The Hills Hub Stage 3 and 4 Mathematics Threshold Concept Project 2010

1. The Hills Hub Stage 3 and 4 Mathematics Threshold Concept Project 2010 Mark Grady 9 November 2010

2. A quick bit about me My role And a personal interest My Background

3. An outline of this afternoon Why are we here today? What are Threshold Concepts? What do we know? How will we go about it?

4. Why are we here today? • This Hills Hub has had great success in transition programs – DG award winning • LMC has run a Science Stage 4 Threshold Project in Biology across 9 schools including Model Farms. • Combining the partnership within this hub, and the knowledge of how Thresholds can support students, it just made sense to pull these 2 aspects together.

5. What are Threshold Concepts? • Jan Meyer • Threshold concepts have been described as a portal or gateway because once acquired, they lead to a new way of thinking and understanding in the discipline. • Because understanding of conceptually difficult ideas are enhanced by explicit teaching of threshold concepts, student learning outcomes are improved.

6. They are understood to possess the following characteristics: • 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.

7. Considering the previous 2 slides, what area/areas of number that you teach do you feel could be described as a Threshold Concept?

8. Is there current Threshold research on Middle Years Mathematics? But this is not a bad thing

9. We could leave it and do nothing But by working smarter, not harder, this could have a major positive impact on student learning and buy us “teaching time” in the classroom

10. What do we currently know? • Evidence (NAPLAN and teacher feedback) suggests students struggle with fractions, and this impacts on a range of skills in stages 3,4, 5 and 6. • WHPS, WHPS and JRPS are feeder schools to Model Farms. Best practice at the 3 feeder schools not only benefits the Stage 3 students, but has a positive flow on effect to Model Farms. • Peter Gould (Manager Mathematics Curriculum K-12 Directorate DET) (5:24 – 9:20)

11. A Sample From NAPLAN 2009 Although these concepts are taught within the Primary and Secondary context, a significant component of students struggle with retaining and reproducing these concepts. MFHS and the 3 feeder are not alone here! • Why 2009? • This is only 1 question, however, it is = 2nd compared to Hills Group showing greatest difference in successful response. • Hills Comparison – be careful • What fraction is halfway between 5/7 and 6/7? • However, another question • And the question referred to by Peter Gould

12. What aspect of fractions do you feel your students have difficulty with? What challenges does this create in the next stage of learning? • Discuss this in groups of 4 as per the colour card you have. • Each group should roughly have a member of JRPS, WHPS, WHPS and MFHS • Group feedback

13. So what can we do? • Use research (Threshold concepts) and proven successful practices within the framework of a “Rich Task” to develop a teaching unit that: • Is engaging, fun and hands on • Has “aha” moments • Supports student understanding • Is part of a Stage 3 & 4 continuum • Brings together our expertise

14. How do we go about it?

15. Questions and discussion

16. Process • Collaboratively determine the aspect of fractions to address • Collaboratively develop fun and engaging teaching units relevant to YOUR students • Pre test the students • Implement the unit • Post test the students • Evaluate/data crunch • Celebrate our success!