Matching Items (22)
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- All Subjects: Mathematics
- Creators: Division of Teacher Preparation
- Status: Published
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
Chapter 1 introduces some key elements of important topics such as; quantum mechanics,
representation theory of the Lorentz and Poincare groups, and a review of some basic rela- ´
tivistic wave equations that will play an important role in the work to follow. In Chapter 2,
a complex covariant form of the classical Maxwell’s equations in a moving medium or at
rest is introduced. In addition, a compact, Lorentz invariant, form of the energy-momentum
tensor is derived. In chapter 3, the concept of photon helicity is critically analyzed and its
connection with the Pauli-Lubanski vector from the viewpoint of the complex electromag- ´
netic field, E+ iH. To this end, a complex covariant form of Maxwell’s equations is used.
Chapter 4 analyzes basic relativistic wave equations for the classical fields, such as Dirac’s
equation, Weyl’s two-component equation for massless neutrinos and the Proca, Maxwell
and Fierz-Pauli equations, from the viewpoint of the Pauli-Lubanski vector and the Casimir ´
operators of the Poincare group. A connection between the spin of a particle/field and ´
consistency of the corresponding overdetermined system is emphasized in the massless
case. Chapter 5 focuses on the so-called generalized quantum harmonic oscillator, which
is a Schrodinger equation with a time-varying quadratic Hamiltonian operator. The time ¨
evolution of exact wave functions of the generalized harmonic oscillators is determined
in terms of the solutions of certain Ermakov and Riccati-type systems. In addition, it is
shown that the classical Arnold transform is naturally connected with Ehrenfest’s theorem
for generalized harmonic oscillators. In Chapter 6, as an example of the usefulness of the
methods introduced in Chapter 5 a model for the quantization of an electromagnetic field
in a variable media is analyzed. The concept of quantization of an electromagnetic field
in factorizable media is discussed via the Caldirola-Kanai Hamiltonian. A single mode
of radiation for this model is used to find time-dependent photon amplitudes in relation
to Fock states. A multi-parameter family of the squeezed states, photon statistics, and the
uncertainty relation, are explicitly given in terms of the Ermakov-type system.
representation theory of the Lorentz and Poincare groups, and a review of some basic rela- ´
tivistic wave equations that will play an important role in the work to follow. In Chapter 2,
a complex covariant form of the classical Maxwell’s equations in a moving medium or at
rest is introduced. In addition, a compact, Lorentz invariant, form of the energy-momentum
tensor is derived. In chapter 3, the concept of photon helicity is critically analyzed and its
connection with the Pauli-Lubanski vector from the viewpoint of the complex electromag- ´
netic field, E+ iH. To this end, a complex covariant form of Maxwell’s equations is used.
Chapter 4 analyzes basic relativistic wave equations for the classical fields, such as Dirac’s
equation, Weyl’s two-component equation for massless neutrinos and the Proca, Maxwell
and Fierz-Pauli equations, from the viewpoint of the Pauli-Lubanski vector and the Casimir ´
operators of the Poincare group. A connection between the spin of a particle/field and ´
consistency of the corresponding overdetermined system is emphasized in the massless
case. Chapter 5 focuses on the so-called generalized quantum harmonic oscillator, which
is a Schrodinger equation with a time-varying quadratic Hamiltonian operator. The time ¨
evolution of exact wave functions of the generalized harmonic oscillators is determined
in terms of the solutions of certain Ermakov and Riccati-type systems. In addition, it is
shown that the classical Arnold transform is naturally connected with Ehrenfest’s theorem
for generalized harmonic oscillators. In Chapter 6, as an example of the usefulness of the
methods introduced in Chapter 5 a model for the quantization of an electromagnetic field
in a variable media is analyzed. The concept of quantization of an electromagnetic field
in factorizable media is discussed via the Caldirola-Kanai Hamiltonian. A single mode
of radiation for this model is used to find time-dependent photon amplitudes in relation
to Fock states. A multi-parameter family of the squeezed states, photon statistics, and the
uncertainty relation, are explicitly given in terms of the Ermakov-type system.
ContributorsLanfear, Nathan A (Author) / Suslov, Sergei (Thesis advisor) / Kotschwar, Brett (Thesis advisor) / Platte, Rodrigo (Committee member) / Matyushov, Dmitry (Committee member) / Kuiper, Hendrik (Committee member) / Gardner, Carl (Committee member) / Arizona State University (Publisher)
Created2016
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
This thesis attempts to explain Everettian quantum mechanics from the ground up, such that those with little to no experience in quantum physics can understand it. First, we introduce the history of quantum theory, and some concepts that make up the framework of quantum physics. Through these concepts, we reveal why interpretations are necessary to map the quantum world onto our classical world. We then introduce the Copenhagen interpretation, and how many-worlds differs from it. From there, we dive into the concepts of entanglement and decoherence, explaining how worlds branch in an Everettian universe, and how an Everettian universe can appear as our classical observed world. From there, we attempt to answer common questions about many-worlds and discuss whether there are philosophical ramifications to believing such a theory. Finally, we look at whether the many-worlds interpretation can be proven, and why one might choose to believe it.
ContributorsSecrest, Micah (Author) / Foy, Joseph (Thesis director) / Hines, Taylor (Committee member) / Computer Science and Engineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2021-05
DescriptionAs an aspiring math teacher, I have created visual representation of my philosophy of education in the form of an embroidered skirt, bringing together my love of sewing and mathematics.
ContributorsOng, Rachel (Author) / Nishimura, Joel (Thesis director) / Johnston, Carmen (Committee member) / Barrett, The Honors College (Contributor) / Division of Teacher Preparation (Contributor)
Created2023-05
Description
As an aspiring math teacher, I have created visual representation of my philosophy of education in the form of an embroidered skirt, bringing together my love of sewing and mathematics.
ContributorsOng, Rachel (Author) / Nishimura, Joel (Thesis director) / Johnston, Carmen (Committee member) / Barrett, The Honors College (Contributor) / Division of Teacher Preparation (Contributor)
Created2023-05
ContributorsOng, Rachel (Author) / Nishimura, Joel (Thesis director) / Johnston, Carmen (Committee member) / Barrett, The Honors College (Contributor) / Division of Teacher Preparation (Contributor)
Created2023-05
ContributorsOng, Rachel (Author) / Nishimura, Joel (Thesis director) / Johnston, Carmen (Committee member) / Barrett, The Honors College (Contributor) / Division of Teacher Preparation (Contributor)
Created2023-05
ContributorsOng, Rachel (Author) / Nishimura, Joel (Thesis director) / Johnston, Carmen (Committee member) / Barrett, The Honors College (Contributor) / Division of Teacher Preparation (Contributor)
Created2023-05
ContributorsOng, Rachel (Author) / Nishimura, Joel (Thesis director) / Johnston, Carmen (Committee member) / Barrett, The Honors College (Contributor) / Division of Teacher Preparation (Contributor)
Created2023-05