Matching Items (224)
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Research on combinatorics education is sparse when compared with other fields in mathematics education. This research attempted to contribute to the dearth of literature by examining students' reasoning about enumerative combinatorics problems and how students conceptualize the set of elements being counted in such problems, called the solution set. In

Research on combinatorics education is sparse when compared with other fields in mathematics education. This research attempted to contribute to the dearth of literature by examining students' reasoning about enumerative combinatorics problems and how students conceptualize the set of elements being counted in such problems, called the solution set. In particular, the focus was on the stable patterns of reasoning, known as ways of thinking, which students applied in a variety of combinatorial situations and tasks. This study catalogued students' ways of thinking about solution sets as they progressed through an instructional sequence. In addition, the relationships between the catalogued ways of thinking were explored. Further, the study investigated the challenges students experienced as they interacted with the tasks and instructional interventions, and how students' ways of thinking evolved as these challenges were overcome. Finally, it examined the role of instruction in guiding students to develop and extend their ways of thinking. Two pairs of undergraduate students with no formal experience with combinatorics participated in one of the two consecutive teaching experiments conducted in Spring 2012. Many ways of thinking emerged through the grounded theory analysis of the data, but only eight were identified as robust. These robust ways of thinking were classified into three categories: Subsets, Odometer, and Problem Posing. The Subsets category encompasses two ways of thinking, both of which ultimately involve envisioning the solution set as the union of subsets. The three ways of thinking in Odometer category involve holding an item or a set of items constant and systematically varying the other items involved in the counting process. The ways of thinking belonging to Problem Posing category involve spontaneously posing new, related combinatorics problems and finding relationships between the solution sets of the original and the new problem. The evolution of students' ways of thinking in the Problem Posing category was analyzed. This entailed examining the perturbation experienced by students and the resulting accommodation of their thinking. It was found that such perturbation and its resolution was often the result of an instructional intervention. Implications for teaching practice are discussed.
ContributorsHalani, Aviva (Author) / Roh, Kyeong Hah (Thesis advisor) / Fishel, Susanna (Committee member) / Saldanha, Luis (Committee member) / Thompson, Patrick (Committee member) / Zandieh, Michelle (Committee member) / Arizona State University (Publisher)
Created2013
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This dissertation report follows a three-paper format, with each paper having a different but related focus. In Paper 1 I discuss conceptual analysis of mathematical ideas relative to its place within cognitive learning theories and research studies. In particular, I highlight specific ways mathematics education research uses conceptual analysis and

This dissertation report follows a three-paper format, with each paper having a different but related focus. In Paper 1 I discuss conceptual analysis of mathematical ideas relative to its place within cognitive learning theories and research studies. In particular, I highlight specific ways mathematics education research uses conceptual analysis and discuss the implications of these uses for interpreting and leveraging results to produce empirically tested learning trajectories. From my summary and analysis I develop two recommendations for the cognitive researchers developing empirically supported learning trajectories. (1) A researcher should frame his/her work, and analyze others’ work, within the researcher’s image of a broadly coherent trajectory for student learning and (2) that the field should work towards a common understanding for the meaning of a hypothetical learning trajectory.

In Paper 2 I argue that prior research in online learning has tested the impact of online courses on measures such as student retention rates, satisfaction scores, and GPA but that research is needed to describe the meanings students construct for mathematical ideas researchers have identified as critical to their success in future math courses and other STEM fields. This paper discusses the need for a new focus in studying online mathematics learning and calls for cognitive researchers to begin developing a productive methodology for examining the meanings students construct while engaged in online lessons.

