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Algebra

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Full-Text Articles in Education

Creating Mandalas For World Peace While Incorporating Mathematics, Art, Literature, Writing, And Technology, Joseph M. Furner Nov 2023

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 …


The Importance Of Implementing Literacy Strategies In A Mathematics Classroom, Lauren Tecca, Joanna Weaver, John Chen Apr 2023

The Importance Of Implementing Literacy Strategies In A Mathematics Classroom, Lauren Tecca, Joanna Weaver, John Chen

Honors Projects

The purpose of this ACTION research study is to explore the influence of literacy on mathematical proficiency levels. The correlation will use the data to formulate some strategies for the classroom in order to increase confidence in both subject areas.


Mathematics Mobility In The Middle Grades: Tracking The Odds Of Completing Calculus, Kristian Edosomwan, Jamaal Young, Jemimah Young, Alana Tholen May 2022

Mathematics Mobility In The Middle Grades: Tracking The Odds Of Completing Calculus, Kristian Edosomwan, Jamaal Young, Jemimah Young, Alana Tholen

Middle Grades Review

High school calculus has become indispensable for students seeking a college degree in a STEM field. However, in the present study, we argue that the mathematics opportunities that students seize (when afforded) in middle grades are the key to earning calculus credit in high school. To take calculus in high school, students usually need to take advanced mathematics in middle school to take the prerequisite courses. We analyzed the probability of earning credit in calculus based on a sample of (n =17,765) students and their eighth-grade mathematics courses. Using descriptive statistics and odds ratio effect sizes we found that …


The Advantages Of Algebra For Learning Proof, Samuel Otten, Mitchelle M. Wambua May 2022

The Advantages Of Algebra For Learning Proof, Samuel Otten, Mitchelle M. Wambua

Colorado Mathematics Teacher

Calls to expand proof beyond geometry are usually based on the general benefits of proving for students, but this essay argues that proof should be extended to algebra because the representational systems in algebra are well suited for understanding the generality and deductive flow of proofs.


Gauss And The First “Rigorous” Proof Of The Fundamental Theorem Of Algebra, Sarah Hagen, Alan Kappler Jan 2022

Gauss And The First “Rigorous” Proof Of The Fundamental Theorem Of Algebra, Sarah Hagen, Alan Kappler

Complex Variables

No abstract provided.


The Luge & Linear Algebra, Kelly Remijan Jan 2022

The Luge & Linear Algebra, Kelly Remijan

Teacher Resources

No abstract provided.


Exploring Algebraic Thinking: In-Service Teacher Experiences, Outcomes, And Perceptions From An Algebra For All Capstone Unit Plan Project, Alexander J. Lord, Tallin Lamonaca Jan 2022

Exploring Algebraic Thinking: In-Service Teacher Experiences, Outcomes, And Perceptions From An Algebra For All Capstone Unit Plan Project, Alexander J. Lord, Tallin Lamonaca

Publications and Research

Taking algebra is often noted as a key component for student preparation for college and career success. However, this course often serves as a barrier for secondary students to overcome due to their lack of preparation for such abstract contexts and due to a lack of meaningful professional experiences available to assist teachers develop those concepts. Initiatives such as Algebra for All were started to help educators at all grade levels develop methods to expose their students to algebraic thinking. In New York City, a five-course Algebra for All sequence was created for in-service public school educators at a local …


How To Develop A Structural Conception Of Algebra In School Students, Vesife Hatisaru Jan 2022

How To Develop A Structural Conception Of Algebra In School Students, Vesife Hatisaru

Research outputs 2022 to 2026

Algebra plays a pivotal role in school students’ mathematics learning. Students, however, have serious difficulties especially with ‘seeing’ the algebraic structures and expressing generality with algebraic symbols. These skills are not gained accidently; developing them in students takes continuous, sustained, and focused effort from both students themselves and teachers. As teachers of mathematics, what kind of classroom experience could we provide our students to prepare them for using algebra successfully? How could we assist them to develop structural conceptions of algebra? In this paper, I describe an approach based on the Mathematical Habits of Mind framework (Cuoco et al., 1996) …


