Connecting culture to geometry - problem based learning across subjects

Scientific Conference (2022, December 16)

Symbols are used to visualise and understand abstract mathematical concepts. According to Duval (1999), visualisations are the core of understanding mathematics and creating a visualisation involves ... [more ▼]

Symbols are used to visualise and understand abstract mathematical concepts. According to Duval (1999), visualisations are the core of understanding mathematics and creating a visualisation involves reasoning and construction. This is also common in culture, for example, in religions where internalisation and externalisation are used for reflection (Vicini, 2017) that might be a visualisation such as geometric art. We want to create learning situations for problem based learning useful for various subjects (i.e., mathematics, history, culture, arts) in primary school based on geometrical shapes. Geometrical shapes are among symbols used in human beliefs (e.g., the cross in Christianity, the star of David in Judaism or the wheel of law in Buddhism) and can be found on buildings and several school books. Visualisations, e.g. in Islam, can be based on polygons, stars or rosettas (Abdullahi & Embi, 2013). Lesson plans combining cultural subjects such as history or art with mathematics are not common, but we believe there is a visible connection with geometric art. Therefore, we aim to find out whether teachers from subjects with a cultural background are interested in such lesson plans and which attributes they should have to combine the subject, geometry and technology in a maker-centred learning experience (Michael & Jones, 2020). We plan on a qualitative approach, first introducing an activity and then interviewing primary school children and their teachers for their perceptions and learnings. For a first orientation of attributes and teacher needs, we created an activity to develop bookmarks in 2D and 3D using chequered paper and the 3D modelling software TinkerCAD for over 50 primary school students. The lesson plan and comments of the student's teachers hinting towards attributes will be presented, and future steps will be discussed. [less ▲]

3D printed mathematics visualisations by STEAM teachers

Scientific Conference (2022, September 12)

Visualising abstract concepts such as for example geometrical objects in mathematics can be a valuable support for learners. Visualisation, however, is a process involving several steps that influence ... [more ▼]

Visualising abstract concepts such as for example geometrical objects in mathematics can be a valuable support for learners. Visualisation, however, is a process involving several steps that influence each other. Duval (1998) uses steps connecting reasoning by an explanation or proof to a construction step involving tools creating a visualisation to a production of a visual representation leading to new insights about a geometrical object. Vágová (2020) argues that visualising geometrical objects needs the ability to create, manipulate, and transform mental images by an internal and an external representation which both require information about the spatial arrangement. 3D modelled and then visualised geometrical objects can support the development and train visualisation skills. Steps of visualisation processes require visuospatial competencies and are also important for other subjects in Science, Technology, Engineering, Arts and Mathematics (STEAM) education (Ng 2017). Being able to understand representations and their spatial rotations, transitions between 2D and 3D and being able to manipulate representations are valuable for STEAM related subjects (Kok 2020). Martin-Dorta et al. (2008) says that spatial abilities can be improved using real and computer-aided models. 3D printing can therefore be an interesting activity as it also combines the mentioned steps in a mathematical modelling way. This approach was used in a beginners course for pre-service mathematics teachers and some of them chose to create mathematical proofs as visualisation. We will look at 3D printed objects, which concepts they visualise and what teachers' ideas behind visualisations were. [less ▲]