity  When a student thinks that effects are equally distributed among the parts of a system (Talanquer, 2006).  Used for the conservation of force idea that if there are more protons than electrons, each electron gets to share a larger portion of the attractive force as though it were a fixed quantity. Analytical  Critically evaluating an initial heuristic response through a slow and controlled process (Evans, 2006).  When a student is able to see inconsistencies, weigh ideas and revise explanations to reach a conclusion based on logical reasoning. Analytical- failure  Defined for this study to denote when a student uses contradictory reasoning and is not aware of it. Analytical- partial  Defined for this study to denote when a student uses contradictory reasoning, is aware of it, but is either unable or unwilling to resolve the tension and change the response. Analogical  Used to form a bridge between what is already known and what is being explained (Dunbar & Klahr, 2012).  The student compares the problem situation to some other more familiar situation and uses the comparison to facilitate thinking and explain causes. 48 Availability  Causes are chosen based on their familiarity or cognitive accessibility (Talanquer, 2006).  The student considers a factor that is unjustified or irrelevant to the situation, but which is very familiar, easily available, or which was recently used in a different context, but which is now unwarranted. Essentialism  The idea that objects or substances have an inherent essence that causes the properties we see (Gelman et al., 1994)  The student explains a trend by referring to the general character or essence of the element. Lexicographic  When factors are considered one at a time until a specific factor differentiates between alternatives (Fishburn, 1974; McClary & Talanquer, 2011).  Redefined for this study as when a student discusses several factors, than chooses one as the basis for a decision and discards or minimizes the rest without justification. Multi-factor  Originally termed ‘multi-variable’, this applies when all factors are taken into consideration to predict whether they will affect the outcome in an additive or interactive manor (Kuhn et al., 2008)  Redefined for this study to apply when a student looks at how two or more factors jointly influence an outcome. Multi-factor failure  After consideration of several factors the decision to defer any choice is made. This is prevalent when the comparisons make a choice too difficult (Dhar, 1996)  When a student attempts to weigh multiple factors, but ends up in confusion either because of a lack of ability to weigh competing factors or when the trend is known, feels that none of the factors considered gives a compelling explanation of the known result and so fails to endorse any explanation. No reason – memorization  The student can offer no answer or responds that they memorized the trend. One-reason  Almost any property is seen as being caused by only one factor (although the factor may change depending on the property) (Talanquer, 2006).  Redefined for this study to apply to any student who used the one, most appropriate factor and justified its use. 49 Proportional  When assertions concerning direct and inverse proportions are made and appropriately justified (Lamon, 2012).  When a student discusses how the increase or decrease in forces affects the properties in question. Representative- ness  Judging whether a target object (situation) belongs to a particular type or class (Shah & Oppenheimer, 2008).  If the student recognizes the relationship of electronegativity or reactivity to ionization energy and uses this relationship to explain trend. Satisficing  Solves a problem by picking the first satisfactory alternative when many alternatives are available (Simon, 1990).  Redefined for this study as when a student is satisfied with using only one (possibly two) factor(s) to explain a phenomenon, ignoring others that either oppose the conclusion or are vital to the context. Similarity  When it is assumed that the cause and effect in a causal relationship have similar features (Talanquer, 2006).  If a student takes an adjective such as large, and thinks if it applies to one characteristic such as charge, than some other characteristic must also be large without applying a scientific principle such as electrostatic forces to explain it. Teleological  If a student asserts that a phenomena changes in response to some internal purpose (Talanquer, 2006).  When the student refers to the atom wanting a full shell or subshell, or wanting to be like a noble gas. Fixation  The tendency of the student to use the same strategy even when the nature of the problem changes and another would be more effective (Talanquer, 2006).  Used as a summary of a student’s responses. This code should be applied when a student uses the same argument that focuses on a single factor to explain more than 50% of the trends. During the coding revision process, four heuristic codes from the literature (one- reason, satisficing, multi-factor, and lexicographic) were redefined to more accurately fit the context of the study. This was done in response to an early problem which was encountered when trying to establish clear boundaries that would differentiate the satisficing and one-reason heuristics since both reduce the number of factors considered. 