Mathematics teacher educator noticing: examining interpretations and evidence of students’ thinking

Noticing is a skill that is not overtly observable yet is consequential to effective mathematics instruction. Researchers have found that prospective and practicing teachers can learn to notice, but little focus has been given to those who teach teachers to notice. The purpose of the study was to characterize mathematics teacher educators’ noticing and their ability to interpret students’ thinking and connect interpretations to evidence. Participants in the study included 16 mathematics teacher educators who took part in a course designed to support noticing. Results indicate the mathematics teacher educators noticed at varying degrees and improved their noticing and incidence of connections between interpretations and evidence. Findings indicated that 19% of participants had no shift in their noticing because they were at the highest level of noticing to begin with (Robust with Strong Evidence), which was considered advanced noticing. Twenty-five percent of the participants did not shift in their noticing at all and remained at Limited, which is considered an intermediate level of noticing. The remaining 56% of the participants improved their noticing. The results of the study reveal that at the end of the course a majority of the participants were able to connect interpretations with evidence. These findings are important because they describe mathematics teacher educators’ interpretations and evidence as they notice.

     

Mathematics anxiety and mathematics teacher efficacy in elementary pre‐service teachers

This study investigated the relationship between mathematics anxiety and mathematics teacher efficacy among 156 elementary pre‐service teachers from a university in the southeastern United States. Data sources included the Mathematics Anxiety Rating Scale (MARS), Mathematics Teaching Efficacy Beliefs Instrument, and pre‐service teacher interviews. Findings revealed a significant, negative relationship between mathematics anxiety and mathematics teachers’ efficacy (r = ?.475, p<.05). Specifically, the pre‐service teachers with the lowest degree of mathematics anxiety had the highest levels of mathematics teacher efficacy. Interviews with pre‐service teachers indicated that their mathematics anxiety is associated with efficaciousness toward mathematics teaching practices and is the basis for their mathematics teaching efficacy beliefs.     

Understanding change through a high school mathematics teacher’s journey to inquiry-based teaching

This article focuses on an experienced high school mathematics teacher who changed her practice without participating in planned interventions aimed at producing this change. It reports on the nature of the teacher’s change from her perspective and an interpretation and understanding of the change from the researcher’s perspective. It illustrates how meaningful change can occur when the process is initiated and rooted in the teacher’s experience based on a tension in self and/or practice that is personal and real to him or her. It discusses three types of change that are possible depending on the level of engagement of the teacher in professional development opportunities: instrumental change, conceptual change, and foundational change.     

Mathematics teacher educator knowledge: What do we know and where to from here?

The knowledge that mathematics teacher educators need has attracted limited but increasing attention in recent years. The papers in this special issue build on emerging themes from that work and raise additional questions that contribute towards a future research agenda in the field. Several of the articles develop conceptualisations of teacher knowledge to apply to mathematics teacher educators, introducing new aspects and drawing attention to unique characteristics of mathematics teacher educators in the process. To some extent the questions these papers raise reflect similar questions in mathematics education more generally but for which the implications for mathematics teacher educators warrant attention. In this paper we review the articles in this special issue and use them as a springboard to examine contemporary developments in the field and posit ways forward for research on mathematics teacher educators’ knowledge.     

The activities of a school‐based teacher educator: a theoretical and empirical exploration

Teacher education all over Europe is increasingly becoming school‐based oriented. This implies new roles for those who support student teachers learning in school. This article describes the way four school‐based teacher educators fulfill their role as educators of student teachers who learn how to teach while participating in the workplace. Based on theoretical notions derived from the literature on teacher education and workplace learning, the Cognitive Apprenticeship Model was specified and used in a case study as a framework to describe the activity of these school‐based teacher educators. They use tools (e.g., apprenticeship assignments) developed within the teacher education institute and rely on their professional knowledge as experienced schoolteachers. This results in student teachers being provided with useful tricks which, however, hardly helps them to interpret and elaborate their experiences from a more conceptual or theoretical perspective. Also the possibilities of the social context of the school as a learning environment are not systematically used.     

A novice mathematics teacher educator–researcher’s evolution of tools designed for in-service mathematics teachers’ professional development

This study documented the process of evolution of the continuous design and revision of the tools of a novice mathematics teacher educator–researcher (MTE-R) as he planned and implemented design-based professional development workshops for in-service mathematics teachers in Taiwan. In order to effectively facilitate teachers designing and implementing their own conjecturing activities during the workshops, the MTE-R fostered their professional learning and growth through reflection upon students’ performance. From the perspective of activity theory, this study examined the evolution of the MTE-R’s mentoring activities and tools whose design gradually changed from being based on the literature content toward being learner-centered activities with teachers as learners. Such evolution not only enhanced teachers’ learning outcomes, but also facilitated the MTE-R’s own professional growth in different areas, including mathematics, mathematics learning, mathematics teaching, teacher education, and, in particular, the extrapolation of generic examples for understanding mathematical concepts.     

