Matching Items (19)
Filtering by
- All Subjects: Mathematics
- All Subjects: STEM
- Creators: Division of Teacher Preparation
- Creators: Kaliszewski, Steven
Description
In this thesis, I investigate the C*-algebras and related constructions that arise from combinatorial structures such as directed graphs and their generalizations. I give a complete characterization of the C*-correspondences associated to directed graphs as well as results about obstructions to a similar characterization of these objects for generalizations of directed graphs. Viewing the higher-dimensional analogues of directed graphs through the lens of product systems, I give a rigorous proof that topological k-graphs are essentially product systems over N^k of topological graphs. I introduce a "compactly aligned" condition for such product systems of graphs and show that this coincides with the similarly-named conditions for topological k-graphs and for the associated product systems over N^k of C*-correspondences. Finally I consider the constructions arising from topological dynamical systems consisting of a locally compact Hausdorff space and k commuting local homeomorphisms. I show that in this case, the associated topological k-graph correspondence is isomorphic to the product system over N^k of C*-correspondences arising from a related Exel-Larsen system. Moreover, I show that the topological k-graph C*-algebra has a crossed product structure in the sense of Larsen.
ContributorsPatani, Nura (Author) / Kaliszewski, Steven (Thesis advisor) / Quigg, John (Thesis advisor) / Bremner, Andrew (Committee member) / Kawski, Matthias (Committee member) / Spielberg, John (Committee member) / Arizona State University (Publisher)
Created2011
Description
Studies have shown that arts programs have a positive impact on students' abilities to achieve academic success, showcase creativity, and stay focused inside and outside of the classroom. However, as school funding drops, arts programs are often the first to be cut from school curricula. Rather than drop art completely, general education teachers have the opportunity to integrate arts instruction with other content areas in their classrooms. Traditional fraction lessons and Music-infused fraction lessons were administered to two classes of fourth-grade students. The two types of lessons were presented over two separate days in each classroom. Mathematics worksheets and attitudinal surveys were administered to each student in each classroom after each lesson to gauge their understanding of the mathematics content as well as their self-perceived understanding, enjoyment and learning related to the lessons. Students in both classes were found to achieve significantly higher mean scores on the traditional fraction lesson than the music-infused fraction lesson. Lower scores in the music-infused fraction lesson may have been due to the additional component of music for students unfamiliar with music principles. Students tended to express satisfaction for both lessons. In future studies, it would be recommended to spend additional lesson instruction time on the principles of music in order help students reach deeper understanding of the music-infused fraction lesson. Other recommendations include using colorful visuals and interactive activities to establish both fraction and music concepts.
ContributorsGerrish, Julie Kathryn (Author) / Zambo, Ronald (Thesis director) / Hutchins, Catherine (Committee member) / Division of Teacher Preparation (Contributor) / Department of Psychology (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05
Description
There are two types of understanding when it comes to learning math: procedural understanding and conceptual understanding. I grew up with a rigorous learning curriculum and learned math through endless drills and practices. I was less motivated to understand the reason behind those procedures. I think both types of understanding are equally important in learning mathematics. Procedural fluency is the "ability to apply procedures accurately, efficiently, and flexibly... to build or modify procedures from other procedures" (National Council of Teachers of Mathematics, 2015). Procedural understanding may perceive as merely about the understanding of the arithmetic and memorizing the steps with no understanding but in reality, students need to decide which procedure to use for a given situation; here is where the conceptual understanding comes in handy. Students need the skills to integrate concepts and procedures to develop their own ways to solve a problem, they need to know how to do it and why they do it that way. The purpose of this 5-day unit is teaching with conceptual understanding through hands-on activities and the use of tools to learn geometry. Through these lesson plans, students should be able to develop the conceptual understanding of the angles created by parallel lines and transversal, interior and exterior angles of triangles and polygons, and the use of similar triangles, while developing the procedural understanding. These lesson plans are created to align with the eighth grade Common Core Standards. Students are learning angles through the use of protractor and patty paper, making a conjecture based on their data and experience, and real-life problem solving. The lesson plans used the direct instruction and the 5E inquiry template from the iTeachAZ program. The direct instruction lesson plan includes instructional input, guided practice and individual practice. The 5E inquiry lesson plan has five sections: engage, explore, explain, elaborate and evaluate.
