Mathematics Commons^™

Qualitative Analysis Of Corequisite Instruction In A Quantitative Reasoning Course, Zachary Beamer

Inquiry: The Journal of the Virginia Community Colleges

In corequisite models of instruction, marginally prepared students are placed directly into college-level coursework, taught with a paired support course. Initial research suggests that such models yield significant improvements in the number of students passing credit-level mathematics when compared to previous models of prerequisite remediation. The present study employs qualitative methods to investigate methods of instruction at one community colleges to understand how instructors identify and respond to student needs. It concludes with recommendations for practice and highlights advantages of small format corequisite classes taught by the same instructor.

Ready To Engage? Urban Middle School Teachers’ Responsiveness To Targeted Engagement Interventions On Their Virtual Instructional Practices: An Action Research Study, Svetlana Nikic

Dissertations

Teachers’ effectiveness is associated with their instructional practices and is ultimately linked to students’ learning outcomes. In order to impact teachers’ effectiveness, schools focus substantial effort and resources on professional development led by an assumption that teachers’ classroom practices can be improved through targeted interventions. Even if this premise is correct, little information is available about how much a teacher’s practice may change through interventions, or which aspects of instructional practice are more receptive to improving teacher effectiveness (Garret et al., 2019).

This study took place at an urban middle school and examined teachers’ responsiveness to targeted engagement intervention in …

Stitching Dedekind Cuts To Construct The Real Numbers, Michael P. Saclolo

Analysis

No abstract provided.

An Astronomer’S Journey Into Quantitative Reasoning, Jeffrey Bennett

Numeracy

The University of Colorado Boulder campus introduced what may have been the world’s first quantitative reasoning (QR) requirement in 1984 and started offering a QR course in 1988. Although I am an astronomer by training, I had the privilege of creating and teaching that course, which led to my co-authorship of the first textbook directed specifically at QR courses. In this “Roots and Seeds” piece, I will discuss how this course and textbook came to be, how I as an astronomer ended up involved in it, and how this work has connected with other aspects of my career.

Interdisciplinary Thinking: Financial Literacy Crosses Disciplinary Boundaries, Marla A. Sole

Publications and Research

Financial literacy is ideally suited to be integrated into mathematics courses and taught in an interdisciplinary manner. Students learn best and are motivated when tackling real-world meaningful questions. This article shares how elementary mathematics was applied to better understand the debate about raising the minimum wage and the United States National Debt. To serve as a guide for other teachers who wish to incorporate financial literacy into their mathematics courses and take an interdisciplinary approach, this article suggests readings, data sets, and pedagogical practices. Students were engaged and enthusiastic to work on problems that challenged their thinking about financial issues.

Interdisciplinary Thinking: Financial Literacy Crosses Disciplinary Boundaries, Marla A. Sole

Publications and Research

Financial literacy is ideally suited to be integrated into mathematics courses and taught in an interdisciplinary manner. Students learn best and are motivated when tackling real-world meaningful questions. This article shares how elementary mathematics was applied to better understand the debate about raising the minimum wage and the United States National Debt. To serve as a guide for other teachers who wish to incorporate financial literacy into their mathematics courses and take an interdisciplinary approach, this article suggests readings, data sets, and pedagogical practices. Students were engaged and enthusiastic to work on problems that challenged their thinking about financial issues.

Factors Impacting Students’ Perceptions Of Mathematics, Amber Souza

Honors Program Theses and Projects

I want to be able to present math in a positive light to all of my future students, regardless of race, gender, and math background. However, for teachers as a whole to be able to take this important step, they must first develop a deeper understanding of why math is a sore spot for many students.

