1. Thinking About My Thinking Working With Friends to Solve Problems Prep students working together

2. Students were focusing on their problem solving skills as a group and as individuals to find a solution to a seemingly simple problem Develop a drawing to represent the game “Cat and Mouse”

3. Problem Solving Is there a situation or process that has some major constraints or limiting condition? Is there a situation or process that could be better understood if constraints or limiting conditions were placed on it?

4. Problem Solving Organiser Goal: Constraining/limiting conditions: Possible solution Selected solution Try another solution Did not work well Problem solved Worked well

5. Problem Solving Organiser Goal: Draw the game cat and mouse Constraining/limiting conditions: Has to be an accurate drawing in terms of positional concepts. Student 1 solutionStudent 3 solutionStudent 2 solution Selected solution Try another solution or adopt one of the original plans. Did not work well Problem solved Worked well

6. We all played Cat and Mouse

7. We then had to draw us playing the game. “I drew my circle first so I would not forget what the game looked like. Then I can draw my friends around the outside” - Chelsea “You have to make sure the children you draw are on the circle; otherwise they are not in the game” - Alana

8. We talked about our drawings “You have to draw some of the people upside down; they are the ones on the other side to me.” - Daffy “I did that too, but they are not really upside down; you just have to draw them that way so you know how they really look.” - Nick

9. Deciding which drawings were the best and why

10. Our Thinking “Greta’s drawing looks best because everyone is on the line, but we are not really upside down” – Daffy “I think Kelsie’s drawing is right, because nobody is upside down in her drawing” – Matt

11. Daffy’s Picture “This is my game of cat and mouse. Everyone is in the circle and they are holding hands”.

12. Checking our ideas Re-enacting the drawings The students had a go of Matt’s drawing first. They agreed that Matt who was the only one with his legs facing inwards was probably drawn wrong. Then they all stood up to see what it really looked like. After lots of giggles they realised that Matt was the only one that was drawn correctly “This isn’t right, we are all the wrong way except for Matt” - Chelsea

13. What about this drawing Students decided to have a go at Kelsie’s drawing next. They were asked to predict if this was more accurate and why: “Yes it is a better drawing because we all have our legs facing downwards like Matt did before” – Nick “Nobody is upside down doing it this way”- Daffy The students then stood up.

14. Maybe this one is right! Students decided they wanted to have a go at Nick’s drawing to see if it was right. They were asked if they thought there was any difference between Nick and Kelsie’s drawing, but they were not sure. When the students stood up they were surprised again that this picture was not right.

15. Thinking about their drawings “Everyone is wrong here; I had a few people right in my drawing” - Kelsie “Maybe we have to draw everyone differently and think about where our faces are” – Greta “Maybe we can draw it while we are standing up so we can see where we should be” - Daffy

16. Proof Prediction: If legs face away from circle, when you stand up you will be facing the wrong way. Prediction: When you can see each other you must be facing the same way. Conclusion or Final Prediction: Drawing must have legs facing inwards and faces looking at each other. Legs have to all face towards the middle of the circle. Faces have to be looking towards middle of circle. Proof Yes No No conclusion – new theory No Yes No conclusion – new theory What type of thinkin g is this?

17. Teacher Direction It is suggested the each individually take turns standing outside the circle and drawing the position of only one person considering, the body, head, legs as well as any distinguishing facial features e.g. could they see the nose or eyes.

18. Individual Drawings Profiles Front and Back

19. Students then cut and pasted their drawings onto a poster “It was easy drawing my position as I could look closely at how they were standing” – Matt “Everyone was standing differently, we just had to look carefully” - Daffy

20. Final Team Drawing Us playing Cat and Mouse

21. Self-assessment Children compare their initial drawings with their final drawings and try and explain the changes they have made Zone of proximal development Learners advance their understanding Vygotsky

22. Reflecting on Predictions Students reflected on their initial drawings and to talk about what they have learnt.

23. Reflection & Feedback “ Your ring-around the rosy is great! The second drawing is a lot more Ring- around-the-rosy! “See that line? That was my first Ring- around-the –rosy but it was not right! Giovanni helped me get a picture of a ring- around-the-rosy in my mind…it was just like I was seeing it, so copying from my mind I got it right”

24. