Browsing by Author "Kreye, Bettibel Carson"
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- Analyzing the Use of Technological/Engineering Design-Based Biotechnical Learning Pedagogical Approaches to Promote Change in Concept Knowledge of Eighth Grade Mathematics StudentsReed, Amanda Marie (Virginia Tech, 2023-12-15)The purpose of this research was to document the ways in which the pedagogical approaches of technology/engineering design-based learning (T/E DBL) were shown to promote change in concept knowledge of eighth grade mathematics students. A mixed method, sequential explanatory multiple embedded case study was used to determine the significance between the T/E DBL intervention and bivariate measurement data concept knowledge. Whole Group quantitative data analysis indicated a statistical significance between pretest and posttest scores. Qualitative data (Interactive Engineering Journals and semi-structured interviews) analyses for the Sub-Group confirmed that students did possess the bivariate data concept knowledge as documented through quantitative results and those gains were directly related to experiences students had while engaged in the T/E DBL intervention. This research demonstrated that the utilization of T/E DBL in an eighth-grade mathematics classroom has the potential to foster a change in concept knowledge of bivariate measurement data through informed design decision-making in a 21st century problem context. This study can be used as a guide for mathematics educators and curriculum developers implementing T/E DBL pedagogy allowing students to learn through contextual experiences. Future research should explore the utilization of T/E DBL to teach additional mathematical concepts at different grade levels.
- Black and White: Race, Culture, and Urban RenewalShepherd, Ann Brogan (Virginia Tech, 2020-09-08)This is a qualitative study using ethnographic methods to collect data and critical autoethnography to reflect on my personal history in the light of what I learned about others (Anderson and Glass-Coffin, 2013; Ellis, 2009; Erickson, 2011; Manning and Adams, 2015; Rennel, 2015). My research focuses on race and culture in relation to perceptions in relationships, community, and education before and after urban renewal. I present my work in two-manuscripts: Growing Up White: I Didn't Know What I Didn't Know and Gainsboro: It's Just the Way Things Were. The first portion of the study looks at growing up in a White neighborhood in Roanoke, Virginia, during the early years of integration and the Civil Rights Movement, while being unaware of the existence of another world beyond my own. The second manuscript presents findings from interviews in the corresponding Black community and archival research interrogating systemic issues associated with urban renewal.
- Evaluating Collaborative Relationships Between K-12 Public and Private Day Schools in VirginiaMazurek, Bethany Christine (Virginia Tech, 2020-03-19)This study is an evaluation of collaborative relationships between K-12 public and private day schools in Virginia when serving students with special needs. Research on the conditions and barriers of collaborative relationships in the educational setting is mostly centered around the dynamic between general education teachers and special education teachers when serving students with special needs. The purpose of the study was to determine the main factors that differ between collaborative relationships that are perceived as strong to those perceived as weak. The study is guided by two research questions: (1) What factors contribute to strong collaborative relationships between K-12 public and private day schools in Virginia? (2) What factors are identified as areas of concern regarding weaker collaborative relationships between K-12 public and private day schools in Virginia. The literature review explores prior research on educational collaboration while methodology addresses the research design and study procedures. Participants were 43 public school special education directors and private day school administrators across the Commonwealth of Virginia. Demographic information was provided by all participants. An online inventory was completed by those participants who had worked with a minimum of two of the opposite provider; special education directors in the public school setting were required to work with two private day schools and vice versa. Responses were recorded from each of the eight regions delineated by the Virginia Department of Education (VDOE, n.d.). Statistical analysis did not reveal any statistically significant differences between the two groups of participants. However, results of the study indicated strengths related to the factors of membership characteristics and purpose for strong relationships. When evaluating a weak collaborative relationship, the factors of process and structure, communication and resources were the primary areas of concern. Regardless of the strength of the collaborative relationship, the resource factor was the lowest scoring factor, indicating it was the primary concern regarding collaborative relationships. This study adds to the field of special education by applying the existing research to the relationship between K-12 public and private day schools when serving students with special needs along the continuum of services.
