Education Commons^™

Tasks For Learning Trigonometry, Sydnee Andreasen

All Graduate Reports and Creative Projects, Fall 2023 to Present

Many studies have been done using task-based learning within different mathematics courses. Within the field of trigonometry, task-based learning is lacking. The following research aimed to create engaging, mathematically rich tasks that meet the standards for the current trigonometry course at Utah State University and align with the State of Utah Core Standards for 7th through 12th grades. Four lessons were selected and developed based on the alignment of standards, the relevance to the remainder of the trigonometry course, and the relevance to courses beyond trigonometry. The four lessons that were chosen and developed were related to trigonometric ratios, graphing …

“Don’T Call On Me!”: Mediating Preservice Elementary Teachers’ Mathematics Anxiety In A Problem-Based Classroom, Christina Koehne, Wenyen Huang, Nataly Chesky

Excelsior: Leadership in Teaching and Learning

This study aims to understand the ways in which problem-based teaching in a mathematics content course can alleviate pre-service elementary school teachers' mathematics anxiety. The significance of this work is to help increase the content and pedagogical knowledge of mathematics education, as outlined in STEM policies. Using a mixed method approach, the teachers-researchers explore what methods, procedures, and other perhaps unknown variables, helped pre-service elementary teachers decrease their mathematics anxiety during two mathematics content courses. The findings illuminate five major themes the authors discuss, which are illustrated by rich descriptions of students’ narratives and interviews. Given the importance of mathematics …

Secondary Math Teachers’ Responses To Errors In The Classroom, Richie Vicinanza

Honors College Theses

This study was conducted in an effort to find out how modern-day secondary math teachers respond to errors in their classrooms and the reasonings behind their responses. To fulfill the purpose of this study, various methods of research were used to gather information. Methods included looking into the scholarly sources surrounding the topic as well as a primary-conducted study in the field. Participants of this study were high school math teachers. The participants engaged in two semi-structured interviews (an initial and a debrief) as well as an observation that was conducted during one of their classes. Through the initial interview, …

Theorizing Mathematical Proof As Becoming: A Deleuzio-Guattarian Investigation, Joshua P. Case

Graduate Theses, Dissertations, and Problem Reports

In this dissertation, I utilize the post-structural philosophy of Gilles Deleuze and Félix Guattari as a lens for investigating the proof process. Deleuze and Guattari were both post- structural philosophers who, like many in this tradition, troubled traditional notions related to stable identities, meaning, language, and mathematics. For Deleuze, sense and meaning is not the result of a sterile, transcendent effect or condition that is associated with propositions and states of affairs. Rather, it is the result of a material production that emerges from the world and that has independence from language and the mind. I apply this framework to …

Supporting Schools’ And Teachers’ Use Of Assessment To Inform Learning Of All Students, Ursula Schwantner, Soumaya Maghnouj

Global education monitoring

Issue 5 of the series Using assessment data in education policy and practice: Examples from the Asia-Pacific documents 4 case studies of promising and effective policies or practices on how education systems can better support teachers and schools in effectively integrating assessment practices in the teaching and learning process, to identify and meaningfully address every learner’s needs. In particular, the case studies show how different tools, approaches and policies help promote and reinforce the use of assessment to support more learner-centred and differentiated approaches to teaching and learning. 1. Using the Progressive Achievement approach to develop data-informed schools by Marc …

The Perceptions Of Elementary Educators Regarding Mathematical Discourse Utilization In The Classroom: A Qualitative Phenomenological Study, Christina Anderson

Doctor of Education Program Dissertations

Given the lack of proper utilization of mathematical discourse in public elementary settings and the stagnation of mathematical proficiency, the purpose of this qualitative phenomenological study was to explore the perceptions of public elementary K-5 educators regarding the use of mathematical discourse as a pedagogical strategy. Because research indicates there are benefits to facilitating mathematical discourse, this study sought to understand the perceptions of public elementary K-5 teachers regarding the use of mathematical discourse as a pedagogical strategy in the classroom, their perceptions of different pedagogical strategies for facilitating mathematical discourse, and their perceptions of students engage in mathematical discourse …

Figured Worlds Of Women Mathematics Education Scholars, Lili Zhou, Jill Newton, Brooke Max, Hyunyi Jung, Lindsay M. Keazer, Bimi Kumari Sapkota, Ricki L. Geller-Mckee

