The purpose of this study was to determine the extent to which the modeling of deductive reasoning and proof-type thinking occurs in a mathematics course in which students are not explicitly preparing to write formal mathematical proofs. Algebra was chosen because it is the course that typically directly precedes a student's first formal introduction to proof in geometry in the United States. The lens through which this study aimed to examine the intended curriculum was by identifying and reviewing the modeling of proof and deductive reasoning in the most popular and widely circulated algebra textbooks throughout the United States. Textbooks have a major impact on mathematics classrooms, playing a significant role in determining a teacher's classroom practices as well as student activities. A rubric was developed to analyze the presence of reasoning and proof in algebra textbooks, and an analysis of the coverage of various topics was performed. The findings indicate that, roughly speaking, students are only exposed to justification of mathematical claims and proof-type thinking in 38% of all sections analyzed. Furthermore, only 6% of coded sections contained an actual proof or justification that offered the same ideas or reasoning as a proof. It was found that when there was some justification or proof present, the most prevalent means of convincing the reader of the truth of a concept, theorem, or procedure was through the use of specific examples. Textbooks attempting to give a series of examples to justify or convince the reader of the truth of a concept, theorem, or procedure often fell short of offering a mathematical proof because they lacked generality and/or, in some cases, the inductive step. While many textbooks stated a general rule at some point, most only used deductive reasoning within a specific example if at all. Textbooks rarely expose students to the kinds of reasoning required by mathematical proof in that they rarely expose students to reasoning about mathematics with generality. This study found a lack of sufficient evidence of instruction or modeling of proof and reasoning in secondary school algebra textbooks. This could indicate that, overall, algebra textbooks may not fulfill the proof and reasoning guidelines set forth by the NCTM Principles and Standards and the Common Core State Standards. Thus, the enacted curriculum in mathematics classrooms may also fail to address the recommendations of these influential and policy defining organizations.

No description available.

This work set out to investigate two questions: 1) what is the state of qualitative understanding of magnetism at various stages of expertise? 2) What approaches to problem-solving are used across the spectrum of expertise? I studied three groups: ten novices (university students who had completed one introductory course in electricity and magnetism), ten experts-in-training (upper division and graduate students) and 11 experts (physics professors and researchers). Data collection involved structured interviews during which participants solved a series of non-standard problems in magnetism while thinking out loud. The problems were designed to test for conceptual understanding. The interviews were audio taped, transcribed, and analyzed using a grounded theory approach. None of the novices and only a few of the experts in training showed a strong understanding of inductance, magnetic energy, and magnetic pressure; and for the most part they tended not to approach problems visually. Novices frequently described gist memories of demonstrations, text book problems, and rules (heuristics). However, these fragmentary mental models were not complete enough to allow them to reason productively. Experts-in-training were able to solve problems that the novices were not able to solve, many times simply because they had greater recall of the material, and therefore more confidence in their facts. Much of their thinking was concrete, based on mentally manipulating objects. Three, however, exhibited traits of experts, albeit not consistently. The experts solved most of the problems in ways that were both effective and efficient. Part of the efficiency derived from their ability to visualize and thus reason in terms of field lines. / text

American musical theater songs are popular with the general public, and many college and university voice students are familiar with them. Some voice teachers also use musical theater repertoire to varying degrees in voice instruction. Such familiarity and interest lend significance to this study of the songs in a teaching context. There is therefore a need for the establishment of repertoire-selection guidelines and pedagogical analysis of selected musical theater songs so that additional teachers will become well informed.Following the introduction in Chapter One, the results of a survey sent to one hundred members of the National Association of Teachers of Singing are presented. The survey posed questions concerning the current use of musical theater songs. Among other things, the results revealed strong interest in the analysis and application of this literature in the voice studio. Guidelines for repertoire selection (also used by the author in selecting songs that address specific aspects of singing) are introduced in Chapter Three, along with a description of analytical procedures. Chapters Four through Eight include summaries of the analyses and suggested applications in the voice studio:Developing the ability to sing longer phrases"You'll Never Walk Alone" (Rodgers)"Where Is Love?" (Bart)"After the Ball" (Harris)• Developing the ability to sing wide intervals in a legato fashion "Lost in the Stars" (Weill)"Warm All Over" (Loesser)"Green Finch and Linnet Bird" (Sondheim)•Developing the ability to articulate words rapidly "My Darling, My Darling" (Loesser) "Seventy-Six Trombones" (Willson) "Soliloquy" (Rodgers)•Developing the ability to move smoothly between registers "Someone to Watch Over Me" (Gershwin) "Where or When" (Rodgers) "O1' Man River" (Kern)•Managing a large range and mature quality "Maria" (Bernstein)"Memory" (Lloyd Webber) "One More Kiss" (Sondheim)Conclusions in Chapter Nine include: (1) teachers should judge musical theater songs by the same criteria as other songs; (2) musical theater literature offers useful material for students who are striving to develop certain aspects of singing; (3) analyses of selected songs demonstrate their suitability for pedagogical use; and (4) there is a need for additional critical analysis of musical theater literature. / School of Music

