Browsing by Author "Johnson, Estrella"
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- Association of malleable factors with adoption of research-based instructional strategies in introductory chemistry, mathematics, and physicsYik, Brandon J.; Raker, Jeffrey R.; Apkarian, Naneh; Stains, Marilyne; Henderson, Charles; Dancy, Melissa H.; Johnson, Estrella (Frontiers, 2022-11)Active learning pedagogies are shown to enhance the outcomes of students, particularly in disciplines known for high attrition rates. Despite the demonstrated benefits of active learning, didactic lecture continues to predominate in science, technology, engineering, and mathematics (STEM) courses. Change agents and professional development programs have historically placed emphasis on develop-disseminate efforts for the adoption of research-based instructional strategies (RBIS). With numerous reported barriers and motivators for trying out and adopting active learning, it is unclear to what extent these factors are associated with adoption of RBIS and the effectiveness of change strategies. We present the results of a large-scale, survey-based study of introductory chemistry, mathematics, and physics instructors and their courses in the United States. Herein, we evaluate the association of 17 malleable factors with the tryout and adoption of RBIS. Multilevel logistic regression analyses suggest that several contextual, personal, and teacher thinking factors are associated with different stages of RBIS adoption. These results are also compared with analogous results evaluating the association of these factors with instructors' time spent lecturing. We offer actionable implications for change agents to provide targeted professional development programming and for institutional leaders to influence the adoption of active learning pedagogies in introductory STEM courses.
- Characteristics of departments with high-use of active learning in introductory STEM courses: implications for departmental transformationLau, Alexandra C.; Henderson, Charles; Stains, Marilyne; Dancy, Melissa; Merino, Christian; Apkarian, Naneh; Raker, Jeffrey R.; Johnson, Estrella (2024-02-12)Background: It is well established in the literature that active learning instruction in introductory STEM courses results in many desired student outcomes. Yet, regular use of high-quality active learning is not the norm in many STEM departments. Using results of a national survey, we identified 16 departments where multiple instructors reported using high levels of active learning in their introductory chemistry, mathematics, or physics courses. We conducted interviews with 27 instructors in these 16 departments to better understand the characteristics of such departments. Results: Using grounded theory methodology, we developed a model that highlights relevant characteristics of departments with high use of active learning instruction in their introductory courses. According to this model, there are four main, interconnected characteristics of such departments: motivated people, knowledge about active learning, opportunities, and cultures and structures that support active learning. These departments have one or more people who are motivated to promote the use of active learning. These motivated people have knowledge about active learning as well as access to opportunities to promote the use of active learning. Finally, these departments have cultures and structures that support the use of active learning. In these departments, there is a positive feedback loop that works iteratively over time, where motivated people shape cultures/structures and these cultures/structures in turn increase the number and level of commitment of the motivated people. A second positive feedback loop was found between the positive outcome of using active learning instruction and the strengthening of cultures/structures supportive of active learning. Conclusions: According to the model, there are two main take-away messages for those interested in promoting the use of active learning. The first is that all four components of the model are important. A weak or missing component may limit the desired outcome. The second is that desired outcomes are obtained and strengthened over time through two positive feedback loops. Thus, there is a temporal aspect to change. In all of the departments that were part of our study, the changes took at minimum several years to enact. While our model was developed using only high-use of active learning departments and future work is needed to develop the model into a full change theory, our results do suggest that change efforts may be made more effective by increasing the robustness of the four components and the connections between them.
