The paper describes aspects of the statistical content knowledge of 46 preservice elementary school teachers. The preservice teachers responded to a written item designed to assess their knowledge of mean, median, and mode. The data produced in response to the written item were examined in light of the Structure of the Observed Learning Outcome (SOLO) Taxonomy (Biggs & Collis, 1982) and Ma's (1999 conception of Profound Understanding of Fundamental Mathematics (PUFM). Four levels of thinking in regard to comparing and contrasting mean, median, and mode are described. Several different categories of written definitions for each measure of central tendency are also described. Connections to previous statistical thinking literature are discussed, implications for teacher education are given, and directions for further research are suggested.Preservice Elementary Teachers' Conceptual and Procedural Knowledge of Mean, Median, and Mode Shulman (1987) used the term "content knowledge" to describe knowledge of the structure and methods of discourse within any given discipline. He stated that the many aspects of content knowledge "are properly understood as a central feature of the knowledge base of teaching" (p. 9). Research illustrates that attaining content knowledge is an important part of a mathematics teacher's development (Putnam, Heaton, Prawat, & Remillard, 1992). At the same time, research illustrates that teachers sometimes lack the content knowledge they need in order to teach elementary school mathematics (Ma, 1999). Ball, Lubienski, and Mewborn (2001) argued that Without such (mathematical) knowledge, teachers lack resources necessary for solving central problems in their workfor instance, using curriculum materials judiciously, choosing and using representations and tools, skillfully interpreting and responding to their students' work, and designing useful homework assignments (p. 433).The statistical measures of mean, median, and mode comprise a fundamental portion of the content knowledge elementary teachers need to possess. Curriculum documents around the world recommend that students develop some understanding of mean, median, and mode before entering secondary school (Australian Education Council, 1994; School Curriculum and Assessment Authority & Curriculum and Assessment Authority for Wales, 1996; National Council of Teachers of Mathematics, 2000). The National Council of Teachers of Mathematics (2000), for example, recommended that students should develop the abilities to "select and use appropriate statistical methods to analyze data" (p. 178) throughout Grades PreK-8. This included attaining proficiency in determining and applying the mean, median, and mode by the end of Grade 8.

A hypothetical framework to characterize statistical knowledge for teaching (SKT) is described.Empirical grounding for the framework is provided by artifacts from an undergraduate course for prospective teachers that concentrated on the development of SKT. The theoretical notion of "key developmental understanding" (KDU) is used to identify landmarks in the development of SKT subject matter knowledge. Sample KDUs are given for the subject matter knowledge categories of common content knowledge, specialized content knowledge, and horizon knowledge. The theoretical notion of "pedagogically powerful idea" is used to describe how KDUs must be transformed to become useful in teaching. Examples of pedagogically powerful ideas for the pedagogical content knowledge categories of knowledge of content and teaching and curriculum knowledge are provided. Knowledge of content and students is hypothesized as a basis for the development of pedagogically powerful ideas.

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Statistics courses for prospective teachers are being developed in response to recent K-12 curriculum recommendations. As these courses are developed, it is important to design accompanying assessments. This manuscript describes a strategy for assessing aspects of statistical knowledge for teaching. The strategy involves analyzing and responding to children's work samples from the National Assessment of Educational Progress. An example is provided to illustrate how such an assessment task can serve to reveal different aspects of respondents' subject matter knowledge as well as their pedagogical content knowledge. Thoughts are provided on how to use the assessment tasks to identify levels of statistical knowledge for teaching.

This paper starts from the premise that teachers’ discourse communities influence how ideas for reform are implemented. In order to understand some of the discourse surrounding the reforms proposed by GAISE, an online focus group activity was conducted. The focus group consisted of pre-service and practicing teachers responsible for teaching statistics at various grade levels. Focus group discourse was used to formulate a set of working hypotheses about actions that need to be taken to facilitate the implementation of GAISE. Working hypotheses emphasized that statistics educators need to play roles in developing teachers’ content knowledge, helping teachers understand the differences between mathematics and statistics, deepening teachers’ pedagogical knowledge, building teachers’ curricular knowledge, and influencing the writing of state-level standards. First published May 2008 at Statistics Education Research Journal Archives

Statistics education has begun to mature as a discipline distinct from mathematics education, creating new perspectives on the teaching and learning of statistics. This commentary emphasizes the importance of coordinating perspectives from statistics education and mathematics education through boundary interactions between the two communities of practice. I argue that such interactions are particularly vital in shared problem spaces related to the teaching and learning of measurement, variability, and contextualized problems. Collaborative work within these shared problem spaces can contribute to the vitality of each discipline. Neglect of the shared problem spaces may contribute to insularity and have negative consequences for research and school curricula. Challenges of working at the boundaries are considered, and strategies for overcoming the challenges are proposed.

The study describes levels of thinking in regard to the design of statistical studies. Clinical interviews were conducted with 15 students who were enrolled in high school or were recent high school graduates, and who represented a range of mathematical backgrounds. During the clinical interview sessions students were asked how they would go about designing studies to answer several different quantifiable questions. Several levels of sophistication were identified in their responses, and are discussed in terms of the Biggs and Collis (1982, 1991) cognitive model.