Paper 3 describes the online Precalculus course intervention we designed around measurement imagery and quantitative reasoning as themes that unite topics across units. I report results relative to the meanings students developed for exponential functions and related ideas (such as percent change and growth factors) while working through lessons in the intervention. I provide a conceptual analysis guiding its design and discuss pre-test and pre-interview results, post-test and post-interview results, and observations from student behaviors while interacting with lessons. I demonstrate that the targeted meanings can be productive for students, show common unproductive meanings students possess as they enter Precalculus, highlight challenges and opportunities in teaching and learning in the online environment, and discuss needed adaptations to the intervention and future research opportunities informed by my results.
ContributorsO'Bryan, Alan Eugene (Author) / Carlson, Marilyn P (Thesis advisor) / Thompson, Patrick W (Committee member) / Milner, Fabio (Committee member) / Roh, Kyeong Hah (Committee member) / Tallman, Michael (Committee member) / Arizona State University (Publisher)
Created2018
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Construction is a defining characteristic of geometry classes. In a traditional classroom, teachers and students use physical tools (i.e. a compass and straight-edge) in their constructions. However, with modern technology, construction is possible through the use of digital applications such as GeoGebra and Geometer’s SketchPad.
Many other studies have

Construction is a defining characteristic of geometry classes. In a traditional classroom, teachers and students use physical tools (i.e. a compass and straight-edge) in their constructions. However, with modern technology, construction is possible through the use of digital applications such as GeoGebra and Geometer’s SketchPad.
Many other studies have researched the benefits of digital manipulatives and digital environments through student completion of tasks and testing. This study intends to research students’ use of the digital tools and manipulatives, along with the students’ interactions with the digital environment. To this end, I conducted exploratory teaching experiments with two calculus I students.
In the exploratory teaching experiments, students were introduced to a GeoGebra application developed by Fischer (2019), which includes instructional videos and corresponding quizzes, as well as exercises and interactive notepads, where students could use digital tools to construct line segments and circles (corresponding to the physical straight-edge and compass). The application built up the students’ foundational knowledge, culminating in the construction and verbal proof of Euclid’s Elements, Proposition 1 (Euclid, 1733).
The central findings of this thesis are the students’ interactions with the digital environment, with observed changes in their conceptions of radii and circles, and in their use of tools. The students were observed to have conceptions of radii as a process, a geometric shape, and a geometric object. I observed the students’ conceptions of a circle change from a geometric shape to a geometric object, and with that change, observed the students’ use of tools change from a measuring focus to a property focus.
I report a summary of the students’ work and classify their reasoning and actions into the above categories, and an analysis of how the digital environment impacts the students’ conceptions. I also briefly discuss the impact of the findings on pedagogy and future research.
ContributorsSakauye, Noelle Marie (Author) / Roh, Kyeong Hah (Thesis director) / Zandieh, Michelle (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / School of International Letters and Cultures (Contributor) / Barrett, The Honors College (Contributor)
Created2020-05
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This honors thesis outlines a method for teaching argument writing in the secondary classroom, including the elements of an argument based upon the Toulmin method, and diverse ways to help students who are all types of learners become engaged and receive the support they need. It includes all elements of

This honors thesis outlines a method for teaching argument writing in the secondary classroom, including the elements of an argument based upon the Toulmin method, and diverse ways to help students who are all types of learners become engaged and receive the support they need. It includes all elements of argument, including evidence, warrants, backing, counterargument, claims, theses, the rhetorical triangle and the rhetorical appeals, including definitions and how they fit together in an argumentative essay. The largest portion of the project is dedicated to activities and resources for teachers based upon all of those elements, along with activities for the writing process as a whole. These activities are based upon the student's individual experience as well as various scholarly resources from leading professionals in the curriculum development field for English Language Arts. This is not meant to be an end-all be-all solution for teaching argument writing, but rather one of many resources that teachers can use in their classroom. This 30-page paper, including references, are condensed into an accessible website for teachers to use more easily. Each tab on the website refers to a different element or focus of the argument writing process, with both a definition and introduction as well as one or more activities for teachers to implement into the classroom. The activities are versatile and general for the purpose of teachers being able to include them into whatever curriculum they are currently teaching. The goal is that they can add argument instruction into what they are already either willingly or being required to teach in an easy and logical way. The website is available for any secondary teachers to use as they see fit at www.teachingargumentwriting.weebly.com.
ContributorsBrooks, Jenna Nicole (Author) / Blasingame, James (Thesis director) / Barnett, Juliet (Committee member) / Division of Teacher Preparation (Contributor) / School of Film, Dance and Theatre (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
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DescriptionThis project is designed to generate enthusiasm for science among refugee students in hopes of inspiring them to continue learning science as well as to help them with their current understanding of their school science subject matter.
ContributorsSipes, Shannon Paige (Author) / O'Flaherty, Katherine (Thesis director) / Gregg, George (Committee member) / School of Molecular Sciences (Contributor) / Division of Teacher Preparation (Contributor) / Barrett, The Honors College (Contributor)
Created2017-12
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This creative project explores the concept of how music is like a language and how, as a teacher, I plan to enforce this concept through my teaching. The aim of this project is to highlight the importance of completing research and acquiring knowledge of aspects, such as the composer's life,

