Space and Shape 94. Space and shape encompasses a wide range of phenomena that are encountered everywhere
in our visual and physical world: patterns, properties of objects, positions and orientations,
representations of objects, decoding and encoding of visual information, navigation and dynamic
interaction with real shapes as well as with representations, movement, displacement, and the
ability to anticipate actions in space. Geometry serves as an essential foundation for space and
shape, but the category extends beyond traditional geometry in content, meaning and method,
drawing on elements of other mathematical areas such as spatial visualisation, measurement and
algebra. For instance, shapes can change and a point can move along a locus, thus requiring
function concepts. Measurement formulas are central in this area. The recognition, manipulation
and interpretation of shapes in settings that call for tools ranging from dynamic geometry software
to Global Positioning Systems (GPS), and to machine learning software are included in this content
category.
95. PISA assumes that the understanding of a set of core concepts and skills is important to
mathematical literacy relative to space and shape. Mathematical literacy in the area of space and
shape involves a range of activities such as understanding perspective (for example in paintings),
creating and reading maps, transforming shapes with and without technology, interpreting views of
three-dimensional scenes from various perspectives and constructing representations of shapes.
96. Geometric approximations: Today’s world is full of shapes that do not follow typical patterns of
evenness or symmetry. Because simple formulas do not deal with irregularity, it has become more
difficult to understand what we see and find the area or volume of the resulting structures. For
example, finding the needed amount of carpeting in a building in which the apartments have acute
angles together with narrow curves demands a different approach than would be the case with a
typically rectangular room.
97. Identifying geometric approximations as a focal point of the space and shape content category
signals the need for students to be able use their understanding of traditional space and shape
phenomena in a range of typical situations.