Connecting Algebra To Geometry: A Transition Summer Camp For At-Risk Students, Mary E. Pilgrim, John Bloemker Jan 2021

Connecting Algebra To Geometry: A Transition Summer Camp For At-Risk Students, Mary E. Pilgrim, John Bloemker

Colorado Mathematics Teacher

The authors share how they designed curriculum for a summer algebra camp, for eighth graders in a district serving high proportions of Latino students. They discuss the impact the algebra camp had on students’ confidence in mathematics and mathematical ability.


Patterns, An Approach To Learning Algebra And Developing Mathematical Thinking In Primary School In Honduras, Johana Elizabeth Thomas Zapata, Alejandra Cáceres Jul 2020

Patterns, An Approach To Learning Algebra And Developing Mathematical Thinking In Primary School In Honduras, Johana Elizabeth Thomas Zapata, Alejandra Cáceres

English Language Institute

No abstract provided.


An Exploration Of Scaffolding Strategies In A Remedial High School Mathematics Course, Pauline Ofure Aikhuele Jan 2020

An Exploration Of Scaffolding Strategies In A Remedial High School Mathematics Course, Pauline Ofure Aikhuele

Walden Dissertations and Doctoral Studies

In a southeastern state school district, the educators understood little about the scaffolding practices of ninth-grade teachers of Foundations of Algebra (FOA), a remedial course. FOA is a mathematics course designed for students who need substantial help to master the required standards. An increasing number of students in 2 high schools failed FOA; hence, they were not prepared for Algebra 1. The purpose of this qualitative exploratory case study was to explore the scaffolding strategies used by FOA teachers. Bruner's constructivist theory and Vygotsky's zone of proximal development (ZPD) theory were used to guide this study. The research questions addressed …


Effects Of Differential Instructional Time In Algebra On Standardized Assessment And Semester Grade Outcomes, Michael S. Wojtowicz Jan 2020

Effects Of Differential Instructional Time In Algebra On Standardized Assessment And Semester Grade Outcomes, Michael S. Wojtowicz

Graduate Research Theses & Dissertations

Building off of other studies that examined the effectiveness of double-dose algebra programs such as Nomi and Allensworth (2009), this dissertation compared the performance outcomes of students enrolled in one of two alternatives to traditional high school algebra, a double-dose and a single-dose algebra program. This work utilized multiple linear regression to assess the degree of association between student race/ethnicity and selected demographic characteristics, including gender, free and reduced lunch status, and IEP status, on standardized assessment and end of semester mathematics course grade outcomes, while controlling for initial mathematics placement test results. This project assessed these outcomes for students …


Preparing New Jersey Community College Students For The Mathematics Placement Tests, Charles Edward Haas Jan 2020

Preparing New Jersey Community College Students For The Mathematics Placement Tests, Charles Edward Haas

Walden Dissertations and Doctoral Studies

Although most new college students had to demonstrate algebraic and basic mathematics mastery to earn a high school diploma or the equivalent, the majority of incoming New Jersey community college students are not showing this knowledge on the mathematics placement tests, thus placing into developmental courses, which must be successfully completed before students can attempt any college-level mathematics courses. Guided by Knowles’ theory of andragogy and developmental mathematics as a core concept, the purpose of this study was to determine ways to help incoming New Jersey community college students prepare for the ACCUPLACER mathematics tests. The research questions addressed testing …


Pengembangan Perangkat Pembelajaran Menggunakan Problem Solving Dalam Problem Posing Berbasis Pendekatan Saintifik, Ahmad Lutfi Dec 2019

Pengembangan Perangkat Pembelajaran Menggunakan Problem Solving Dalam Problem Posing Berbasis Pendekatan Saintifik, Ahmad Lutfi

