Making the transition from calculus to advanced calculus/real analysis can be challenging for undergraduate students. Part of this challenge lies in the shift in the focus of student activity, from a focus on algorithms and computational techniques to activities focused around definitions, theorems, and proofs. The goal of Realistic Mathematics Education (RME) is to support students in making this transition by building on and formalizing their informal knowledge. There are a growing number of projects in this vein at the undergraduate level, in the areas of abstract algebra (TAAFU: Larsen, 2013; Larsen & Lockwood, 2013), differential equations (IO-DE: Rasmussen & Kwon, 2007), geometry (Zandieh & Rasmussen, 2010), and linear algebra (IOLA: Wawro, et al., 2012). This project represents the first steps in a similar RME-based, inquiry-oriented instructional design project aimed at advanced calculus. The results of this project are presented as three journal articles. In the first article I describe the development of a local instructional theory (LIT) for supporting the reinvention of formal conceptions of sequence convergence, the completeness property of the real numbers, and continuity of real functions. This LIT was inspired by Cauchy's proof of the Intermediate Value Theorem, and has been developed and refined using the instructional design heuristics of RME through the course of two teaching experiments. I found that a proof of the Intermediate Value Theorem was a powerful context for supporting the reinvention of a number of the core concepts of advanced calculus. The second article reports on two students' reinventions of formal conceptions of sequence convergence and the completeness property of the real numbers in the context of developing a proof of the Intermediate Value Theorem (IVT). Over the course of ten, hour-long sessions I worked with two students in a clinical setting, as these students collaborated on a sequence of tasks designed to support them in producing a proof of the IVT. Along the way, these students conjectured and developed a proof of the Monotone Convergence Theorem. Through this development I found that student conceptions of completeness were based on the geometric representation of the real numbers as a number line, and that the development of formal conceptions of sequence convergence and completeness were inextricably intertwined and supported one another in powerful ways. The third and final article takes the findings from the two aforementioned papers and translates them for use in an advanced calculus classroom. Specifically, Cauchy's proof of the Intermediate Value Theorem is used as an inspiration and touchstone for developing some of the core concepts of advanced calculus/real analysis: namely, sequence convergence, the completeness property of the real numbers, and continuous functions. These are presented as a succession of student investigations, within the context of students developing their own formal proof of the Intermediate Value Theorem.

My research measured completion and retention of procedural learning tasks, and declarative and procedural components of engagement in indoor and outdoor settings. Instructor-assisted Self-Directed Learning and Non-instructor-assisted Self-Directed Learning were implemented in the context of an Experiential Learning approach. Experimental covariates included student-specific variables such as background and experience, and environment-specific variables such as temperature, and humidity. AIC model averaging was used to identify the best-fitting mixed GLM models. Neither location, nor pedagogic method, proved to be a significant predictor of the probability that a student would complete the most complex of the procedural learning tasks, and the percent of students completing this task was not significantly higher in outdoor groups than in indoor groups. Neither location nor pedagogic method was a significant predictor of retention of procedural knowledge or engagement with learning materials. The level of voluntary collaboration was higher in outdoor groups than in indoor groups. / Includes bibliography. / Thesis (M.S.)--Florida Atlantic University, 2014. / FAU Electronic Theses and Dissertations Collection

This essay presents an ecocritical reading of water imagery in selected poems by Carol AnnDuffy, with focus on Duffy’s personified water-voices, how water illuminates history, andDuffy’s metaphor of language as water. After a consideration of the problematics of teachingpoetry in the EFL classroom, the essay concludes that Duffy’s poetry holds potential forstudents to develop environmental literacy, both in content and in form.

In the US, an estimated 25% of four-year college students and up to 80% of community college students suffer from a moderate to high degree of mathematics anxiety (MA) (Chang & Beilock, 2016). Many scholars have noted that mathematics anxiety can be regarded as a significant factor in determining a student's achievement and mathematics related jobs. In the existing literature body, many researchers noted that MA may stem from teaching methods that are more conventional and rule-bounded such as lecture-style classroom models. On the other hand, MA can be mitigated by inquiry-based learning classroom models where students construct knowledge through inquiry, communication, critical thinking, and group work. However, the current literature has not built the connection between different teaching styles and students' individual differences with respect to MA. The individual differences are associated with the personality of the learner, learning styles, learning speed, and needs and interests of the learner. Depending on a student's learning style and a compatible teaching style, the student may actively participate in their own learning with less mathematics anxiety. Thus, the purpose of this study is to determine the influence of different teaching styles on MA, when interacted with Kolb’s and Gregorc’s (1984) four different learning and thinking styles. The research questions investigated in this study are: 1) What is the difference between a lecture classroom model (LCM) and an inquiry-based learning classroom model (IBL) on students’ mathematics anxiety levels over a fifteen-week semester of a college-level remedial mathematics course?; 2) What is the difference between a lecture classroom model (LCM) and an inquiry-based learning classroom model (IBL) on mathematics anxiety levels for students with different learning and thinking styles (as defined by Kolb’s and Gregorc’s learning styles) over a fifteen-week semester?; and 3) What aspects of instructional approaches (LCM and IBL) do students with different learning and thinking styles report as being related to mathematics anxiety? The abbreviated version of the mathematics anxiety rating scale (A-MARS), Kolb’s learning styles inventory, Gregorc’s thinking styles, and Written questionnaire were used to measure students’ MA levels and identify their learning and thinking styles. The results provided evidence that IBL instruction is beneficial for the students with MA, especially with mathematics test anxiety and mathematics course anxiety. Only numerical task anxiety was not significant. Thus, student-centered learning pedagogies turned out to be an effective and engaging method for lowering MA. However, there was no evidence to support the overall relationship between the constructs of learning and thinking styles and MA levels, above and beyond the instructional approaches. Classifying students according to learning and thinking styles did not influence students’ MA levels in this study over the 15 academic weeks. Moreover, after a 15 academic weeks, students in both LCM and IBL classes responded positively to key components of LCM and IBL classroom models. This implies that both LCM and IBL approaches still are important models regardless of students’ MA levels.