52 be seen by looking at the following quote by Corban when he explained the changes in ionization energy within a group: If there’s more shells there’s going to be repulsion, like between the inner-most shell and the shell next to it. So this one [sodium] isn’t close, even remotely close to the eleven protons, so there’s going to be little attraction between the protons and the electrons on the way out. In lithium, there’s only two orbitals, so it has two orbitals, one inner, and there’s one valence electron [in outer shell]. It still is going to be closer to the nucleus rather than the one electron in sodium. Corban discussed sodium having more orbitals than lithium, and that more orbitals caused more repulsion. He then went on to state that sodium is larger (in radius) than lithium (probably due to the repulsion factor that he started with). Corban links distance and repulsion, two appropriate factors which interact to affect the final prediction, but he fails to explain the causal factor that would modify the results of repulsion, thus he was not coded as multi-factor. Instead, he was coded as satisficing, because he ignored a factor (increased nuclear attraction) that would negate the effect of the increased repulsion that he did discuss. The last code that was redefined was lexicographic. The literature definition (Fishburn, 1974; McClary & Talanquer, 2011; Svenson, 1979) is that the problem solver looks at factors one by one, often in order of attractiveness or importance, comparing their values, but stops as soon as a factor helps in differentiating between alternatives. This presented a problem in the interviewing situation because the student would often start with the factor that differentiated between the alternatives and ignore those that were 53 the same, even when aware of them, which resulted in a one-reason code. The lexicographic code was redefined as referring to the student that considered several factors, but settled on only the one that seemed most attractive as the basis for a decision and appeared to discard the rest. This is not the same as the student that was able to discuss the effect of interactions between various factors in making a decision (multi- factor reasoning). An example can be seen in the explanation that Nathan gave for the decreasing ionization energy going down a group. He stated: More protons would have an effect in the sense of drawing electrons towards it in the center. . . . Well, also as you go down the periodic table, you get more core electrons. And so with more core electrons, there’s more of a repulsive force that’s going to push. It’s going to push those outer electrons away, so making it easier to pull one away when there’s more forces pushing out. Nathan correctly assessed the effect of proton attraction and electron repulsion and knew that the effect was opposite. Since he had memorized the trend, he simply ignored the effect of the protons and decided that the repulsion from core electrons was the reason for the decrease in the trend. He never explained why the attractive force from the protons did not counterbalance the repulsion from the core electrons, but rather seemed to dismiss the attraction argument. After the final coding rules had been established and the first round of coding was complete, it became clear that many of the students exhibited a consistency in the flow of their explanations, using the same limited factors and justifications for many of the 54 periodic trends. The fixation code (Talanquer, 2006) was instituted in order to reflect the totality of the students’ explanations rather than a single isolated reasoning strategy. This heuristic describes the tendency of students’ to overgeneralize the use of a particular rule or principle regardless of any change in the problem context. Fixation was coded for any student using the same factor and justification for at least 50% of the periodic trends. The first round of coding was completed by the researcher of record with the collaboration of a second researcher who had several years’ experience teaching undergraduate chemistry. The second researcher participated in about one-third of the coding, deciding on codes independently and then collaborating until consensus was reached. As a part of this collaboration, coding definitions were reviewed and refined as discussed previously, until the final definitions were arrived at by the end of the first round of coding. A second round of coding occurred in which the researcher of record reviewed all codes that had been assigned, flagged any questionable codes, and then collaborated with the second researcher until agreement occurred. Lastly, explanations with the same code were compared to each other to ensure consistency. The code assignments continued to be evaluated until it was felt that no further questionable codes were being found. After coding was complete, and the frequency of code utilization had been compiled, a decision was made to simplify the results by eliminating five codes from any further analysis. The first code to be eliminated was proportional reasoning. Proportional reasoning could be defined as the ability to compare two quantities using a mathematical justification involving direct or inverse proportions (Lamon, 2012). All of the periodic 57 The criteria for adequate DSK concerning atomic structure was that students needed to understand the Bohr model of the atom in order to predict most trends, but when explaining the exceptions to the ionization energy in a period, they also needed to understand the orbital structure that is part of the quantum model (Taber, 2003b). After the pilot study, it was determined that an understanding of the wave properties of the atom was not important at the level of student reasoning expected. The criteria for understanding the electrostatic forces within the atom was based on the principles of Coulomb’s Law about attractive and repulsive forces (Taber, 2003b). Table 3.8 Criteria Used to Assess Students’ DSK Topic DSK needed to predict periodic trends Assessment instrument and question number* Atomic Structure  Is able to draw a correct Bohr representation of an atom.  