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.
In most teacher training programs for Dutch mathematics teachers, history of mathematics is a required part of the curriculum. The courses provide historical background knowledge of certain mathematical developments to the students. This knowledge could also affect prospective teachers’ views on the nature of mathematics and the pedagogical choices they make for their classrooms. These effects have been examined in a small qualitative research project with two different groups of students from a teacher-training program in Amsterdam. The results are discussed in this paper and can be useful in describing and evaluating the relation between knowledge of history of mathematics and classroom activities.
Society continues to place an exaggerated emphasis on women's skins, judging the value of lives lived within, by the colour and condition of these surfaces. This artistic research will explore how the skin of a painting might unpack this site of judgement, highlight its objectification, and offer women alternative visualizations of their own sense of embodiment. This speculative renovation of traditional concepts of portrayal will explore how painting, as an aesthetic body whose material skin is both its surface and its inner content (its representations) can help us imagine our portrayal in a different way, focusing, not on what we look like to others, but on how we sense, touch, and experience. How might we visualise skin from its ghostly inner side? This feminist enquiry will unfold alongside archival research on The Ten Largest (1906-07), a painting series by Swedish Modernist Hilma af Klint. Initial findings suggest the artist was mapping traditional clothing designs into a spectral, painterly idea of a body in time. Fundamental methods research, and access to newly available Af Klint archives, will expand upon these roots in maps and women’s craft practices and explore them as political acts, linked to Swedish Life Reform, and knowingly sidestepping a non-inclusive art history. Blending archival study with a contemporary practice informed by eco-feminism is an approach to artistic research that re-vivifies an historical paradigm that seems remote today, but which may offer a new understanding of the past that allows us to also re-think our present. This mutuality, and Af Klint’s rhizomatic approach to image-making, will therefore also inform the pedagogical development of a Methods Research programme, as part of this post-doc. This will extend across MA and PhD study, and be further enriched by pedagogy research at Cal-Arts, Los Angeles, and Konstfack, Stockholm.
