An Autoethnography of Transitioning Mathematics Content Courses for K-8 Preservice Teachers to Online Learning during COVID-19

The context in which preservice teachers (PSTs) learn the mathematical knowledge required for teaching in an elementary classroom is still less obvious. This chapter addresses the complexity of PSTs (re)learning the mathematical knowledge for teaching multiplication of fractions in a mathematics content course. The existing literature on PSTs' learning in a mathematics content course has focused on models for designing the course and efforts for designing innovative pedagogies. In addition, more recent studies have explored the design and implementation of mathematical tasks in a content course. However, studies that have provided insights into the affordances and complexity involved in developing fraction concepts using the basic principles of critical thinking are limited. The aim of this chapter is to explore the extent to which PSTs can develop a conceptual understanding of multiplication of fractions in the context of a mathematics content course designed using the basic principles of critical thinking. The complexities, challenges and tensions confronted by PSTs and the instructor as they (re) learn the meaning of multiplication in more nuanced ways will be discussed.

The present study aims to explore the use of assessment in mathematics content courses for future elementary school teachers. Analysis of self assessment data on mathematical understanding and peer assessment data on oral mathematical presentation showed that pre-service teachers had a balanced understanding of procedural knowledge and problem solving. Conceptual understanding was not in the structure of pre-service teachers’ mathematical knowledge. Understandings of conceptual knowledge, procedural knowledge, and problem solving had no meaningful effects on gains in mathematics performance. Aspects of oral mathematical presentation were associated with improved understanding of procedural knowledge and in particular conceptual knowledge. The result of the study calls for a conceptual approach to mathematical knowledge and sufficient mathematical problem solving in college-level mathematics content courses and in particular the infusion of assessment into college-level mathematics education for pre-service teachers.

This longitudinal study examines the effects of changes in an elementary teacher preparation program on mathematics beliefs and content knowledge for teaching of two groups of prospective teachers (N = 276): (1) those who completed a program with three mathematics content courses and two mathematics methods courses and (2) those who completed a program with four mathematics content courses and a single mathematics methods course. The results reveal salient benefits of a second methods course that were not evident in the new program with only one methods course. Further, the addition of a fourth content course did not result in notable differences in mathematical knowledge for teaching. In addition, mathematical knowledge for teaching was positively linked to change in pedagogical beliefs about learners, further illuminating the interwoven nature of knowledge and beliefs.

Enhancing teachers’ pedagogical content knowledge (PCK) is essential to improving the teaching and learning of mathematics. Mathematics teacher educators (MTEs) need to help prospective teachers enhance PCK (Marks in J Teach Educ 41(3):3–11, 1990. doi: 10.1177/002248719004100302 ; Mason 2008). However, we know very little about the practices of MTEs, especially in mathematics content courses, as these practices are not widely researched or disseminated (e.g., Bergsten and Grevholm, in: Jaworski, Wood (eds) The international handbook of mathematics teacher education, vol 4, Sense Publishers, Rotterdam, pp 223–246, 2008; Floden and Philipp, in: Lester, Ferrini-Mundy (eds) Proceedings of the NCTM research catalyst conference, National Council of Teachers of Mathematics, Reston, pp 171–176, 2003). This phenomenographical study offers empirical findings on commonly identified purposes across ten expert MTEs who provided K-8 prospective teachers with opportunities to develop PCK in their mathematics content courses. Furthermore, our emergent findings indicated that expert MTEs also provided opportunities for prospective teachers to develop orientations toward teaching the subject, which prompted framework adaptations and articulations of “orientations” as a construct discussed in the broader literature outside of mathematics teacher education research (Magnusson et al., in: Gess-Newsome, Lederman (eds) Examining pedagogical content knowledge, Kluwer, Dordrecht, pp 95–132, 1999). Research and practitioner implications from this study provide specific PCK-related learning opportunities of prospective teachers through the lenses of expert MTEs’ (personal and professional) purposes and reflections on teaching, as a foundation on which the field can continue building future research and MTEs can continue building their practice in mathematics content courses.