- Evaluating the impact of malleable factors on percent time lecturing in gateway chemistry, mathematics, and physics coursesYik, Brandon J.; Raker, Jeffrey R.; Apkarian, Naneh; Stains, Marilyne; Henderson, Charles; Dancy, Melissa H.; Johnson, Estrella (2022-02-10)Background Active learning used in science, technology, engineering, and mathematics (STEM) courses has been shown to improve student outcomes. Nevertheless, traditional lecture-orientated approaches endure in these courses. The implementation of teaching practices is a result of many interrelated factors including disciplinary norms, classroom context, and beliefs about learning. Although factors influencing uptake of active learning are known, no study to date has had the statistical power to empirically test the relative association of these factors with active learning when considered collectively. Prior studies have been limited to a single or small number of evaluated factors; in addition, such studies did not capture the nested nature of institutional contexts. We present the results of a multi-institution, large-scale (N = 2382 instructors; N = 1405 departments; N = 749 institutions) survey-based study in the United States to evaluate 17 malleable factors (i.e., influenceable and changeable) that are associated with the amount of time an instructor spends lecturing, a proxy for implementation of active learning strategies, in introductory postsecondary chemistry, mathematics, and physics courses. Results Regression analyses, using multilevel modeling to account for the nested nature of the data, indicate several evaluated contextual factors, personal factors, and teacher thinking factors were significantly associated with percent of class time lecturing when controlling for other factors used in this study. Quantitative results corroborate prior research in indicating that large class sizes are associated with increased percent time lecturing. Other contextual factors (e.g., classroom setup for small group work) and personal contexts (e.g., participation in scholarship of teaching and learning activities) are associated with a decrease in percent time lecturing. Conclusions Given the malleable nature of the factors, we offer tangible implications for instructors and administrators to influence the adoption of more active learning strategies in introductory STEM courses.
- Examining Connections among Instruction, Conceptual Metaphors, and Beliefs of Instructors and StudentsRupnow, Rachel Lynn (Virginia Tech, 2019-07-29)In this study, I will examine the beliefs and conceptual understanding of instructors and students from two abstract algebra classes. This research takes the form of a case study in which I answer four research questions, each addressing a relationship between instruction and beliefs or conceptual understanding. Specifically, these research questions are: 1. What beliefs do the instructors have about math, teaching, and learning and what relationship exists between these beliefs and instructional practice? 2. What is the relationship between instructional practice and students' beliefs about math, teaching, and learning? 3. What conceptual metaphors do the professors use to describe isomorphisms and homomorphisms and what relationship exists between these metaphors and the mathematical content in instruction? 4. What is the relationship between the mathematical content in instruction and conceptual metaphors the students use to describe isomorphisms and homomorphisms? In terms of beliefs, the instructors articulated considered positions on the nature of math, math learning, and math teaching. These beliefs were clearly reflected in their overall approaches to teaching. However, their instruction shifted in practice over the course of the semester. Students' beliefs seemed to shift slightly as a result of the ways their instructors taught. However, their core beliefs about math seemed unchanged and some lessons students took away were similar in the two classes. In terms of conceptual understanding, the instructors provided many conceptual metaphors that related to how they understood isomorphism. They struggled more to provide an image for homomorphism, which requires thinking about a more complicated mathematical object. Their understandings of isomorphism and homomorphism were largely reflected in their instruction with some notable differences. Students took away similar understandings of isomorphism to the instructors, but did not all take away the same level of structural understanding of homomorphism. In short, relationships between instructors' beliefs and instruction and between instructors' conceptual understanding and instruction were evident. However, certain elements were not made as clear as they perhaps intended. Relationships between instruction and students' beliefs and between instruction and students' conceptual understanding were also evident. However, relationships between instruction and beliefs were subtler than between instruction and conceptual understanding.
- Examining whether and how instructional coordination occurs within introductory undergraduate STEM coursesCouch, Brian A.; Prevost, Luanna B.; Stains, Marilyne; Whitt, Blake; Marcy, Ariel E.; Apkarian, Naneh; Dancy, Melissa H.; Henderson, Charles; Johnson, Estrella; Raker, Jeffrey R.; Yik, Brandon J.; Earl, Brittnee; Shadle, Susan E.; Skvoretz, John; Ziker, John P. (Frontiers, 2023-04)Instructors' interactions can foster knowledge sharing around teaching and the use of research-based instructional strategies (RBIS). Coordinated teaching presents an impetus for instructors' interactions and creates opportunities for instructional improvement but also potentially limits an instructor's autonomy. In this study, we sought to characterize the extent of coordination present in introductory undergraduate courses and to understand how departments and instructors implement and experience course coordination. We examined survey data from 3,641 chemistry, mathematics, and physics instructors at three institution types and conducted follow-up interviews with a subset of 24 survey respondents to determine what types of coordination existed, what factors led to coordination, how coordination constrained instruction, and how instructors maintained autonomy within coordinated contexts. We classified three approaches to coordination at both the overall course and course component levels: independent (i.e., not coordinated), collaborative (decision-making by instructor and others), controlled (decision-making by others, not instructor). Two course components, content coverage and textbooks, were highly coordinated. These curricular components were often decided through formal or informal committees, but these decisions were seldom revisited. This limited the ability for instructors to participate in the decision-making process, the level of interactions between instructors, and the pedagogical growth that could have occurred through these conversations. Decision-making around the other two course components, instructional methods and exams, was more likely to be independently determined by the instructors, who valued this autonomy. Participants in the study identified various ways in which collaborative coordination of courses can promote but also inhibit pedagogical growth. Our findings indicate that the benefits of collaborative course coordination can be realized when departments develop coordinated approaches that value each instructor's autonomy, incorporate shared and ongoing decision-making, and facilitate collaborative interactions and knowledge sharing among instructors.