This creative project explores the concept of how music is like a language and how, as a teacher, I plan to enforce this concept through my teaching. The aim of this project is to highlight the importance of completing research and acquiring knowledge of aspects, such as the composer's life, historical background and literary references, when learning a piece of music. Through this project, I address connections between the brain and music pertaining to memorization, the components of language, the similarities between language and music, the role of the teacher and the development of a "toolbox" of knowledge for studying a piece of music. I present my own research on Schumann's Novelette Op. 21, No. 8 in f-sharp minor as well as my own experiences of learning the piece to demonstrate an example of the process and discoveries I hope my students will make in their own studies of repertoire.
ContributorsLee, Kara Jia-Shan (Author) / Pagano, Caio (Thesis director) / Creviston, Hannah (Committee member) / Division of Teacher Preparation (Contributor) / School of Music (Contributor) / Barrett, The Honors College (Contributor)
Created2017-12
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The SolarSPELL is an offline, ruggedized, digital library, created by Dr. Laura Hosman for the U.S. Peace Corps. It has thousands of pieces of educational content that can be accessed through a self-contained Wi-Fi hotspot on the device itself. Currently, there are more than 200 deployed in several Pacific Island

The SolarSPELL is an offline, ruggedized, digital library, created by Dr. Laura Hosman for the U.S. Peace Corps. It has thousands of pieces of educational content that can be accessed through a self-contained Wi-Fi hotspot on the device itself. Currently, there are more than 200 deployed in several Pacific Island nations. After visiting one of these nations, Tonga, in December of 2016, I learned that almost all of the Peace Corps volunteers stationed around the Pacific Islands suffered from a lack of resources due to a variety of reasons. While the SolarSPELL helps to remedy that, the device is lacking classroom activities and resources for creative work and educational drama. Furthermore, for many students in these environments, schools are for learning information and producing high scores on exams, not for learning about creative strengths and identity. After researching curriculum development and the use of drama in an educational setting, I compiled over 50 pieces of content to include on the SolarSPELL involving art, drama, music, movement, and most importantly, imagination. These resources will allow Peace Corps volunteers to explore additional ways to teach English in their schools, while also creating a classroom environment that allows for creative expression. All the content is compiled into one folder as "Teaching Resources", and is then broken down into seven sub- categories. In the first sub-category, Art Projects, there is a collection of several hands-on projects, many of which involve recyclable or readily available materials. These projects will allow for a greater understanding of conservation and "green" living, concepts that are crucial to the stability of these island nations. The next 5 categories are Drama Readings, Music, Movement, and Video, Group Exercises, Creative Writing, and Worksheets. The second sub- category is a collection of beginner-level "Reader's Theater" scripts. The third sub-category involves music and video to engage students in movement activities. The fourth sub-category is a compilation of group games and activities to help students express themselves and learn social skills. The fifth sub-category includes a collection of activities such as fill-in-the-blank story worksheets and journal prompts which will aid in creative thinking and the practice of the English language. The sixth sub-category involves a collection of worksheets that mainly focus on self-reflection and identity. The seventh and final sub-category, Content Guide and Information, works to explain the benefits of using of drama and creative play in the classroom, as well as strategies teachers can implement in order to further engage their students in dramatic learning and play. Overall, these pieces of content are meant to be used as resources for the Peace Corps volunteers in order to provide alternative ways to practice reading, writing, and speaking the English language, a critical part of education in the Pacific Islands.
ContributorsTaylor, Amanda Nicole (Author) / Hosman, Laura (Thesis director) / McAvoy, Mary (Committee member) / School of Film, Dance and Theatre (Contributor) / Division of Teacher Preparation (Contributor) / Barrett, The Honors College (Contributor) / School for the Future of Innovation in Society (Contributor)
Created2017-12
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In an effort to combat the lack of diversity in Children's Literature, this project displays a piece of literature titled Stories & Stages: A Tale of Two Sisters, in the form of a children's chapter book for a middle grade audience. Focusing on characters of a Hispanic background without relying

