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The Language of Mathematics Education

An Expanded Glossary of Key Terms and Concepts in Mathematics Teaching and Learning


Shannon W. Dingman, Laura B. Kent, Kim K. McComas and Cynthia C. Orona

The Language of Mathematics Education: An Expanded Glossary of Key Terms and Concepts in Mathematics Teaching and Learning offers mathematics teachers, mathematics education professionals and students a valuable resource in which common terms are defined and expounded upon in short essay format. The shared vocabulary and terminology relating to mathematics teaching and learning, and used by mathematics educators is an essential component of work conducted in the field.

The authors aim to provide an overview of more than 100 terms commonly used in mathematics teaching and learning. Each term is defined and is followed by a short overview of the concept under discussion that includes several bibliographic references the reader can use for further investigation. In addition to terms specific to the domain of mathematics education, select key terms common across all fields of education (e.g., curriculum, epistemology, metacognition) are included. The goal for this book is to serve as a resource for those entering the field as they navigate the language and terminology of mathematics education and as an asset for more established professionals who wish to gain additional insights into these ideas.

Barnes-Johnson Joy, Saman A. Aryana and Jacqueline Leonard


This chapter reports findings from a larger Noyce study on the internship experiences that supported STEM undergraduate students’ transition to elementary teaching at a public university in the Rocky Mountain region—a rural, high-need context. The central research question addressed in this chapter is how can pre-professional mentoring and Noyce internship programs be used to support STEM majors to become equity-minded STEM educators? An underlying assumption embedded in this question is that teachers who espouse equity as a guiding principle for teaching will be more committed to teaching in high-need contexts, a requirement for participation in the Noyce scholarship program. This chapter reports on training experiences provided to Noyce scholars at various stages of commitment to the two- to three-year program. The identity development of a mentor and three interns were explicated as a cross-case study of this Noyce scholars’ program. The patterns of support that improved self-efficacy and cultivated equitable STEM teacher identity development may be used as a model for STEM teacher preparation programs in other high-need communities.

Building Computational Thinking

Design and Making in Teacher Education

Laurie O. Campbell and Samantha Heller


While the importance of teaching computational thinking has received national attention over the last decade, many educators continue to lack the understanding and awareness to implement computational thinking as a problem-solving framework in their daily instruction. In this mixed methods study, preservice teachers participated in Pop-Up Makerspace activities designed to introduce and explore computational thinking as a framework for problem solving. After determining the participants’ level of confidence teaching STEM-related content was lowest in problem-solving and engineering, the study examined how affective factors such as disposition and attitude were evident during the Pop-Up learning experiences. In this study, educators demonstrated the affective traits of resilience, failure, persistence, and frustration. Each factor of computational thinking was observed during the design and making experience. The effects of participation in a Pop-Up Makerspace motivated the preservice teachers to incorporate these experiential learning experiences into their own teaching practices.

Belinda P. Edwards, Desha Williams, Karen Kuhel and Adrian Epps


This chapter describes how a professional development project engaged mathematics preservice teachers and teacher educators in an ongoing conversation about teaching culturally and linguistically diverse students enrolled in high-need schools. Qualitative research methods were employed to examine preservice teachers’ perspectives about the process of learning to teach culturally and linguistically diverse students and how their identities and cultural competence evolved as they progressed through five professional development workshops and a semester long clinical field experience in an urban high-need school.

Lillie R. Albert


This study documents the experience of eight beginning teachers, eight experienced teachers, and six mathematicians participating in a professional learning community. The hallmark of the professional learning community is a two-way mentoring model, designed to incorporate content and pedagogical knowledge for teaching mathematics, whereby the beginning teachers have a mathematician and an experienced practicing teacher as mentors. Applying Vygotsky’s concept of sociocultural historic theory, the mentor-mentee relationship is examined through the lens of intersubjectivity. Findings suggest that the development of intersubjectivity can move the mentoring process ahead, where this relationship is characterized by achieving a common understanding of mathematical activities and ideas.

