FEATURE ARTICLE At the Intersections of the Embodiment and Emergence for a Mathematics Teacher Educator (original) (raw)
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At the intersections of the embodiment and emergence for a mathematics teacher educator
2011
Carolina at Greensboro ESEARCH IN MATHEMATICS EDUCATION and curriculum theory currently has a very limited set of intersections. Few education researchers claim to work in both fields. I draw on the work of those few researchers for my own understandings as a mathematics teacher educator. Now as a part of this small community, I continue to struggle with what it means to be a mathematics educator from a curriculum theorist's perspective. In my journey and in my research, I have come to realize that mathematics is often perceived as an external truth, a fixed set of ideas, and based on that perception, mathematics pedagogy is proffered as basics-asbreakdown (Jardine, Clifford, & Friesen, 2003). As an alternative, I propose that a different way to consider mathematics education is to imagine how one can experience being in the world with mathematics. This being with idea emerged by reviewing two topics in particular: curriculum and the history of mathematics, which are central to my understandings of teacher education, specifically mathematics teacher education. Coupled with this investigation is an autobiographical reflection of how I have experienced being in the world with mathematics and how this investigation allows for a more meaningful engagement in the teaching and learning of mathematics. The intertwining of the personal with the contextual displays how the idea of being with is an interconnected and dynamic notion. The Being With So what does it mean to experience being in the world with mathematics? Many models of schooling lend themselves to the banking metaphor of education, where the teachers are the depositors and the students the depositees of information (Freire, 1970). In this model, teachers are on the "outside" of learning-watching, evaluating, and judging. Creating this inside/outside perspective is prevalent among the discourses and practices of mathematics. Watching mathe
Symposium on the Occasion of the 100th Anniversary …, 2008
Teacher education, both pre-service and ongoing professional development, is increasingly in the spotlight, indexing a recognition that the production of quality teaching is central to any education system. In South Africa an interesting and challenging feature of a new undergraduate Bachelor of Education degree and a variety of formalised inservice mathematics teacher education programmes is what and how mathematical knowledge and practices are distributed, and the consequent opportunities for the education of teachers. While programmes vary across institutions, there is a commonly stated desire to impact on teachers' mathematical knowledge and practices. This is a function of a context of rapid and intense educational change generated by national imperatives to impact generally on the quality of mathematics education and specifically on attempts to eradicate apartheid's legacy of the reproduction of deep educational (and more general) inequality.
Mathematics Educational Research potentials for Mathematics-curriculum-teacher-researchers
2017
DOI: 10.13140/RG.2.2.21419.59681 Teaching- and Research-Methods of Critical Mathematics Education (CME) have to deal with the dichotomy of the social and the individualist aspect of collaborative learning (Nunes and Bryant, 1996; Lerman, 2001; Valero, 2002). Collaboration refers mostly to the formulation and elaboration of a “dialogical learning framework” (discourse) (Civil & Planas, 2004) within which learning happens as the adoption of certain norms, values and notions of importance. The above give rise to elaborations of “social interactions” as tools to interpret the “classroom dialectics”. To that, let us consider tutors and learners as “active social individuals” whose engagement in social interactions abides to principles of “autonomies” and “heteronomies” (Castoriades in: Straume, 2016) defined against an established collection of normative regulations (the instituted society, (ibid.)): these consist also of “established epistemologies” or, in our frame, “established pedagogical contexts and methods”. Within the same contextual trading of the educational frame, Critical Educational Research and, especially, Emancipatory/Transformational Action Research (AR) tend towards the “(self-) institutionalising society” (ibid.) of Learning, that conceptualizes and contains the collective potentials of its autonomous members, preferably “breaking the didactical contracts along the way” (Brousseau, 1997; Brousseau et al., 2014). Diminishing the “autonomous potential” in these dialectical scheme is one of the main reasons of criticism towards Critical Pedagogies, as e.g. in (Giroux, 1983), and supports tendencies towards “social (establishment) reproduction”. It is of no surprise that classical Mathematical Pedagogies tend to adopt Socio-Cultural aspects that support norms and questions of diverse educational-political establishments, be it the cognitive-skills-approach (Freudenthal, 1981; Stinson et al., 20012; Bishop, 2008; Schoenfeld, 2013; Mason, 1998; Kinard & Kozulin, 2008), or CME (Winter, 1996; Elliott, 1994; Skovsmose, 1994; Stinson et al., 2012; Bishop, 2008; Valero, 2002); even if mathematics teachers usually have no means of describing the corresponding demands and principles (Bishop, 2008). In the above sketched conceptual frame, we shall try to describe the position and potential impact of Teacher-Researchers that engage in Transformational and Emancipatory AR on Teaching and Curriculum, and comment on the sought-for characteristics – both educational and civilian – that would facilitate the intervention of the active practitioners in the context of the established pedagogies themselves via critical curriculum research. Let us add to these the need – raised by the engagement in AR-procedures – to learn to “observe in a critical and, at the same time, self-reflecting manner” the procedures of learning themselves; a need that is preferably supported in ME, given its metacognitive aspects.
