Supporting novice mathematics teacher educators teaching elementary mathematics content courses for the first time

This study examines prospective elementary teachers' growth and development of competencies, conceptions, and perceptions of mathematical modelling in a mathematics content course for elementary teachers. A series of lessons were implemented that engaged students in the modelling process through modelling tasks. The goal was to capture prospective teachers' thoughts and perceptions on the meaning of mathematical modelling and their conceptions of teaching and learning modelling at the elementary and middle school level. The research questions were: (1) How do prospective teachers translate the mathematical modelling cycle into their practice of doing modelling? and (2) How do prospective teachers' conceptions of modelling and teaching and learning modelling evolve throughout the implementation of a series of mathematical modelling lessons? Data sources included posters, modelling reports, responses to a pre- and post-intervention questionnaire, and semi-structured interview dialogue. Data analyses included mixed methods using provisional coding, open coding, and a categorical rubric. Findings from this study indicate that (1)Prospective elementary teachers translated the modelling cycle into their practice by developing their range of modelling competencies including multiple components of the modelling cycle, and (2) They developed a professionally appropriate conception of mathematical modelling along with productive perceptions of the benefits of teaching and learning modelling.

The expertise of novices: A framework for prospective teacher’s noticing of children’s mathematical thinking

The transition from learner to teacher of mathematics is often a difficult one for prospective elementary teachers to negotiate. Learning to teach necessitates the opportunity to practice the discourse of teacher of mathematics. The undergraduate mathematics content classroom provides a setting for prospective teachers to practice the discourse of teacher through their interactions with each other while also learning the mathematical concepts presented in class. This qualitative study sought to examine what roles prospective teachers adopt while engaged in a cooperative problem-solving task. Discourse analysis was applied to analyze the verbal interactions between three participants in a mathematics content course. Key disruptions in the conversation revealed instances of the fluid relationship between learner and teacher of mathematics in the roles they adopted while solving an application problem: self as learner-in-teacher, collaborator as learner-in-teacher, and unlikely learner-in-teacher. The presence of this fluid relationship led to the proposal of a model of learner-in-teacher-in-learner of mathematics. This proposed model suggests that prospective teachers have the opportunity to learn how to teach in and through each other when given the opportunity to engage in dialogue with one another.

Prospective elementary teachers may enter their teacher education program having experienced science more as a collection of definitions and facts than in ways that support rich engagement with scientific phenomena. As a result, their visions of themselves as science teachers may not align with the most recent understandings about how to teach science to support student learning. Science methods courses are settings that have the potential to shift prospective teachers’ visions of science teaching. We used an explanatory sequential mixed methods approach with collection of survey data followed by interviews with selected participants. We analyzed how prospective elementary teachers’ visions of science teaching shifted over the course of a one-semester science methods course and what experiences they felt most influenced their visions of teaching science. We found that the visions of science teaching shifted towards or maintained alignment with the principles of science teaching introduced in the science methods course. Additionally, the prospective teachers identified model science activities and explicit connections between these activities and how students learn science as having influenced them in terms of how they thought about teaching science.

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.

There is compelling evidence on the effectiveness of bibliotherapy for facilitating one’s development. Arguably, in teacher education, bibliotherapy has been shown to facilitate prospective teachers’ professional development. However, teacher educators may experience difficulties in finding relevant reading to stimulate prospective teachers’ identification process, which is essential if the application of pedagogical bibliotherapy is to be successful. This study is situated in a mathematics education course for prospective elementary school teachers and explores the features of relevant pedagogical reading via analysis of four prospective elementary school teachers’ identification processes with two case descriptions. The identification here relates to the reading of the so-called true stories; prospective teachers read stories of other prospective teachers from the same teacher education context. We outline the recommendations for the selection of reading material when applying pedagogical bibliotherapy in order to assist prospective teachers’ professional development.

