The representation of numerical and non-numerical ordered sequences was investigated in children from preschool to grade 3. The child's conception of how sequence items map onto a spatial scale was tested using the Number-to-Position task (Siegler & Opfer, 2003) and new variants of the task designed to probe the representation of the alphabet…

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…

Two experiments using the "projection of shadows" paradigm investigated multidimensional reasoning, implicit and explicit knowledge, and the nonlinearity concept in 5-, 9-, and 13-year-olds and adults. Participants estimated the resulting shadow lengths of differently sized objects, placed at varying distances from a light source. Experiment 1…

This action research project devised a program designed to increase the use of visual elements in middle school core subjects and assessed its impact on student recall, teacher awareness, and use of visual/spatial elements. Observation, surveys, and interviews documented teachers' and students' limited knowledge and use of visual/spatial elements…