Science and Mathematics Education Commons^™

An Analysis Of The Essential Understandings In Elementary Geometry And A Comparison To The Common Core Standards With Teaching Implications, Helen Crompton, Sarah Ferguson

STEMPS Faculty Publications

Geometry and spatial reasoning form the foundations of learning in mathematics. However, geometry is a subject often ignored by curriculum writers and teachers until high school, leading to students lacking in critical skills in geometric reasoning. As the United States moves into a new curriculum epoch, heralding the commencement of the national common core standards (CCS), one could question if CCS in geometry align with the essential understandings children need to be successful geometric thinkers. This paper begins with an examination of the essential understandings of geometric reasoning leading to an interpretation and critique of the elementary geometry CCS. Finally, …

Examining The Influence Of Secondary Math And Science Teacher Preparation Programs On Graduates' Instructional Quality And Persistence In Teaching, Danielle M. Rhemer, Will Rogers, Sherry Ann Southerland

Teaching & Learning Faculty Publications

This quantitative, non-experimental study explored the relationship between the features of math and science teachers’ preparation programs and their graduates’ instructional rigor and persistence in teaching. Five math and science teacher preparation programs from across the United States were examined. Six sets of instructional tasks were collected from forty-six recent graduates of these programs to provide insights into novices’ instructional rigor, and employment data were collected for thirty-seven of these graduates three to eight years after graduation. Regardless of the program’s features, all teachers could design and implement instruction with moderate to high rigor. However, this ability was not the …

Prospective Teachers' Conceptions Of Area, Betsy Mcneal, Sayonita Ghosh Hajra, Michael Battista, Ayse Ozturk

Teaching & Learning Faculty Publications

This study explored 10 prospective teachers’ (PTs’) understanding of the area of a rectangular region using square and non-square rectangular area-units. In an hour-long interview, each PT was first asked to explain how they would find the area of a given rectangular region in terms of a non-square notecard. For several PTs, this task prompted discussion of a square unit defined by the edge of the notecard. In a second task, PTs were presented with a rectangular array of squares and were asked to explain to a fictional child why multiplying length times width does not count the top left …

Payday Power-Up: Let's Make A Raise Distribution, Ayse Ozturk

Teaching & Learning Faculty Publications

This study illustrates a problem-solving activity reflective of a real-life situation wherein high school students articulate their reasoning while contemplating the effectiveness and fairness of distributing raises. Study data were gathered via teaching experiment methodology in problem-solving sessions at a mathematics camp for secondary students. Examination of the data indicated that students sought entry points for problem-solving by making assumptions and pinpointing crucial variables. Framing mathematics within the concept of fairness encouraged students to review their work, engage in active listening, and find purpose in mathematical reasoning.

Mathematics Education Researchers' Practices In Interdisciplinary Collaborations: Embracing Different Ways Of Knowing, Elizabeth Suazo-Flores, Wiliam S. Walker Iii, Signe E. Kastberg, Mahtob Aqazade, Hanan Alyami

Faculty Publications – Mathematics

Mathematics education researchers (MERs) use practices unique to the mathematics education discipline to conduct their work. MERs’ practices, i.e., ways of being, interacting, and operating, define the field of mathematics education, are initially learned in doctoral preparation programs, and are encouraged and sanctioned by conferences and publications. Disciplinary practices facilitate MERs’ interactions within mathematics education. When working in interdisciplinary groups, differences in disciplinary ways of being, interacting, and operating can create challenges with completing research and other work. Since MERs’ engagement in interdisciplinary collaborations is encouraged and can result in products contributing to the evolution of the mathematics education discipline, …

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 …

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

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

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. …

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 …

“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 …

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 & 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. …

The Impact Of Personal And Service-Related Factors On The Perceived Academic Success Among College Students, Ronnie Davis, Geraldine Doucet, Terayana Lamb, Sonya Sneed, David Fletcher

The Journal of the Research Association of Minority Professors

In recent years, student completion of the first year and second-year college curriculum has become a significant barrier to student success and retention especially at Historically Black Colleges and Universities. Despite low pass and retention rates, many degree programs in the U.S. require at least one college-level mathematics course, and the failure in this math course has contributed disproportionately to the failure to complete the first- and second-year curriculum.

