Education Commons^™

Creating Mandalas For World Peace While Incorporating Mathematics, Art, Literature, Writing, And Technology, Joseph M. Furner

Transformations

Across the USA there are more and more students whose parents are from around the world. It is important teachers can effectively teach mathematics to reach all students, particularly those with limited English proficiency, while establishing interdisciplinary and cultural connections and even working toward world peace. The purpose of this paper is to share how a class of students from an elementary school in South Florida with their teacher created mandalas to teach mathematics, art, writing, and even world peace to their students. Math teachers should strive to bridge the cultural gap among all students by incorporating innovative ideas as …

Area Activity, Admin Stem For Success

STEM for Success Showcase

Lesson plan to teach students about area including an activity plan, activity description, activity video, and additional activity materials

How To Guard An Art Gallery: A Simple Mathematical Problem, Natalie Petruzelli

The Review: A Journal of Undergraduate Student Research

The art gallery problem is a geometry question that seeks to find the minimum number of guards necessary to guard an art gallery based on the qualities of the museum’s shape, specifically the number of walls. Solved by Václav Chvátal in 1975, the resulting Art Gallery Theorem dictates that ⌊n/3⌋ guards are always sufficient and sometimes necessary to guard an art gallery with n walls. This theorem, along with the argument that proves it, are accessible and interesting results even to one with little to no mathematical knowledge, introducing readers to common concepts in both geometry and graph …

Making Upper-Level Math Accessible To A Younger Audience, Allyson Roller

WWU Honors College Senior Projects

Symmetry is all around us. It appears on fabrics and on the buildings that surround us. Believe it or not, there is actually quite a bit of math that goes into generating these patterns, which are known as the seven frieze patterns. In my work, I explain how each unique pattern is generated using different types of symmetries. I also created a PDF of a children’s book about frieze patterns to ensure that people of all ages have the opportunity to learn about seemingly complex patterns.

Preservice Elementary Teachers’ Beliefs About The Role Of Definition In The Learning Of Mathematics, Dana C. Cox, Suzanne Harper, Jane M. Keiser

Journal of Educational Research and Innovation

Answering a call to emphasize the act of defining over the learning of definitions, we have shifted the content of a geometry course for preservice elementary teachers (PSETs) away from comparing and applying pre-written classification structures to classroom episodes centered on authoring definitions for special quadrilaterals. PSETs complete activities using geometry software, and collaboratively create definitions for specific quadrilaterals. In order to fully understand the potential of this curricular shift, we asked preservice elementary mathematics teachers’ to share their perceptions of the process of writing mathematical definitions. Data from participant reflections were analyzed for themes related to mathematical definition and …

Young Adolescents’ Opportunity To Develop Concept Images Of Polygons In Middle School Mathematics Textbooks, Megan N. Cannon

USF Tampa Graduate Theses and Dissertations

Young adolescents build notions of figures through experiences. When young adolescentsbegin middle school mathematics, they already have prior assumptions and conceptualizations about shapes (Herbst, Fujita, Halverscheid, & Weiss, 2017). Over years of experiences, interactions, and exposures with a particular concept, these students develop concept images consisting of all the visual information, pictures, mental images, or properties associated with the particular mathematical concept (Vinner, 1983). Seminal works in the field of mathematics education research found that without an opportunity to engage with varied representations, young adolescent students may not develop robust concept images (Aspinwall, Shaw & Presmeg, 1997; Hasegawa, 1997; Mesa, …

Possible Adventures In Impossible Figures, Knarik Tunyan

The STEAM Journal

This interdisciplinary article aims to engage student into stepping outside traditional disciplinary boundaries by combining the arts, math, and programming. First, we explore a geometric pattern in the Penrose triangle. Then using the fundamental concepts of geometry, we find geometric relationship, calculate the vertices coordinates, and digitally reconstruct the Penrose triangle using coding. Students are encouraged to further explore this topic by finding another pattern, creating modifications of the Penrose triangle by changing measurements, or considering other impossible figures.

Strategy To Estimate Size, Hui Fang Huang Su, Dylan Mandolini, Bhagi Phuel, Shawlyn Fleming, Chloe Johnson

Transformations

Have you ever wondered exactly how much land and space are included in a national park? In this paper, we will explore the vastness of a fictitious Park and calculate its total area.