- Evaluation of the Externship Within a Master's Degree Program for Mathematics Specialists at Virginia TechKreye, Bettibel Carson (Virginia Tech, 2009-03-31)The purpose of this evaluation was to determine the effectiveness of an Externship as the capstone experience of a Master's degree program in preparing seventeen teachers to be Mathematics Specialists. This formative evaluation was based on the teacher's perspective and was naturalistic in design utilizing both qualitative and quantitative research methods. Data sources included a teacher survey, teacher interviews, writing prompts, teacher observations, and teacher final project presentations. This evaluation was designed to answer the question: Do the teachers feel that the requirements of this Masters' Degree Externship have prepared them for their role as a Mathematics Specialist? The success and effectiveness of the Externship was tied directly to the teachers chosen school-based experiences which were designed based on a mathematics needs assessment of their schools. Teachers were found to be involved in all five of the essential components of an externship as outlined in the theoretical framework — application, collaboration, reflection, expectations, and the cohort structure. In addition, teachers were found to integrate their leadership and teaching skills through the engagement of their school colleagues in the improvement of educational experiences for all students. Overall, the teachers felt that the experiences throughout the Externship adequately prepared them for their roles of a mathematics specialist; working effectively with stakeholders; working with issues around curriculum and instruction; planning and delivering professional development; and working as leaders within their schools.
- Examining the Relationship Between Students' Measurement Schemes for Fractions and Their Quantifications of AngularityMullins, Sara Brooke (Virginia Tech, 2020-06-26)In the basic understanding of measurement, students are expected to be able to subdivide a given whole into a unit and then change the position of that unit along the entire length of the whole. These basic operations of subdivision and change of position are related to the more formal operations of partitioning and iterating. In the context of fractions, partitioning and iterating play a fundamental role in understanding fractions as measures, where students are expected to partition a whole into an iterable unit. In the context of angle measurement, students are expected to measure angles as a fractional amount of a full rotation or a circle, by partitioning the circle into a unit angle and then iterating that unit angle to find the measure of the given angle. Despite this link between measurement, fractions, and angles, research suggests that there is a disconnect between students' concepts of measurement and geometry concepts, including angle and angle measurement. Therefore, one area of study that might help us understand this disconnection would be to investigate the relationship between students' concepts of measurement and their concepts of angle measurement. This current study documents sixth, seventh, and eighth grade students' measurement schemes for fractions and their quantifications of angularity, and then investigates the relationship between them. This research is guided by the following question: What is the relationship between middle school students' measurement schemes for fractions and their quantifications of angularity? Results indicate that the majority of students involved in this study do not possess a measurement concept of fractions nor a measurement concept of angularity. However, these results demonstrate that there is a relationship between students' measurement schemes for fractions and their quantifications of angularity. It is concluded that students who construct more sophisticated fraction schemes tend to construct more sophisticated quantifications of angularity.
- Exploring Middle School Students' Heuristic Thinking about ProbabilityMistele, Jean May (Virginia Tech, 2014-05-04)This descriptive qualitative study examines six eighth-grade students' thinking while solving probability problems. This study aimed to gather direct information on students' problem solving processes informed by the heuristics and biases framework. This study used purposive sampling (Patton, 1990) to identify eighth-grade students who were knowledgeable about probability and had reached the formal operational stage of cognitive development. These criterion were necessary to reduce the likelihood of students' merely guessing answers and important so that the researcher could distinguish between reasoning and intuition. The theoretical framework for this study was informed by Kahneman and Fredrick's (2002) recent revision to the heuristics and biases framework grounded in the research of Amos Tversky and Daniel Kahneman. Kahneman and Fredrick (2002) drew on dual process theory to explain systematic and predictable heuristic ways of thinking. Dual process theory hypothesizes that human thinking is divided into two different modes of processing. One mode, called System 1, is fast and linked to intuition, and the other, called System 2, is slow and linked to reasoning (Evans, 2008; Stanovich and West, 2000). Within dual process theory, System 1 thinking provides a credible system for explaining why people use heuristic thinking (Kahneman and Frederick, 2002). The recent revision to the heuristics and biases framework is focused on three heuristics, representativeness, conjunction fallacy, and availability. These three heuristics are believed to share the same