Jurnal Riset Pendidikan Matematika

Penelitian ini bertujuan untuk menghasilkan produk berupa perangkat pembel-ajaran aljabar menggunakan problem solving dalam problem posing berbasis pendekatan saintifik yang valid, praktis dan efektif ditinjau dari keyakinan terhadap pelajaran matematika (KTM) dan kemampuan berpikir kreatif (KBK) siswa SMA. Penelitian pengembangan ini menggunakan model Plomp. Hasil penelitian ini adalah perangkat pembelajaran aljabar menggunakan problem solving dalam problem posing berbasis pendekatan saintifik yang berorientasi pada keyakinan terhadap pelajaran matematika dan kemampuan berpikir kreatif siswa SMA berupa RPP dan LKS. Kualitas perangkat pembelajaran yang dikembangkan ditinjau dari aspek kevalidan, aspek kepraktisan dan aspek keefektifan. Hasil penelitian menunjukkan bahwa RPP dan LKS valid dan …


Completing The Square: From The Roots Of Algebra, Danny Otero Oct 2019

Completing The Square: From The Roots Of Algebra, Danny Otero

Pre-calculus and Trigonometry

No abstract provided.


Solving Equations And Completing The Square: From The Roots Of Algebra, Danny Otero Jul 2019

Solving Equations And Completing The Square: From The Roots Of Algebra, Danny Otero

Pre-calculus and Trigonometry

No abstract provided.


Kesalahan Siswa Dalam Menyelesaikan Soal Olimpiade Smp Konten Aljabar, Yoga Baskara Setiawan, Hapizah Hapizah, Cecil Hiltrimartin Dec 2018

Kesalahan Siswa Dalam Menyelesaikan Soal Olimpiade Smp Konten Aljabar, Yoga Baskara Setiawan, Hapizah Hapizah, Cecil Hiltrimartin

Jurnal Riset Pendidikan Matematika

Penelitian ini merupakan penelitian deskriptif kualitatif yang bertujuan untuk mengetahui dan mendeskripsikan kesalahan siswa dalam menyelesaikan soal olimpiade SMP konten aljabar. Jenis penelitian yang digunakan adalah studi kasus. Subjek penelitian adalah perwakilan siswa kelas IX SMP Negeri 1 Palembang dengan jumlah siswa 22 orang. Teknik pengumpulan data pada penelitian adalah tes tertulis dan wawancara. Analisis data tes dan wawancara mengikuti prosedur Newman Error Analysis. Hasil penelitian menunjukkan bahwa kesalahan-kesalahan yang dilakukan siswa dalam menyelesaikan soal olimpiade SMP konten aljabar terdiri dari kesalahan dalam memahami soal, kesalahan dalam transformasi meliputi penggunaan rumus atau prosedur tidak relevan dan tidak mengetahui prosedur …


Exploring The Knowledge Of Algebra For Teaching., Jonathan David Watkins Dec 2018

Exploring The Knowledge Of Algebra For Teaching., Jonathan David Watkins

Electronic Theses and Dissertations

For the past few decades, researchers in mathematics education have been exploring the concept of pedagogical content knowledge (PCK)—or knowledge related to teaching content—and applying it to various areas of mathematics, such as algebra. Research related to teacher knowledge of algebra is critical because researchers (e.g., Hill, Rowan, & Ball, 2005) have found correlations between some types of teacher knowledge and student achievement in mathematics; students from around the world are outperforming U.S. students on international assessments of mathematics, including algebra (Organization for Economic Cooperation and Development, 2014, 2016); and algebra plays an integral role in the K-12 mathematics curriculum …


Relationship Of Supplemental Instruction And Attitude Of Students Enrolled In College Algebra, Kele Anne Mckaig Jul 2018

Relationship Of Supplemental Instruction And Attitude Of Students Enrolled In College Algebra, Kele Anne Mckaig

OTS Master's Level Projects & Papers

The problem of this study was to determine the relationship of supplemental instruction on the attitudes of college algebra students at a Southeastern university. The population for this study consisted of college algebra students enrolled in M102 and M103 courses in the Summer 2018 semester. While M102 and M103 cover the same material, M103 requires mandatory tutoring in addition to the classroom instruction. A survey of these students provided data on their attitudes toward mathematics at the beginning and end of their college algebra course. The first research question of this study asked to what extent attitudes differ, if at …


