Growing from the commognitive framework, this study is concerned with objectification -- a special way of talking about mathematical objects, which is key to one's concept formation. The study explores how objectification can be manifested in the discourse on square roots that unfolds in writing. The data comes from a class in a foundation…

The ubiquitous practice of providing worked solutions to exercises in mathematics education has been under-researched. Little is known about what elements of a worked solution are valued by students. This exploratory study sought in-depth feedback from six undergraduate students who experienced a range of worked solutions designed to encourage…

In this study, we considered how four teachers reasoned about proportional situations involving geometry. We used pilot interviews conducted with in-service middle grades teachers around a set of proportional tasks. Analysis relied on a knowledge in pieces lens to uncover the resources that each teacher used in solving the tasks and which…

It is generally assumed that students possess the ability to apply abstract reasoning to content material in a variety of disciplines when they enter college. Yet many college students have not reached the level of formal operations defined by Jean Piaget; thus they experience difficulty in coping with their work. A solution to this dilemma can be…

Students in college basic writing courses need to consider their own written language and to compare it with other students' work before they can develop a sense of the symbolic relationship between language and experience. Because of a lack of previous writing experience, basic writers have no sense that the "facts" about which they…

The distinction between the participant and spectator functions of language are used to describe the teaching skills of a fourth grade teacher during a unit of instruction. This study documented the science instruction of a teacher who 20 years ago majored in teaching reading. In recent years she has taken steps to develop skill and knowledge in…