Active learning—a cultural change needed in teacher education and schools

In this article, the purpose is to evaluate how teacher education may promote active learning and what the main obstacles are to reach this target. The problem is investigated from the perspective of student teachers, teacher educators, teachers and pupils in schools. All these groups have evaluated how active learning is applied and what the obstacles are to active learning. The results clearly indicated that schools and teacher education departments are in the middle of a cultural change. Many indicators of active learning can be seen, but there are many obstacles which should be overcome.     

Principal–teacher interactions and teacher leadership development: beginning teachers’ perspectives

Teacher leadership lies at the heart of school improvement. Leadership development among beginning teachers, however, is often neglected. This paper examines the role of principal–teacher interactions in the leadership development of a group of beginning teachers. Using a case study design, interviews were conducted and documentary evidence was collected. The results showed that the beginning teachers were able to take up leadership roles in schools both formally and informally. Development of teacher leadership requires constructive and regular communication with teachers and encouragement of their continuing professional development. Three types of effects on principal–teacher interactions in developing teacher leadership were identified: ‘inspirational’, ‘empowering’ and ‘allowing’. These interaction patterns contribute to the international knowledge on teacher leadership development in schools. Implications for school leadership are discussed.     

Grounding practice in scholarship,grounding scholarship in practice: Knowledge of a mathematics teacher educator–researcher

Despite the acknowledged complexity of the expertise of teacher educators (Cochran-Smith, M. (2003). Learning and unlearning: the education of teacher educators. Teaching and Teacher Education, 19, 5--28), there is limited research attending to what teacher educators need to know and how they develop this expertise. This self-study draws from multiple frameworks of teacher knowledge to investigate knowledge content, structure, and growth of a novice mathematics teacher educator-researcher (MTE-R) from her doctoral program into her third year of a tenure-track faculty position at a large southwestern United States university. Narrative inquiry was used to both examine past artifacts and create new data. The findings highlight how the multiple roles of MTE-Rs elicit different kinds of knowledge and how frameworks for studying mathematics teachers can be utilized for studying teacher educator-researchers.     

The teacher educator’s role as enacted and experienced in school-based development

ABSTRACT

This article focuses on teacher educators’ role and how it was enacted and experienced by teachers and leaders in a school-based development project. The arena for the teachers’ professional development was the school, and teacher educators at one teacher-education institution and three schools took part in the research. Teacher educators, teachers and school leaders were interviewed two years and two months after they formally took part in the project, for one year in a pilot program and afterward for three semesters. The findings show that the teacher educators enacted their roles differently, and that they realise that they should have collaborated more and coordinated their experiences from collaborations with teachers and leaders to learn from their experiences in school. The leaders and teachers were satisfied with the teacher educators’ lectures, but the teachers wanted more dialogue with teacher educators and felt that teacher educators should have helped them transform their knowledge into teaching actions in practice. Teacher educators taking part as supporters in teachers’ practice truly could infiltrate instruction and learning. The study demonstrates that culture, structure and content need to be coordinated to enhance school-based development.     

MOOCs in teacher education: institutional and pedagogical change?

We study the implementation of a MOOC initiative which involved two distinct teacher education institutions at HEIs, and where the implementation was led by a governmental body. Our aim was to see in what ways this initiative changed the teacher education involved, in terms of institutional organisation and pedagogics. Based on interviews with stakeholders from the government and from the two HEIs, we found that the process of implementing and piloting the MOOC faced various sorts of resistance. Our study might serve as a contribution to researchers and practitioners involved in development and running MOOCs as cross institutional initiatives, in that it addresses the diversity of challenges new study models are facing within HEIs. It may also be of interest to teacher education departments responsible for continuing education programs, since it demonstrates the opportunities that comes with a MOOC to provide larger groups of in-service teachers with new educational possibilities.     

Understanding a high stakes teacher performance assessment in mathematics through elementary prospective teachers’ lived experiences

Journal of Mathematics Teacher Education - Within a global context of more standardization of teacher preparation, programs in the USA are increasingly using standardized teacher performance...     

Mathematics in and through social justice: another misunderstood marriage?

The current push to marry off mathematics with social justice compels one to ask such critical questions as “What is social justice?” and “How does (or can) mathematics look and act when viewed in/through the lenses of social justice?” Taking a critically reflective approach, this article draws the reader into a discussion of what is amiss in the currently promoted picture-perfect marriage of mathematics and social justice, presenting perspectives on both the content and context of mathematics teaching and learning. In this article, the author’s account of her experience in teaching a mathematics curriculum course for prospective middle years' teachers highlights a call to re-imagine the relationship between mathematics and social justice as more than a perfunctory integration of a “statistics and figures” approach. The author’s reflections acknowledge the complexity and potentiality of the relationship while challenging current status quo practices and paradigms in mathematics education.