Education Faculty Publications

Drawing on the concept of figured worlds (Holland et al., 1998), this project focuses on addressing, responding to, and understanding the self within the figured world of the mathematics education community. Specifically, we examine a group of women with diverse backgrounds in terms of race, class, and cultural contexts, who are engaged in various roles as mathematics education scholars, including teachers, teacher educators, and researchers. Using a dialogical self approach, we facilitate both internal and external discourses, exploring personal histories, narratives, and the development of evolving identities. Our findings reveal that culture and social positions, such as gender, class, and …

More Than Free Textbooks: Labor And Pedagogy In Implementing Open Resources In A Trigonometry Course, Caleb Holloway

Journal of Humanistic Mathematics

This paper reports the implementation of open educational resources (OER) in a university trigonometry class, with an emphasis on the pedagogical considerations and academic labor involved. To date these two matters have been underreported in the literature on OER. I provide an account of the work involved both in choosing an open textbook and in creating hundreds of accompanying homework exercises for an online learning platform. I also present the pedagogical lens that informed this implementation, discuss how it informed my adoption of an open textbook, and provide specific examples of how it guided the creation of these exercises. Based …

Analyzing The Influence Of Mathematics Intervention Teacher Actions On Students' Mathematics Identities: An Examination Of Bipoc Student Perceptions And Past Learning Experiences., Sydni P. Morris

Electronic Theses and Dissertations

This dissertation examines mathematics education's past and present state in the United States, emphasizing mathematics intervention instruction. This dissertation includes a complex and critical analysis of intervention practices and historical and structural inequities based on race present in these interventions and mathematics education. In combination, it examines the construct of mathematics identities, their role in student success with mathematics, and trends surrounding mathematics education and its impact on populations of students of color. Using Critical Race Theory as an underlying framework and Critical Counter-Narrative as a methodology, it argues a need for marginalized student voices to be present in the …

What Pre-Service Teachers Want “Math” To Know: Examining Self-Identified Relationships And Critical Experiences With Mathematics, Claudia M. Bertolone-Smith, Alison Puliatte, Samantha Sommers, Michelle Unigarro, Danielle Vantassell

Excelsior: Leadership in Teaching and Learning

This study examines the self-reported critical experiences that undergraduate pre-service teachers (PSTs) choose to share when writing a letter directly to “Math” and creating a self-portrait of a math learning experience. The letters sought to initiate a personification of math and the self-portraits to further explore math learning experiences of the PSTs. The letters and portraits were examined to understand the types of math relationships and critical events PSTs reported and their impact on PST identity and agency as a future teacher. Portraits were analyzed by PST research partners. The relationship between the categories of critical events and mindset …

Learning To Teach Prospective Elementary Teachers: A Narrative Inquiry Of A Newer Mathematics Content Instructor, Kelsey Quaisley

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

Learning to teach mathematics content courses designed for prospective elementary teachers (PTs) is challenging. Mathematics content instructors must be prepared to not only teach mathematics content, but engage PTs in understanding children’s mathematical thinking strategies, learning trajectories, and misconceptions (Carpenter et al., 1996; Carpenter & Moser, 1982; I et al., 2020). When considering how instructors might best be prepared and supported, however, one must recognize that there is significant variation in the backgrounds and expertise of mathematics content instructors (Masingila et al., 2012; Yow et al., 2016) and little is known about the preparation, knowledge, and experiences of mathematics content …

Data-Wisdom As A Framework For Building Data Literacy, Rita Swartzentruber

Masters Theses

In a world where “big-data” rules, the need for data literate citizens is critical. Not only do we need citizens who can read data, but also citizens who are critical of data practices that perpetuate racist practices. One potential answer for this call is to create “data-wise” citizens. The purpose of this design-based research study was to explore how secondary and post-secondary students can develop data-wisdom through the analysis of three data-inspired artistic data visualizations. This study examined the growth of data-wisdom in participants, the development of classroom norms, and the increase in positive perceptions of mathematics in participants. Data …

Classroom Social Support: A Multiple Phenomenological Case Study Of Mathematics Graduate Teaching Assistants’ Decision Making In The Classroom, Brittany Johnson