Is able to construct correct electron configurations and orbital diagrams. ASSE 1 E 1, 2, 5, 6 I Forces  Can describe what gives rise to attractive and repulsive forces  Can differentiate the effect of core and valence electrons in shielding outer electrons from the nucleus, or can use the concept of effective nuclear charge. ASSE 5 E 3 I Ionization Process  Is able to correctly describe the meaning of ionization energy  Can produce a chemical equation that represents the ionization process.  Can differentiate first and second ionization energy ASSE 6a-b E 4, 7 I *ASSE = Atomic Structure Student Evaluation; E = Unit Exam; I = Interview 58 Students needed to understand that protons attract electrons, electrons repel other electrons, and core electrons cause more nuclear shielding by their repulsion than the valence electrons (Wang & Barrow, 2013). The criteria for the ionization process was based on the concepts that would be needed to predict the different periodic trends that related to ionization energy. This included an understanding of the definition of ionization energy as well as being able to represent the ionization process using a chemical equation. Trustworthiness Dual role of instructor and researcher. As mentioned previously, the researcher of record also served as the instructor for the course. As the instructor of the general chemistry course at the institution where the present study took place for the previous seven years, the researcher had both understanding and control over the instructional setting ensuring that every participant in the study had been exposed to the same content and instructional activities. This type of prolonged engagement by the researcher with the students had the potential to encourage the establishment of rapport and trust (Guba & Lincoln, 1989) so that students might feel less hesitation in proffering their ideas and explanations. Evidence for this sort of trust was seen when 29% of the students in the course volunteered for the pilot study done in the Spring of 2015, at a very busy time in the semester, when no extra credit was offered. Hammersley (2006) suggests that the established relationship between an instructor and students also has the potential to enhance the depth of data collected. 59 The disadvantage of the dual role of instructor and researcher is the possibility of introducing bias by creating expectations for the type of reasoning that individuals might use based on past performance. To guard against this bias, the interview transcripts were thoroughly reviewed several times, with a critical attitude concerning any previous interpretations. When there was any uncertainty about the interpretation, the second researcher was brought into the decision-making process to discuss alternative interpretations and arrive at a consensus. If the meaning of a particular explanation was unclear, it was compared to other explanations made by the same student to gain insight into the student’s understanding and mindset. While it is not possible to eliminate all bias, significant effort was made to interpret the results in a manner that truly reflected the data collected. Another possible disadvantage of the dual role of instructor/researcher is that the instructor had a position of power in the relationship with students which might cause the students to feel that their participation status could influence future treatment in the course. This threat was minimized by the clear assurance conveyed during the invitation process and just before the interview took place, that participation was voluntary and would have no bearing on the instructor’s attitude or interactions with the student in the future. Limitations. Inherent limitations of qualitative studies dependent on interview data are the level of participant motivation (Maeyer & Talanquer, 2013; Sjöström & Dahlgren, 2002) and willingness of participants to verbalize their thought process due to either verbal ability or comfort level (Taber & Bricheno, 2009). Given the low-stake 62 CHAPTER 4: FINDINGS This chapter will present and interpret the findings of this study. As a reminder for the reader, the research questions that guided this study were: 1. Reasoning Strategies: What are the reasoning strategies used by undergraduate general chemistry students in their explanations of periodic trends including atomic radii, ionic radii, ionization energy, electronegativity and reactivity? 2. Domain Specific Knowledge (DSK): How does domain specific knowledge concerning atomic structure, electrostatic forces operating within the atom, and the ionization process shape the reasoning strategies of undergraduate general chemistry students in regard to the above trends? 3. Unfamiliar Trend: What effect will an unfamiliar periodic trend problem have on the reasoning strategies utilized by undergraduate general chemistry students? The first section presents an overview of the types of reasoning strategies that were used by students to explain various periodic trends. The second section explores the relationship between domain specific knowledge (DSK) and specific reasoning strategies. The third section will investigate how patterns of reasoning are affected when an unfamiliar problem is presented. All student names are pseudonyms. Research Question 1: Reasoning Strategies This section addresses the frequency and distribution of reasoning strategies used by students in explaining periodic trends as summarized in Figure 4.1. The focus of the section is on those reasoning strategies with the highest frequency of utilization having at least 30 coded references, as well as those strategies that were used primarily for one 63 trend. It was found that