mental process identified by Kahneman and Fredrick (2002), as the attribute substitution process. The clinical task based interview method was used in this study. This technique allowed the researcher to better observe and interact with the participants while exploring the students' probability thinking. The researcher also used think-aloud protocols to better reveal the organic thinking patterns of the students in real time (Ericsson and Simon, 1980; Fox, Ericsson, and Bets, 2010; Van Someren, Barnard, and Sandberg, 1994). The data from the interviews were analyzed using the constant comparison method (Glaser, 1965). This analysis revealed three categories that were combined with other analyses to create profiles for various thinking patterns observed by the researcher. The researcher identified patterns of thinking by students that were consistent with System 1 thinking and associated with the attribute substitution process (Kahneman and Fredrick, 2002). There were also situations in which students demonstrated ways of thinking consistent with System 2 thinking. However, unexpected ways of thinking were also identified by the researcher. For example, there were occasions when students substituted their fraction knowledge when solving probability problems and even seemed to equate probability with fractions. This type of thinking was referred to as the content substitution process in this study. This process occurred when students were using System 1 thinking as well as other types of thinking. In addition, the researcher observed students with thinking patterns that contained characteristics of both System 1 and System 2, which is referred to as slow intuition in this study. Slow intuition seemed to affect students' problem solving strategies as they wavered between multiple problem solving strategies that included either of the two substitution processes: attribute substitution and content substitution. This study contributes to the body of knowledge related to probabilistic thinking. In particular, this study informs our understanding of heuristic thinking used by eighth-grade students when solving probability problems. Further, teaching practices that draw on Fischbein's (1975, 1987) general notion of intuition might be developed and used to improve probability reasoning skills. These teaching practices target students that depend on the attribute substitution process and/or the content substitution process. Each of these heuristic ways of thinking may require different instructional techniques to help students develop more sound ways of thinking about probability. Regardless, teachers need to be informed of the extent that some students rely on their fraction knowledge when solving probability problems.
- Finding Voice along the Appalachian Mountains: An Autoethnographic Journey of a Female Immigrant StudentChang, Rong Bai (Virginia Tech, 2019-08-05)Using autoethnography (Ellis, 2004), this study explores a female immigrant student's lived experiences in education in China, and in the United States. The theoretical framework of this study is critical autoethnography. In the study, I present my lived experiences in poems, narratives, and stories as the storied scholarship (Boylorn and Orbe, 2014). Through the study, I make sense of how a female non-traditional immigrant student navigated schooling in the complex social, cultural environment in the United States, and schooling experiences of my youth in China. I utilize the study to examine the deeper meaning of my story as an inquiry (Denzin and Lincoln, 2005; Richardson and St. Pierre, 2005). In doing so, to not only make sense of the complex lifelong experiences (Berger, 2004) of an immigrant student, but also to make connections with many other female immigrant students, and to bring new light to the understanding of their struggles, difficulties, and challenges. I use various literary styles and the metaphor of finding the voice in my writing to illustrate the process (Forber-Pratt, 2015; Luke, 2009).
- Foreign Language Teachers' Beliefs and Practices in Language Education: What to Teach and How to TeachLiu, Yuning (Virginia Tech, 2021-08-06)This dissertation is a combination of two manuscripts. By using autoethnography in manuscript one, this study first reflects on my learning English as a foreign language journey and the influences that brought to my life. The seven stories in this study cover many aspects of foreign language education, including teaching contents, teaching methods, and teacher preparation. Through the lens of autoethnography, I will further explore factors that influence foreign language education. Through detailed analysis, I discover language learning is not isolated. Foreign language teaching and learning will be influenced by economy, politics, cultures, and society. Based on these findings, I ask many thought-provoking questions on foreign language education, such as teaching contents and teaching methods. Manuscript two is traditional qualitative research using ethnographic methods. I use in-depth interviews to explore teachers' beliefs and practices of one supervisor and three foreign language teachers. I first present findings on their beliefs and practices in foreign language teaching and learning, including changes and challenges in the division's language education and foreign language teachers' beliefs and practices and their alignment with the ACTFL Standards. I will also use the ACTFL Standards as a lens to analyze how their beliefs and practices match with the 5Cs: Communication, cultures, connections, comparisons, communities. Finally, I will provide suggestions for future similar studies.