Reflections On Inquiry-Based Learning In A First-Year Algebra Classroom: Implications For Practitioners, Gregory P. Sand Jul 2018

Reflections On Inquiry-Based Learning In A First-Year Algebra Classroom: Implications For Practitioners, Gregory P. Sand

Department of Teaching, Learning, and Teacher Education: Dissertations, Theses, and Student Research

This self-study examines the learning by the teacher and students in a first-year Algebra class in a medium sized Midwestern city. The author, a secondary mathematics teacher, overviews two problems of practice and outlines methodology used to study these problems within the standard curriculum of first-year Algebra taught using inquiry-based methodology. Three units of study, Inequalities, Exponents, and Parabolas are analyzed to identify the learning of students and the mathematical and pedagogical learning of the teacher. Emergent mathematical and pedagogical themes from the analysis chapters are discussed with implications for practice.

Advisor: Stephen A. Swidler


Teacher Graphing Practices For Linear Functions In A Covariation-Based College Algebra Classroom, Konda Jo Luckau Jul 2018

Teacher Graphing Practices For Linear Functions In A Covariation-Based College Algebra Classroom, Konda Jo Luckau

Theses and Dissertations

Graphing is a fundamental topic in algebra that is notoriously difficult for students. Much of the past research has focused on conceptions and misconceptions. This study extends past research by looking at the mathematical practices of a practitioner, specifically one instructor of a function-based covariation-focused algebra class in the linear functions unit. Considering practices in addition to conception adds dramatically to our understanding of mathematical activity because it leads to explicit descriptions of normative purposes that are connected to particular situations or problems and also specifies how tools and symbols are coordinated to achieve these purposes. The results of this …


A Program Evaluation Of Double-Period Algebra, Jason Major Dec 2017

A Program Evaluation Of Double-Period Algebra, Jason Major

Dissertations

Students in ninth grade traditionally take algebra courses, but many students come in lacking foundational skills in mathematics. High schools have tried to solve this problem by introducing double-period algebra courses with sporadic results. During this program evaluation, I interviewed an administrator and a teacher from two different high schools about the methods they used to begin and evaluate the program; I found that student-teacher relationships were the most important factor in the effectiveness of the program. Using quantitative data was a good starting point to determine the students who would benefit from the program and who would be successful, …


Connecting Advanced And Secondary Mathematics, Eileen Murray, Erin Baldinger, Nicholas Wasserman, Shawn Broderick, Diana White Aug 2017

Connecting Advanced And Secondary Mathematics, Eileen Murray, Erin Baldinger, Nicholas Wasserman, Shawn Broderick, Diana White

Department of Mathematics Facuty Scholarship and Creative Works

There is an ongoing debate among scholars in understanding what mathematical knowledge secondary teachers should have in order to provide effective instruction. We explore connections between advanced and secondary mathematics as an entry point into this debate. In many cases, advanced mathematics is considered relevant for secondary teachers simply because the content is inherently related. In this paper, we instead argue that there are connections between advanced mathematics and secondary mathematics that directly influence teaching. These are not discussions of the mathematical connections, per se, but rather discussions of specific ways in which knowing mathematical connections might influence secondary teachers’ …


A Quantitative Reasoning Approach To Algebra Using Inquiry-Based Learning, Victor I. Piercey Jul 2017

A Quantitative Reasoning Approach To Algebra Using Inquiry-Based Learning, Victor I. Piercey

Numeracy

In this paper, I share a hybrid quantitative reasoning/algebra two-course sequence that challenges the common assumption that quantitative literacy and reasoning are less rigorous mathematics alternatives to algebra and illustrates that a quantitative reasoning framework can be used to teach traditional algebra. The presentation is made in two parts. In the first part, which is somewhat philosophical and theoretical, I explain my personal perspective of what I mean by “algebra” and “doing algebra.” I contend that algebra is a form of communication whose value is precision, which allows us to perform algebraic manipulations in the form of simplification and solving …