those codes with at least 20 references were broadly used for many trends, whereas, the majority of the codes that had between seven and twenty coded references were restricted to only a few periodic trends. Most frequently used reasoning strategies. While a wide variety of reasoning types were used, four stood out as being of particular prominence. The four most frequently used reasoning strategies in this study in order of decreasing frequency were satisficing, teleological, multi-factor, and one-reason. This is not surprising as each of these strategies, with the exception of teleological, could be considered useful, in explaining any periodic trend. Satisficing. Satisficing is a blend of the words sufficing and satisfying (Gigerenzer & Goldstein, 1996), and occurs when a person picks the first satisfactory explanation that will solve the problem rather than searching for the optimal solution (Simon, 1990). In this study, the satisficing heuristic was redefined as the type of Figure 4.1. Reasoning strategies used by thirteen students to explain periodic trends 0 10 20 30 40 50 60 N u m b er o f R ef er en ce s Codes # of References # of Students using Code 64 reasoning used when a student was satisfied to use one primary factor that did not adequately explain the periodic trend while ignoring other more scientifically appropriate factors that either opposed their conclusion or were essential to fully explain the trend. Satisficing was the most frequently coded heuristic in this study with 57 coding references out of a total of 291, or roughly 20% of the codes. Twelve of the thirteen students in the study used satisficing at least one time. This result is consistent with the singularity, relevance, and satisficing principles postulated by Evans (2006) that people consider a single hypothetical possibility at a time, choosing what they feel to be most relevant in the current context and will accept it if it seems satisfactory, often without any additional validation. The solution is usually chosen by means of an implicit process that requires only shallow processing of context requirements. This implicit processing competes with more explicit processing that considers all relevant factors and carefully works through their scientific justification. Satisficing was often used to code a student who referred to either attractive or repulsive forces but did not balance their explanation with an assessment of the opposing force. This was considered to be a partial explanation that biased whichever force was most convenient in providing an explanation for a prediction the student had already decided on. Two examples illustrate how students used this reasoning strategy to validate a prediction. The first was Corban’s explanation as to why the atomic radius increases in a group: 67 In this study, 35 responses were coded as multi-factor out of 291, or roughly 12% of all codes. Nine of the thirteen students used multi-factor thinking at least one time. An example of multi-factor reasoning is shown in the following interview excerpt by Karla when she discussed the change in ionization energy across a period: It takes the most energy in the top right corner, and that’s because as you’re moving across a period, you have the same amount of core electrons. . . . So you know the effective nuclear charge is getting bigger, and so the protons have more attraction on the electrons. So they are like holding on to them tighter, or pulling them closer, and because of that, because the protons are so much, outnumber the core electrons, because the core electrons are staying the same, it takes a lot more energy to take away an electron. So that’s why as you move across a period, they’re gaining protons, but keep the same amount of core electrons and so the ionization just gets bigger and bigger. Karla used two ideas: proton attraction, and core electrons. She wove them together to give the concept of effective nuclear charge. While she did not explicitly discuss electron repulsion in this trend, she gives a more complete explanation of effective nuclear charge later stating: “The effective nuclear charge is increasing as you go to the right. The positive charge has more attraction than there is repulsion between the electrons.” She then related effective nuclear charge to the energy required to overcome that attraction and take away the electron. She was the only student in the study who was able to both explain and use the concept of effective nuclear charge. This is a complex property that takes into account the total nuclear attraction as well as the electron repulsion. Since the 68 majority of the electron repulsion is due to the core electrons, rather than the valence electrons, effective nuclear charge is often simplified to the number of protons minus the number of core electrons. Teleological. Teleological reasoning was coded with the second highest frequency with 37 of the 291 responses or about 13% being coded in this category. Twelve of the thirteen students in the study used teleological reasoning at least once showing that it was a major part of their thinking about this topic. Teleological reasoning involves an inversion of cause and effect, such that the effect of a change is seen as the purpose which drives the change to occur, as described in Chapter 2. The explanation might reference a chemical principle or rule without explaining the interactions that cause the principle to work. In this study, teleological reasoning was coded whenever the student described the atom as needing to fill the outer shell, subshell or orbital, fulfill the octet rule, or trying to become like a noble gas. A fundamental human bias toward teleological thought as proposed by Kelemen et al. (2013) is supported by the almost universal use of the full shells explanation by students in this study. Some examples of how these ideas were expressed are given below: It’s just because everything wants to be filled. So this is like if magnesium has eight [electrons] but has just one valence electron, it’s going to be more willing to just want to lose that electron. (Corban on the second ionization energy of magnesium.) If you take the next one [electron] from that full orbital, then that would want, it doesn’t want to give it away so it would take more ionization energy to get it. . . . 