- Homework Journaling in Undergraduate MathematicsJohnston, Alexis Larissa (Virginia Tech, 2012-03-23)Over the past twenty years, journal writing has become more common in mathematics classes at all age levels. However, there has been very little empirical research about journal writing in college mathematics (Speer, Smith, & Horvath, 2010), particularly concerning the relationship between journal writing in college mathematics and college students' motivation towards learning mathematics. The purpose of this dissertation study is to fill that gap by implementing homework journals, which are a journal writing assignment based on Powell and Ramnauth's (1992) "multiple-entry log," in a college mathematics course and studying the relationship between homework journals and students' motivation towards learning mathematics as grounded in self-determination theory (Ryan & Deci, 2000). Self-determination theory predicts intrinsic motivation by focusing on the fundamental needs of competence, autonomy, and relatedness (Ryan & Deci, 2000). In addition, the purpose of this dissertation study is to explore and describe the relationship between homework journals and students' attitudes towards writing in mathematics. A pre-course and post-course survey was distributed to students enrolled in two sections of a college mathematics course and then analyzed using a 2Ã 2 repeated measures ANOVA with time (pre-course and post-course) and treatment (one section engaged with homework journals while the other did not) as the two factors, in order to test whether the change over time was different between the two sections. In addition, student and instructor interviews were conducted and then analyzed using a constant comparative method (Anfara, Brown, & Mangione, 2002) in order to add richness to the description of the relationship between homework journals and students' motivation towards learning mathematics as well as students' attitudes towards writing in mathematics. Based on the quantitative analysis of survey data, no differences in rate of change of competence, autonomy, relatedness, or attitudes towards writing were found. However, based on the qualitative analysis of interview data, homework journals were found to influence students' sense of competence, autonomy, and relatedness under certain conditions. In addition, students' attitudes towards writing in mathematics were strongly influenced by their likes and dislikes of homework journals and the perceived benefits of homework journals.
- The Importance of Reflection within the Academic Assignments of Study Abroad ProgramsPlaza, Raymond Vidal (Virginia Tech, 2016-08-16)Today, almost 305,000 U.S. college students are taking advantage of study abroad opportunities throughout the world. While study abroad experiences have has been increasing in number and scope, there continue to be questions about the importance and value of study abroad on the students' growth and development. This study highlights a summer study abroad program at Virginia Tech from 2008 – 2012. Reflection and transformative learning serve as the primary theoretical frameworks for this study. The work of Dewey (1933), Mezirow (1991, 1997), Moon (2004), Whitney and Clayton (2011) and others help to provide additional insight into better understanding reflection and transformative learning. The methodological framework is a qualitative case study focusing on the student participants from summer 2012 and examines the role of reflection in the academic components of the program and whether or not reflection helped to further enhance the influence and impact of the experience on the students. I collected data from photo journals, weekly reflection papers and their final exam paper, all of which comprised the academic requirements for this credit-bearing course. The participants consisted of seven female identified students and four male identified students, representing the following academic disciplines: Human Development, Geography, Political Science, Journalism, Studio Art and International Studies. Through content analysis (Mayan, 2009; Merriam, 1998), I discovered the themes of self-awareness and visibility and presence. These two themes provide a deeper understanding about how the study abroad experience has a distinct influence on the students, as can be evidenced through their academic work. While the two themes help to further reinforce the importance of reflective practice, the study also reveals that reflection can be problematic as well.
- The Induction and Mentoring Experiences of New English as a Second Language and Bilingual TeachersRaab, Rebecca Raine (Virginia Tech, 2020-10-14)The focus of this dissertation is on the induction and mentoring experiences of new English as a Second Language (ESL) and bilingual teachers. Included in the dissertation are three manuscripts: a systematic literature review of the experiences of and supports for new ESL/bilingual teachers, a descriptive analysis of their induction, and an inferential analysis (i.e., regression) of the extent to which working with a mentor improved their first-year instruction. The first manuscript (Chapter 2) is a systematic review of peer-reviewed articles documenting the experiences of and supports for new ESL/bilingual teachers in U.S public schools. Findings from 32 studies published from 2002-2020 were synthesized into three overarching themes (i.e., instructional contexts and roles; social contexts of teaching; formal induction supports). Many new teachers experienced challenges in their instructional contexts and roles and struggled to connect socially with others in their schools, leading to physical segregation and marginalization. Moreover, only a few studies elaborated on specific induction and mentoring supports. Manuscript 1 concludes with suggestions for researchers and implications for K-12 school leaders, teacher educators, and new ESL/bilingual teachers. The second manuscript (Chapter 3) presents the findings of a secondary descriptive analysis of new ESL/bilingual teacher induction using the nationally representative 2011-12 Schools and Staffing Survey Teacher Questionnaire. Findings provide a first of its kind national profile of their induction supports, levels of perceived preparedness for the first year, and demographic characteristics, as well as a comparison to new general educators. Findings indicate that a lower percentage of new ESL/bilingual teachers than general educators received important induction supports (i.e., administrator feedback, same-subject mentoring, and frequent mentoring) and were not well prepared for critical teaching tasks (e.g., assessing students). Demographically, a higher percentage of new ESL/bilingual teachers than general educators were teachers of color. The manuscript concludes with directions for future research and implications for teacher educators and school leaders. The third manuscript (Chapter 4) investigated which mentoring components (i.e., same-subject mentors, frequency of mentoring, and other mentoring activities), predicted new ESL/bilingual teachers' perceptions that their mentors helped improve their first year of teaching. Using a nationally representative sample of ESL/bilingual teachers. I found that frequent weekly mentoring, help with developing student assessment tools, and help with paperwork/record keeping were statistically significant predictors of the extent to which new ESL/bilingual teachers indicated their mentors improved their first-year teaching. I conclude with suggestions for future research and improving mentoring programs for new ESL/bilingual teachers.