The purpose of this study was to examine the predictability of the relationship between selected personal, academic, and service-related factors and the perceived academic success in mathematics among college students. Specifically, …

Teaching Mathematics With Technology: Tpack And Effective Teaching Practices, Christopher R. Rakes, Michele L. Stites, Robert N. Ronau, Sarah B. Bush, Molly H. Fisher, Farshid Safi, Siddhi Desai, Ashley Schmidt, Janet B. Andreasen, Jon Saderholm, Lisa Amick, Margaret J. Mohr-Schroeder, Julian Viera

Science, Technology, Engineering, and Mathematics (STEM) Education Faculty Publications

This paper examines how 17 secondary mathematics teacher candidates (TCs) in four university teacher preparation programs implemented technology in their classrooms to teach for conceptual understanding in online, hybrid, and face to face classes during COVID-19. Using the Professional Development: Research, Implementation, and Evaluation (PrimeD) framework, TCs, classroom mentor teachers, field experience supervisors, and university faculty formed a Networked Improvement Community (NIC) to discuss a commonly agreed upon problem of practice and a change idea to implement in the classroom. Through Plan-Do-Study-Act cycles, participants documented their improvement efforts and refinements to the change idea and then reported back to the …

Middle School Students Generating Mathematical Problems From A Real-Life Situation, David Coffland, Ying Xie

Journal of Humanistic Mathematics

In this study, we examined the effect of different presentation formats of a realistic situation on students’ mathematical problem-posing behavior. We divided thirty-six middle school students into two groups, gave them a pretest, and then showed them a realistic, problem-posing situation in Artifact or Video format. We used Silver’s core dimensions of creativity, namely fluency, flexibility, and originality, to measure participants’ problem-posing activity. The results for the fluency measures showed that the Artifact group wrote more questions than the Video group but the same number of mathematics problems. The Video group posed problems in more mathematical domains than the Artifact …

Learning Mathematics While Black In Rural Appalachia: Black Students' Counterstories And Freedom Dreams About Mathematics Education, Sean P. Freeland

Graduate Theses, Dissertations, and Problem Reports (ETD)

This dissertation aims to illuminate and uncover the experiences of Black students’ learning mathematics in rural Appalachia and specifically West Virginia. The focal theory for this study is Critical Race Theory (CRT) which centers the experience of Black students and their voices. The intersection of race, mathematics education, and the context of rural Appalachia contribute to the analysis of these experiences in specific ways. Participants for this study included six Black high school students from various communities throughout West Virginia. Through interviews and mathematical autobiographies, these students shared their experiences learning mathematics across their schooling experiences and also considering their …

Preparing Preservice Mathematics Teachers To Teach For Social Justice, Jodie Cahill

Honors Projects

As a preservice teacher, I have always been taught that mathematics should be relatable to students. My future students live in a tumultuous society with many social justice issues affecting them. In the endeavor to connect mathematics to the real world, I sought to intertwine social justice topics into mathematics lessons. My research question is: How do social justice topics support preservice mathematics teachers’ endeavors to enrich their future students’ educations? I conducted a two-part professional development workshop for preservice teachers at Bowling Green State University about teaching mathematics for social justice in order to answer this question. There was …

The Impact Of Covid-19 On Mathematics Education Curriculum, Kristen Ferguson

The Journal of Purdue Undergraduate Research

No abstract provided.