Year 7 Students’ Interpretation Of Letters And Symbols In Solving Routine Algebraic Problems, Madihah Khalid Dr., Faeizah Yakop Dr., Hasniza Ibrahim

The Qualitative Report

In this study wefocused on one of the recurring issues in the learning of mathematics, which is students’ errors and misconceptions in learning algebra. We investigated Year 7 students on how they manipulate and interpret letters in solving routine algebraic problems to understand their thinking process. This is a case study of qualitative nature, focusing on one pencil and paper test, observation, and in-depth interviews of students in one particular school in Brunei Darussalam. The themes that emerged from interviews based on the test showed students’ interpretation of letters categorized as “combining” - which involved the combining of numbers during …

Effectiveness Of Mayer’S Problem Solving Model With Visual Representation Teaching Strategy In Enhancing Year Four Pupils’ Mathematical Problem Solving Ability, Sharmilla Palanisamy

Student Works (2020-2029)

This study aims to determine the effectiveness of Mayer’s problem solving Model with Visual Representation (MMVR) teaching strategy in enhancing Year 4 students’ mathematical problem solving ability in Klang Valley, and its interaction with gender. A quasi-experimental research design was employed in this study. A sample of 203 Year 4 students consisting of 101 males and 102 females from a private school in Klang Valley were drawn using a convenient sampling technique with two classes assigned as the experimental groups namely Mayer’s problem solving Model (MM) and MMVR groups, and the other one as the control group. The MM group …

Changes And Deltas, Jim Wolper

Journal of Humanistic Mathematics

Lecturing about Mathematics is like playing Jazz.

A Study Of Problem Posing As A Means To Help Mathematics Teachers Foster Creativity, Deborah Moore-Russo, Amanda A. Simmons, Michael J.D. Tulino

Journal of Humanistic Mathematics

Research suggests that mathematical creativity often results from extended periods of mathematical activity and reflection based on the use of deep and flexible content knowledge [14, 15]. This implies that instruction can influence creativity. However, for teaching to foster creativity in mathematics, there should be purposefully designed instructional tasks. It is doubtful that routine, mechanical exercises would foster creativity. Moreover, mathematical creativity may neither be explicitly promoted, nor fully appreciated, by students when a learning space involves only problem solving, even if the problems are challenging and engaging. For students to get an authentic sense of mathematics and to develop …

Cross-Cultural Comparisons: The Art Of Computing The Greatest Common Divisor, Mary K. Flagg

Number Theory

No abstract provided.

Pemahaman Ungkapan Algebra Dalam Kalangan Murid Tingkatan Dua, Hamid Azizah

Student Works (2020-2029)

Pemahaman tentang konsep ungkapan algebra penting bagi murid sekolah menengah kerana ia merupakan asas kepada pembelajaran matematik di peringkat menengah dan peringkat pengajian tinggi memandangkan kesukaran dalam pembelajaran algebra menjadi semakin kritikal. Kajian ini adalah untuk mengenal pasti pemahaman murid Tingkatan Dua tentang ungkapan algebra dengan berlandaskan konstruktivisme radikal. Penyelidikan ini menggunakan kajian kes sebagai reka bentuk kajian, yang membabitkan data berbentuk kualitatif. Peserta kajian membabitkan enam murid dari tiga kategori pencapaian akademik dengan menggunakan teknik persampelan bertujuan. Data kajian terkumpul melalui tiga sesi temu duga klinikal dengan menggunakan perakam video, catatan murid dan pengkaji. Data kajian dianalisis dengan menggunakan …

Pemahaman Murid Tingkatan Lima Tentang Konsep Dalam Topik Janjang Aritmetik, Edwar Siti Zaharah

Student Works (2020-2029)

Janjang Aritmetik merupakan tajuk yang sangat penting bagi murid Tingkatan Lima yang mengambil matapelajaran elektif Matematik Tambahan. Tujuan kajian ini dijalankan adalah untuk mengetahui pemahaman murid Tingkatan Lima tentang konsep dalam topik janjang aritmetik. Seramai empat orang murid Tingkatan Lima dipilih dalam kajian ini menggunakan kaedah persampelan bertujuan. Mereka belajar di sebuah sekolah menengah di Selangor. Kajian ini dijalankan berlandaskan teori konstruktivisme radikal. Kajian kes digunakan bagi mengumpulkan data melalui empat sesi temu bual klinikal yang melibatkan gambaran mental, perwakilan, makna dan penyelesaian masalah. Setiap sesi temu duga dirakam dengan alat perakam video. Data kajian dalam bentuk jawapan bertulis dan …

Teaching And Learning Of Fluid Mechanics, Ashwin Vaidya

Department of Mathematics Faculty Scholarship and Creative Works

Fluid mechanics occupies a privileged position in the sciences; it is taught in various science departments including physics, mathematics, environmental sciences and mechanical, chemical and civil engineering, with each highlighting a different aspect or interpretation of the foundation and applications of fluids. Doll’s fluid analogy [5] for this idea is especially relevant to this issue: “Emergence of creativity from complex flow of knowledge—example of Benard convection pattern as an analogy—dissipation or dispersal of knowledge (complex knowledge) results in emergent structures, i.e., creativity which in the context of education should be thought of as a unique way to arrange information so …

Investigations Into Bolzano's Bounded Set Theorem, Dave Ruch

Analysis

No abstract provided.

Investigations Into D'Alembert's Definition Of Limit (Real Analysis Version), Dave Ruch

Analysis

No abstract provided.

Written Reflections And Discussion Forums-- Math For Elementary School Teachers (Q2s-Ep: Math 301aqbr And Math 301bqbr ), Stephanie Creswell

Q2S Enhancing Pedagogy

Preparing for the transition from quarters to semesters, instructors of the mathematics sequence for future elementary teachers (Math 301ABC, Math 308 and their semester equivalents 3011, 3012 and 3013) applied research about best practices for online learning in mathematics to the quarter bridge courses Math 301AQBR and 301BQBR that each include 0.5 units of online activities. Successful activities piloted in the quarter bridge courses may be implemented in the 3011-3012-3013 semester sequence and their associated lab courses 3011L-3012L-3013L. This paper focuses on written reflections and group discussion forums associated with the class textbook Powerful Problem Solving by Max Ray.

Development And Assessment Of A Continuing Education Unit In Quantitative Literacy For High School Stem Teachers, Craig P. Mcclure

Numeracy

Influencing the teaching of quantitative literacy at all levels of education can be difficult due to the many demands placed on educators. In a continuing education course, public high school science teachers participated in a pilot study of a program on quantitative literacy, involving defining quantitative literacy, how it is beneficial to students, examples of quantitative literacy education, and how it may be supported in the science classroom. Surveys administered before and after the unit indicate an improvement in the teachers’ understanding of quantitative literacy, and a follow-up survey indicates that the unit impacted classroom practice. Results support the conclusion …

The Wright Stuff: An Integrative Approach To Stained Glass, Cassandra Wissink Armstrong

Professional Learning Day

In this session we'll explore the scientific and mathematical influences behind the artistic stained glass creations of Frank Lloyd Wright, and use them to create our own Wright-inspired stained glass designs. This is a truly integrative lesson that touches on properties of glass, linear functions, and artistic design.

Black And Brown Students’ Mathematics Anxiety In Elementary School: The Use Of Restorative Justice Circles And Critical Concepts Of Care, Hope, And Love, Mariana E. Winnik

Dissertations, Theses, and Capstone Projects

Children navigate their world and are constantly making meaning of their experiences. Through this meaning making, children are also constructing their identities. Black and Brown children have an added layer of identity construction compared to their White peers. Black and Brown students develop their racial identity in conjunction with multiple other identities. This paper focuses specifically on how Black and Brown students construct a "mathematics identity" that is meaningful to their racial identity in order to help lessen their mathematics anxiety. I argue that the use of Restorative Justice Circles (RJC) in classrooms will allow for students to bring their …

The Mobius Function And Mobius Inversion, Carl Lienert

Number Theory

No abstract provided.

