Teacher's Pedagogical Content Beliefs in Mathematics

Comparative studies of mathematics teaching: does the means of analysis determine the outcome?

“…Also, structural knowledge, reflecting relationships between concepts and topics is a higher order learning outcome resonant with notions of relational understanding as described by Skemp (1976). Finally, the characteristics of this factor reflect well current perspectives on reform mathematics teaching, whereby learners actively construct rather than passively receive knowledge (Cady et al 2007;Peterson et al 1989) and, "through interaction, are able to challenge one another's constructions in ways that facilitate the construction of increasingly shared and powerful knowledge" (Beswick 2005, p. 43) in classrooms that emphasise the making of mathematical connections (Cady et al 2007;Peterson et al 1989;Spillane and Zeuli 1999). In sum, we construe this factor as a relational participation.…”

“…On the one hand, the activation of prior knowledge, matches reform expectations that teachers take account of learners' prior knowledge when making decisions about lesson progression (Beswick 2005;Cady et al 2007;Peterson et al 1989). On the other hand, reform classrooms are also characterised by an emphasis on problem solving (Cady et al 2007;Peterson et al 1989;Spillane and Zeuli 1999). Such findings highlight the fact that effective mathematics teaching is a complex interaction of many factors and that these may not, depending on circumstances, be complementary.…”

In-Service Mathematics Teachers’ Beliefs About Teaching, Learning and Nature of Mathematics and Their Mathematics Teaching Practices

“…Also, findings indicated that teacher preparation programs had a limited effect on teachers' beliefs or practices. Peterson, Fennema, Carpenter & Loef (1989) has tested the relationship between the beliefs of first grade teachers and their pedagogical knowledge and accomplishments on the subject of mathematics. In this study, questionnaires were used and interviews were held with teachers to explore their beliefs and their knowledge of teaching.…”

“…A number of studies found that teachers' classroom practices related to the teaching of mathematics are affected by their beliefs (Cam, 2015;Sapkova, 2014;Memnun & Hart, 2012;Huang & Shiomi, 2007;Stipek, Givvin, Salmon, & MacGyvers, 2001;Peterson, Fennema, Carpenter, & Loef, 1989). While numerous others refute and contradict this claim, for example, (Mohammad, 2005;Wilkins, 2008;Shi, Zhang, & Lin, 2014), one cannot ignore teachers' beliefs and perceptions when aiming to enhance the math learning and math teaching processes and improve student performance in the subject area.…”

Supporting Mathematics Coaches’ Learning of Probability through Professional Development Tasks

“…Research has provided the mathematics community with a great deal of attention to knowledge as it relates to teaching mathematics and preparing novice or experienced teachers to carry out instruction (Carpenter, Fennema, Peterson, & Carey, 1988;Hill, Schilling, & Ball, 2004;Peterson, 1988;Peterson, Fennema, Carpenter, & Loef, 1989;Shulman, 1986Shulman, , 1987Wilson, Shulman, & Richert, 1987). In some instances, teachers have strong content knowledge but weak pedagogical knowledge or vice versa.…”