Prospective teachers bring countless stories of success and failure from different mathematics classrooms to their post-field teacher education courses. These reflective stories often glorify school mathematics classrooms and dominant traditions within, instead of confronting the marginalization of diverse groups in school environments. Mathematics teacher educators have a significant role to play in teaching prospective teachers to reflect critically on their field experiences and, in doing so, create spaces for disruption and disruptive pedagogies. Drawing on critical and equity-based theories applied within the fields of mathematics education and teacher education research, we propose a disruptive pedagogy analytical framework that enables us to study the roles and practices of mathematics teacher educators as they conduct their work in these post-field contexts of teacher education. In this paper, we introduce our disruptive pedagogy framework and present the results that followed from using it to analyze data from a research study in which mathematics teacher educators from across Canada and Norway were interviewed. We claim that our analytical framework can be used to identify those disruptive and transformative practices initiated by mathematics teacher educators—practices that are necessary to bring about shifts in inequitable and unjust classroom practices of school mathematics and in becoming a teacher. Unfortunately, however, results reported here point to the need for further shifts and growth toward more explicitly disruptive practices initiated by mathematics teacher educators in the post-field context.

Epistemological beliefs refer to an individual’s thinking and beliefs about the nature of knowledge and knowing. The present study examined two research questions: (1) how do prospective elementary teachers’ epistemological beliefs in science change as a result of instruction specifically designed to improve their epistemological beliefs and (2) what role does the conceptual ecology for epistemological beliefs play in their development? The study was correlational with a sample of 161 prospective elementary teachers (148 female, 13 male). Self-report questionnaires tapping four dimensions of epistemological beliefs (certainty-simplicity, justification, source, attainability of truth) were given to prospective elementary teachers at two time points during an introductory science course. Results indicated that prospective elementary teachers became more sophisticated in their beliefs across all four dimensions of epistemological beliefs. It was found that one component of conceptual ecology for epistemological beliefs, thinking dispositions, was related to the development of epistemological beliefs. Prospective teachers with high thinking dispositions developed more sophisticated beliefs in comparison to prospective teachers with low thinking dispositions.

Inferentialism has emerged as a valuable theoretical resource in mathematics education. As a theory of meaning about the use and content of concepts, it offers a fresh perspective on traditional epistemological and linguistic questions in the field. Despite its emergence, important inferentialist ideas still need to be operationalized. In this paper, I operationalize multiple inferentialist concepts to analyze prospective secondary mathematics teachers’ learning about graphs and quantitative and covariational reasoning in a mathematics content course. I use Robert Brandom’s ideas about upstream, downstream, and incompatible inferences to illustrate the inferentialist mastering metaphor for learning and Brandom’s ideas about objectivity. My analysis shows (a) inferentialism’s capacity to address epistemological issues like objectivity and conceptual understanding, (b) the importance of attending to different types of inferences to assess learning from an inferentialist perspective, and (c) how the development of mastery is associated with virtues. I conclude by identifying the study’s potential limitations and trajectories for future research.

This article describes the 3rd cycle of an intervention in a mathematics content course that was designed to foster awareness among middle school mathematics preservice teachers (PSTs) of the challenges that English language learner (ELL) students face and the resources they draw on as they learn mathematics and communicate their thinking in English-only classrooms. Pairs of PSTs engaged 2 different ELL students in a videotaped task-based interview using 4 measurement tasks. Following each interview, the PSTs wrote a structured report guided by Mason's (2002) framework of noticing. The results of the intervention indicated that the PSTs went beyond awareness of ELLs' needs and challenges and also adopted strategies outlined in the literature that were aligned with best practices for teaching ELLs. The article also discusses the potential of the intervention and how it can be used by other mathematics educators.

An elementary mathematics teacher once argued that she and her students held four Rights of the Learner in the classroom: (1) the right to be confused; (2) the right to claim a mistake; (3) the right to speak, listen and be heard; and (4) the right to write, do, and represent only what makes sense. Written as an emerging framework to promote equity in the mathematics classroom through divergent formative assessment, the RotL assumes that students can take more explicit ownership of their learning, both in writing and in oral communication. Foregrounded in the literature, this paper discusses how the RotL can help children and teachers to embrace productive struggle and mistakes as valuable steps in the process of learning mathematics (and learning to teach mathematics). The paper also frames the RotL with divergent formative assessment as a tangible means of honoring students’ mathematical resources (e.g., native language, out-of-school knowledge and experiences) to help all students learn mathematics. The paper also presents the experiences of a mathematics teacher educator as she learned about and incorporated the RotL with her prospective elementary mathematics teachers in a university methods course. Implications for mathematics education and teacher education are discussed.