- Facilitating Instructional Change: A Case Study on Diffusion of Curriculum InnovationMitchell, Corinne Beloved (Virginia Tech, 2023-08-15)While much research has been conducted on train-the-trainer models for diffusing curriculum innovations at the K-12 level, not much is known about how such models play out at the undergraduate level, especially with newer curriculum innovations using student-centered instruction. I present findings from one such project: a case study on the second-generation facilitation of a professional development group focused on supporting instructors teaching with the Inquiry-Oriented Abstract Algebra (Larsen et al., 2013) curriculum materials. I investigate the relationship between the intent of the instructional support model and the facilitator's beliefs and goals for the professional development, using video data collected from a series of online meetings and from the facilitator's classroom in the year prior to his facilitation. Results indicate that the facilitator's orientations and goals around sharing authority and creating supportive learning environments, especially for women participants, both modify and stabilize the intentions of the TIMES project (NSF Awards: #1431595, #1431641, #1431393) as a whole, and the train-the-trainer model as a subsidiary.
- Factors contributing to students and instructors experiencing a lack of time in college calculusHagman, Jessica Ellis; Johnson, Estrella; Fosdick, Bailey K. (SpringerOpen, 2017-06-14)Background: Calculus is a foundational course for STEM-intending students yet has been shown to dissuade students from pursuing STEM degrees. In this report, we examine factors related to students and instructors reporting a lack of time in class for students to understand difficult ideas and relate this to students’ and instructors’ perceptions of opportunities to learn using a hierarchical linear model. This work is part of the US national study on college calculus, which provides an ideal landscape to examine these questions on a large scale. Results: We find a number of student factors associated with students experiencing negative opportunities to learn, such as student gender, lacking previous calculus experience, and reports of poor and non-student-centered teaching. Factors weakly associated with instructor reports of lack of time were a common final and reporting that approximately half of the students lacked the ability to succeed in the course. Conclusions: This analysis offers insight into how we might create more positive opportunities to learn in our own classrooms. This includes preparing students before they enter calculus, so they feel confident in their abilities, as well as weakening the internal framing of the course by engaging in teaching practices that provide students opportunities to communicate and influence their learning (e.g., discussion and group work). We argue that this is especially important in introductory college calculus courses that are packed with material, taught to a diverse population of students in terms of demographics, mathematical preparation, and career goals.
- Failure to Reject the p-value is Not the Same as Accepting it: The Development, Validation, and Administration of the KPVMI InstrumentKeller, Rachel Elizabeth (Virginia Tech, 2019-05-08)The purpose of this study was to investigate on a national scale the baseline level of p-value fluency of future researchers (i.e., doctoral students). To that end, two research questions were investigated. The first research question, Can a sufficiently reliable and valid measure of p-value misinterpretations (in a research context) be constructed?, was addressed via the development and validation of the Keller P-value Misinterpretation Inventory instrument (KPVMI). An iterative process of expert review, pilot testing, and field testing resulted in an adequately reliable measure (Alpha = .8030) of p-value fluency as assessed across 18 misinterpretations and 2 process levels as well as an independently validated sub-measure of p-value fluency in context as assessed across 18 misinterpretations (Alpha = .8298). The second research question, What do the results of the KPVMI administration tell us about the current level of p-value fluency among doctoral students nationally?, was addressed via analysis of a subset of the field test data (n = 147) with respect to performance on the subset of items considered sufficiently validated as developed in Phases I-III (KPVMI-1). The median score was 10/18 items answered correctly indicating that future researchers on the aggregate struggle to properly interpret and report p-values in context; furthermore, there was insufficient evidence to indicate training and experience are positively correlated with performance. These results aligned with the extant literature regarding the p-value misinterpretations of practicing researchers.
