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Tools to Teach 8th Grade Geometry: A 5-Day Lesson Kit

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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

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.

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2015-12

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Fractions, Mathematics, and Music: Developing Conceptual Understanding in Fourth Grade Students

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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

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.

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2016-05

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Addressing Childhood Trauma in the Classroom

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Over the past few years, the issue of childhood trauma in the United States has become significant. A growing number of children are experiencing abuse, neglect, or some other form of maltreatment each year. Considering the stressful home lives of

Over the past few years, the issue of childhood trauma in the United States has become significant. A growing number of children are experiencing abuse, neglect, or some other form of maltreatment each year. Considering the stressful home lives of maltreated children, the one sure sanctuary is school. However, this idea requires teachers to be actively involved in identifying and caring for the children who need it most. Traumatic childhood experiences leave lasting scars on its victims, so it is helpful if teachers learn how to identify and support children who have lived through them. It is unfortunate that teachers will most likely encounter children throughout their career who have experienced horrendous things, but it is a reality. With this being said, teachers need to develop an understanding of what traumatized children live with, and learn how to address these issues with skilled sensitivity. Schools are not just a place where children learn how to read and write; they build the foundation for a successful life. This project was designed to provide teachers with a necessary resource for helping children who have suffered traumatic experiences. The methodology of this project began with interviews with organizations specializing in working with traumatized children such as Arizonans for Children, Free Arts for Abused Children, The Sojourner Center, and UMOM. The next step was a review of the current literature on the subject of childhood trauma. The findings have all been compiled into one, convenient document for teacher use and distribution. Upon completion of this document, an interactive video presentation will be made available through an online education website, so that distribution will be made simpler. Hopefully, teachers will share the information with people in their networks and create a chain reaction. The goal is to make it available to as many teachers as possible, so that more children will receive the support they need.

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2016-05

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College Students’ and Inservice Teachers’ Evoked Concept Images and Ways of Understanding Congruence

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Eleven years after being put into practice, the Common Core State Standards for Mathematics still take a back seat as traditional approaches drive many secondary geometry classrooms, specifically in regard to congruence. This thesis explores how university students reason about

Eleven years after being put into practice, the Common Core State Standards for Mathematics still take a back seat as traditional approaches drive many secondary geometry classrooms, specifically in regard to congruence. This thesis explores how university students reason about congruence based on their high school learning experience, as well as how in-service geometry teachers reason about and teach congruence. During the Summer of 2020, two distinct surveys were distributed to 33 undergraduate students at Arizona State University and two in-service geometry teachers in Arizona to characterize the ways they understand congruence and reflect on their experiences in secondary geometry classrooms. The results of the survey indicate that students who understood congruence either in terms of corresponding measurements or transformations were successful in identifying congruent shapes, while only students who understood congruence in terms of transformations were successful in constructing congruent shapes. Transformational reasoning was both the most productive and the least prominent way of understanding congruence among students. Their responses to activities and reflections on their experiences also suggested that deductive reasoning is not practiced or prioritized in many secondary geometry classrooms. Teacher understandings of congruence varied, and reflections suggested that development of materials and training that are aligned with the goals of CCSSM for both pre-service and in-service teachers would help teachers create an environment conducive to a transformational understanding of congruence and that promotes deductive reasoning.

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2020-12