An Investigation Of Palindromes And Their Place In Mathematics, Ryan Andrew Nivens May 2017

An Investigation Of Palindromes And Their Place In Mathematics, Ryan Andrew Nivens

Ryan Andrew Nivens

What do the Honda Civic, the Mazda 626, and the Boeing 747 have in common? What about Weird Al's song Bob, the first name of Miley Cyrus' alter ego, and the 70s sensation Abba? What do all these things have in common? They all contain palindromes. While some people recognise a palindrome when they see one, fewer realise that a palindrome is a special case of a pattern and that these patterns are all around. Palindromes frequently occur in names, both of vehicles and people, and in music.


The Impact Of An Elementary Algebra Course On Student Success In A College-Level Liberal Arts Math Course And Persistence In College, Lori Ann Austin Mar 2017

The Impact Of An Elementary Algebra Course On Student Success In A College-Level Liberal Arts Math Course And Persistence In College, Lori Ann Austin

Theses and Dissertations

Many students enter community college underprepared for college-level math and are placed into developmental elementary algebra without consideration if the algebra will provide a foundation for their needed college-level math course. Large percentages of those students are unable to succeed in the developmental course and, therefore, are unable to graduate (Bahr, 2008; Bailey, Jeong, & Cho, 2010). This quasi-experimental design focused on students who are not in math-intensive majors, needing only a general liberal arts math course. The purpose was to determine the impact of the elementary algebra course on success in college-level math and persistence in college. Student performance …


Developing Conceptual Understanding And Procedural Fluency In Algebra For High School Students With Intellectual Disability, Andrew J. Wojcik Jan 2017

Developing Conceptual Understanding And Procedural Fluency In Algebra For High School Students With Intellectual Disability, Andrew J. Wojcik

Theses and Dissertations

Teaching students with Intellectual Disability (ID) is a relatively new endeavor. Beginning in 2001 with the passage of the No Child Left Behind Act, the general education curriculum integrated algebra across the K-12 curriculum (Kendall, 2011; National Governors Association Center for Best Practices & Council of Chief State School Officers, 2010), and expansion of the curriculum included five intertwined skills (productive disposition, procedural fluency, strategic competence, adaptive reasoning, and conceptual understanding) (Kilpatrick, Swafford, & Findell, 2001). Researchers are just beginning to explore the potential of students with ID with algebra (Browder, Spooner, Ahlgrim-Delzell, Harris & Wakeman, 2008; Creech-Galloway, Collins, Knight, …


A Matter Of Time: The Relationship Of Class Length And Demographics On The South Carolina Algebra I End-Of-Course Test In South Carolina Middle Schools, Jennifer Addie Ramsey Dec 2016

A Matter Of Time: The Relationship Of Class Length And Demographics On The South Carolina Algebra I End-Of-Course Test In South Carolina Middle Schools, Jennifer Addie Ramsey

Education Dissertations and Projects

For middle school students taking Algebra 1 as a high school credit, having sufficient instructional time to understand and explore the course content is crucial. While the focus of the literature review helps lend understanding to the study, there has been limited information concerning assessment scores in middle school math classes and the length of class time. This study investigated the differences in the End-of-Course Examination Program (EOCEP) test scores of middle school students in Algebra 1 as influenced by schedules used in South Carolina public middle schools for each individual year in a 5-year span of the 2010-2015 academic …


Addressing The Stem Challenge Through Targeted Teaching : What’S The Evidence?, Dianne Siemon Aug 2016

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 …


Richard Dedekind And The Creation Of An Ideal: Early Developments In Ring Theory, Janet Heine Barnett Jul 2016

Richard Dedekind And The Creation Of An Ideal: Early Developments In Ring Theory, Janet Heine Barnett

Abstract Algebra

No abstract provided.