- Individual and situational factors related to undergraduate mathematics instructionJohnson, Estrella; Keller, Rachel E.; Peterson, Valerie; Fukawa-Connelly, Timothy (2019-06-28)Background In the US, there is significant interest from policy boards and funding agencies to change students’ experiences in undergraduate mathematics classes. Even with these reform initiatives, researchers continue to document that lecture remains the dominant mode of instruction in US undergraduate mathematics courses. However, we have reason to believe there is variability in teaching practice, even among instructors who self describe their teaching practice as “lecture.” Thus, our research questions for this study are as follows: what instructional practices are undergraduate mathematics instructors currently employing and what are the factors influencing their use of non-lecture pedagogies? Here, we explore these questions by focusing on instruction in algebra courses, an upper-division mathematics course that is particularly well positioned for instructional reform. Results We report the results of a survey of 219 abstract algebra instructors from US colleges and universities concerning their instructional practices. Organizing our respondents into three groups based on the proportion of class time spent lecturing, we were able to identify 14 instructional practices that were significantly different between at least two of the three groups. Attempting to account for these differences, we analyzed the individual and situational factors reported by the instructors. Results indicate that while significant differences in teaching practices exist, these differences are primarily associated with individual factors, such as personal beliefs. Situational characteristics, such as perceived departmental support and situation of abstract algebra in the broader mathematics curriculum, did not appear to be related to instructional differences. Conclusions Our results suggest that personal bounds in general, and beliefs in particular, are strongly related to the decision to (not) lecture. However, many of the commonly cited reasons used to justify the use of extensive lecture were not significantly different across the three groups of instructors. This lack of differentiation suggests that there may be relevant institutional characteristics that have not yet been explored in the literature, and a transnational comparison might be useful in identifying them.
- Instructors' Orientation on Mathematical MeaningChowdhury, Ahsan Habib (Virginia Tech, 2021-06-11)Students often ask "when is this ever going to be useful?", "why are we doing this?", etc. when speaking about mathematics. If we take this as a question about 'meaningfulness', how can instructors respond and how do they even understand the terms 'meaningful' and 'meaning'? My dissertation looked at how college instructors see their instruction as meaningful or not. Drawing on social and cognitive perspectives of learning, I define four ways to think of what's 'meaningful' about mathematics. From a cognitive perspective, instructors can understand 'meaningful' as mathematical understanding versus understanding the significance of mathematics. From a social perspective where meaning is taken as the experiences of everyday life within communities, teachers can understand 'meaningful' as anything that engages students in practices the mathematics community engage in versus practices non-mathematics communities engage in (e.g. pushing computation or critical thinking as a means for maintaining social hierarchies). Using these four conceptions to categorize instructors' goals, this work focuses on how four undergraduate mathematics instructors thought of their instruction as meaningful and contextual and background factors that influenced those views.
- A Lacanian Ideology Critique of Gender in Mathematics EducationMoore, Alexander Stone (Virginia Tech, 2023-09-14)In this study I employ Lacanian psychoanalysis and ideological criticism to analyze the development of "gender and mathematics" research over the past fifty years. This study is motivated by the original Marxist-Lacanian claim by Valerie Walkerdine in the 1980s that women's relationship with mathematics must always be considered as fundamentally problematic, and by the complex and often contradictory claims that are made in research artifacts that report on this topic. Many approaches to this topic that focus on "closing the gender gap" or aiming for "gender equity" warrant an ideological critique to situate these motivations within the political realm of mathematics education research. Artifacts analyzed in this study were gleaned from a comprehensive electronic library search of over 600 entries, where 178 were retained as yield. A complete ideological critique was performed on a subset of these. Findings include (1) historical alignment of the ideologies evidenced in the research with the ideological influences of the political situation at the time of publication, including scientism, neoliberalism, evolutionism, and solutionism, (2) the ideology of interpellationism which indicates the role of scientific ways of knowing in capitalist political economy, and (3) theoretical foundations of what I call the feminine-quilted-speech indicate how at the present moment in the field, we have the opportunity to shift the ideological underpinnings of research on gender and mathematics. The study avows the role of gender as an agent of capitalist accumulation in school mathematics, through a notion I develop called the masculine-quilted-speech.