69 Because it [electron] wants to stay with all the valence electrons. Once it [potassium ion] has a full set, it doesn’t want to give them away, it wants to just keep them. (Tina on the second ionization energy of potassium.) Because the attraction between the nucleus and electrons are strong because atoms want to become fully shelled, like have all the electrons in the shell. They want to become a noble gas so they’re less likely to release the electrons so they’re going to pull them in closer. (Katie on the atomic radius in a period.) While an important goal of science instruction is to encourage the development of scientifically sound, causal reasoning, one must still ask whether there is any positive function that teleological reasoning might fulfill. Talanquer (2007) suggests that teleological explanations can be useful in chemistry particularly when a general rule predicts directionality in the transformation of a chemical system. A teleological explanation takes complex chemical systems with many interactions and simplifies them in a way that allows students to more easily organize their knowledge around major concepts, giving them a powerful means with which to make predictions (Taber, 2003b; Talanquer, 2007). The octet rule provides a useful rule of thumb to determine the number of electrons that must be transferred or shared in a chemical reaction because it is straight-forward and easy to remember (Tan et al., 2008). The utility of teleological reasoning involving the octet rule can be seen in several of the interviews when students were initially undecided about a trend, but the octet rule helped to steer their thinking in productive directions. When discussing the ionization energy in a period, Ronald initially predicted that it would decrease as you go from left to 72 atom to achieve a noble gas configuration or full shell. Since calcium is able to achieve the noble gas configuration only with the loss of the second electron, she determined that the energy would be less for the second electron than the first since the loss of the first electron achieves a configuration that does not involve a full shell. She had a bias toward the teleological octet reasoning even though she realized that it was contradictory to the argument she had used previously for the second ionization of potassium where she discussed the increased attraction of protons. After giving her teleological argument for calcium, she stated, “Proton logic is not helping me here,” tacitly acknowledging her previous explanation for potassium. Corban used an identical teleological argument for the second ionization energy trend stating: Magnesium already lost one electron. I guess the ionization energy would be less than its first ionization energy because it just has one valence electron outside instead of two. . . . Everything wants to be filled. So this is like if magnesium has eight [electrons] but has just one valence electron, it’s going to be more willing to just want to lose that electron. In other cases, the use of teleological reasoning may not have resulted in an incorrect prediction, but it was overgeneralized and misapplied to a situation in which its use was not warranted. Such was the case in the following excerpt in which Ronald was trying to explain why beryllium required more energy to lose an electron than boron. He first noticed that in the valence shell, boron had two electrons in the s-orbital, and only one in the p-orbital. 73 Just having one electron in that energy level will make a huge difference because you’d only be pulling away, acting on the one electron in there. I mean you’d be fighting however many, the five protons that are in there, but there’s only one electron in that energy level. . . . Once it’s full [the 2s-orbital/subshell] it’s harder to pull away [the electron]. In this situation, the decrease in energy for the removal of the 2p-electron is not because it is by itself in an orbital. There is actually less repulsion when the electron is not paired which would tend to increase the amount of energy needed to remove it. The decrease in energy for ionization is instead related to the increase in the energy of the 2p-orbital relative to the 2s. Ronald has overgeneralized the full shell rule to include subshells as well as shells and he disregards the fact that the atom will not achieve the octet of electrons or a noble gas configuration. Six other students used an identical argument for exceptions to the general ionization trend. Karla used a similar argument when thinking about the electronegativity in a period. She stated: If you look at lithium, it only has one electron in that energy level, in 2s, and so it wants to fill up that one. So I feel like lithium would attract electrons more than beryllium will. She then began to consider the radius and effective nuclear charge and decided to reverse her prediction to the correct one. In this case, while her first intuitive reasoning was teleological, when given the time to reflect, she was able to generate a more scientifically correct causal/mechanical reason. This does not mean that she saw the error of applying the full shells argument