This chapter examines preservice teachers' (PSTs) perceptions on the design of both an online and face-to-face mathematics content course for elementary and middle school preservice teachers. The chapter describes the instructor's design goals, considerations, and describes PSTs' experiences in the process of completing the course. Further, the chapter describes the features of the course that provided productive learning opportunities for PSTs. Drawing from PSTs' reflection after completing an online course and face-to-face course, the chapter compares PSTs' experiences and learning outcomes from the online course compared to a traditional face-to-face course. Finally, the authors explicate the affordances and constraints encountered by both the instructor and the students as they completed the online course.

Active learning mathematics classrooms incorporate meaningful activities that emphasize reasoning, thinking and active interaction with mathematics. Current mathematics standards and curricula recommend that Mathematics Teacher Educators (MTEs) use elements of active learning in their mathematics content courses specifically designed for Prospective Teachers (PTs) as they prepare PTs to learn and teach mathematics. However, it can be very difficult for PTs to shift their pedagogical dispositions towards instruction associated with active learning because they typically have not experienced mathematics taught in this way. This article focuses on two instructional practices for MTEs to use with PTs. First, selecting tasks that promote reasoning and problem solving. This includes practices to open tasks for multiple entry points or solution strategies, tasks that allow for analysis of examples and counterexamples, and tasks that evaluate multiple strategies. Second, facilitating meaningful mathematical discourse. This includes practices for whole class and small group discourse. When MTEs use active learning strategies with PTs in their mathematics content courses, PTs begin their journey in shifting their beliefs and understandings about what it means to teach and learn mathematics. By offering PTs valuable active learning experiences during their mathematics content courses and highlighting how these experiences can enhance both PTs’ own understanding and their future students’ mathematical understanding, MTEs will provide a valuable foundation for PTs to meet the expectations for teaching and learning in mathematics classrooms.

There are long-standing and ongoing calls for making mathematics meaningful, relevant, and applicable outside the classroom. In other words, to help students see mathematics as a tool for understanding, analyzing, and changing the world. However, there are also tensions between a focus on classical mathematics goals and a focus on analyzing and understanding social and political issues, which does not always lend itself to focusing on a specific mathematical concept. In this study, we redesigned a mathematics content course for prospective elementary teachers (PTs) to examine whether we could engage PTs in learning both about the classical mathematics content and about understanding and critiquing the world. We examined their learning in both areas and their evolving views of mathematics teaching throughout the course. We found that PTs learned both the mathematics and about the world and in addition they reconceived of mathematics as a tool to make sense of the world. Thus, mathematics content courses can be designed to allow PTs to develop their knowledge in both areas and experience a classroom where teaching math for social justice is a focus.

As mathematics teacher educators, we grapple with determining the depth of mathematical knowledge required of prospective elementary school teachers in our mathematical content courses. We struggle with identifying the mathematics appropriate for these courses as well as making the mathematics relevant for these teachers. If these classes are housed in a department of mathematics, as ours are, this discussion must take into account the expectations of our departmental colleagues. We examined these issues in spring 2001, when we were asked to redesign a mathematics content course for preservice elementary school teachers. In this article, we describe some of our experiences, including our decision to use middle school mathematics curricular materials as the primary textbooks.

Differentiated instruction is a promising approach for supporting the diverse needs of students. To support prospective teachers with the challenge of implementing differentiated instruction in their future instruction and to meet their diverse needs as college students, we decided to incorporate differentiated instruction in our mathematics content course for them. The specific objective of this study was then to examine how the prospective elementary teachers experienced differentiated instruction in the mathematics content course, whether it met their varying instructional needs, and how it may impact their future mathematics teaching. Qualitative and quantitative analyses revealed that the prospective teachers found the differentiated instruction supportive of their diverse needs and that they plan to incorporate similar features in their future instruction. However, the prospective teachers' comments did reveal additional aspects about differentiated instruction to learn and strengthen. Suggestions for revising the mathematics content course and enhancing the differentiated instruction are provided along with directions for further research.