- On the role of student understanding of function and rate of change in learning differential equationsKuster Jr, George Emil (Virginia Tech, 2016-07-22)In this research, I utilize the theoretical perspective Knowledge In Pieces to identify the knowledge resources students utilize while in the process of completing various differential equations tasks. In addition I explore how this utilization changes over the course of a semester, and how resources related to the concepts of function and rate of change supported the students in completing the tasks. I do so using data collected from a series of task-based individual interviews with two students enrolled in separate differential equations courses. The results provide a fine-grained description of the knowledge students consider to be productive with regard to completing various differential equations tasks. Further the analysis resulted in the identification of five ways students interpret differential equations tasks and how these interpretations are related to the knowledge resources students utilize while completing the various tasks. Lastly, this research makes a contribution to mathematics education by illuminating the knowledge concerning function and rate of change students utilize and how this knowledge comes together to support students in drawing connections between differential equations and their solutions, structuring those solutions, and reasoning with relationships present in the differential equations.
- Predictors of Positive Change in Teaching Practices: A Quantitative StudySanchez Robayo, Brigitte Johana (Virginia Tech, 2023-03-21)Change in educational settings is a complex and multifaceted process that commonly implies change in teaching practices. Different initiatives have shown the significance of teachers and their perceptions when change in teaching practices is intended. Additionally, various factors may influence change in teaching practices at three different moments: before it happens, during, and after its implementation. Considering teachers' perceptions, I studied different factors that may be related to positive change in teaching practices. I studied the relationship between three groups of factors and positive change in teaching practices: motivational factors, including teachers' self-efficacy and autonomy; learning opportunities that include professional development, feedback, and leadership; and the academic and community domains as part of the school climate factor. In particular, I answered the following research question: To what extent do learning opportunities, teacher motivational factors, and school climate predict positive change in teaching practices? In this study I posited that teacher factors such as self-efficacy and school factors such as leadership influence positive change in teaching practices. I also posited that school factors influence the relationship between teacher factors and positive change in teaching practices. To study these relationships, I analyzed data from the Teaching and Learning International Survey (TALIS). This survey provides clustered data: teachers are clustered by schools and schools by countries. I used multilevel modeling statistical methods (i.e., a two-level hierarchical linear model) to examine the Colombian and United Stated datasets. Before estimating the hierarchical linear models, I conducted an exploratory factor analysis (EFA) to identify the teacher-level variables. One follow-up EFA focused on teacher self-efficacy yielded three variables that allowed me to focus on three specific teaching tasks: managing student behavior, motivating students, and varying instructional strategies. I found that learning opportunities, motivational factors, and school climate predict positive change in teaching practices. Learning opportunities, such as feedback from the principal has a stronger effect than feedback from colleagues. The impact of feedback from the principal has significant unnoticeable variability across schools, and it is negatively influenced by the feedback received by the teachers at the same school. Additionally, teachers' self-efficacy in different teaching tasks predicts positive change, however, these relationships differ by country. Finally, distributed leadership as part of school climate is a significant predictor of positive change that also affects it by influencing teacher interactions positively. Implications of these findings are also discussed as it relates to the existing literature and the educational system in each of the two countries.
- Prospective Teachers' Knowledge of Secondary and Abstract Algebra and their Use of this Knowledge while Noticing Students' Mathematical ThinkingSerbin, Kaitlyn Stephens (Virginia Tech, 2021-08-03)I examined the development of three Prospective Secondary Mathematics Teachers' (PSMTs) understandings of connections between concepts in Abstract Algebra and high school Algebra, as well as their use of this understanding while engaging in the teaching practice of noticing students' mathematical thinking. I drew on the theory, Knowledge of Nonlocal Mathematics for Teaching, which suggests that teachers' knowledge of advanced mathematics can become useful for teaching when it first helps reshape their understanding of the content they teach. I examined this reshaping process by investigating how PSMTs extended, deepened, unified, and strengthened their understanding of inverses, identities, and binary operations over time. I investigated how the PSMTs' engagement in a Mathematics for Secondary Teachers course, which covered connections between inverse functions and equation solving and the abstract algebraic structures of groups and rings, supported the reshaping of their understandings. I then explored how the PSMTs used their mathematical knowledge as they engaged in the teaching practice of noticing hypothetical students' mathematical thinking. I investigated the extent to which the PSMTs' noticing skills of attending, interpreting, and deciding how to respond to student thinking developed as their mathematical understandings were reshaped. There were key similarities in how the PSMTs reshaped their knowledge of inverse, identity, and binary operation. The PSMTs all unified