In an effort to combat the lack of diversity in Children's Literature, this project displays a piece of literature titled Stories & Stages: A Tale of Two Sisters, in the form of a children's chapter book for a middle grade audience. Focusing on characters of a Hispanic background without relying on stereotypes or false characterizations, the novel works to inspire young minds and reflect a true representation of the world children are living in. This is done using research on different aspects of Children's Literature, including: the definition of children's literature, diversity, girlhood, and sibling relationships. This research provides the basis for the project, as does personal experience and background. Following the novel is a recording of the background research involved and a documentations of the creative process. Keywords: Children's Literature, Diversity
ContributorsFlores, Abriana Lorraine (Author) / Elliott, Lisa (Thesis director) / Haddy, Lana (Committee member) / Division of Teacher Preparation (Contributor) / Department of English (Contributor) / Barrett, The Honors College (Contributor)
Created2017-12
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This creative project created and implemented a seven-day STEM curriculum that ultimately encouraged engagement in STEM subjects in students ages 5 through 11. The activities were incorporated into Arizona State University's Kids' Camp over the summer of 2017, every Tuesday afternoon from 4 to 6 p.m. with each activity running

This creative project created and implemented a seven-day STEM curriculum that ultimately encouraged engagement in STEM subjects in students ages 5 through 11. The activities were incorporated into Arizona State University's Kids' Camp over the summer of 2017, every Tuesday afternoon from 4 to 6 p.m. with each activity running for roughly 40 minutes. The lesson plans were created to cover a myriad of scientific topics to account for varied student interest. The topics covered were plant biology, aerodynamics, zoology, geology, chemistry, physics, and astronomy. Each lesson was scaffolded to match the learning needs of the three age groups (5-6 year olds, 7-8 year olds, 9-11 year olds) and to encourage engagement. "Engagement" was measured by pre- and post-activity surveys approved by IRB. The surveys were in the form of statements where the children would totally agree, agree, be undecided, disagree, or totally disagree with it. To more accurately test engagement, the smiley face Likert scale was incorporated with the answer choices. After implementation of the intervention, two-tailed paired t-tests showed that student engagement significantly increased for the two lesson plans of Aerodynamics and Chemistry.
ContributorsHunt, Allison Rene (Co-author) / Belko, Sara (Co-author) / Merritt, Eileen (Thesis director) / Ankeny, Casey (Committee member) / Division of Teacher Preparation (Contributor) / Harrington Bioengineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2017-12
Description
This project seeks to investigate the ways in which the W.P. Carey School of Business, at Arizona State University, can improve student retention and engagement efforts. The analysis is being completed through an audit of the business school's current efforts towards student engagement, an examination of the internal and external

This project seeks to investigate the ways in which the W.P. Carey School of Business, at Arizona State University, can improve student retention and engagement efforts. The analysis is being completed through an audit of the business school's current efforts towards student engagement, an examination of the internal and external environments of business schools across the nation, and a review of scholarly data/research on student retention risk factors and methods for improving engagement. The study highlights what exactly contributes to the success of the W.P. Carey School of Business, concluding with recommendations for how its engagement and retention efforts can be further improved to continue to serve students at a nationally ranked level.
ContributorsStinger, Rio W. (Author) / Hillman, Amy (Thesis director) / Mader, Michael (Committee member) / Division of Teacher Preparation (Contributor) / Department of Management (Contributor) / W. P. Carey School of Business (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05