ContributorsLeung, Miranda Wing-Mei (Author) / Kurz, Terri (Thesis director) / Walters, Molina (Committee member) / Division of Teacher Preparation (Contributor) / Barrett, The Honors College (Contributor)
Created2015-12
Description
STEM has increasingly become a buzz word in the world of education. According to Briener, et. al. (2012), the most common perspective of STEM education is teaching the integrated disciplines of science, technology, engineering, and mathematics as "one cohesive entity" instead of as separate subjects (p. 5). Prioritizing a STEM focus is a tactic many schools are beginning to adapt and one the United States government is financially backing, contributing significantly to the popularity of the movement (Briener, et.al., 2012). Across the nation, schools are making strides towards incorporating more STEM activities, and many school districts are designating entire schools as STEM schools. These STEM schools distinguish themselves with consistent commitment and attention to aspects of the STEM fields within instruction, including research opportunities for students, 21st Century skills, and a variety of learning environments. Bridges Elementary is one such identified STEM school that exemplifies these criteria, amongst others, setting a precedent for STEM schools to come.
ContributorsFefolt, Molly Lynn (Author) / Walters, Molina (Thesis director) / Oliver, Jill (Committee member) / Division of Teacher Preparation (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
Description
As a Country, the United States is continually falling behind academically when compared to other Nations. Therefore, the purpose of my Honors Thesis is to enlighten others on the importance of incorporating science, technology, engineering, and mathematics (STEM) into our classrooms. When students have the chance to partake in hands on, inquiry based lessons, their new knowledge for the subject increases drastically. However, completing STEM lessons in the classroom is a challenging task. For this reason, I have designed a unit's worth of lesson plans, where the unit encompasses science, technology, engineering, and mathematics. These STEM lessons are inquiry-based so that students get an understanding that science is a learning process, not just a group of facts to be memorized. The lessons are written in the 5E format, as this format is based on the way human beings learn. I wanted to make this as easy as possible for teachers to bring inquiry-based STEM learning into the classroom. When students are allowed to take control of their own learning and make discoveries for themselves, they are going to realize the excitement that comes with STEM. This will lead more students to pursue STEM careers, thus helping bring the United States back to a competitive level academically.
ContributorsPiatak, Mary Frances (Author) / Oliver, Jill (Thesis director) / Walters, Molina (Committee member) / Division of Teacher Preparation (Contributor) / Barrett, The Honors College (Contributor)
Created2016-12
Description
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 examined the need for Science, Technology, Engineering, and Math (STEM) activities within a specific modality (centers) and their potential influence on elementary students with a particular emphasis on gender. STEM is an interdisciplinary curriculum that seeks to seamlessly incorporate science, technology, engineering, and math. Due to the increasing demand for STEM professions and proficiency within each aspect, the education system and individual educators require lessons and modalities that motivate learning in each of these areas. Administrators and teachers need creative ways to provide effective STEM implementation. Currently, the education system as a whole lacks creative and motivating material for these four domains. Not only this, but there has been a misunderstanding in regard to what effective STEM implementation entails, as well as a dearth of classroom ready lessons for educators. As a result, this thesis project developed a way to implement STEM through the use of learning centers. Learning centers are defined as designated areas within a classroom that allow easy access to a variety of learning materials. Within these centers are activities that reinforce concepts by using inquiry-based learning. Learning centers are effective in developing additional concepts or providing students with a greater breadth of knowledge on a concept. This thesis project developed three STEM learning center activity boxes and two STEM learning center outlines. Creating effective STEM learning centers and outlines was a multistep process. The first step was to develop a 3E lesson plan for each activity. Once the lesson plans were revised and complete, the creation of the three activity boxes was next. To create the activity boxes, all the required materials and worksheets were gathered and printed. From there, the next step was to implement the learning centers in a classroom to observe the results and propose any modifications. Afterwards, a reflection detailing the results and modifications was made. In the end, the goal of this project was to develop easily implemented STEM activities for my future classroom. Coming up with a creative way to get kids curious and excited about STEM is key in building STEM awareness. Not only did my project create STEM activities I can implement, but it also allowed me the opportunity to share my activities with other teachers. As a result, influencing the spread of STEM amongst future and current teachers.
ContributorsSchott, Nicole Elizabeth (Author) / Walters, Molina (Thesis director) / Oliver, Jill (Committee member) / Division of Teacher Preparation (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
Description
Clean and accessible drinking water is a crucial and limited resource. As the world's population grows and demand increases, water resources will become more limited. This project aims to educate students on water resources, drinking water, and how biomimicry can allow society to improve its water usage. The project consists of a ten day unit plan which addresses several water topics such as: the various uses of water, water distribution, where drinking water comes from, the water treatment process, and more. After establishing background knowledge on water and surrounding issues, the students will be challenged to design a water bottle using biomimicry. Biomimicry is looking at nature to draw and inspire solutions to human problems. This unit has been optimized for use by elementary teachers. The ten day unit consists of a lesson summary, objectives, standards, and recommended activities for each day. Of the ten days, three lesson plans were fully developed using the 5E format. The research supporting this project is compiled in the following report.