Department of Mathematics: Dissertations, Theses, and Student Research

Research suggests that support offered by an instructor can have a significant impact on the student experience, both in terms of classroom performance and affective well-being. Research also suggests that there are different types of support that instructors can offer (e.g., emotional support, instrumental support, informational support, and appraisal support). Although such research suggests that students perceive and are affected by these different types of support in different ways, there does not appear to be research surrounding the decision-making process behind instructors offering the support or the extent to which social support is a priority for them in the classroom. …

Conceptualizing Social Mathematical Empowerment: What Is The Curricular Connection?, Alicia C. Gonzales

Doctoral Dissertations

As a result of everchanging goals and visions for mathematics education in the United States, this study builds on an initial theoretical framework of empowerment and further conceptualizes one domain, namely Social Mathematical Empowerment [SME]. I used concept analysis to define processes and outcomes more precisely and identified SME as a multi-layered, dialectic construct. This approach results in two components of action and awareness with various instructional and theoretical approaches. I then applied that conceptualization and created an analytical tool to examine mathematics teaching materials to engage learners in SME. This study adds to the existing knowledge base by providing …

Trends Of Mathematics Education Research Studies Published In Journal Of Mathematics Education From 2017 To 2021, Hisham Barakat Hussein Prof.

International Journal for Research in Education

The study aimed to analyze the trends of mathematics education research published in the Journal of Mathematics Education in the last five years and to propose a future map for mathematics education research in the light of the analysis results, professors’ and experts’ views, and the contemporary international trends. The study used a simplified model to classify research in seven domains. Also, the researcher used a questionnaire for professors and experts to determine a future map for mathematics education research. The results showed the research trends in the Journal of Mathematics Education were most of the articles were single authored …

The Difference In Geometry Achievement Between Students Who Utilize Lfm Strategies And Those Who Do Not: A Nonequivalent Control-Group Pretest/Posttest Study, Amanda Nicol

Doctoral Dissertations and Projects

The purpose of this quantitative, quasi-experimental nonequivalent control-group pretest/posttest study was to identify whether there is a difference in Geometry achievement between students who utilize Learning for Mastery (LFM) strategies compared to those who do not at the high school level. This study provided insight into instructional and assessment strategies that may increase student achievement, understanding, and retention. Seventy-three high school mathematics students enrolled in Geometry courses, grades nine through twelve, from a suburban high school in Northwestern New Jersey were assessed in this study. Students were given a pretest, participated in daily classwork and instructional strategies for ten weeks, …

The Nothing That Really Matters, Szilárd Svitek

Journal of Humanistic Mathematics

Zero has (a) special role(s) in mathematics. In the current century, we take negative numbers and zero for granted, but we should also be aware that their acceptance and their emergence in mathematics, and their ubiquity today, have not come to happen as rapidly as, for example, that of natural numbers. Students can quickly become confused by the question: is zero a natural number? The answer is simple: a matter of definition. The history of zero and that of negative numbers are closely linked. It was in the calculations of debts that the negative numbers first appeared, where the state …

Teaching Routines And Student-Centered Mathematics Instruction: The Essential Role Of Conferring To Understand Student Thinking And Reasoning, Eva Thanheiser, Kathleen Melhuish

Mathematics and Statistics Faculty Publications and Presentations

We compare two lessons with respect to how a teacher centers student mathematical thinking to move instruction forward through enactment of five mathematically productive teaching routines: Conferring To Understand Student Thinking and Reasoning, Structuring Mathematical Student Talk, Working With Selected and Sequenced Student Math Ideas, Working with Public Records of Students’ Mathematical Thinking, and Orchestrating Mathematical Discussion. Findings show that the lessons differ in the enactment of teaching routines, especially Conferring to Understand Student Thinking and Reasoning which resulted in a difference in student-centeredness of the instruction. This difference highlights whose mathematics was being centralized in the classroom and whether …

“Should Wellbeing Be The Same As Perfection?” A Case Study On Student Wellbeing In Higher Mathematics Education, Marcelo Alonso Almora Rios

Graduate Student Theses, Dissertations, & Professional Papers

Previous research has given the impression that reticent is our hunt for optimal teaching practices, educational goals, and nature of mathematical workings. In this regard, we have (seemingly) ended up with the following inquiries:

• What could the math classroom be for? and
• What has the math classroom been for?

