2. Empowering students through inquiry resolve is an Australian Government funded project to develop and disseminate a suite of high quality, innovative mathematics resources for students and teachers from F to Year 10 incorporating contemporary mathematics pedagogy exemplifying an inquiry approach.

3. Partners The Australian Academy of Science The Australian Association of Mathematics Teachers The project $6.4m from 1 November 2015 to 30 June 2018 Website http://science.org.au/reSolve

4. Two interpretations of inquiry Inquiry: significant, complex, extended, problems inquiry: promoting a spirit of inquiry through asking “what if…?”, “I wonder when…”. “Is this always…?”

5. The protocol reSolve mathematics is purposeful reSolve mathematics is challenging yet accessible. reSolve mathematics has a supportive knowledge-building culture.

6. reSolve mathematics is purposeful It seeks to emphasise: Connections within mathematics Mathematical modelling Conceptual depth Abstraction and generalisation Creative and critical thinking

7. reSolve mathematics is challenging yet accessible It uses tasks that: Have low floor and high ceiling Contain enabling and extending prompts Require sustained inquiry, problem solving, decision making and communication Provide opportunity for all students irrespective of background and experience Are designed to maximise students’ mathematical development

8. reSolve mathematics has a supportive knowledge-building culture It promotes: The active role of both teacher and student Collaborative inquiry, action and reflection Mistakes as a vehicle for learning Productive dispositions such as the motivation and willingness to take risk.

9. Some examples from the year 6 Directed Numbers unit Elevator Challenge Roller Coaster World Climate Data Snakes on a Plane

10. Another example: sums of squares 363644 111111111111 62626262 62626262 22222222 22222222 12121212 12121212 12121212 12121212 12121212 12121212 12121212 12121212 12121212 12121212 12121212 12121212 4646

11. 62626262 62626262 22222222 22222222 12121212 12121212 12121212 12121212 12121212 12121212 12121212 12121212 12121212 12121212 12121212 12121212 22222222 22222222 4646

12. 62626262 62626262 12121212 12121212 22222222 22222222 12121212 12121212 22222222 22222222 4646 32323232 32323232 Can we do better?

13. What might students notice?

14. Some inquiries What numbers only ever require 2 squares? Why do all the numbers in column 3 and 6 require 3 squares, and all the numbers in column 7 require 4 squares? Can some numbers be written as the sum of two, three or four squares in more than one way? Can every number be written as the sum of four squares? How many perfect cubes do you need to sum to be able to write very natural number?

15. Using technology

16. Public Domain, https://commons.wikimedia.org/w/index.php?curid=575665 Diophantus

17. By Twice25 - Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=3853693 Lagrange

18. Please complete the survey

19. Contact Executive Director: Dr Steve Thornton steve.thornton@science.org.au +61 6201 9430 steve.thornton@science.org.au