This descriptive case study examines six mathematics teacher educators’ (MTEs) perspectives on their design of content courses for elementary preservice teachers. By focusing on MTE’s design goals and considerations for their mathematics content courses, the means by which they achieved these course design goals, and the challenges they encountered as they carried out their design goals, this study adds to the image of mathematics content courses, and sheds light on the work of MTEs. Our findings indicate that MTEs design content courses that take a learner-centered approach to instruction and that in designing learner-centered content courses, MTEs face a variety of challenges. Implications for the professional development of MTEs are discussed.

Secondary mathematics pre-service teachers (PSTs) are required to take university-level mathematics content courses to develop their mathematical content knowledge. Although PSTs’ experiences as students play a major role in the types of teachers they become, there is limited research investigating the experiences of PSTs engaging in these courses. Thus, our study used a series of semi-structured interviews to provide first-hand accounts of PSTs’ experiences. Findings suggest that PSTs experienced a range of challenges, including difficulties connecting with and understanding course content, and being ignored and dismissed by mathematics instructors. To cope with these challenges, PSTs became reflective practitioners and considered how their experiences in these courses applied to their learning as future teachers. PSTs also developed a community with each other that grew out of needing support with mathematical content, but evolved into collegial friendships. While PSTs were able to find positive features within negative experiences, this study highlights the need to understand PSTs’ experiences in these courses so that effective improvements can be made.

Preservice teachers often hold deficit views about the students they will teach and their communities. These limiting beliefs can result in lower expectations of and poor outcomes for the students, and need to be addressed in all areas of teacher education, including mathematics courses. In particular, mathematics content courses for preservice teachers offer numerous opportunities for investigating social justice issues and challenging preservice teachers’ beliefs. The assignment described in this manuscript provides an example of the work that can take place in mathematics content courses for preservice K-8 teachers. As part of the assignment, preservice teachers used mathematics to investigate negative perceptions that their campus community has of the surrounding neighborhood. They wrote reflections and created mathematical arguments about household income, poverty rates, educational attainment, crime, and diversity in the neighborhood. Through working on the assignment many preservice teachers began to question their stereotypes about the community. Because of the preservice teacher interest in the topic, and because some problematic beliefs were displayed in the reflections, there is a need for similar assignments in this and other courses, in order to help preservice teachers see the strengths of diverse communities, instead of just their shortcomings.

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 education, particularly the need for strengthening it at the childhood level, this work contributes to a growing body of research that can help future elementary education teachers become exemplary educators.

This study examined the development of prospective teachers’ (PTs) understanding of productive struggle using video episodes which PTs analyzed through the lens of professional teacher noticing. Our qualitative study included 66 PTs in four sections of a semester-long mathematics content course for prospective elementary and middle school teachers that focused on numbers and operations. The goal was to give PTs opportunities to observe students struggling with the course content the PTs were studying and to enact their specialized content knowledge and pedagogical knowledge for teaching simultaneously. Findings suggest that the PTs develop the ability to attend to and interpret the mathematics underlying the student struggles through video analyses. They also begin to identify teaching strategies and practices that appear potentially useful for supporting productive struggle. The use of a productive struggle framework helped the PTs develop a language for discussing productive struggle. Findings also suggest that PTs who had very little knowledge of productive struggle became more aware of what it looks like in practice, discuss ways to support students’ struggle and suggest its potential value in supporting students’ understanding of mathematics. One implication for this study is to carefully weave opportunities to develop teaching practices such as support of productive struggle into the content course for teaching. The PTs may better bridge the stance between being a student and becoming a teacher in what productive struggle looks like in learning mathematics.

Prospective elementary school teachers (PTs), at the completion of their mathematics content course, often feel that (1) they did not learn anything new in the course, (2) they “knew it all along,” and (3) they just needed a refresher. Thus, PTs often undervalue both their own learning in the mathematics content course and the complexity of the elementary mathematics content they learned. In this study, I replicate prior work in which I found that conducting a videotaped interview with PTs at the beginning of the course can help them recognize, before taking the course, that they have mathematics content to learn. I also extend that work by having PTs view their videotaped interviews at the end of the course. I argue that reviewing of the interview and thus remembering what they did not know before the course can help PTs recognize, after they have taken the course, that they have learned content. This remembering led the PTs not only to appreciate the content they learned but also to be aware of the complexity of elementary mathematics, an essential aspect of Mathematical Knowledge for Teaching.