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This paper focuses on high school mathematics teachers and what they do when they use digital technology in their lessons. It is essentially a discursive paper but it uses data from a project on teachers using technology to illustrate points. The main aim of the paper is to present an holistic account of factors influencing teachers' practice. A secondary aim is to present the integration of technology into lessons as a complex issue. Saxe's four parameter model of goal-linked practice is employed to show how different dimensions of teachers' activities interrelate in this complex undertaking. The paper ends with a consideration of approaches related to Saxe's model.

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Concept image and concept definition is an important construct in mathematics education. Its use, however, has been limited to cognitive studies. This article revisits concept image in the context of research on undergraduate students' understanding of the derivative which regards the context of learning as paramount. The literature, mainly on concept image and concept definition, is considered before outlining the research study, the calculus courses and results which inform considerations of concept image. Section 6 addresses three themes: students' developing concept images of the derivative; the relationship between teaching and students' developing concept images; students' developing concept images and their departmental affiliation. The conclusion states that studies of undergraduates' concept images should not ignore their departmental affiliations.

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The framework for this paper is a recently developed theory of abstraction in context. The paper reports on data collected from one student working on tasks concerned with absolute value functions. It examines the relationship between mathematical constructions and abstractions. It argues that an abstraction is a consolidated construction that can be used to create new constructions. Newly formed constructions are fragile entities. In the course of consolidating a construction this student creates connections between the new construction and already established mathematical knowledge and develops a language to describe and guide mathematical actions related to the construction. The resulting abstraction is a more resilient form of the construction and the student is able to justify his assertions. The paper also examines issues in designing tasks to consolidate a construction.