Threshold Concepts with Space and Geometry (Stages 1-3)

1. Threshold Concepts with Space and Geometry (Stages 1-3) Mark Grady August 2011

2. So what lies ahead? • 2 minute recap on Threshold Concepts • What are the Threshold Concepts related to Space and Geometry? Does NAPLAN inform us? • Ideas to support the teaching of aspects of Space and Geometry

3. A 2 minute reminder of Threshold Concepts • Threshold concepts have been described as a portal or gateway • Transformative - once acquired it shifts perception of the subject • Irreversible- once learners have come to see the world in terms of the threshold concept they cannot return to their former, more primitive, view • Integrative- acquisition of the threshold concept illuminates the underlying inter-relatedness of aspects of the subject • Troublesome- a threshold concept may be counterintuitive and initially very difficult for learners to accept. In grasping a threshold concept the learner moves to a new perception of the world that may be in conflict with previously held perceptions.

4. Threshold Concepts within Space and Geometry • What do you consider to be Threshold Concepts within Space and Geometry? • Discuss in pairs or small groups at your site (3 minutes)

5. What does NAPLAN tell us? • Let’s investigate a few questions from 2008, 2009 and 2010. • These are Yr 7 NAPLAN, but Stage 3 outcome questions

6. 2010

9. 2009

13. My view on Threshold Concepts and Space / Geometry • There is no formal research on this, so it is my view (though discussed with a number of colleagues) Given the characteristics of Threshold Concepts : • Once acquired it shifts perception of the subject • Once learners have come to see the world in terms of the threshold concept they cannot return to their former, more primitive, view • Acquisition of the threshold concept illuminates the underlying inter-relatedness of aspects of the subject • Troublesome

14. Not necessarily containing Threshold Concepts, but certainly full of troublesome concepts • Position when given an angle not measured from North. See NAPLAN 2011 for a great example of this (smallest angle turn) • Converting text into mathematics – metalanguage e.g. Position question above • Recognising shapes in different orientations or views • Which is a right angled triangle?

15. Despite, in my view, no real Threshold Concepts in Stages 1 - 3 S and G, we have to carefully consider how best to program activities and experiences to best meet our students needs. • That is a real strength of this course – a chance to discuss, reflect and adapt

16. Teaching Ideas • Euler’s formula: V + F – E = 2 • Although not formally in the syllabus to Stage 4, the discovery element of counting corners, faces and edges appears in earlier Stages. Polyhedra with straight edges

17. Smart software – vortex • Hands on 3D shapes • Allow students to experience position, angle questions as both practical and theoretical activities. Orienteering • Sketching and describing from different views – give them 3D shapes to hold etc, then sketch. A bit of work with a hammer, a few nails (or glue) can make some great shapes. • Spinning and stacking (Stage 2) • Viewfinder (Stage 2,3,4) • Nature by Numbers has some relevant parts – to stimulate interest and discovery (SGES1.2)