In this paper, we extend our previous work on challenges teachers face when engaging with proportional reasoning contexts to investigate two contexts that included four problems for middle grades teachers to solve as well as eight student solutions. Analysis included coding for correct solving of the problem as well as making sense of and…

Spatial visualisation is a subset of spatial ability and is exemplified in predicting whether or not a net will fold to form a target solid. The researchers examined video of interviews to explore the schemes of Year 5 students for determining the validity of nets for a cube and pyramid. Findings suggest the significance of imaged actions, shown…

Fifteen elementary and secondary teacher candidates solved sixteen integer addition and subtraction problems during think-aloud interviews. Investigators further probed participants' solution strategies as well as what they noticed first when starting a new problem. Task analyses of participants' solutions led to the creation of two distinct maps…

What is involved in consolidating a new mathematical abstraction? This paper examines the work of one student who was working on a task designed to consolidate two recently constructed absolute function abstractions. The study adopts an activity theoretic model of abstraction in context. Selected protocol data are presented. The initial state of…

In order to study two aspects of the composing process, goal-setting and risk-taking, English and reading graduate students were given a set of readings on the topic of introspection and asked to write weekly papers in response. The papers were summaries, reaction statements, synthesis essays, and position papers, and students kept ongoing…

In this report, we address the following questions: What aspects of information do preservice elementary teachers rely on when performing inductive reasoning? What contexts enable them to perceive the inherent invariant relationships from a finite sample and, thus, formulate viable generalizations? To what extent are they able to justify inductive…

This paper describes the task analysis of performance-based science tasks that were designed for the 1994 National Assessment of Educational Progress (NAEP) science assessment, now postponed until 1996, and field tested in 1993. A brief description of the science performance tasks is followed by a description of the task analyses performed and a…