We will:

1. Create a fictitious Park, determine a scale that can be used to perform

calculations using a practical unit of measurement.

2. Develop a strategy that students can use to find the area of the Park.

3. Demonstrate the use of the strategy by solving for the area of the fictitious park.

Creative Geometry Games, Hui Fang Huang Su, Dylan Mandolini, Bhagi Phuel

Transformations

The geometry game presented in this article was inspired by Bright and Harvey's (1988) Learning and fun with geometry games. In their article, Bright and Harvey (1988) propose three interactive games: Polyhedron Rummy, Polygon Rummy and That are Stretching it. Polygon Rummy is a game pertaining to plane geometry where the instructional objective is to construct a figure using lines and angles, whereas the goal of polyhedron rummy is to construct a solid using faces and angles. Although Bright and Harvey focused on constructing shapes, they also suggested presenting pre-constructed shapes to students, allowing them to classify and identify them …

The Effect Of Augmented Reality On Learning In The Mathematics Classroom, Justin Thomas Maffei

Doctoral Dissertations and Projects

This study examined the impact of two treatments, augmented reality or concrete materials, on the Geometry knowledge of high school students. Participating classes were chosen from two secondary schools between two rural Virginia school districts. The sampling method selected for the study employed a convenience sample. There were 87 total participants in the study. The importance of this study emerged from a lack of research relating the use of augmented reality in the classroom to its effect on student learning. The purpose of this quantitative pretest-posttest, non-equivalent control group quasi-experimental study was to evaluate the difference in achievement scores, as …

Applying Quantitative Reasoning To Clarify Arc Measurements, David Glassmeyer, Daniel Barton

Georgia Educational Researcher

The importance of reasoning quantitatively is reflected in both mathematics education research and mathematical standards for K-12 students. In this article, we detail how a quantitative reasoning framework can be used to help differentiate two quantities we have found students often struggle with: arc length and the measure of a central angle. We argue that taking the time to define all four components of a quantity can support students’ understanding of theorems involving these quantities.

Exploring Zimbabwean Mathematics Teachers’ Integration Of Ethnomathematics Approaches Into The Teaching And Learning Of Geometry., Gladys Sunzuma, Aneshkumar Maharaj Prof

Australian Journal of Teacher Education

This article reports on a study that explored how a group of in-service mathematics teachers integrated ethnomathematics approaches into the teaching and learning of geometry. The study used a convergent parallel mixed-methods design, which combined both quantitative and qualitative methods, to provide a deeper understanding of how the participants integrate ethnomathematics approaches into the teaching and learning of geometry. The data for the study were gathered from 40 in-service mathematics teachers through the use of questionnaires and focus group discussions. Results showed that the in-service teachers integrate ethnomathematics approaches into the teaching and learning of geometry as learning …

Pengembangan Perangkat Pembelajaran Geometri Dengan Mengadaptasi Model Core Untuk Meningkatkan Efikasi Diri, Danis Agung Nugroho

Jurnal Riset Pendidikan Matematika

Penelitian ini bertujuan untuk menghasilkan perangkat pembelajaran yang diadaptasi dari model CORE (Connecting, Organizing, Reflecting, dan Extending) yang valid, praktis, dan efektif untuk meningkatkan efikasi diri siswa. Pengembangan perangkat menggunakan model pengembangan Borg dan Gall yang dimodifikasi oleh peneliti dengan tahapan: (1) studi pendahuluan, (2) perencanaan, (3) pengembangan rancangan produk awal, (4) uji coba terbatas, (5) revisi tahap I, (6) uji coba operasional, (7) revisi tahap II, dan (8) desiminasi produk akhir. Uji coba produk dilakukan di SMA Negeri 1 Prambanan Sleman dengan melibatkan 52 siswa dan seorang guru matematika. Instrumen yang digunakan terdiri atas …

Pengembangan Alat Pembelajaran Geoklik Untuk Pembelajaran Geometri, Aan Hendroanto, Harina Fitriyani

