Science and Mathematics Education Commons^™

An Analysis Of Ohio's Advanced Quantitative Reasoning Course, Ethan A. Douglas

Williams Honors College, Honors Research Projects

Beginning in about 2018, The Ohio Department of Education and Workforce partnered with the Ohio Department of Higher Education and the Ohio Math Initiative to create a mathematics transition course to provide high school students with a class that could prepare them for a college entry-level mathematics course if they had not previously earned a remediation-free score. This course was titled “Mathematical Modeling and Reasoning” and has since been named, “Advanced Quantitative Reasoning” (AQR) and has become an Algebra II equivalent course where students can receive their final math credit to graduate. This study looked to compare students in Algebra …

From Textbook To Classroom: Gaps In Mathematical Representation And Translation In Nepali Education, Deepak Basyal

Mathematics and Statistics

Translating real-world problem contexts into mathematical symbols is a key skill in curricula worldwide. This study examines Nepali students’ abilities to translate words into symbols and how Nepali textbooks from earlier grades support the development of these skills. To investigate this phenomenon, a sequential explanatory study was conducted with a test for 10th graders and an analysis of Grades 6—9 textbooks. Results show that students struggle to convert real-world contexts into mathematical symbols, while textbooks provide limited opportunities for practice. In particular, students have difficulty translating symbols back into real-world situations, suggesting a link between textbook opportunities and achievement. These …

A Comparative Analysis Of Early Algebraic Thinking Activities From U.S. And Singapore Primary Textbooks, Christian Joel Hernandez

Theses and Dissertations

Many studies highlight the challenges students face when transitioning to algebra at the secondary level. Introducing algebraic concepts and fostering algebraic thinking at the primary level can help mitigate these difficulties. Prior to formal algebra instruction, early algebra can be cultivated as a mode of thinking known as algebraic thinking. Several international curricula, such as Singapore Math, incorporate early algebraic thinking into the early stages of schooling. Singapore Math, renowned for its high performance in international assessments, has been widely adopted by schools seeking to replicate its success.

This study compares two primary-level mathematics curricula—CCSSM-aligned textbooks and Singapore Math—specifically focusing …

Designing An Educational Robotics Curriculum To Teach Mathematical Concepts While Fostering A Growth Mindset: A Self-Study, Lauren Harter

Electronic Theses and Dissertations

This study explores the development and implementation of a five-day curriculum designed to enhance students' understanding of algebraic concepts through the integration of educational robotics and growth mindset principles. The study is structured around three research questions that investigate influences on decision-making in curriculum design, the alignment of teaching intents with practices, and the impact of self-study on integrating algebra, robotics, and growth mindset principles. Findings reveal themes focused on the importance of research and collaboration, using the Understanding by Design (UbD) framework, intentional curriculum creation, starting somewhere, personal growth and self-reflection, and experiencing and embodying constructivism in action. The …

Building Painted Cubes Task: Serena’S Case, Elizabeth Suazo-Flores, Lisa Roetker

Teaching, Leadership & Professional Practice Faculty Publications

The Building Painted Cubes Task is a groupworthy algebraic task. Students build cubes using linking unit cubes, search for algebraic patterns, and report findings on posters. This task can create spaces for students to see themselves as doers of mathematics.

Mathematical Connections In Preservice Secondary Mathematics Teachers’ Solution Strategies To Algebra Problems, Vesife Hatisaru, Kaye Stacey, Jon R. Star

Research outputs 2022 to 2026

This study investigated the mathematical connections found in the solutions provided by 22 preservice secondary mathematics teachers to a set of algebra problems. Interest in, and research on, mathematical connections has gained prominence of the past decade. Here, we use the Extended Theory of Mathematical Connections or ETMC to explore the types of connections that this framework does and does not capture in the preservice teachers’ solutions. The ETMC surfaced four types of mathematical connections across four problems: ‘different representations’, ‘procedural’, ‘part-whole’ and ‘meaning’. The other types of connections defined in ETMC such as ‘reversibility’ or ‘feature’ were not found …

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

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.

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.

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

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 …

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

Complex Variables

No abstract provided.

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

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

International Programs

No abstract provided.

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 …

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 …

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 …

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

Pre-calculus and Trigonometry

No abstract provided.

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

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

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 …

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

Department of Teaching, Learning, and Teacher Education: Theses and Other 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

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 …

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

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

Department of Mathematics Faculty 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

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 …

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 …