School mathematics tends to have developed from the major cultures of Asia, the Mediterranean and Europe. However, indigenous cultures in particular may have distinctly different systematic ways of referring to space and thinking mathematically about spatial activity. Their approaches are based on the close link between the environment and cultural activity. The affinity to place strengthens the efficient, abstract, mathematical system behind the reference and its connection to the real world of place and a holistic worldview. This paper sets out to present an overview of various approaches to aspects of space and geometry by drawing on linguistic and cultural literature, my collaborative research in Papua New Guinea, and from personal communications with indigenous colleagues in Australia and elsewhere. This diversity provides a challenge by which teachers can deconstruct their thinking about mathematics and subsequently to review the content of teaching and to be more responsive to the diversity of cultural backgrounds of students. To assist with recognising ecocultural mathematics on space and geometry, 4 principles are established and discussed on language structures, reference lines and points, measures of space and worldviews and interpretations of space as place.