1. core standards for teaching mathematics

2. what is the notion of standards? what is the purpose of standards?
principles which inform both the content and the expertise required for the teaching of school mathematics:
a deep understanding of the content that they need to teach
knowledge of appropriate pedagogies
knowledge of the learners and their contexts

3. what nomenclature are you using to describe standards?
quantifying
spatial reasoning
habits of mind within mathematical processes
effective teaching
understanding of concept
developing awareness of
teachers ability to recognise sense making
core knowledges
subject matter knowledge

4. what is the architecture of the standards?
identifying “big ideas” within “related” content areas
what are numbers?
what is subtraction?
are arcs figures or lines?
which rectangles are also squares?
incorporating “habits of mind” in relation to mathematical processes
conjecturing
classifying
describing…

5. how are the standards being developed?
(using geometry and measurement as an example)

6. Firstly, geometry focus skills and content topics from the South African curriculum were listed.
We then set out to identify common areas by noting key words and terms which mentioned focus skills and content within each document’s content outline, which were common across the seven curricula and the NCTM’s Principles and Standards on geometry in school mathematics. It is important to note that the skills and content were matched to what had been elicited from the South African curriculum.
The study of Space and Shape improves understanding and appreciation of the pattern, precision, achievement and beauty in natural and cultural forms. It focuses on the properties, relationships, orientations, positions and transformations of two-dimensional shapes and three-dimensional objects.

7. Natural / Cultural Surroundings
Visualization
Once a list of terms had been compiled, these were arranged accordingly within a framework of the natural and cultural surrounds, and how this is visualized (perceived).
Natural / Cultural Surroundings

8. Natural / Cultural Surroundings
Visualization
Properties
Describe
Define
Habits of the mind: Occurring and encouraged, but NOT in the absence of the properties of geometric elements – (Cuoco, Goldenburg, Mark)
Investigate
Generalize
Compare
Classify
Visualize
Natural / Cultural Surroundings

9. Natural / Cultural Surroundings
Measurement
Describe
Compare
Investigate
Visualization
Properties
Visualize
Estimate
Natural / Cultural Surroundings

10. Natural / Cultural Surroundings
Describe
Define
Measurement
Generalize
Investigate
Invariance
Compare
Classify
Visualize
Visualization
Properties
Natural / Cultural Surroundings

11. Natural / Cultural Surroundings
Describe
Define
Transformations
Measurement
Generalize
Investigate
Invariance
Compare
Classify
Visualize
Visualization
Properties
Natural / Cultural Surroundings

12. Natural / Cultural Surroundings
Transformations
Measurement
Invariance
MATHEMATICAL PROCESSES
Visualization
Properties
Natural / Cultural Surroundings

13. Natural / Cultural Surroundings
Transformations
Measurement
Invariance
SPATIAL REASONING
MATHEMATICAL PROCESSES
Visualization
Properties
Natural / Cultural Surroundings