The Participation, Beliefs, and Development of Arithmetic Meaning of a Third-Grade Student in Mathematics Class Discussions

An Investigation of Relationships between Seventh-Grade Students' Beliefs and Their Participation during Mathematics Discussions in Two Classrooms

“…Mathematics education researchers have begun to examine links between students' beliefs and classroom norms and practices (e.g., Bowers & Nickerson, 2001;Cobb et al, 2001;Lo, Wheatley, & Smith, 1994;Stephan, Cobb, & Gravemeijer, 2003); these studies primarily emphasized the analysis of classroom norms and mathematical practices in single classrooms, complemented by analyses of students' beliefs that focus on case studies of small JANSEN numbers of students. In this study, I coordinated analyses of students' beliefs with the analysis of social interactions by shifting the emphasis onto individual students and analyzed a larger number of cases (N = 15) of students' participation and beliefs, with complementary analyses of typical patterns of interaction during whole-class discussions in two classrooms.…”

Pedagogical, Mathematical, and Real-World Conceptual-Support Nets: A Model for Building Children's Multidigit Domain Knowledge

“…Thus, conceptual supports can be useful in enabling children to carry out and communicate solution methods, but teachers must also use them in class activities that are structured to help children learn knowledge that is required for more advanced methods. Without such activities, children may continue to use unitary methods of counting all of the ones, even in third or fourth grade and even in projects focused on meaning-making (Cobb, 1995;Drueck, 1997;Lo, Wheatley, & Smith, 1994;Steinberg, Carpenter, & Fennema, 1994).…”

“…Cobb, Wood, & Yackel, 1993;Cobb & Bauersfeld, 1996) did use models of tens and ones (often unifix cubes stored in columns of ten), but few teachers seem to have used systematic activities with such models to facilitate all children's construction of generative tens conceptual structures. Some children in third grade (Lo, Wheatley, & Smith, 1994) and in the fourth grade (Steinberg, Carpenter, & Fennema, 1994) were still using unitary methods. In our experience, all second graders, even those coming from backgrounds of urban poverty, can come to carry out and explain generalisable addition and subtraction methods involving tens by several months into the school year if they have experiences to help them construct the conceptual prerequisites for such methods (Fuson, 1996;Fuson & Smith, 1995;.…”

Teacher Education Does Matter: A Situative View of Learning to Teach Secondary Mathematics

“…These calls for more meaningful discourse in mathematics classrooms are grounded in research demonstrating the social nature of learning mathematics (Cobb, Boufi, McClain, & Whitenack, 1997) and a vision of school mathematical practice that reflects the essence of mathematical practice within the discipline (Lampert, 1990). It is through participation in A SITUATIVE VIEW OF TEACHING MATH classroom discourse that students become initiated into the community of mathematical practice (Lo, Wheatley, & Smith, 1994). Mathematical discourse in the classroom provides an arena in which the students learn how to represent mathematics through thinking, talking, agreeing, and disagreeing about mathematics, rather than learning from the talk (Lave & Wenger, 1991).…”