the additive identity, multiplicative identity, and identity function as instantiations of the same overarching identity concept. They each deepened their understanding of inverse functions. They all unified additive, multiplicative, and function inverses under the overarching inverse concept. They also strengthened connections between inverse functions, the identity function, and function composition. They all extended the contexts in which their understandings of inverses were situated to include trigonometric functions. These changes were observed across all the cases, but one change in understanding was not observed in each case: one PSMT deepened his understanding of the identity function, whereas the other two had not yet conceptualized the identity function as a function in its own right; rather, they perceived it as x, the output of the composition of inverse functions. The PSMTs had opportunities to develop these understandings in their Mathematics for Secondary Teachers course, in which the instructor led the students to reason about the inverse and identity group axioms and reflect on the structure of additive, multiplicative, and compositional inverses and identities. The course also covered the use of inverses, identities, and binary operations used while performing cancellation in the context of equation solving. The PSMTs' noticing skills improved as their mathematical knowledge was reshaped. The PSMTs' reshaped understandings supported them paying more attention to the properties and strategies evident in a hypothetical student's work and know which details were relevant to attend to. The PSMTs' reshaped understandings helped them more accurately interpret a hypothetical student's understanding of the properties, structures, and operations used in equation solving and problems about inverse functions. Their reshaped understandings also helped them give more accurate and appropriate suggestions for responding to a hypothetical student in ways that would build on and improve the student's understanding.
- Relating Understanding of Inverse and Identity to Engagement in Proof in Abstract AlgebraPlaxco, David Bryant (Virginia Tech, 2015-09-05)In this research, I set out to elucidate the relationships that might exist between students' conceptual understanding upon which they draw in their proof activity. I explore these relationships using data from individual interviews with three students from a junior-level Modern Algebra course. Each phase of analysis was iterative, consisting of iterative coding drawing on grounded theory methodology (Charmaz, 2000, 2006; Glaser and Strauss, 1967). In the first phase, I analyzed the participants' interview responses to model their conceptual understanding by drawing on the form/function framework (Saxe, et al., 1998). I then analyzed the participants proof activity using Aberdein's (2006a, 2006b) extension of Toulmin's (1969) model of argumentation. Finally, I analyzed across participants' proofs to analyze emerging patterns of relationships between the models of participants' understanding of identity and inverse and the participants' proof activity. These analyses contributed to the development of three emerging constructs: form shifts in service of sense-making, re-claiming, and lemma generation. These three constructs provide insight into how conceptual understanding relates to proof activity.
- The Role of Students' Gestures in Offloading Cognitive Demands on Working Memory in Proving ActivitiesKokushkin, Vladislav (Virginia Tech, 2023-02-03)This study examines how undergraduate students use hand gestures to offload cognitive demands on their working memory (WM) when they are engaged in three major proving activities: reading, presenting, and constructing proofs of mathematical conjectures. Existing research literature on the role of gesturing in cognitive offloading has been limited to the context of elementary mathematics but has shown promise for extension to the college level. My framework weaves together theoretical constructs from mathematics education and cognitive psychology: gestures, WM, and mathematical proofs. Piagetian and embodied perspectives allow for the integration of these constructs through positioning bodily activity at the core of human cognition. This framework is operationalized through the methodology for measuring cognitive demands of proofs, which is used to identify the set of mental schemes that are activated simultaneously, as well as the places of potential cognitive overload. The data examined in this dissertation includes individual clinical interviews with six undergraduate students enrolled in different sections of the Introduction to Proofs course in Fall 2021 and Spring 2022. Each student participated in seven interviews: two WM assessments, three proofs-based interviews, a stimulated recall interview (SRI), and post-interview assessments. In total, 42 interviews were conducted. The participants' hand gesturing and mathematical reasoning were qualitatively analyzed. Ultimately, students' reflections during SRIs helped me triangulate the initial data findings. The findings suggest that, in absence of other forms of offloading, hand gesturing may become a convenient, powerful, although not an exclusive offloading mechanism: several participants employed alternative mental strategies in overcoming the cognitive overload they experienced. To better understand what constitutes the essence of cognitive offloading via hand gesturing, I propose a typology of offloading gestures. This typology differs from the existing classification schemes by capturing the cognitive nuances of hand gestures rather than reflecting their mechanical characteristics or the underlying mathematical content. Employing the emerged typology, I then show that cognitive offloading takes different forms when students read or construct proofs, and when they present proofs to the interviewer. Finally, I report on some WM-related issues in presenting and constructing proofs that can be attributed to the potential side effects of mathematical chunking. The dissertation concludes with a discussion of the limitations and practical implications of this project, as well as foreshadowing the avenues for future research.
