How can visualisation be harnassed to promote mathematical abstraction and generalization. Daniel F JUnius.

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Presentation transcript:

How can visualisation be harnassed to promote mathematical abstraction and generalization. Daniel F JUnius

Theoretical Framework Visualization in Mathematical learning could be described as the ability of the brain to create a mental image of a variety of mathematical concepts/entities, including plane /two-dimensional diagrams with its manipulation and various dimensions, numerical series, algebraic manipulation DIAGRAMS, colours/pictures and algorithms, as an aid to solve mathematical problems. (work In Progress )

Constructivism Visualisation Strands of learning Radical How the brain organizes information about abstract concepts, In Algebra.

RESEARCH PROCESS The human brain has several “regions” Identify Topics Of concern INTERVENTION Develop applets with teachers. Community of Practise: Train teachers Geogebra Find together areas that have similar outcomes. TRAIN Learners Geogebra? (INTERVENTION) IDENTIFY the successful/not sucessful features. Develop learner applets (OBSERVE). TEST APPLETS within larger areas. The human brain has several “regions” that do specific kinds for spatial understanding of abstract concepts.

Research Questions to be answered: Can abstract Algebraic concepts be taught through visualisation? Will visualisation enhances conceptual understanding and generelisation? Will abstraction through visualisation lead towards a productive disposition towards learning mathematics in learners?

Scientific conclusion : The human brain has a number of separate, independent structures that help us organize abstract information Important take home message for educators/administrators: There are significant individual differences In student inclination and ability to use different modes of spatial thinking.