to subshells, but that in this case she recognized overriding 74 factors that caused her to change her prediction. Loni also used an argument regarding the stability of a full s-orbital when describing the reactivity of atoms in a period. The widespread use of the overgeneralization of full shells to full subshells or orbitals lends support to the appeal that the teleological octet argument has for students. Reasoning strategies associated with specific trends. While satisficing, multi- factor, one-reason and teleological strategies were used most frequently in part due to their more general applicability to all of the periodic trends, there were other heuristics that seemed to be more uniquely applied to only one or two of the trends, as seen in Figure 4.2. Additivity, availability, essentialism, representativeness, and similarity were each used primarily for one trend, rather than being more evenly distributed as the other Figure 4.2. Heuristics associated with specific trends. 0 2 4 6 8 10 12 14 16 Additivity Availability Essentialism Representativeness Similarity 77 Reactivity differed from the other trends in that it was the most unfamiliar of the trends and students were provided with a greater variety of resources to support their reasoning. Resources included the periodic table (available for all the questions), chemical equations representing the reactions that occurred, and a table that included the first through fourth ionization energies for all of the elements involved (Appendix B). Both the unfamiliarity and the resources that were available may have had an effect on the types of reasoning used. The unfamiliarity issue will be addressed in detail by the third research question later in this chapter. Availability. Availability is a type of reasoning based on the familiarity or cognitive accessibility of the causal factors used (Talanquer, 2006). The access to resources available only for the reactivity trend may have influenced reasoning strategies as seen by the increase in the use of factors prompted by the information provided by the ionization table. Nine of the sixteen availability references were coded for the reactivity trend. Availability was coded when a student inappropriately used a factor which was unjustified or irrelevant to the situation, but which is familiar, or readily available in the form of a reference chart. In the case of the reactivity trends, if the ionization chart was used in an inappropriate manner, then the response was coded as availability. Examples of inappropriate use of the available chart occurred in the interviews with several students and usually focused on the jump in ionization energy that occurs after all of the valence electrons have been lost. In responding to the reactivity in a period, Katie initially stated: I believe that potassium will react, it reacts more vigorously because of the large jumps between the first ionization energy and the second and the third and the 78 fourth compared to calcium which also has large jumps, but not as large of jumps as potassium. And then iron has very small jumps compared to the other two. As Katie continued to ponder the question, eventually she was able to come up with a more scientifically appropriate reason, but her first response was based on the availability of the chart and the large change in energy that she saw after potassium lost the first electron. Rhonda used a similar rationale for the reactivity in a period. She said: Like for potassium, it has a really high jump between ionization energies. Like it’s not as big of a jump from ionization energies. . . . It takes a bigger ionization energy from first to second then for calcium or iron. I think that it would make it react more. It is difficult to determine from this excerpt whether Rhonda understood what ionization energy meant. She was simply using the chart and noticed the large change between the first and second ionization energy for potassium. She may have remembered this as something important from class discussions and so assumed incorrectly that it was the cause of the increased reactivity of potassium. Later Rhonda responded, “It’s gaining electrons because it is bonding with the oxygen and the hydrogen.” It became clear that while Rhonda knew electrons are involved, she has no real understanding of the process. Sonya and Ronald appropriated almost identical reasoning, not understanding that the reactivity of a metal increases when the ionization energy is low so that the electrons can be more easily lost. Nathan was also coded as using the availability heuristic when responding to the reactivity trend. His response was interesting as he initially used the ionization chart in a 79 scientifically appropriate manner, but failing to mention electrons he was asked if potassium had lost an electron in the reaction. His response after considering the equations was, “Potassium has a charge of plus one, H has a charge of [pause] nope, it is not losing an electron.” When asked the next question, which concerned the reactivity in the group, he responded: You have that chart because it has something to do with the ionization energy. So all I can think of is just that the ionization energy gets less and less as you go down the periodic table, so it becomes, it basically becomes what I would consider less stable in the sense that it is more reactive. Nathan knew that the ionization chart that was provided must be the key to reactivity, but because he had not yet mastered how to recognize the loss of electrons in an equation, he was left at a loss as to how to explain why the ionization energy was relevant. While students used availability reasoning most often when responding to the reactivity trend, it was also used