ED3662 Lecture Notes - Lecture 7: Semiregular Polyhedron, Regular Polygon, Subjective Constancy
Week Seven
Lecture Seven: Visualisation, 2D Shapes and 3D objects
Developing Visualisation
- Mathematical visualisation is the process of forming images (mentally, or with pencil and paper
or with the aid of technology) and using such images effectively for mathematical discovery and
understanding
o Zimmerman and Cunningham, 1991
- Visualisation is an important aspect of geometry and mathematics in general. It is more than
just seeig iages i the id. ‘ather spatial isualisatio is the ailit to geerate ad
aipulate iages.
o Siemon et. al, 2015
Visualisation
- Figure ground perception
o The ability to identify and isolate shapes within shapes
▪ Can you see some triangles? Squares? Pentagons? Hexagons?
- Mental rotation
o Visualise movement
- Perception of spatial positions
o the ability to relate an object, picture, or mental image to oneself
o blue counter is right in front of me and the black counter is to the left of me.
- Perception of spatial relationships
o the ability to relate several objects, pictures or mental images to each other, or
simultaneously to oneself.
o The sofa is in front of the painting which is to the left of the lamp, and the table is
directly in front of me.
- Perceptual constancy
o the ability to recognise that some characteristics of an object are independent of size,
colour, texture or position. e.g. an upside down triangle is still a triangle, a small blue
triangle and a large red triangle are both triangles. These are all triangles
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Document Summary
Lecture seven: visualisation, 2d shapes and 3d objects. Mathematical visualisation is the process of forming images (mentally, or with pencil and paper or with the aid of technology) and using such images effectively for mathematical discovery and understanding: zimmerman and cunningham, 1991. Visualisation is an important aspect of geometry and mathematics in general. It is more than just (cid:858)seei(cid:374)g i(cid:373)ages i(cid:374) the (cid:373)i(cid:374)d(cid:859). Ather spatial (cid:448)isualisatio(cid:374) is the (cid:858)a(cid:271)ilit(cid:455) to ge(cid:374)erate a(cid:374)d (cid:373)a(cid:374)ipulate i(cid:373)ages(cid:859): siemon et. al, 2015. Perception of spatial positions the ability to relate an object, picture, or mental image to oneself: blue counter is right in front of me and the black counter is to the left of me. Visual discrimination: the ability to compare several figures and to determine how they are similar and how they are different. All angles are equal and all sides are the same length. Regular polygons are both equiangular and equilateral. Any polygon that is not a regular polygon.