These two questions touch on the scary horns of two other charged philosophical dandruffs. Namely:“What are the aims of teaching mathematics?” and “What should be our objectives in learning it?”

The term ‘positive education’ refers to an educational system engendering both the skills of positive wellbeing and traditional, academic achievement (Seligman …

Fostering Spatial Ability Development In And For Authentic Stem Learning, Caiwei Zhu, Chloe Oi-Ying Leung, Eleni Lagoudaki, Mariana Velho, Natalia Segura-Caballero, Dietsje Jolles, Gavin Duffy, Gunter Maresch, Marianna Pagkratidou, Remke Klapwijk

Articles

Empirical interdisciplinary research has explored the role of spatial ability in STEM learning and achievement. While most of this research indicates that fostering spatial thinking in educational contexts has the potential to positively impact students’ enrollment and performance in STEM subjects, there is less agreement on the best approach to do so. This article provides an overview of various types of effective spatial interventions and practices in formal or informal educational contexts, including targeted training of STEM-relevant spatial skills, spatialized curricula embedded in schools, integrated STEM practices addressing students’ use of spatial skills, and spatial activities in informal STEM education. …

Sustaining At Scale: District Mathematics Specialists’ Adaptations To A Teacher Leadership Preparation Program, Michael Jarry-Shore, Victoria Delaney, Hilda Borko

Curriculum, Instruction, and Foundational Studies Faculty Publications and Presentations

A common approach to scaling up a professional development program is for the researchers who designed the program to prepare teacher leaders to facilitate it at their schools. When researchers eventually leave, however, teacher leaders may receive less support. To ensure that teacher leaders continue receiving support, researchers can prepare district mathematics specialists to assume responsibility for preparing the teacher leaders. Little is known, however, about district mathematics specialists’ role in sustaining, and potentially adapting, professional development programs. We examined district mathematics specialists’ facilitation of an adaptive teacher leadership preparation program. Program sessions were originally facilitated by researchers then by …

Pre-Service Elementary Teachers' Framing Of Mathematical Discussions After Problem-Solving Through Mursion™ Simulation, Sezai Kocabas, Melva Grant, Signe Kastberg, Hanan Alyami

Teaching & Learning Faculty Publications

Research on pre-service teachers' discussion practices has focused on decompositions of practice into subskills, while acknowledging the importance of the role of context, identity, and relationships between interactive moves. We focused on 66 elementary preservice teachers' (PSTs') framing-launching moves in discussions after problem-solving in a MursionTM custom simulation. PSTs used five moves: gathering information about student processes, focusing on problem features, task and non-task oriented social interactions, and partner talk. Empirical findings of PSTs' intentions and tacit actions coupled with study findings of the diversity in PSTs' framing moves, highlight the complexity of teacher decision making involved in discussion subsills …

Pre-Service Teachers’ Perceptions Of Problem-Based Learning For Developing Their Mathematics Teaching Pedagogy, David A. Martin, Romina Jamieson-Proctor

Research outputs 2022 to 2026

The study reported in this paper was part of a larger study that explored pre-service teachers’ perceptions of the effectiveness of a problem-based learning (PBL) teaching approach for developing their mathematics pedagogical content knowledge (PCK) and their ability to enact their PCK in a tertiary mathematics education subject. This paper reports the qualitative semi-structured interviews used to capture the student voice with respect to the impact of the PBL approach used on the development of their mathematics PCK in comparison to their previous experiences with teacher-directed instruction. Overall, responses from the interviews revealed the pre-service teachers considered the PBL method …

An Investigation Of Active Learning On Students' Understanding Of Infinite Series Convergence, Zachary Coverstone

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Many students encounter infinite series for the first time as part of their single-variable calculus coursework. As part of this initial engagement with infinite series convergence, students grapple with infinity in ways that they haven't had to before. For instance, the fact that summing infinitely many terms sometimes yields a finite value, but at other times diverges, poses significant conceptual challenges.