- An Investigation of Black and Hispanic Participation and Performance in Advanced Placement Courses in a School Division that has Targeted Increased Participation as a GoalByrd, Tyrone Qovodis (Virginia Tech, 2023-04-04)Participation in Advanced Placement (AP) courses and success on associated exams has become the standard bearer for post-secondary admission. While AP began as a mechanism to support the academic needs of the most advanced students, today it is offered to a diverse range of students. Increasing AP participation and improving AP performance for traditionally underrepresented populations to include Blacks, Hispanics, students with disabilities, and those from lower socioeconomic families has been an ambition of American school districts for the past several decades. This study used AP participation and performance data to investigate the progress one school district has made regarding Black and Hispanic students for the eight school years between 2011-19. Progress was measured by increases in percentages of Black and Hispanic students enrolled in AP courses who sat for an associated AP exam and the percentage of each cohort who earned scores of three or higher on those exams. Significance was determined using Pearson's chi-square and one-way ANOVA tests. Study results show that, among other findings, there was no significant relationship in AP participation for either Black or Hispanic students and that both Black and Hispanic students demonstrated significant improvement in AP performance between school years.
- A Meta-Analysis on The Impact of Professional Development Programs for K-12 Mathematics Teachers on Students' AchievementFranklin, Anita Valentina (Virginia Tech, 2015-11-24)Over the past decade there has been a growing investment in professional development (PD) programs for K-12 mathematics teachers. Researchers and policy makers often inquire about the effect of professional development programs and whether they are having a positive impact on students' learning, and which type of programs aid in students ' academic improvements. In view of the continued concern about the low achievement of U.S. students in mathematics there is a strong need to better understand the effect of PD on student learning and more specifically, which components of PD are more beneficial and are likely to enhance students' math learning. This study offers evidence in an effort fill the gap in the literature by examining the relationship between professional development and student achievement. A meta-analysis methodology was used to synthesize quantitatively and aggregate the results of the prior studies that have used scientific methods and reported numerical results. The time period for the selection of studies is from 2003 to 2014. Findings in this study confirm earlier literature and offers guidance about three effective components (duration, content, and intervention modality) in professional development programs that have been found to have a positive relationship with students' achievement. The results also highlighted the importance of content focus, sufficient duration and multiple modalities of professional development programs aiding teachers in their ability to become more effective in the classroom leading to increased students' achievement in math.
