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AbstractionTeaching today, in the 21st century, in the age of drones, 3D printers and artificial intelligence, can no longer be the same as it was 10 or 40 years ago. Everything is anchanging. intellectualThe competencequestion is whether we can still teach in the same traditional way? Can students only acquire new knowledge in a dynamic everyday life in the traditional way? Only with chalk and a blackboard? How can we strike a balance between traditional teaching and the use of technology? How can we use technology as a tool for acquiring new skills in combination with traditional math/geometry skills instead of just using technology for technology's sake? People who love math/geometry know that enablesit is all around us, in our lives, in the mindworkplace, in science, in business, in art ... It is not possible to analysegive an answer to all these questions, but the main idea is to try. To answer some (or all) of these questions, we have prepared activities for students and comprehendteachers. conceptsWe want to developshow newthem solutions. The abilityhow to translateteach abstractand spatiallearn concepts into abstract sculptural artifacts, commonmath/geometry in architecturala design,different needsenvironment, namely art. It is well known that art and mathematics have been very closely linked throughout history. From the artists of ancient Greece to bethe practicedgreats throughoutof lifethe Renaissance and canthe beoutstanding transferred to contexts outsidedesigners of architecturaltoday. practice. This way, intellectual hypotheses fromIn the humanitiesall cantoo berich representedworld visuallyof withoutart, abandoningwe science.have chosen neoplasticism as our artistic environment. By abstraction,combining theclassical critical thinking of science can be transferred to artistic artifacts. This will be presented through visualizations developed closelywork with the Germanuse Archaeologicalof InstituteSketchpad, (DAI),a Colognedynamic Cathedral,program orfor Bernteaching Minster.mathematics, Thestudents scientificand hypothesistheir teachers discover a new world, a combination of mathematics and art. They learn new skills. However, the best thing is translatedthat they apply the adopted outcomes through skills"play" math/geometry (from architecture:elementary modellingto high school) in art and photography.vice Firstly,versa. genuineThis formstakes teaching and learning to a higher level. New research skills (dynamic geometry) and correlations between math and art are designed. These are then projected as if they were built. This second step can be termed virtual photography. In conclusion, artistic creativity promotes competences and skills to cope with the uncertainties of the 21st century by practicing imagination and critical thinking through art, as taught in our architectural courses.adopted.
The methods are recording of the geometry, assignment of hypotheses, concepts of idealizations and abstractions, abstract modelling, identification of historical viewpoints,
Projection and iterative exchange between disciplines. The tools are hand sketches, CAD, projection, and image editing.
Applicable to any age: In pre-school, it makes more sense to work with physical models; from school age, we have good experiences with CAD; from high school, almost the same can be achieved at universities because the core competencies are fundamental. Antiproportional is the acceptance of abstraction, therefore starting early is particularly fruitful.
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