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Previous research has shown that instruction followed by problem solving (I-PS) is an effective pedagogical approach in many procedural domains, but engaging students in problem solving before instruction (PS-I) can benefit conceptual learning and transfer. However, it is unclear which order of instruction is optimal for domains that rely heavily on both procedural and conceptual knowledge, such as symbolic modeling. This study investigates optimal order of instruction for learning modeling when instruction is based on incorrect examples. In an experiment with 97 eighth graders, we tested which order of instruction, I-PS or PS-I, was most beneficial for learning to create and evaluate mathematical models of rate-based situations, and for transferring learning to create models with different structures. The study also investigated whether optimal order of instruction depended on a student’s prior knowledge. Students in the I-PS condition performed better on model generation, regardless of prior knowledge, but no condition differences were found in model evaluation or transfer outcomes. Students in the PS-I condition reported more instances of confusion. Confusion negatively predicted transfer and showed a trend toward negatively predicting model evaluation. However, confusion did not mediate the relationship between condition and learning outcomes. This study extends the research on the role of instructional order in learning, and its impact on students’ affective experiences.

Young people tend to witness and experience the ubiquitous nature of conflicts that emanate from dominant socio-political, economic, and cultural forces and often tend to shape school practices. In this study, I listened to the voices of students who attend schools that aspire to resist this socialization for conflict through their focus on peace education. The research questions that guided my study are, ‘In this world of conflict, how are young people imagining, engaging, and enacting a peaceful world?’ which is complemented with a question on, ‘How are middle school students interacting with notions of peace and conflict as they make meaning of their social worlds?’ Inspired by a methodological approach of youth participatory action research (YPAR), 12 students across two schools in New Delhi, India, participated in a YPAR process across 13 virtual sessions, which were held twice weekly. Guided by a critical peace education and critical hope framework, I found that despite living in a world that is embedded in conflict, these young people move beyond despair and offer hope and possibilities for imagining, engaging with, and enacting a peaceful world. With an orientation to peace, these young people illuminate their imaginations of peace, which help us to think about ways in which we can live as peaceful beings characterized by harmonious co/existence with the self, one another, and the environment. Living in this world of conflict, these young people do demonstrate an awareness of existing conflict, and their engagement with conflict also tends to take them back to a place of peace. Starting from and returning to a place of peace could contribute towards building a peaceful world.

Education for adolescents in middle-level schools is a topic of great interest for many educators. Reaching a consensus on what constitutes an effective education for middle-level learners has been a challenge. The purpose of this study was to contribute to this discussion. Although the study was designed to report on effective middle schools, the respondents reported their perspectives on good middle schools. The findings of this study about good middle schools may be beneficial to middle-level educators that are interested in improving educational environments and outcomes for the adolescent learner. A cross-case study methodology was used to investigate the perspectives on a good middle school of teachers and administrators in two middle schools in a school system in a southeastern state. Seventeen face-to-face interviews were conducted with a researcher-developed protocol, and document analyses were conducted. Data were analyzed with the constant comparative method. The perspectives of the participants were organized into ten categories of what they believed constitutes a good middle school: culture, personnel, the needs of diverse adolescent learners, organizational structures, transitions, instructional practices, parental involvement, curricular aspects, physical environment, and progress. The teacher and administrator perspectives on a good middle school were analyzed in three ways: (a) a descriptive analysis of the characteristics of a good middle school as viewed by the teachers and administrators of Dorchester Middle School and J. K. Walters Middle School; (b) a comparison of the characteristics of a good middle school as viewed by teachers and administrators of the two schools and the characteristics of a good middle school as identified by the National Association of Secondary School Principals Council on Middle Level Education in 1985, the Association for Middle Level Education in 2010, and the Carnegie Corporations Council on Adolescent Development in 1989; and (c) a comparison of the characteristics of a good middle school identified by the teachers and administrators of Dorchester Middle School and the characteristics of a good middle school identified by the teachers and administrators of J. K. Walters Middle School (pseudonyms). Middle school educators have struggled with the nature of an appropriate education for middle-level learners for decades. When combined with other studies of the perspectives on middle-level schooling of practicing teachers and administrators, those who work with middle-level learners every day, the data in this study may help in efforts to reach a consensus on the elements that should be a part of a good middle school. / Ed. D.

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Although proof has long been viewed as a cornerstone of mathematical activity, incorporating the mathematical practice of proving into classrooms is not a simple matter. In this dissertation I aim to advance research on proof by addressing this issue. In particular, I explore the role proof might play in promoting the learning of mathematics in the classroom. I do this in a series of three articles (organized as three chapters), which are preceded by an introductory chapter. The introductory chapter situates the remaining chapters in the context of mathematics education research. In the second chapter I explore what the literature on proof tells us about what role proof might play in the promotion of learning in the mathematics classroom. In this chapter I also compare the ways in which proof is purported to promote learning in the mathematics classroom with the roles it is purported to play in the field of research mathematics. In the third chapter I look at empirical data to explore ways engaging in proof and proving might create opportunities for student learning. In particular, my analysis led me to focus on how identifying and reflecting on the key idea of a proof can create opportunities for learning mathematics. The final chapter is an article for a practitioner journal and discusses implications for practice based on the two preceding articles.

This study documented the changes in understanding a class of eighth grade high school-level biology students experienced through a biology unit introducing genetics. Learning profiles for 55 students were created using concept maps and interviews as qualitative and quantitative instruments. The study provides additional support to the theory of learning progressions called for by experts in the field. The students' learning profiles were assessed to determine the alignment with a researcher-developed learning profile. The researcher-developed learning profile incorporated the learning progressions published in the Next Generation Science Standards, as well as current research in learning progressions for 5-10th grade students studying genetics. Students were found to obtain understanding of the content in a manner that was nonlinear, even circuitous. This opposes the prevailing interpretation of learning progressions, that knowledge is ascertained in escalating levels of complexity. Learning progressions have implications in teaching sequence, assessment, education research, and policy. Tracking student understanding of other populations of students would augment the body of research and enhance generalizability.

This descriptive study uses a qualitative, content analysis to examine the middle school visual arts and core Texas Essential Knowledge and Skills (TEKS) to determine the potential common learning activities that can be aligned between the two. By performing an alignment of the potential common learning activities present in the middle school visual art TEKS and the middle school core TEKS, I demonstrate that there is a foundation for curriculum integration in the Texas middle school visual arts classroom.