PYTHAGORAS : Jurnal Matematika dan Pendidikan Matematika

Objek matematika sebagian besar bersifat abstrak dan sulit untuk dibayangkan sehingga banyak siswa yang kesulitan untuk memahaminya. Salah satu solusi untuk membantu siswa dalam hal ini yaitu dengan menggunakan alat-alat Euclid seperti penggaris, jangka, dan busur untuk menggambar objek geometri di papan tulis atau whiteboard. Namun, penggunaan alat-alat Euclid untuk menggambar terkadang tidak maksimal dikarenakan kurang efisien dan merepotkan. Akibatnya, banyak guru yang kemudian justru menggambar objek geometri tanpa menggunakan alat-alat ini sehingga gambar yang seharusnya membantu siswa memahami materi, justru malah membuat mereka semakin tidak paham. Penelitian ini bertujuan untuk menghasilkan alat yang dinamakan GeoKlik untuk mendukung kegiatan …

The Van Hiele Analysis Of Curricular Materials: A Comparative Study, Vinay Kumar Kalyankar

Graduate Theses and Dissertations

The goal of this study is to investigate K-8 geometry curriculum standards and textbooks for their effectiveness in preparing students for high school geometry. The basis for the study is van Hiele theory pioneered by the Dutch educators and researchers of geometric understanding in adolescents, Dina van Hiele Geldof and Pierre van Hiele. Another driving force for this dissertation is research into mathematics textbooks and curriculum standards of school mathematics as seen in CCSSM and state specific standards documents, both of which influence the mathematics students have the opportunity to learn.

The K-8 geometry curriculum standards and textbook instructional segments …

How To Calculate Pi: Buffon's Needle (Non-Calculus Version), Dominic Klyve

Pre-calculus and Trigonometry

No abstract provided.

Sliding Into An Equitable Lesson, Kelley E. Buchheister 6872059, Christa Jackson, Cynthia E. Taylor

Department of Child, Youth, and Family Studies: Faculty Publications

A kindergarten teacher uses Gutierrez's four dimensions of equity to design and facilitate geometry instruction.

Equitable instruction is reflected in how students are positioned in the classroom and how their identities evolve through purposeful interactions that value and recognize the intellectual capacity of each student (Gutiérrez 2013; Lemons-Smith 2008). These integral interactions occur when teachers and students exchange problem-solving strategies, discuss relations among various mathematical representations, and listen to the viewpoints of others (NCTM 2000; 2014).

Students’ Opportunity To Learn Surface Area And Volume In Middle Grades Mathematics Textbooks, Sofia Hatziminadakis

USF Tampa Graduate Theses and Dissertations

I conducted a content analysis to examine the treatment of the surface area and volume concepts within four published middle-grades mathematics textbook series. In particular, I examined the treatment of the surface area and volume concepts in terms of the location of surface area and volume lessons in the textbook and the number of pages and lessons devoted to these concepts. I also investigated the sequence of the instructional blocks of surface area and volume lessons. In addition, I evaluated the tasks included in these lessons in regards to the performance expectations of students, the types of visual representations of …

Tinkering With Logo In An Elementary Mathematics Methods Course, Keri Duncan Valentine

Interdisciplinary Journal of Problem-Based Learning

With an increased push to integrate coding and computational literacy in K–12 learning environments, teacher educators will need to consider ways they might support preservice teachers (PSTs). This paper details a tinkering approach used to engage PSTs in thinking computationally as they worked with geometric concepts they will be expected to teach in K–5. Experiences programming in Logo to construct authentic artifacts in the form of two-dimensional geometric graphics not only supported PSTs’ understanding of core geometric and spatial concepts, but also helped them to make connections between mathematics and computational literacy. Artifacts and discourse are discussed as they relate …

Generating Pythagorean Triples: A Gnomonic Exploration, Janet Heine Barnett

Number Theory

No abstract provided.

Shape Shifting: The Impact Of Student And Teacher Choice On Differentiation In A Detracked, Standards-Based High School Geometry Classroom, Kristin M. Weller

Journal of Practitioner Research

To gain insight into how using differentiated instruction and standards-based assessment supported my students’ learning in a detracked, honors geometry classroom, I employed the methodology of practitioner research to examine and reflect on the development and implementation of a standards-based differentiated unit based on the Pythagorean Theorem. Data collected and analyzed included field notes during classroom activities, student artifacts from classroom assessments and activities, verbatim transcripts from audiotaped student interviews, and practitioner researcher journal entries chronicling significant events and actions taken during the development and implementation of the unit. As I reviewed, analyzed, and reflected upon the data, my findings …

Generating Pythagorean Triples: The Methods Of Pythagoras And Of Plato Via Gnomons, Janet Heine Barnett

Number Theory

No abstract provided.

