Literature Index

The introduction of statistics into local mathematics syllabuses in 1984 has stimulated much activity in the field of teacher education, in both pre- and in-service courses. Bearing in mind that "the teaching of statistics is substantially more difficult than many other branches of mathematics", that most of our teachers have an inadequate background in statistics and that few of them have taken a methods course covering the teaching of the subject, it was clear that there was a need for some form of in-service education and training to help teachers at the junior high school level to implement the new syllabus. Thus a short in-service course was designed to meet the needs of these teachers.

We address the telling/not-telling dilemma in mathematics education. Telling is instructionally important, but has been downplayed because of (a) perceived inconsistencies between telling and constructivism, (b) increased awareness of the negative consequences of relying too heavily on telling, and (c) a focus on "non-telling" actions as pedagogical implications of constructivism. In response, we advance a theoretical reformulation of telling as the set of teaching actions that serve the function of stimulating students' mathematical thoughts via the introduction of new ideas into a classroom conversation. We reformulate telling in three ways: (a) in terms of the function (which involves attention to the teacher's intention, the nature of the teaching action, and the students' interpretations of the action) rather than the form of teachers' communicative acts; (b) in terms of the conceptual rather than procedural content of the new information; and (c) in terms of its relationship to other actions rather than as an isolated action. This reformulation resolves some of the concerns with teaching as telling and helps establish the legitimacy of providing new information within a constructivist perspective on learning.

We investigate business undergraduate mathematics-based courses in a blended environment of online assignments and exams and offline lectures, and report the impact on academic performance of factors such as classroom attendance, web-based course supplements, and homework. We present results from both ordinary least squares and fixed effects, where the latter method controls for unobserved heterogeneity among students. We discuss biases in estimation when the ordinary least squares method is used, resulting from the fact that it ignores unobserved heterogeneity. The fixed effects results suggest that (1) class attendance has a positive impact on exam score, (2) a student who achieves proficiency in a greater number of Khan Academy skillsets to prepare for an exam takes longer to complete an exam but does not experience a significant change in exam score, (3) a student who spends more time completing the homework spends more time completing the exam but does not experience a significant change in exam score, and (4) students who score relatively higher in homework tend to score relatively higher in exams and finish in less time than other students.

In this study, we seek a better understanding of how individuals and their daily interactions shape and reshape social structures that constitute a classroom community. Moreover, we provide insight into how discourse and classroom interactions shape the nature of a learning community, as well as which aspects of the classroom culture may be consequential for learning. The participants in this study include two teachers who are implementing a new environmental science program, Global Learning through Observation to Benefit the Environment (GLOBE), and interacting with 54 children in an urban middle school. Both qualitative and quantitative data are analyzed and presented. To gain a better understanding of the inquiry teaching within classroom communities, we compare and contrast the discourse and interactions of the two teachers during three parallel environmental science lessons. The focus of our analysis includes (1) how the community identifies the object or goal of its activity; and (2) how the rights, rules, and roles for members are established and inhabited in interaction. Quantitative analyses of student pre- and posttests suggest greater learning for students in one classroom over the other, providing support for the influence of the classroom community and interactional choices of the teacher on student learning. Implications of the findings from this study are discussed in the context of curricular design, professional development, and educational reform.