Be The Change: Re-Ignite Student’S Passion For Problem Solving & Mathematics, Joseph Bolz, Marti Shirley

Faculty Publications & Research

Outcomes!

• I will be able to facilitate an open ended and open middle problems in the classroom, complete with questioning techniques and student prompts.
• I will experience how to modify a textbook problem into a richer open task that encourages discussion and multiple approaches, with a focus on tailoring them to real world applications.
• I will leave with a list of questions, perfect for posing to students while engaged in the problem solving process, and also useful for any class period when students are lacking persistence

Beauty, Bees, And God: The Fibonacci Sequence As A Theological Springboard In Secondary Mathematics, John D. Brahier

Journal of Catholic Education

Catholic schools primarily should be in the business of making saints. This article identifies and explores a meaningful, engaging point of contact between mathematics and theology for high school math classes, the Fibonacci Sequence. This sequence serves as an engaging introduction to sequences and series; more importantly, the topic can be used as a springboard to theological discussions. The paper will provide a brief historical background to the Fibonacci Sequence, an explanation of how it can be used in a high school math classroom, and an exploration of three different theological touchpoints that the Fibonacci Sequence offers.

Exercises Integrating High School Mathematics With Robot Motion Planning, Ronald I. Greenberg, George K. Thiruvathukal

Computer Science: Faculty Publications and Other Works

This paper presents progress in developing exercises for high school students incorporating level-appropriate mathematics into robotics activities. We assume mathematical foundations ranging from algebra to precalculus, whereas most prior work on integrating mathematics into robotics uses only very elementary mathematical reasoning or, at the other extreme, is comprised of technical papers or books using calculus and other advanced mathematics. The exercises suggested are relevant to any differerential-drive robot, which is an appropriate model for many different varieties of educational robots. They guide students towards comparing a variety of natural navigational strategies making use of typical movement primitives. The exercises align …

Mathematics Out Of Nothing: Talking About Powerful Mathematical Ideas With Children, Matthew Oldridge

Journal of Humanistic Mathematics

Parents and educators have powerful opportunities to introduce children to big mathematical ideas, when those ideas become necessary. Children are capable and curious. They don’t need to be sheltered from big mathematical ideas. Bring out mathematical ideas when kids are ready, or when they are needed. This article describes one such instance, when I helped my six-year-old son move beyond zero in the negative direction when subtracting.

Mathematics Students As Artists: Broadening The Mathematics Curriculum, Marshall Gordon

Journal of Humanistic Mathematics

Mathematics has often been referred to as an art. For some it is “the purest of the arts”, where the mathematicians’ art is “asking simple and elegant questions about our imaginary creations, and crafting satisfying and beautiful explanations”. Yet with classroom time given primarily to “covering the curriculum”, testing, and practicing problem-solving procedures, students’ opportunities to appreciate the aesthetic dimension of mathematics are often limited. To promote a responsive environment in an effort to enable students to become artists of their own mathematics experience, I consider in this paper two facets of the mathematics classroom. Content-wise I make the argument …

Telling Women's Stories: A Resource For College Mathematics Instructors, Sarah Mayes-Tang

Journal of Humanistic Mathematics

Stereotypes about mathematicians that conflict with ``traditionally feminine" identities are widely held by people from middle-school-age onwards, and can influence their participation in mathematics and related fields. Simply being exposed to women in mathematics is not enough to change students' perceptions of mathematicians, and may even decrease girls' interest in mathematics. This paper proposes a storytelling strategy to help change students' perceptions of mathematicians. It includes several activities for intentionally incorporating women's stories into the post-secondary classroom and a list of resources for finding existing powerful stories. The diverse stories of women mathematicians, including details of their personal lives and …

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

Pre-calculus and Trigonometry

No abstract provided.

Connectedness- Its Evolution And Applications, Nicholas A. Scoville

Topology

No abstract provided.