Charles (2005) or Siemon et al. (2012)
choose their own ‘big idea’ based on one contained in articles by Charles (2005) or Siemon et al. (2012).
The task is designed to allow students to demonstrate their mathematical content knowledge and how that knowledge is based on rich understanding ofkey concepts and how those concepts are linked to a range of other ideas. The task is NOT based on any particular content strand ofthe AC: M (Number & Algebra,Measurement & Geometry or Statistics & Probability) but rather allows students to show how a ‘big idea’ of mathematics incorporates
component parts from more than one content strand.
Similarly, the task DOES NOT focus on a particular year level. Students should identify key aspects or component parts ofthe ‘big idea’ (i.e., parts that help develop the ‘big idea’ in combination with other parts). In
doing so, students will necessarily show aspects of previous knowledge that children would be expected to have at various levels.
The task should be linked to, and should reflect ideas expressed in the philosophy statement. Similarly, it should be reflected in the other
portfolio elements that follow, as far as is possible. The portfolio should be a ‘seamless’ document that has clarity and coherence and which clearly identifies the writer’s thoughts and beliefs about effective mathematics teaching. This particular part ofthe portfolio enables each student to demonstrate his/her content knowledge and to show that s/he understands how ‘big ideas’ help to make explicit the many connections that exist between mathematical ideas.
What to present.
1. Brief descriptive overview/rationale about the ‘big idea’ what it broadly encompasses, how it links to other ideas, why it is important etc.
2. Concept map, mind map, or some otherform of graphic organizer- show key component parts ofthe big idea and expand to show other elements and examples of each component part.
Table or some other method of presentation showing how the component parts ofthe ‘big idea’ are identified in the Australian Curriculum:
Mathematics. Show specific year level content descriptors. In this section, select six ofthe content descriptors and give a brief overview of a task that could develop that descriptor in relation to the ‘big idea’.
4. Lesson Plan – develop ONE ofthe six activities/tasks described above into a concise lesson plan showing the mathematical focus, a specific learning objective, focus questions, basic description
of what children will do, clear and specific assessment pointers, and plan for review/reflection related to the focus/objective.
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