- A Mixed Methods Study of Chinese Students' Construction of Fraction Schemes: Extending the Written Test with Follow-Up Clinical InterviewsXu, Cong Ze (Virginia Tech, 2023-01-12)Understanding fractions is fundamental for expanding number knowledge from the whole number system to the rational number system. According to the National Council of Teachers of Mathematics (NCTM) Principles and Standards for School Mathematics (2000), learning fractions is an important mathematical goal for students in grades three through five in the U.S. Moreover, the NCTM suggests that fraction instruction start in Pre-K and continue through 8th grade. At the same time, the Common Core State Standards for Mathematics (CCSSM) suggests that fraction instruction should occur from Grade 3 to 7. In contrast to the time spent on learning fractions in the U.S., students in China spend a relatively short time learning fractions (Zhang and Siegler, 2022). According to the Chinese national curriculum standards, the Chinese National Mathematics Curriculum Standards (CNMCS) for five-four system, the fundamental fraction concepts are taught in grades 3 and 5 only. However, Chinese students continue to have higher performance on fraction items in international assessments when compared with American students (Fan and Zhu, 2004). Consequently, over the last several years, researchers have investigated subject content knowledge and pedagogical content knowledge of Chinese in-service teachers and pre-service teachers via fraction division (e.g., Li and Huang, 2008; Ma, 1999). There are also studies exploring Chinese written curricula of fraction division (e. g., Li, Zhang, and Ma, 2009). Recently, a quantitative study from Norton, Wilkins, and Xu (2018) investigated the process of Chinese students' construction of fraction knowledge through the lens of fraction schemes, a model established by western scholars Steffe (2002) and his colleague Olive (Steffe and Olive, 2010). However, there is a lack of qualitative research that attempts to use fraction schemes as an explanatory framework to interpret the process of Chinese students' construction of fraction knowledge. The main purpose of this study was to investigate Chinese students' understanding of the fundamental fraction knowledge in terms of their understanding of the "fraction unit," referred to as a "unit fraction" in the U.S., using Steffe and Olive's (2010) fraction schemes as the conceptual framework. A sequential mixed methods design was used in this study. The design included two consecutive phases, namely a quantitative phase followed by a qualitative phase (Creswell and Plano Clark, 2011). During the quantitative phase, five hundred and thirty-four Chinese fourth and fifth grade students were administered an assessment. The quantitative data was first analyzed using a Cochran's Q test to determine if the Chinese participants in this study follow the same progression of fraction schemes as their American peers. Results indicate that the development of fractional schemes among Chinese 4th and 5th grade participants in this study is similar to their U.S. counterparts and the Chinese participants in Norton et al.'s (2018) study regardless of the curricula differences across countries or areas in the same country, the textbook differences, and the language differences. Next, two different analysis of variances (ANOVA), a three-way mixed ANOVA and a two-way repeated measures ANOVA were conducted. The three-way mixed ANOVA was used to inform the researcher as to the fraction schemes these students had constructed before the concept of fraction unit is formally introduced and after the concept of fraction unit is formally introduced. The results showed that the fraction knowledge of the students in this study developed from 4th grade to 5th grade. The analysis of clinical interview data confirmed this conclusion. The two-way repeated measures ANOVA was used to determine which model (i.e., linear, circular, or rectangular) is more or less problematic for Chinese students when solving fraction tasks. The results suggest that generally students' performance on linear model tasks was better than their performance on circular model tasks, but there was no statistically significant difference between performance on circular model and its corresponding rectangular model tasks. The results from the quantitative analyses were also used to screen students to form groups based on their highest available fraction scheme for a clinical interview in the second phase, the qualitative phase. In the qualitative phase, a clinical interview using a think-aloud method was used to gain insight into the role of students' conceptual understanding of the fraction unit in their construction of fraction knowledge. In this phase, students were asked to solve the tasks in the clinical interview protocol using the think aloud method. Two main findings were revealed analyzing the clinical interview data. First, a conceptual understanding of fraction units as well as a conceptual understanding of a unit whole play a critical role in the construction of Chinese students' fraction knowledge. Second, the lack of the understanding of a fraction unit as an iterable unit may be one of the reasons that obstructs students move from part-whole concept of fractions to the measurement concept of fractions. This study also demonstrates that a conceptual understanding of fraction units and the unit whole are a necessary condition for constructing of a conceptual understanding of fraction knowledge. Thus, implications of this study suggest that teachers not only should help students build a conceptual understanding of fraction units, but also need to confirm that students have constructed the concept of what the unit whole is before asking students to identify the fraction units for the referent whole. On the other hand, the tasks used in the present study only include continuous but not discrete wholes. Therefore, future research may focus on investigating how students identify fraction units and in what way the iterating operation could be used when students encounter a discrete whole.
