In this article, Presmeg talks about visualization as a significant research area in mathematics education. Here, visualization encompasses sight, hearing, smell, taste, touch, and their interactions and interconnections. And mathematics as a subject consisting of "diagrams, tables, spatial arrangements of signifiers such as symbols, and other inscriptions as essential components." It appears to me that the theoretical underpinning of visualization in mathematics education is based on the constructivist approach. Presmeg alludes to the rise in interest in constructivism, which is somewhat of a deviation from the influences of existing teaching and learning theories based on behaviourism, cognitivism, and communication.
Presmeg takes the following position in this article: when a learner creates a mathematical inscription, the learner generates, guides, and constructs visual images in their mind. This author prefers to use inscription rather than representation, because the term 'representation' was insufficient to provide an accurate definition. Visual images are assumed to be mental constructs depicting visual or spatial information. Presmeg identifies numerous types of visual images: Figurative (purely perceptive), Concrete (purely in the mind), Operative (operates on/with the carrier), Kinaesthetic (physical movement), Relational (transformation of concrete carrier), Dynamic (image itself is moved or transformed), Symbolic (formulas and spatial relations), Memory of formulae, and Pattern (pure relationships stripped of concrete details).
Presmeg's research on visualizers (learners who prefer to use visual methods when there is a choice) reveals that: 52/54 visualizers used concrete imagery, 32 preferred memory images, pattern imagery (18), and kinaesthetic imagery (16). It was surprising to note that dynamic imagery was used but rarely. This is a surprise because both pattern and dynamic imagery are thought to be involved with rigorous analytical thought processes. This implies that learners are capable of generating visual images, but are unable to use these images for analytical reasoning.
Presmeg takes the following position in this article: when a learner creates a mathematical inscription, the learner generates, guides, and constructs visual images in their mind. This author prefers to use inscription rather than representation, because the term 'representation' was insufficient to provide an accurate definition. Visual images are assumed to be mental constructs depicting visual or spatial information. Presmeg identifies numerous types of visual images: Figurative (purely perceptive), Concrete (purely in the mind), Operative (operates on/with the carrier), Kinaesthetic (physical movement), Relational (transformation of concrete carrier), Dynamic (image itself is moved or transformed), Symbolic (formulas and spatial relations), Memory of formulae, and Pattern (pure relationships stripped of concrete details).
Presmeg's research on visualizers (learners who prefer to use visual methods when there is a choice) reveals that: 52/54 visualizers used concrete imagery, 32 preferred memory images, pattern imagery (18), and kinaesthetic imagery (16). It was surprising to note that dynamic imagery was used but rarely. This is a surprise because both pattern and dynamic imagery are thought to be involved with rigorous analytical thought processes. This implies that learners are capable of generating visual images, but are unable to use these images for analytical reasoning.
Presmeg, N. C. (2006). Research on visualization in learning and teaching mathematics. Handbook of research on the psychology of mathematics education, 205-235.
No comments:
Post a Comment