In this study I attempt to develop a rationale for the role of student writing in advancing learning in Zoology. To this end, I use the informed and insightful voices of five academics from the University of Cape Town's Department of Zoology to present a picture of the goals of the discipline, how they view the role that student writing plays in advan~ing these goals, a sense of the tensions they face in dealing with student diversity, and the promise and challenges of innovative approaches. My interest in how staff view student writing stems from a belief that staff make use of student writing in different ways, depending on their assumptions about writing. I explore these assumptions by means of interviews with members of staff, in which I ask about how they understand the pursuit of science, the qualities a scientist needs to develop, the best ways to develop these qualities in students, and the part that student writing plays in this development. What emerges in this study is the understanding that the kinds of writing we ask students to do reflect the forms of educational practice that we sustain. On the one hand, certain forms of writing may support forms of transmission pedagogy that are viewed as being at odds with progressive science education. On the other hand, if we are to develop alternative teaching approaches which are in keeping with contemporary views of science and learning, then we need to develop new genres of student writing that give expression to these goals and methods. The study concludes with suggested avenues into curriculum review that would operationalise the insights developed by this study.

The purpose of this collaborative inquiry (CI) dissertation study was to examine pedagogical strategies designed to open Western classical music to improvisation. Piano teacher-participants formed a collaborative inquiry cohort as co-researchers to design and implement pedagogical strategies for use with their piano students, ages 8 to 10. Improvisation appears to occupy a limited role in practices commonly associated with Western classical music. Since the body of evidence found in Western music history and performance practice reveals traditions that encompassed improvisation, this study was designed to challenge existing pedagogical models associated with Western classical music through experimentation and improvisation. The prior attitudes and practices of the three participants were assessed through introductory interviews, as well as the collection of videos of teaching practices and preliminary survey data. Three two-hour in-person sessions of the cohort took place, interspersed with interviews and the sharing of video excerpts and co-researcher memos and blogs in an online forum on Canvas. During in-person sessions of the cohort, pedagogical strategies were designed and revisited through reflection following participants’ teaching experiences in their piano studios. Participants explored musical improvisation within a creative community by investigating the processes and experiences of treating Western classical music as an impetus to creative thought and improvisatory realization by their students. Findings illuminate patterns of interaction that illustrate the function of strategies for musical creativity and the applicability to pedagogical practices. Several overarching themes, addressing the purpose of the study, emerged through my analysis of data, pertaining to the dynamic nature of music, call and response as formative, and knowledge and novelty as means and ends. Participants demonstrated distinct operational definitions of improvisation, each of which appeared to connect to a model of awareness and responsiveness through the expression of interrelated themes. Whether spontaneously generated or chosen intentionally, limitations promoted improvisation as the exploration of novelty, advancing and emanating from a knowledge base. By revealing pedagogical practices that demonstrate heuristic models for experimentation through variability practices, this study illuminates patterns of interaction that open works of musical art to the sociocultural activity of improvisation, through which a multiplicity of meanings can take form.

Typescript (photocopy). / Digitized by Kansas Correctional Industries

There is no abstract available for this dissertation.

The purpose of this study was to determine if one hour of field instruction by a specialist would significantly increase fifth graders' knowledge and understanding of the concepts of ecological succession in abandoned fields at the Trumbull Area Land Laboratory in Trumbull County, Ohio.The research included the development of educational objectives and a curriculum to teach these objectives. An evaluation instrument was administered to a sampling of six classes before and after instruction. The results were analyzed to determine each question's discrimination index and difficulty level. A control group was utilized to measure the test's reliability.Data proved the test to have high reliability, but too high a degree of difficulty. A positive discrimination was shown on all items, but five were less than satisfactory. Three questions were shown to be invalid and none of the objectives were completely achieved. The conclusion reached was that the topic "Ecological Succession in Abandoned Fields" is too difficult to effectively convey in one hour to fifth graders at the level of understanding which the objectives were written.

The purpose of this study was to determine the relationship of a programmed study skills unit to the academic achievement of a selected group of eighth grade students.