- Perceptions of Technology/Engineering Education Influence on Integrated STEM Teaching and LearningGreene, Clark Wayland (Virginia Tech, 2024-06-27)The dynamics of successfully integrating science, technology/engineering and math content, practice, and delivery in K-12 education is still evolving. "A number of questions remain about the best methods by which to effectively teach engineering at the K-12 level and how they play into the integration of other STEM disciplines" (Moore, Glancy, Tank, Kersten, Smith, and Stohlmann, 2014). The International Technology and Engineering Educators Association (ITEEA) has declared that technology and engineering within STEM education as delivered by the technology education content area is defined by the Standards for Technological Literacy™ (ITEEA, 2000). Lack of applied technology/engineering pedagogical content knowledge via technology teacher collaboration may be excluding valuable contributions to more effective STEM teaching and learning. Absence of developed and identified perceptions resulting from such collaborations could be an impediment to application of valuable technology/engineering practices, beliefs, content, and structure within integrated STEM instruction. Collaboration inclusive of all STEM subject teachers is critical to effective practice and delivery of integrated STEM teaching. To achieve this, integrated STEM experiences need "to be researched and evaluated to build knowledge and understanding about the effectiveness of these experiences in promoting STEM learning and engagement within and across disciplines." (Honey et al., 2014). The purpose of this study was to examine and identify science, math, and technology education teacher perceptions of technology/engineering education influence within existing STEM collaborations. The objective was to provide useful information pertinent to further improving STEM education practice and effectiveness. A three round, mixed method, Delphi approach was employed to determine common perceptions among all STEM teachers included in this study. Consensus among study participants identified strategies specific to technology/engineering education that were perceived to positively impact STEM education. The results of this study illustrate that content, practice, and pedagogical attributes specific to technology education do exist and that those attributes are perceived to enhance student learning of STEM content and practice. Synthesized from initial qualitative responses in Round One, of the 28 presented technology/engineering strategies, 24 achieved consensus as determined by an applied two factor threshold of a 7.5 median agreement score and interquartile rating of 2.0 or less from among all participants. In a comparison of represented STEM subjects taught, there also appeared significant agreement among all groups. The level of agreement between science and the other groups was weakest, although still sizeable. Engineering design knowledge, skilled use of tools and materials to produce models and prototypes, promotion of designerly critical thinking and problem-solving skills, and both tacit and contextual knowledge of technology and engineering applications were found to be general themes specific to technology/engineering education teachers.
- Perceptions of the Initial Steps a Planning Principal Takes to Open a New Plus One Elementary SchoolDubiel, Karen Lee (Virginia Tech, 2024-06-21)The purpose of this study was to identify the initial steps that a planning principal takes to open a new plus one elementary school. Too often, the focus is on the completion of the bricks and mortar of the facility instead of what takes place in the building once construction is complete (Lane, 2008). "Effective planning for the opening of a new school produces an environment in which teachers can teach and students can learn effectively and efficiently" (Lane, 2008, p. 2). Thus, the opening of a new plus one school requires a well-planned, detailed, organized approach for occupying the facility as the success or failure of the school opening process weighs heavily on the ability of the planning principal (Lane, 2008). New plus one schools are continuing to be built regularly within the United States to address student enrollment increases in existing schools with limited capacity, yet there is no set of instructions to guide a planning principal. With new school construction still needed to address increasing student enrollment in local school districts, the perceptions of the initial steps planning principals take to open a new plus one elementary school are valuable. This study involved interviewing four planning principals in the Mid-Atlantic region of the United States. Interview questions sought the actions that planning principals take to start a new plus one elementary school. All four planning principals indicated that they had no playbook or guide, were self-directed and initiated support when needed, and exercised a high level of autonomy with decision making, specifically with staffing, developing a school vision, and determining the school mascot and school colors. Implications for practitioners were identified including the need for a guide or handbook, a structure of support, and training or professional development. The outcome of the study provided opportunities for future planning principals to identify the key responsibilities, experiences, and guidance recommended for opening new plus one elementary schools.
- 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.
- Resolving Apparent Inconsistencies in the Belief Systems of High School Geometry TeachersLaCroix, Tiffany Jo (Virginia Tech, 2020-03-30)This qualitative research seeks to identify and understand the beliefs of 10 high school geometry teachers that help resolve apparent inconsistencies between their espoused and enacted beliefs. Data was collected using an initial interview, classroom observations, and a follow-up interview to gather evidence of teacher beliefs based on what they say, do, and intend respectively. Open coding, analytical coding, cluster identification, coding memos, and analytical memos were used to analyze the data and write summaries of the teachers' explanatory beliefs with beliefs as the unit of analysis. It was identified that teachers consistently and inconsistently enact their espoused beliefs, but there are also instances when teachers both consistently and inconsistently enact particular espoused beliefs. This endeavor necessitates a shared understanding of terms, and it was found what it means to "understand" needs to be clarified with a definition and examples from teachers. When teachers appear to not enact their espoused beliefs, explanatory beliefs were pinpointed that resolve the conflict and found the explanatory beliefs exist in at least seven macro clusters. These explanatory beliefs interact with espoused beliefs by overriding, limiting, or preventing the espoused beliefs to resolve the apparent inconsistency in teachers espoused and enacted beliefs. The explanatory beliefs with limiting and overriding interactions were found to coexist for some teachers around a teaching practice as overriding interactions are connected to constraints on the classroom whereas limiting interactions are not. It was also found that belief clusters are nested within clusters of beliefs, and these clusters allow for beliefs to cluster in isolation in different ways. This work also shows empirically that some geometry teacher beliefs are socially constructed due to the presence of common cultural artifacts and influence from mathematics teacher educators. This work has implications and future research directions in the areas of using beliefs as the unit of analysis, mapping teacher's belief systems, considering the social construction of beliefs and role of community, connecting beliefs to specific teaching practices, and educating teachers.
