Children Expressing Mathematics - Bárbara M. Brizuela

My background is in psychology and education, and I am interested in general in cognitive development and educational processes. My research focuses on children's learning of written mathematical representations: written numbers, graphs, tables, algebraic notation, representations for space, data, and measurement, and idiosyncratic notations. My interests lie in understanding the interactions between children's written representations and their understanding of the conceptual aspects of mathematics. I am also interested in the role of notations within mathematics itself, both historically and in the development of children.

In this project, I investigate children's early learning of mathematical notations. I assume that conventional knowledge is built on prior understandings. From this assumption, it follows that children's ideas about mathematical notations could be constitutive of their later conventional understandings. One of the central tasks of the investigation is to document how children initially represent numerical and mathematical understandings and how they gradually assimilate conventional representations into their expressive repertoire.

The data collected in this research project is recorded through the use of digital video. The digital videos are edited and logged using iMovie and Final Cut Pro, and assembled into DVDs through iDVD and DVD Studio Pro. These DVDs of children's learning of mathematical notations and of curricular activities implemented are used in teacher workshops, courses, and in teacher education programs and are an invaluable tool in the development of a focus on mathematical notations in pre- and in-service teachers' professional development.