Conditions of progress in mathematics teacher educ

Authors: João Pedro da Ponte

Publish Date: 2009/09/25

Volume: 12, Issue: 5, Pages: 311-

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Abstract

The progress of mathematics teacher education as a field of study depends on theoretical and empirical work Both kinds of work are intimately related Any scientific article that reports an empirical study needs to be based in theoretical constructs and at the very end should contribute to a better understanding of these concepts or at least of their power for understanding specific problems and any theoretical work to make sense requires some sort of empirical applicationThe articles in this issue of JMTE draw on several key theoretical concepts in mathematics teacher education content knowledge and pedagogical content knowledge Davis teachers’ beliefs Cross Davis teachers’ practices Cross Ryken and teacher learning Ryken As a subfield of the social sciences we cannot expect that all the authors share the same view about such notions However we must be able to understand how they conceptualize their major theoretical concepts relate them to each other note their similarities and differences and regard the implications of the different choicesTeachers’ knowledge of mathematics includes teacher knowledge of mathematical facts and representations concepts procedures and other information as well as the ability to solve problems to construct and use models to establish connections within and outside mathematics to reason to prove and to evaluate results In this issue Davis in his article titled “Understanding the influence of two mathematics textbooks on prospective secondary teachers’ knowledge” draws on the distinction between factual knowledge and conceptual knowledge that points toward different levels of elaboration Other dimensions of knowledge in action which are captured by the notions of problem solving modeling proving and evaluating are at the core of the current mathematics curriculum orientations for students’ learning and also need the attention of mathematics teacher education researchersTeachers’ pedagogical content knowledge blends “pedagogy” and “content” in a special way Davis stresses two aspects the educative representations that include “the most powerful analogies illustrations examples explanations and demonstrations” and topic perceptivity “an understanding of what makes the learning of specific topics easy or difficult” Pedagogical content knowledge is an appealing notion as it resonates with the experience and concerns of teachers and teacher educators for whom both content and pedagogy are important elements This notion has proved to be very fruitful in research with teachers However it is also a notion that has been reframed over and over again both regarding its content and its nature Is it declarative and formal knowledge that can be learned and assessed using verbal language or is it essentially practical and implicit knowledge that has to appraised and developed through practice Pedagogical content knowledge is the knowledge of experienced teachers seen by their colleagues as professional leaders or is it the knowledge that researchers posit teachers must haveTeachers’ beliefs is another key notion that frames much research on teachers Beliefs are closely related to knowledge establishing a bridge between the cognitive and the affective domain For some researchers beliefs are a special kind of knowledge for others they have different epistemic status In this issue Cross in the article titled “Alignment cohesion and change Examining mathematics teachers’ belief structures and their influence on instructional practice” sees beliefs as “embodied conscious and unconscious ideas and thoughts about oneself the world and one’s position in it developed through membership in various social groups” and gives special attention to teachers’ “mathematics beliefs”—beliefs about the nature of mathematics about mathematics teaching and about student learning Davis also refers to beliefs about mathematics and mathematics teaching There is little doubt that beliefs are a useful concept to describe teachers’ activity However we are still in need of a better understanding about how beliefs develop change and what factors mediate their influence on practiceThe notion of teachers’ practices is another central construct Often practices are regarded as “actions” “acts” “behaviours” or “gestures” that can be observed and categorized in an objective way However teachers may be doing similar actions with quite different purposes in rather different activity systems An element of stability and recurrence in a given context is essential in the notion of practice In addition there is a reflexive relationship between individual activities and social practices—the activities of the individual are constitutive of social practices and at the same time social practices give form and meaning to the activities of the individual In this issue Cross looks at instructional practices with special attention to organizing the classroom environment the classroom discourse and interactions promoted and the types and use of assessments Ryken also looks at assessment practicesFinally another key notion is that of teacher learning or teacher professional development Teachers learn about mathematics curriculum frameworks and management ways of teaching mathematics classroom materials handling classroom discourse students’ strategies and difficulties assessment instruments procedures and implications institutional social and professional values opportunities and constrains Teachers develop professionally as they become more able to use their resources to solve the professional problems that they face in their daily activity Through these processes they develop their professional identity as teachers another notion hinted at by Ryken in the article titled “Multiple representations as sites for teacher reflection about mathematics learning” As this author indicates teacher learning has been analyzed from both a cognitive perspective putting emphasis in developing concepts and problem solving strategies and a socialization perspective balancing choices and constraints within institutional cultures Both perspectives address different issues and shed light on different phenomena How can we connect them in a meaningful and productive ways What price do we pay in making such connectionLooking at other issues of this Journal we could expand this list The fact that we have a handful of major concepts in mathematics teacher education is an important sign of progress However such concepts will only be useful if we take care to discuss and clarify the meaning we give to them and if we establish connections and relations among them which help a better understanding of the ways teachers work think and learn at the different stages of their careers and institutional working conditions

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