Teachers’ Interactions with Curriculum Materials in Mathematics Education
Acta Scientiae
From the 1990s, teachers have been provided with a considerable number of materials produced and distributed by different governments to develop a mathematics curriculum to perform as curriculum implementers and promote the mathematical reform of different teaching systems. These resources have been researching tools. However, the types of use that teachers make of them are still little explored. In this article, we present the results of a study that aimed to understand the relationship between teacher-curriculum materials in the area of mathematics education, which takes discussions about teaching competencies of curriculum design as theoretical contributions. The research analysed a research report, and meta-analysis was the methodology adopted. The results indicate that affordances and constraints qualify the materials and potentiate the agency and its displacement, both for teachers and for materials, thus imparting different interactions between these two agents of curriculum ...
Teacher Education Does Matter: A Situative View of Learning to Teach Secondary Mathematics
Educational Psychologist, 2000
The visions of mathematics classrooms called for by current educational reform efforts pose great challenges for kindergarten through Grade 12 schools and teacher education programs. Although a number of colleges and universities throughout the country are making changes in their teacher education programs to reflect these reform recommendations, we have little systematic information on the nature of these programs or their impact on prospective teachers. These issues are of central concern in the study-Learning to Teach Secondary Mathematics in Two Reform-Based Teacher Education Programs-that we draw on in this article. The article focuses on 1 preservice teacher's (Ms. Savant) knowledge, beliefs, and practices related to proof, tasks, and discourse. A situative perspective on cognition and components of teachers' professional knowledge frame our research. We examined data on Ms. Savant's experiences in her teacher education program to understand the influences of teacher education on her development as a mathematics teacher. This research indicates that Ms. Savant's teacher education experiences did make a difference in her development as a teacher. Her mathematics methods course provided a large collection of tasks, engaged her and her preservice colleagues in discourse, and provided her with both formal and informal experiences with proof-all of these experiences reflecting reform-based visions of mathematics classrooms. The situative perspective on cognition directed our attention to issues of compatibility of goals and visions across the various university and kindergarten through Grade 12 classroom settings, and it helped us to understand why some aspects of reform-based pedagogy are more easily learned than others: Why some ideas and practices learned as a student in the university setting are more easily transported to the novice teacher's kindergarten through Grade 12 field setting. We conclude that compatibility of these settings on several key dimensions is essential for the settings to reinforce each other's messages, and thus work in conjunction, rather than in opposition, to prepare reform-minded teachers.
Knowledge of curriculum embedded mathematics: exploring a critical domain of teaching
Educational Studies in Mathematics, 2017
This paper proposes a framework for identifying the mathematical knowledge teachers activate when using curriculum resources. We use the term knowledge of curriculum embedded mathematics (KCEM) to refer to the mathematics knowledge activated by teachers when reading and interpreting mathematical tasks, instructional designs, and representations in mathematics curriculum materials. The KCEM framework is situated within existing research on content-specific teacher knowledge. Through analysis of elementary mathematics teacher's guides from the USA, we identified elements of curriculum resources teachers interact with when using them to plan instruction. These findings were complemented by interviews of teachers using curriculum guides to plan lessons, uncovering how they interacted with different elements of their guides. From this analysis, we propose four overlapping dimensions of KCEM: foundational mathematical ideas, representations and connections among these ideas, problem complexity, and mathematical learning pathways. Using an excerpt from one elementary curriculum guide and one of the teacher interviews on using this guide to plan a lesson, we illustrate how these dimensions might be activated as teachers read and use their guides. Keywords Teacher knowledge. Teacher curriculum use. Mathematics knowledge for teaching 1 Introduction Knowledge used in teaching is currently receiving tremendous attention, both in research and in practice. Since Shulman's (1986, 1987) seminal work proposing a knowledge base for Educ Stud Math
Opening Another Black Box: Researching Mathematics for Teaching in Mathematics Teacher Education
Journal for Research in Mathematics Education, 2006
This article describes an investigation into mathematics for teaching in current teacher education practice in South Africa. The study focuses on formal evaluative events across mathematics teacher education courses in a range of institutions. Its theoretical orientation is informed by Bernstein's educational code theory and the analytic frame builds on Ball and Bass' notion of "unpacking" in the mathematical work of teaching. The analysis of formal evaluative events reveals that across the range of courses, and particularly mathematics courses designed specifically for teachers, compression or abbreviation (in contrast to unpacking) of mathematical ideas is dominant. The article offers theoretical and practical explanations for why this might be so, as well as avenues for further research.
International Journal of Educational Research, 2019
In this study we explore the interactions between teachers and resources during lesson preparation from different perspectives. We ask in which ways the crossing of perspectives help to develop deeper understandings of teacher interactions with curriculum resources. For doing this, we have chosen the following three theoretical frames: (1) Documentational Approach to Didactics (DAD); (2) Anthropological Theory of the Didactic (ATD); and (3) Cultural-Historical Activity Theory (CHAT). We chose data concerning two experienced mathematics teachers (at lower secondary school level) working together, preparing lessons on the topic of " algorithmics " , a topic newly introduced in grade 6 of the French curriculum, and hence a topic they had never taught before.