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To make teacher preparation and professional development effective, it is important to find out possible deficiencies in teachers' knowledge as well as teachers' own perceptions about their needs. By focusing on preservice teachers' knowledge of fraction division in this article, we conceptualize the notion of pre-service teachers' knowledge in mathematics and pedagogy for teaching as containing both teachers' perceptions of their preparation and their mathematics knowledge needed for teaching. With specific assessment instruments developed for pre-service middle school teachers, we focus on both pre-service teachers' own perceptions about their knowledge preparation and the extent of their mathematics knowledge on the topic of fraction division. The results reveal a wide gap between sampled pre-service middle school teachers' general perceptions/confidence and their limited mathematics knowledge needed for teaching fraction division conceptually. The results suggest that these pre-service teachers need to develop a sound and deep understanding of mathematics knowledge for teaching in order to build their confidence for classroom instruction. The study's findings indicate the feasibility and importance of conceptualizing the notion of teachers' knowledge in mathematics and pedagogy for teaching to include teachers' perceptions. The applicability and implications of this expanded notion of teachers' knowledge is then discussed.

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In this study, we aimed to examine mathematics teachers' daily lesson plans and associated practices and thinking in lesson plan development. By focusing on teachers' preparation for teaching fraction division, we collected and analyzed a sequence of four lesson plans from each of six mathematics teachers in six different elementary schools in China. Interviews with these teachers were also analyzed to support the lesson plan analysis and reveal teachers' thinking behind their practices. The results show that Chinese teachers placed a great consideration on several aspects of lesson planning, including content, process, and their students' learning. Teachers' lesson plans were similar in terms of some broad features, but differed in details and specific approaches used. While the textbook's influence was clearly evident in these teachers' lesson plans, lesson planning itself was an important process for Chinese teachers to transform textbook content into a script unique to different teachers and their students. Implications obtained from Chinese teachers' lesson planning practices and their thinking are then discussed in a broad context.

A sample of 134 sixth‐grade students who were using the Connected Mathematics curriculum were administered an open‐ended item entitled, Vet Club (Balanced Assessment, 2000). This paper explores the role of misconceptions and naïve conceptions in the acquisition of statistical thinking for middle grades students. Students exhibited misconceptions and naïve conceptions regarding representing data graphically, interpreting the meaning of typicality, and plotting 0 above the x‐axis.

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