ContributorsSalik, Rachael (Co-author) / Burke, Aurora (Co-author) / Walters, Molina (Thesis director) / Larson, Kelli L. (Committee member) / Civil, Environmental and Sustainable Engineering Programs (Contributor) / Division of Teacher Preparation (Contributor) / Barrett, The Honors College (Contributor)
Created2016-12
Description
In recent education trends, an emphasis has been placed on teaching students in STEM (Science, Technology, Engineering, and Mathematics) disciplines. Many researchers have advocated for integrating Arts education as well, changing STEM education to STEAM (STEM + Arts) education. This paper describes an original 8th Grade physics curriculum integrating Science, Technology, Engineering, Arts, and Mathematics (STEAM). The curriculum was designed to teach core science concepts through inquiry and dance activities. The curriculum uses the 5E inquiry format, specifically using dance and movement activities to elaborate on the learned science content. The unit curriculum is designed to be implemented in an 8th Grade science classroom based on best practices in Science Instruction and Dance Education. The curriculum was not implemented as a research study this year, but is designed to support research in the future. The curriculum was however presented to Term 6 Pre-service Teachers in Mary Lou Fulton Teacher's College at ASU, whom evaluated the effectiveness of the lessons and offered feedback. This paper includes a review of current literature on STEAM education and dance integration, rationale for the curriculum's 5E Format and dance integration, the entire physics unit curriculum in 5E format, Pre-service Teacher feedback, and implications for a future research study with the unit curriculum.
ContributorsHarris, Carson Donald (Author) / Chen, Ying-Chih (Thesis director) / Atkinson, Laura (Committee member) / Division of Teacher Preparation (Contributor) / School of Film, Dance and Theatre (Contributor) / Barrett, The Honors College (Contributor)
Created2016-12
Description
This dissertation will cover two topics. For the first, let $K$ be a number field. A $K$-derived polynomial $f(x) \in K[x]$ is a polynomial that
factors into linear factors over $K$, as do all of its derivatives. Such a polynomial
is said to be {\it proper} if
its roots are distinct. An unresolved question in the literature is
whether or not there exists a proper $\Q$-derived polynomial of degree 4. Some examples
are known of proper $K$-derived quartics for a quadratic number field $K$, although other
than $\Q(\sqrt{3})$, these fields have quite large discriminant. (The second known field
is $\Q(\sqrt{3441})$.) I will describe a search for quadratic fields $K$
over which there exist proper $K$-derived quartics. The search finds examples for
$K=\Q(\sqrt{D})$ with $D=...,-95,-41,-19,21,31,89,...$.\\
For the second topic, by Krasner's lemma there exist a finite number of degree $n$ extensions of $\Q_p$. Jones and Roberts have developed a database recording invariants of $p$-adic extensions for low degree $n$. I will contribute data to this database by computing the Galois slope content, inertia subgroup, and Galois mean slope for a variety of wildly ramified extensions of composite degree using the idea of \emph{global splitting models}.
factors into linear factors over $K$, as do all of its derivatives. Such a polynomial
is said to be {\it proper} if
its roots are distinct. An unresolved question in the literature is
whether or not there exists a proper $\Q$-derived polynomial of degree 4. Some examples
are known of proper $K$-derived quartics for a quadratic number field $K$, although other
than $\Q(\sqrt{3})$, these fields have quite large discriminant. (The second known field
is $\Q(\sqrt{3441})$.) I will describe a search for quadratic fields $K$
over which there exist proper $K$-derived quartics. The search finds examples for
$K=\Q(\sqrt{D})$ with $D=...,-95,-41,-19,21,31,89,...$.\\
For the second topic, by Krasner's lemma there exist a finite number of degree $n$ extensions of $\Q_p$. Jones and Roberts have developed a database recording invariants of $p$-adic extensions for low degree $n$. I will contribute data to this database by computing the Galois slope content, inertia subgroup, and Galois mean slope for a variety of wildly ramified extensions of composite degree using the idea of \emph{global splitting models}.
ContributorsCarrillo, Benjamin (Author) / Jones, John (Thesis advisor) / Bremner, Andrew (Thesis advisor) / Childress, Nancy (Committee member) / Fishel, Susanna (Committee member) / Kaliszewski, Steven (Committee member) / Arizona State University (Publisher)
Created2019