- Subitizing Activity: Item Orientation with Regard to Number AbstractionMacDonald, Beth Loveday (Virginia Tech, 2013-12-23)Subitizing, a quick apprehension of the numerosity of a small set of items, is inconsistently utilized by preschool educators to support early number understandings (Sarama & Clements, 2009). The purpose of this qualitative study is to investigate the relationship between children’s number understanding and subitizing activity. Sarama and Clements (2009) consider students’ subitizing activity as shifting from reliance upon perceptual processes to conceptual processes. Hypothesized mental actions carried into subitizing activity by children have not yet been empirically investigated (Sarama & Clements, 2009). Drawing upon Piaget’s (1968/1970) three mother structures of mathematical thinking, the theoretical implications of this study consider expanding the scope of Piaget’s (1968/1970) definition of topological thinking structures to include patterned orientations. Increasing the scope of this definition would allow for the investigation of the development of topological thinking structures and subitizing activity. An 11-week teaching experiment was conducted with six preschool aged children in order to analyze student engagement with subitizing tasks (Steffe & Ulrich, in press). To infer what perceptual and conceptual processes students relied upon when subitizing, tasks were designed to either assess or provoke cognitive changes. Analysis of interactions between students and the teacher-researcher informed this teacher-researcher of cognitive changes relative to each student’s thinking structure. Results indicated that students rely upon the space between items, symmetrical aspects of items, and color of items when perceptually subitizing. Seven different types of subitizing activity were documented and used to more explicitly describe student reliance upon perceptual or conceptual processes. Conceptual subitizing activity was redefined in this study, as depending upon mental reversibility and sophisticated number schemes. Students capable of conceptual subitizing were also able to conserve number. Students capable of conserving number were not always capable of conceptual subitizing. The symmetrical aspects of an item’s arrangement elicited students’ attention towards subgroups and transitioning students’ perceptual subitizing to conceptual subitizing. Combinations of counting and subitizing activity explained students’ reliance upon serial and classification thinking structures when transitioning from perceptual subitizing to conceptual subitizing. Implications of this study suggest effectively designed subitizing activity can both assess students’ number understandings, and appropriately differentiate preschool curriculum.
- Teaching in the Real World: Autoethnography Meets Meta-Autoethnography from a Practicing Teacher's PerspectiveArnold, Brandy (Virginia Tech, 2021-07-30)In "Who are You," I narrate seven vignettes of my lived experiences from childhood through the beginning of my Ph. D. I examine how they directly relate to the relationships I build with my students as a teacher in an urban public high school. I deconstruct how my experiences push me to break standard professional teacher boundaries in order to support and advocate for my students. I discuss the realities of my lived experiences and the impact they have had on me personally, educationally, and professionally. I explain my choice for using narrative vignettes tied to the Lewis Carroll novels Alice in Wonderland and Through the Looking Glass and their connection with my adolescent and professional experiences. I explain my choice of autoethnography as my method and how I have come to terms with the vulnerability necessary to successfully use this genre of qualitative research while learning about the difficulties and benefits of the method. In "Where Soul Meets Body," I reflect on occurred during those experiences, and how they shaped the person and the teacher I am today. I reflect on the collapse of family, the effects of divorce on my actions, the seeking of solace and emotional repair, the effects of abusive relationships, the changes in my identity, the rebuilding of my identity, and the impact of my lived experiences on my teaching pedagogy. I reflect on the need for transparency and vulnerability in teaching. I explore how the acceptance and realization of my lived experiences has a deep impact on personal pedagogy, practices, and meaningful relationships with students, specifically in an urban school setting. I explore how my personal experiences intertwine with my students' personal experiences and how all teachers need to acknowledge the importance of transparency and vulnerability in their pedagogy.