I recently designed and implemented a curriculum for second-semester calculus centered in doing problems to help students develop ideas surrounding infinite series convergence, rather than using direct instruction. The unit design was patterned after a workshop at the Park …

Mathematics Education As Dystopia: A Future Beyond, Peter Appelbaum, Charoula Stathopoulou, Constantinos Xenofontos

Journal of Humanistic Mathematics

We argue that scholars and practitioners of mathematics education need to find new directions through recognition of its dystopic characteristics, and embrace these characteristics as both the source of challenges and method of response. This contrasts with the generally utopic approach of most scholarship in the field. We offer critical ethnomathematics education as a model, since it has its own origins in lingering dystopic legacies. A perpetual hopelessness and disempowerment is one implicit curriculum of contemporary mathematics education, where the mathematics one learns might help to describe things, yet hardly assists in transforming the reification of power and agency in …

Collaborative Learning With A Geometry Video Game: The Role Of Elaboration And Game Design In Motivation And Learning, Ethlyn Saltzman

Dissertations, Theses, and Capstone Projects

The study examined the effects of a new game mechanic on collaborative learning and mathematical discourse when playing a digital geometry puzzle game. For this study, two new versions of the game “Noobs vs. Leets” were developed. Both versions of the game teach the concepts of complementary and supplementary angles and the angle sum theorem of triangles. It was hypothesized that the version of the game that included a game mechanic that allow players to manipulate the angles, thus creating a more open-ended task, would be more intrinsically motivating, promote elaboration of the geometric concepts, and lead to greater learning …

Hearing Silence: Understanding The Complexities Of Silence In Democratic Classrooms And Our Responsibility As Teachers And Teacher Educators. A Response To "Creating A Democratic Mathematics Classroom: The Interplay Of The Rights And Responsibilities Of The Learner.", Kersti Tyson, Allison Hintz, Andrea English, Diana Murdoch

Democracy and Education

This response to Priya Prasad’s and Crystal Kalinec-Craig’s article on the interplay of the Rights and Responsibilities of the Learner aims to engage with and add on to the authors’ exploration of learners overexercising or opting out of their rights. While grappling with these challenges alongside the authors, our curiosity deepened about a significant and understudied facet of democratic classrooms: silence. Through this response, we consider the multifaceted dimension of silence and how a focus on silence may help us more fully understand the tension between learners’ rights and responsibilities to self, each other, and the collective. Specifically, we engage …

Pre-Service Elementary School Teachers’ Perceptions Of Themselves As Learners Of Mathematics And Science, Diana L. Moss, Rachel Wilson, Danielle Divis

Journal on Empowering Teaching Excellence

Access the online Pressbooks version of this article here.

This study investigated how prospective elementary teachers view themselves as learners of mathematics and science during their last year in a teacher preparation program at an American university. Using drawing and reflections as the method for collecting data, prospective teachers were prompted to draw themselves and reflect on learning mathematics and draw themselves and reflect on learning science prior to and after their mathematics and science methods courses. Drawings (n = 147) were coded according to the presence or absence of several themes including physical objects, teachers, students, and environment. …

Full Issue: Journal On Empowering Teaching Excellence, Volume 6, Issue 1, Spring 2022

Journal on Empowering Teaching Excellence

The full-length 2022 Special Issue (Volume 5, Issue 3) of the Journal on Empowering Teaching Excellence

Access the online Pressbooks version (with downloadable EPUB format) here.

The Spring 2022 issue begins with research that explores the perceptions of pre-service teachers relative to learning mathematics and science, with suggestions for how findings can impact curriculum and further research. The focus on pre-service teachers continues with research into their sense of self-efficacy with instructional technologies and whether specific techniques increase comfort level with technologies. Next, researchers explore the products that Generation Z students value most in their learning of a second language, …

Teaching Innovation Learned From The 2022 Amte Conference: Prepare Future Mathematics Educators, Yi-Jung Lee

TFSC Publications and Presentations

The role of mathematics has transformed from gatekeeper to launchpad in K-12 schools and been considered as a critical factor in career readiness in a diverse society (CDE, 2022). Therefore, teacher education programs must adopt effective teaching approaches with cultural awareness while preparing future mathematics teachers. I shared a revised teaching design framework (Rhodes, 2021) along with the Culturally Responsive Mathematical Modeling perspectives to help educators integrate a) productive disposition, b) the instructional design with modeling tasks, and c) equity-minded practice into their teaching preparation and practices.