Browsing by Subject "mathematics teaching"
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ItemAn exploration of students' statistical thinking(2006) Groth, Randall E.The statistical thinking exhibited by 14-19 year old students during clinical interview sessions is described. The students’ thinking in regard to fundamental statistics concepts is reported in order to help inform instructional practice. ItemAn exploration of two online approaches to mathematics teacher education(2009) Groth, Randall E.; Burgess, Claudia R.The purpose of the present study was to examine the nature of the discourse generated by two different online approaches to mathematics teacher professional development. Thirty mathematics teachers participated in online activities involving analysis and discourse about artifacts of teaching practice. Half were randomly assigned to a group that analyzed and discussed students work samples, and the other half to a group focused upon descriptions of classroom teaching episodes. Teachers formed threads of conversation on asynchronous discussion boards as they considered the different aspects of each artifact. Within the threads, different orientations toward the reform agenda in mathematics education were shown. Some messages were strongly rooted in the reform paradigm, others in the traditional paradigm, and many others contained elements characteristic of each paradigm. The distribution and characteristics of the messages reflected teachers’ frequent attempts to try to reconcile the largely incompatible paradigms undergirding reform-oriented and traditional approaches to mathematics instruction. This paper describes the nature of the discourses occurring within each group of teachers with the aim of providing empirical grounds to inform the actions of teacher educators and researchers designing online learning environments that attempt to bring teachers more fully into the reform-oriented discourse about teaching mathematics. ItemHigh school students’ levels of thinking in regard to statistical study design(2003) Groth, Randall E.The study describes levels of thinking in regard to the design of statistical studies. Clinical interviews were conducted with 15 students. Each student was enrolled in high school or was a recent graduate. The students interviewed 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. The levels of sophistication in response are discussed in terms of the Biggs and Collis (1982, 1991) cognitive model. ItemPreservice elementary teachers' conceptual and procedural knowledge of mean, median, and mode(2006) Groth, Randall E.; Bergner, Jennifer A.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, 1991) 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.