core standards for teaching mathematics

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

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

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…

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

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.

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

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

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

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

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

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

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