Discussions about the importance of the built environment for healthcare delivery extend at least as far back as Hippocrates 1 (400 BC). The iconic Florence Nightingale (1859) also strongly believed in the influence the indoor environment has on the progress of disease and recovery. Today, the role of the built environment in the healing process is of growing interest to healthcare providers, environmental psychologists, consultants, and architects. Although there is a mounting evidence 1 linking healthcare environments to health outcomes, because of the varying quality of that evidence, there has also been a lack of clarity around what can and cannot be achieved through design. Given the ageing of society and the ever increasing numbers of persons with dementia in the Western World, the need for detailed knowledge about aged care environments has also become increasingly important. The mental and physical health state of these persons is extremely fragile and their needs demand careful consideration. Although environmental interventions constitute only a fraction of what is needed for people with dementia to remain as independent as possible, there is now sufficient evidence (2, 3) to argue they can be used as a first-line treatment, rather than beginning with farmalogical interventions.
It is a challenge for mathematics teachers to provide activities for their students at a high level of cognitive demand. In this article, we explore the possibilities that history of mathematics has to offer to meet this challenge. History of mathematics can be applied in mathematics education in different ways. We offer a framework for describing the appearances of history of mathematics in curriculum materials. This framework consists of four formats that are entitled speck, stamp, snippet, and story. Characteristic properties are named for each format, in terms of size, content, location, and function. The formats are related to four ascending levels of cognitive demand. We describe how these formats, together with design principles that are also derived from the history of mathematics, can be used to raise the cognitive level of existing tasks and design new tasks. The combination of formats, cognitive demand levels, and design principles is called the 4S-model. Finally, we advocate that this 4S-model can play a role in mathematics teacher training to enable prospective teachers to reach higher cognitive levels in their mathematics classrooms.