Prevalence Of Typical Images In High School Geometry Textbooks, Megan N. Cannon

USF Tampa Graduate Theses and Dissertations

Visualization in mathematics can be discussed in many ways; it is a broad term that references physical visualization objects as well as the process in which we picture images and manipulate them in our minds. Research suggests that visualization can be a powerful tool in mathematics for intuitive understanding, providing and/or supporting proof and reasoning, and assisting in comprehension. The literature also reveals some difficulties related to the use of visualization, particularly how illustrations can mislead students if they are not comfortable seeing concepts represented in varied ways. However, despite the extensive research on the benefits and challenges of visualization …

Polygons, Pillars And Pavilions: Discovering Connections Between Geometry And Architecture, Sean Patrick Madden

Journal of Catholic Education

Crowning the second semester of geometry, taught within a Catholic middle school, the author's students explored connections between the geometry of regular polygons and architecture of local buildings. They went on to explore how these principles apply famous buildings around the world such as the monuments of Washington, D.C. and the elliptical piazza of Saint Peter's Basilica at Vatican City within Rome, Italy.

Using Mobile Learning To Supports Students' Understanding In Geometry: A Design-Based Research Study, Helen Crompton

Teaching & Learning Faculty Publications

The use of mobile learning offers new affordances to teaching and learning. In this study, students from two fourth grade classes used iPads in dyads and groups to learn about angle. Using a design-based research methodology, which included observations, video, researcher journals, and artefact collection, a local instruction theory was developed on how students can learn about angle concepts through mobile learning activities. The local instruction theory is comprised of two components: (a) a seven lesson curriculum for 4th grade students on developing an early understanding of angle utilizing a mobile learning approach, and (b) additions to the scholarly theories, …

Addressing The Stem Challenge Through Targeted Teaching : What’S The Evidence?, Dianne Siemon

2009 - 2019 ACER Research Conferences

Numerous public reports are pointing to the critical importance of STEM (science, technology, engineering and mathematics) to Australia’s future, but the number of students studying STEM subjects in senior years is declining, and many students in the primary and middle years of schooling do not have access to the ways of thinking and learning needed to succeed in school mathematics. Research over the past 10 years has established the critical role of multiplicative thinking in building student knowledge and confidence at this level of schooling, but there is a need for an expanded, evidence-based learning and teaching framework to support …

Mathematics Uncovered Through Action Science, William H. Robertson

William H. Robertson

The Exigency Of The Euclidean Parallel Postulate And The Pythagorean Theorem, Jerry Lodder

Geometry

No abstract provided.

Mathematics Anxiety In Society: A Real Phenomena And A Real Solution, Joseph M. Furner, Carol A. Marinas

Transformations

While math anxiety still remains a real issue affecting student performance and confidence, today it is even more critical with the greater emphasis on producing more students for careers in STEM fields. In an effort to understand ways to ease math anxiety and encourage adaptive achievement behaviors to deal with such anxiety, this paper will explore the topic and provide research-based practices in providing a solution to this existing problem in our schools. There are many studies that show using technology in the teaching of mathematics will help to alleviate math anxiety and encourage students to enjoy learning mathematics. GeoGebra, …

Assessing Awareness, Interest, And Knowledge Of Fractal Geometry Among Secondary Mathematics Teachers In The United States And China, Suanrong Chen

Dissertations

Fractal geometry has gained great attention from mathematicians and scientists in the past three decades (Fraboni, & Moller, 2008). As a new geometry language and subject, fractal geometry has significant value in teaching and learning secondary mathematics. The present study focused on investigating the current state of mathematics teachers’ awareness, interest, and knowledge of fractal geometry in the U.S. and China, as well as the factors that influence them.

The instrument of the study included a survey and a test designed by the researcher and validated by five experts. The results of the study indicated that secondary math teachers in …