Timss 2019 Australia. Volume Ii: School And Classroom Contexts For Learning, Sue Thomson, Nicole Wernert, Sarah Buckley, Sima Rodrigues, Elizabeth O'Grady, Marina Schmid

TIMSS 2019

This is the second of two reports that look at the results of TIMSS 2019 and Australia’s performance. Volume I focuses specifically on the achievement results, detailing Australia’s results within the international context, and presents results for the Australian jurisdictions, and for the different demographic groups within Australia, including male and female students. This report, Volume II, presents the results from the contextual questionnaires, and examines the contexts in which learning and achievement occur, including home, school, and classroom contexts, as well as student attitudes. Each chapter focuses on different indicators that cover the school community, the school learning environment, …

Impact Of The Order Of Eac And Sos During Instruction On Ratios, Josephine Marlene Derrick

Boise State University Theses and Dissertations

The purpose of this study was twofold. First, a set of instructional materials surrounding proportional reasoning with ratios (particularly the understanding of the multiplicative relationship between the quantities within the ratio, referred to as functional reasoning throughout this thesis) were created using the free online tool, Desmos, with a goal of determining the impact of the lesson materials on student understanding. The second goal was to explore the impact of the order in which two instructional strategies, Explicit Attention to Concepts (EAC) and Students’ Opportunity to Struggle (SOS), had on student understanding. The lesson materials consisted of 5 lessons. These …

Using Logistic Regression To Examine The Relationship Between Early Alert Systems And Success In Mathematics, Jennifer-Anne Tekawitha Hill

Graduate Research Theses & Dissertations

Early alert systems are an intervention at community colleges that aim to identify and informally intervene with students who are struggling in their courses. This study examined the relationship between early alert systems and student success in developmental and gateway math courses. This study also examined if the impact of early alert referrals differed by class modality, as students in online classes were often unaware of resources available to them. Method: The sample was taken from one large primarily midwestern community college. Data was sourced from the institutional research department. Individual student transcript records were used, early alert referral information, …

Creating A Culturally Relevant Statistics Assignment On Z-Scores, Grace Pai

Publications and Research

Culturally relevant teaching or pedagogy has become increasingly popular both in practice and in research, but there are still few curricular resources for instructors to use, particularly for a college-level mathematics course. Departing from the question “relevant to whom,” this article illustrates how to design a statistics assignment on z-scores that is culturally relevant to students based on their prior experiences. Ultimately, the author shares design principles—which includes the importance of considering student trauma—that can be transferable to any statistics or quantitative analysis/reasoning class.

Teaching Statistics For Social Justice - An Autoethnographic Research Report, Sheffield L. Dacia, Sierra Brooks, Basil M. Conway, Ha Nguyen

Georgia Educational Researcher

The following autoethnography was completed by two graduate students at University A learning to enact teaching for social justice while building content underpinnings in statistics at University B. The authors present a research base for teaching for social justice followed by a description of their lesson, observations during enactment, and reflection of change in beliefs about teaching for social justice afterward. Findings in this study are shared from the authors’ personal perspectives through the enactment of teaching a lesson for social justice in an undergraduate statistics course at University B. Implications provide encouragement that the inclusion of social justice topics …

Teacher Understanding Of Instructional Strategies In Elementary Mathematics, Erica Boatwright Glover

Walden Dissertations and Doctoral Studies

Synergizing Elementary School (pseudonym) consistently experiences low state-required mathematics test scores in grades 3 and 4 below district and state proficiency rates in mathematics. The purpose of this qualitative case study was to investigate what instructional practices used by Grade 3 and Grade 4 teachers are, aligned or not aligned, with research-based planning, standards-based instruction, attention to conditions of learning, and professional responsibilities of teachers to support students’ achievement in mathematics. This study's conceptual framework was grounded in Robert Marzano's model of teaching effectiveness called the focus teacher evaluation model. Data for this case study were gathered from semi-structured interviews …

Critical Connections Between Numeracy And Mathematics: Supplementary Materials, Dave Tout

Student learning processes

This publication contains three professional development activities targeted at teachers of mathematics. The activities for both groups and individuals focus on the challenge of word problems in maths and connecting maths to the real world. Also included are references, materials and resources related to the issue of the connections between numeracy and mathematics.