With rapid development of information technologies, especially the Internet technology, people can communicate more flexibly via various media, in which knowledge can be also shared. In gaining knowledge through the Internet, either digital content retrieval or inter-personal interaction, learning activities conducted on the Web are getting popular. This research has two main objectives. One is to develop incentive mechanisms to enhance the quantity and quality of information shared through peer-to-peer (P2P) networks. The other objective is to implement and evaluate the proposed mechanisms for inquiry-based learning on P2P networks. The pricing-like incentive mechanism is embedded on each peer to determine the price to share a document, to issue a question, and respond to a question. Through experiments, this study evaluates the effects on mitigating the free-riding problems and exchanging information through the P2P network. The results show the effectiveness of the incentive mechanisms for inquiry-based learning on P2P networks.

Walden's Paths, created by the Center for the Study of Digital Libraries, provides a mechanism for leveraging student learning with the incredible amount of educational material on the web by organizing selected web pages into a structured learning activity. Applying specialized templates to the creation of Walden's Paths can aid a path author in creating pedagogically sound, Web-based activities, by assisting in the collection of information and organization of the activity. Authoring templates may be based on established educational frameworks, learning theories or specific activity type. This research project investigates how using pedagogically based templates affects the authoring process for paths created using Walden's Paths. A template based on the educational framework Inquiry-Based Learning was created and tested by a group of users to determine what effects the template has on creating paths as compared to creating similar paths using the existing Walden's Paths interface.

The purpose of this report is to describe the course, Analysis of the Real Line, taught at The University of Texas at Austin. Course materials are presented using the inquiry based learning method. Students work a series of warm up problems before being presented rigorous problems in calculus, including topics on integration, exponential functions, and real number line analysis. Additionally, students consider aspects of these problems that could be incorporated into a high school curriculum. Typical problems in several major areas are summarized along with warm up problems that introduce or extend the topics. / text

This study examined the content knowledge and pedagogical content knowledge (PCK) constructed by a group of 24 pre-service elementary teacher participants as they learned about the moon’s phases, inquiry learning, and use of the Internet message boards as a teaching tool as a part of their science teaching methods course. The MOON Project (More Observations On Nature), an exploration of inquiry teaching via e-learning, matched the pre-service elementary teacher participants with schoolchildren in grades 4-8 around the world. Upon completion of a 4-week moon observation phase, the participants led the schoolchildren in a discussion of their observations via Blackboard™. This mixed methods study followed a quasi-experimental non-equivalent control group design. The participants’ content knowledge, pedagogical content knowledge and perceptions about their knowledge were documented using questionnaires, essays, and tests as they entered this experience and again as they exited. Qualitative and quantitative methods and analysis established that the increase in pre-service teachers’ content and pedagogical content knowledge (PCK) as well as their perceptions of the knowledge gained was statistically significant at the conclusion of the project. However, they took away understandings of why the moon changes shape that were basic at best and fraught with a statistically significant increase in misconceptions. None of the instruments supported the pre-service teachers’ perceptions of increased PCK. The pre-service teachers had mixed perceptions about teaching over the Internet, mostly due to the degree to which their elementary student groups responded with focus to questions and discussions or, in some cases, participated at all. The findings and recommendations speak to teacher educators about the methodology used in teacher education programs. / Department of Biology

Thesis (M.S.)--Miami University, Dept. of Chemistry and Biochemistry, 2008. / Title from first page of PDF document. Includes bibliographical references (p. 115-118).

Philosophiae Doctor - PhD / The purpose of this study is to investigate the role of school libraries in supporting an inquiry based approach for teaching and learning science subjects in senior secondary schools in Ekiti State, Nigeria. The significance of this study revolves round the prominence given to science education being a mechanism for realising national advancement in Nigeria. This was emphasised in the Nigeria National Policy on Education (2013) as the Federal Government of Nigeria adopted science education as an instrument for effecting national development. This study addressed the following research questions: What is the status of secondary school libraries in Ekiti State, Nigeria? To what extent does the quality of library resources influence science curriculum implementation? To what extent do science teachers advocate using information resources beyond textbooks?