Introduction A common response when questioning in-service mathematics teachers about their mathematical preparation for teaching is that their college mathematics courses did not adequately prepare them to teach school mathematics because the college courses often failed to connect the mathematics they were learning with the school mathematics that they would be teaching. Though the courses were rich in mathematical ideas, their connections to important concepts in school mathematics were not always explicitly detailed. Several factors contributed to this deficiency, but the most prominent one was the lack of high quality textbooks that identify and explain the critical connections. Without such materials, it is challenging and time consuming for mathematicians, who primarily teach content courses for pre-service teachers and who are typically unfamiliar with school mathematics curricula, to make these critical connections. To help address the need for specialized courses and materials for pre-service mathematics teachers, the Conference Board of Mathematical Sciences, and the Mathematical Association of America (with funding provided by the United States Department of Education), developed the Mathematical Education of Teachers Report(MET) , [2]. It gives a framework for mathematics content courses for prospective teachers that is built on the premise that “The mathematical knowledge needed for teaching is quite different from that required by college students pursuing other mathematics-related professions. Prospective teachers need a solid understanding of mathematics so that they can teach it as a coherent, reasoned activity and communicate its elegance and power.”

Fractions are important in young students’ understanding of rational numbers and proportional reasoning. The teacher is fundamental in developing student understanding and competency in working with fractions. The present study spanned five years and investigated prospective teachers’ competency and confidence with fraction operations as they entered a college mathematics content course designed for teachers. Results indicate prospective teachers’ levels of competence vary by fraction operation. Many of the same error patterns exhibited in the 1980s and early 1990s are still exhibited today. Many prospective teachers inaccurately predict their performance on multiplying fractions with relatively prime denominators and dividing reciprocal fractions.

Traditional teaching methods have become obsolete in modern society, especially in preparing prospective elementary school teachers to face the challenges of the 21st century. Therefore, a new educational approach is needed that is able to develop globally relevant knowledge, skills, and character values. This study aims to analyze the effect of science, technology, engineering, and mathematics (STEM)-based hybrid learning on the 21st-century skills and character values ​​of prospective elementary school teachers. This study uses a mixed-methods method with an explanatory sequential design, where quantitative data is collected first and then continued with qualitative data to deepen the findings. The sample consisted of 156 students from four universities in Indonesia: Universitas PGRI Yogyakarta, STKIP Majenang, Universitas Islam Sultan Agung, and Universitas PGRI Semarang. The validity of the instrument was tested through expert judgment, while reliability was tested using Cronbach's alpha. The research instruments included an essay test to measure critical thinking skills and creativity, as well as a Likert scale questionnaire (1–5) to assess communication, collaboration, and character. Data were analyzed using Multivariate Analysis of Variance (MANOVA), with results showing significant F values ​​for all indicators (Pillai’s Trace = 7.709; Wilks’ Lambda = 8.115; Hotelling’s Trace = 8.344; Roy’s Largest Root = 14.295; p < 0.001), indicating that the hybrid-STEM model has a significant effect on improving 4C skills (critical thinking, creativity, collaboration, and communication) and students’ character values. Surveys and observations also showed a positive response to this model, which was proven to improve conceptual understanding, problem-solving skills, and active involvement in learning. This study recommends strengthening STEM-based learning in higher education as a strategy to produce prospective teachers who excel academically and in character. The limitations of the study lie in the scope of the institution and the number of samples, which are still limited, so it is recommended to conduct further studies with a broader context to strengthen the generalization of the findings.

The purpose of this study is to explore preservice teachers’ (PTs’) ability to implement multiple strategies using standard algorithms and alternative strategies and to investigate their conceptual knowledge of decimal operations. There were 37 PTs who participated in this study, all of whom attended a mathematics course in the K-8 Teacher Education Program at a mid-western university. These participants were asked to solve the Decimal Knowledge Test (DKT) in multiple ways. A qualitative approach was used to analyze PTs’ responses to the problems on the DKT. The results indicated that using standard algorithms, PTs demonstrated higher ability in solving decimal addition, subtraction, and multiplication involving a whole number. Alternative strategies posed difficulties in solving decimal multiplication problems involving two decimals, and division problems. Similarly, when examining operations, showing smooth or difficult translations between the representations, PTs found it difficult to translate representational modes in operations with multiplication involving two decimals, two division problems. The same results were seen when examining PTs’ conceptual understanding based on the Lesh Translation Model. The results provide teacher education programs with opportunities to create various instructional approaches involving translations among multiple representations in mathematics methods and content courses.