David Segura, Maria Varelas, Daniel Morales-Doyle, Brezhnev Batres, Phillip Cantor, Diana Bonilla, Angela Frausto, Carolina Salinas and Lynette Gayden Thomas


In this chapter, we examine how teaching that is oriented towards equity and social justice was co-constructed between two experienced high-school science teachers and their four student teachers. Using the lenses of structure-agency dialectic and culturally responsive mentoring, along with case study design, we studied ways in which structures (e.g., curricular, pedagogical, material, symbolic, and programmatic) influenced, and were influenced by, the experienced teachers’ and their student teachers’ agency to conceptualize and enact such practices. The findings unpack the complicated nature of learning to teach science in ways that promote equity and social justice. The cooperating teachers’ mentoring was structured differently based on how each interpreted the structures impeding their students’ agency. Moreover, the student teachers constructed their cooperating teachers’ guidance differently, using their own agency to support student agency. Although the teachers and student teachers foregrounded specific dimensions of culturally responsive mentoring, other dimensions of the framework intermingled to inform and shape the practices of experienced and novice teachers.

Noyce at Vanderbilt

Exploring the Factors That Shape the Recruitment and Retention of Black Teachers

Heather J. Johnson, Teresa K. Dunleavy and Nicole M. Joseph


The recruitment and retention of Black STEM teachers is a nation-wide challenge for the field of teacher education. In this chapter, we start to unpack the recruitment and retention challenges faced by Vanderbilt’s Noyce STEM teacher education program. We share the analysis of lived-experience interviews from two Black teacher candidates who earned their STEM degrees from an HBCU (Fisk University) and then transitioned to a PWI (Vanderbilt University) to earn their master’s in education (M.Ed.) degree. The analysis of their lived experiences revealed four themes: (a) the need for more visible partnerships between the HBCU and PWI; (b) the identification of mentors for scholar success; (c) the investigation for understanding Black teacher candidates as role models for their students; and (d) the institutionalized racism that still challenges Black teacher candidates at PWIs. These findings have implications for how programs situated within a PWI might consider the recruitment and retention of Black mathematics and science teachers.

Retention through Community Building

Secondary Science and Math Noyce Scholars’ Use of a Chat Room

Andrea C. Burrows


A study funded by the National Science Foundation through the Robert Noyce Scholarship program targeted degree holding science, technology, engineering, and mathematics (STEM) graduates to support licensure in secondary science or math. The grant, entitled Sustaining Wyoming’s Advancing Reach in Mathematics and Science (SWARMS), provided the study’s pool of 24 participants. This chapter highlights the SWARMS chat room to document the study’s successes and challenges as well as the participants’ interactions. Throughout the four-year study (2014–2018), qualitative and quantitative data showed consistent chat room interactions, especially as these data relate to classroom activities. However, some of the participants used the chat room with more frequency and self-reflection than others. Based on responses in the chat room and via email communication, community was built among participants and their self-efficacy was enhanced.

Rise, Defy, Teach, and Lead


Justina Ogodo, Karen E. Irving, Patti Brosnan and Lin Ding


Teaching in urban high-need schools can be challenging for teachers, which is one major reason for high teacher turn-over. Inadequate teacher enculturation can also contribute to high teacher attrition. The Empowering Noyce Apprenticeships by Leadership Engagement in STEM Teaching (ENABLE STEM) project is a study funded by the National Science Foundation (NSF) that is designed to recruit students into the Master of Education program at The Ohio State University (OSU) with the goal of empowering them to become successful learners and productive innovators in STEM fields. OSU preservice teachers are prepared as quality teachers, empowered to rise and defy the challenges that prevent others from remaining in urban high-need schools. They are equipped to teach students effectively through a four pronged-focused and intensive teacher training program: (a) Urban Teaching Seminar; (b) informal teaching experience at the Center of Science and Industry; (c) science methods with scientists and science educators; and (d) leadership focused induction and mentoring.

Seeking to Stay

Job Search Process and Teacher Retention

Lora Bartlett and Alisun Thompson


This qualitative longitudinal research follows thirty science and math teachers across five cohorts from their preparation program into the early career years to better understand the conditions of professional retention and attrition. Findings indicate that these teachers exhibit little agency or discernment in the job search process and typically accept the first position offered with little to no information about the school, students, colleagues, or teaching assignment. This decision has profound consequences for teacher turnover. Retention differences exist between teachers who choose their schools with robust information and those with very limited information. Furthermore, how and why teachers choose schools have profound consequences for their professional success and their persistence in high-need schools. This research study contends that professional retention of math and science teachers in high-need schools starts with teacher articulation of workplace priorities and is coupled with a rich information hiring process.