This survey on the theme of Geometry Education (including new technologies) focuses chiefly on the time span since 2008. Based on our review of the research literature published during this time span (in refereed journal articles, conference proceedings and edited books), we have jointly identified seven major threads of contributions that span from the early years of learning (pre-school and primary school) through to post-compulsory education and to the issue of mathematics teacher education for geometry. These threads are as follows: developments and trends in the use of theories; advances in the understanding of visuo spatial reasoning; the use and role of diagrams and gestures; advances in the understanding of the role of digital technologies; advances in the understanding of the teaching and learning of definitions; advances in the understanding of the teaching and learning of the proving process; and, moving beyond traditional Euclidean approaches. Within each theme, we identify relevant research and also offer commentary on future directions.
Glendon Lean collated data on nearly 900 counting systems of Papua New Guinea, Oceania, and Irian Jaya (West Papua). Lean's data came from a questionnaire completed by students and talks with village elders. He read old documents written in English, German, and Dutch. He made comparisons between older and new accounts of the counting systems and compared neighbouring counting systems from both Austronesian and non-Austronesian languages. His, work drew attention to the rich diversity of the systems and suggested that systems based on body parts and cycli拢: systems developed spontaneously. Digit tally systems were also relatively common. Lean's thesis on spontaneous developments of these ancient cultures challenged traditional theories describing the spread of number systems from Middle East cultures.If my life is richer for the people I have met and the books I have read, then let me share it with others. If the ethnomathematics that I have read, heard, seen, and explored has influenced me, then I am pragmatic enough to think that it will influence others. Some argue that ethlnomathematics should only be available to those whose culture and mathematics it is. Sound ethical reasons suggest that consideration of ownership and context has to be taken into account. Cultural roots, however, should be recognised by students in all disciplines. I recently undertook an interview study of some Papua New Guinea (PNG) architecture students (Owens, 1999). The response that impacted on me most was the affective and somewhat intangible response by students that their PNG heritage was. significant in their designing. It was as if their pride in the PNG design tradition meant they were good designers. Design was part of their culture; their culture was part of their designing. In some cases, this was evident in specific aspects of their sculptures, but at other times it was not obvious or explainable by them. A fishing tool, a house roof, spirals, weaving, a symmetrical face, sea devils, and abstract design were represented, but many students did not express their culture in a specific design feature.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations鈥揷itations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.