The complexity of mathematics teaching and learning in mathematics teacher education and research

Abstract

Coping with the complexity of mathematics teaching and learning in the practice ofteaching is an everyday task for a mathematics teacher, teacher educator, and researcher.Krainer (2003) considers that the field of mathematics education has moved toward a betterunderstanding of this complexity: ‘‘The growth of mathematics education as a scientificfield can be regarded as a continuous process of having a deeper and deeper understandingof the complexity of learning and teaching’’ (p. 93). In mathematics teacher educationresearch, as reported in a number of articles of the Journal of Mathematics TeacherEducation (JMTE), this complexity is tackled in different ways and contexts. Some studiesare exploratory with a focus on how teachers cope with the classroom complexity. Othersare developmental in the sense of creating contexts for teachers, which would promotetheir awareness of the complexity of teaching and learning mathematics and support themto cope with this in the classroom.At the exploratory level, the complexity lies in the classroom interactions and the waysthat the teacher is balancing mathematical goals, students’ reasoning and thinking, andclassroom management. As Wood (2002) argues, the alternate forms of teaching and theresearch on them have brought under consideration situations such as classroom norms,patterns of interaction, supporting students’ mathematical thinking, and reasoning asimportant issues in mathematics teaching that pose new challenges for the teacher, theteacher educator, and the researcher. Moving beyond this micro level of the mathematicsclassroom and addressing wider social factors that frame mathematics learning andteaching, Valero (2010) addresses another layer of complexity involving a network ofdifferent practices that seem to frame the didactical triangle and emphasizes the need formathematics education research to consider the connections between these differentpractices and mathematics teaching and learning. Sullivan (2006), in his editorial, alsooffers specific examples to indicate that ambiguities that exist in curriculum goals and inresearch findings create dilemmas to teachers and teacher educators who try to balancedifferent and often dichotomous goals of mathematics teaching. These complexities raised