- A structural equation model looking at student’s participatory behavior and their success in Calculus IKeller, Rachel E.; Johnson, Estrella; DeShong, Steven (2017-11-10)Background Government projections in the USA indicate that the country will need a million more science, technology, engineering, and mathematics (STEM) graduates above and beyond those already projected by the year 2022. Of crucial importance to the STEM pipeline is success in Calculus I, without which continuation in a STEM major is not possible. The STEM community at large, and mathematics instructors specifically, need to understand factors that influence and promote success in order to mitigate the alarming attrition trend. Previous work in this area has defined success singularly in terms of grades or persistence; however, these definitions are somewhat limiting and neglect the possible mediating effects of affective constructs like confidence, mindset, and enjoyment on the aforementioned markers of success. Using structural equation modeling, this paper explored the effect of participation on grades in freshman college calculus and investigated whether these effects were mediated by affective variables. Results Results indicated that participation had no significant direct effect on any of the success components in the final model—a finding that was not only counterintuitive but actually contradicted previous research done on this data. Participation was however highly correlated with two other exogenous variables indicating it would be inappropriate to dismiss it as being unrelated to success. Furthermore, the results suggested a cluster of affective success components and an achievement component with confidence being the intermediary between the two. Conclusions This paper extends upon previous work with this data set in which the effect of participatory behaviors on success was investigated wherein success was measured singularly with expected course grade and affective components of success were not considered. The limited explanatory power of the model, coupled with the seemingly contradictory results, indicates that participatory behaviors alone might be insufficient to capture the complexity of the success response variable.
- Students' Conceptions of NormalizationWatson, Kevin L. (Virginia Tech, 2020-10-13)Improving the learning and success of students in undergraduate science, technology, engineering, and mathematics (STEM) courses has become an increased focus of education researchers within the past decade. As part of these efforts, discipline-based education research (DBER) has emerged within STEM education as a way to address discipline-specific challenges for teaching and learning, by combining expert knowledge of the various STEM disciplines with knowledge about teaching and learning (Dolan et al., 2018; National Research Council, 2012). Particularly important to furthering DBER and improving STEM education are interdisciplinary studies that examine how the teaching and learning of specific concepts develop among and across various STEM disciplines...
- Teachers' Reflection on Inquiry-Oriented Instruction in Online Professional DevelopmentKelley, Marilin Annie (Virginia Tech, 2021-01-11)In light of the expansion of student-centered instructional approaches in mathematics education and a brightening spotlight on virtual teacher supports, I look to Inquiry-Oriented Instruction (IOI) and explore how instructors reflect on and plan for their implementation of IOI in online professional development. I focus specifically on two teachers' comments on their implementation of IOI materials covering Abstract Algebra topics in online work groups developed to support teachers in implementing IOI. I analyze both reflection and enactment through the components of IOI characterized through the Instructional Triangle. Analysis of the teachers' reflections, viewed through their participation in the roles of sense maker, inquirer, and builder, revealed interesting differences in the teachers' approaches to IOI. I detail these two teachers' approaches to IOI and ultimately shed light on the intricacies of IOI and online professional development. Such findings support the growing bodies of research centered around IOI and corresponding professional development.
- What really impacts the use of active learning in undergraduate STEM education? Results from a national survey of chemistry, mathematics, and physics instructorsApkarian, Naneh; Henderson, Charles; Stains, Marilyne; Raker, Jeffrey R.; Johnson, Estrella; Dancy, Melissa H. (2021-02-25)Six common beliefs about the usage of active learning in introductory STEM courses are investigated using survey data from 3769 instructors. Three beliefs focus on contextual factors: class size, classroom setup, and teaching evaluations; three focus on individual factors: security of employment, research activity, and prior exposure. The analysis indicates that instructors in all situations can and do employ active learning in their courses. However, with the exception of security of employment, trends in the data are consistent with beliefs about the impact of these factors on usage of active learning. We discuss implications of these results for institutional and departmental policies to facilitate the use of active learning.