with other trends. In Monica’s response concerning the atomic radius trend in a period, she stated: As you go from left to right in a period, you get larger because the atomic mass grows. . . . As you go from left to right you have more electrons, valence or just electrons in general. Because like say I was at aluminum, I would have three electrons in the last orbital so that could expand the [break in sentence] because you’re taking more space. Monica used the common sense reasoning that when something has more mass and more particles, it will take up more space rather than a more scientific argument dealing with 82 reactivity trend. An example of the use of the similarity heuristic occurred when Ronald explained the trend in reactivity moving across a period. He stated: Potassium, it jumps from 419 [kJ/mole] to 3042 [kJ/mole] then another thousand jump . . . That would be the amount of energy that has to be expelled and acted on potassium. . . . Big reactions give off a lot of heat generally or they take away a lot of a lot of heat. . . . There’s more heat involved so it becomes hot enough to burn. So I was just thinking that intensity probably comes a lot from how much energy is actually required to pull away that first electron. Ronald assumes that a large ionization energy (or increase in successive ionization energies) causes the release of a large amount of energy or heat as a result. Rather than thinking about how an increase in required energy needed might increase the difficulty of breaking bonds and slow the reaction down, he has the conception that a large amount of energy at one stage of a reaction must result in a large amount of energy at all stages of that reaction. Representativeness. The representativeness heuristic was also used primarily to explain reactivity trends. Representativeness thinking is used when students recognize the target problem as belonging to a particular class of problems (Shah & Oppenheimer, 2008). The representativeness code was used primarily if the student recognized the relationship of the trend in question, to the ionization process when it was not ionization energy that they were being asked to explain. Given this requirement, the heuristic could only be used for the electronegativity and reactivity trends. In other words, to use the 83 representativeness heuristic, the student would need to recognize how the ionization process compared to electronegativity or that ionization is actually the controlling issue in the reactivity of metals. Katie recognized the relevance of the ionization data to the reactivity of metals across a period when she stated: It [potassium] wants to lose the first electron because it has such a low first electron ionization energy. So, it wants to lose it, the valence electron, so it will react with the water in order to have that exchange. . . . Iron has a very high first ionization energy. So, it means that it doesn’t really want to lose the first electron, or at least less so compared to the other two, so it will be less likely to give away that electron and react with the water. Katie knew that ionization energy (IE) was the energy needed to lose an electron and recognized that the amount of energy required was relevant to the reactivity of metals. She then compared the first IE of potassium to that of iron, made the connection that a lower IE made it easier for an exchange of electrons to occur, and drew the conclusion that a lower IE promoted higher levels of reactivity for a metal with water. Used in this manner, the representativeness heuristic is very useful to the solution of problems when applied appropriately. Summary for Research Question One. The first research question sought to determine the reasoning strategies used by undergraduate general chemistry students in their explanations of periodic trends in atomic radii, ionic radii, ionization energy, electronegativity and reactivity. This section has highlighted those strategies that were 84 used with the greatest frequencies as well as those that were particularly important in explaining specific periodic trends. It was found that the satisficing, teleological, multi- factor, and one-reason strategies were used with the highest frequency. Each of these strategies are generally applicable to all of the trends as opposed to the additivity, availability, representativeness, and similarity strategies that were used primarily for a more limited number of trends. A comparison of the one-reason and satisficing strategies showed that they were both very similar in that they relied on the use of primarily one factor which reduced the level of cognitive processing for students, allowing them to use less time to come up with an answer. Although the students were not limited in the time allowed, they still had a preference for these strategies. Many students also used the multi-factor strategy which required a greater level of cognitive processing, as more factors had to be considered and their effect integrated. The teleological strategy was used both with high frequency and by almost all students. It is possible that teleological thinking is a fundamental aspect of human thought (Kelemen, 1999). Reasoning strategies that were limited to a few specific trends included additivity, used only for trends involving the ionization process, and the strategies of availability, essentialism, representativeness and similarity which were all used primarily with the reactivity trend. It is probable that the unique nature of the problem context which included more resources and which was also unfamiliar to the students affected these choices. Research Question 2: Domain Specific Knowledge Overview of DSK by domain. The second research question to be investigated