Cheryl A. Lubinski

The mathematical tale of two teachers: A longitudinal study relating mathematics instructional practices to level of intellectual development

In this article the development of two teachers as they make the transition from pre-service teachers to experienced teachers is examined. While these teachers participated in the same mathematics methods course and similar collaborative environments in their practicum experiences, their mathematics classroom instructional practices revealed stark differences by the time they were experienced teachers. In an effort to investigate these differences, the teachers’ beliefs were explored in relation to those promoted in their pre-service course and in relation to their implementation of current mathematics education reform practices.

The Effects of Poverty and Language on Mathematics Achievement for English Language Learners

This chapter acknowledges that access to mathematics plays a role in potential earnings and that this access is closed to English language learners (ELLs) and to students living in poverty. We provided evidence that poverty, academic language development, and discourse diversities are intertwined and cannot be easily separated when it comes to mathematical achievement. In fact, evidence is provided to suggest that English-speaking students living in poverty may be more severely impacted by discourse diversities and academic language development than ELLs. Even the discourse practices espoused by reform curricula can have a negative influence on the achievement of students in poverty. The authors suggest a pedagogical approach, such as Cognitively Guided Instruction, to aid both ELLs and students in poverty because of its focus on identifying and using what students already know to plan instruction and its focus on developing mathematical language through negotiation and discussion of students’ thinking.

Levels of Introspection in Mathematics Instruction

Case studies of five teachers who participated in a three-year staff-development project formed the basis for this grounded study which focused on primary factors that dominated teachers’ instructional decision making. As the analysis progressed, qualitatively different levels of introspection, rank ordered by the degree to which children’s thinking was utilised in the decision-making process, were identified. These distinct levels were robust in that they consistently reappeared across all coded categories of decisions made by these teachers. Moreover, these levels were positively correlated with the quality of students’ thinking based on what they said or did during instruction (ρ = .60). Further, when all project teachers were categorisation the basis of their dominant level of introspection, a positive correlation was found between these levels and their belief scores on a mathematics teaching and learning survey (ρ = .61).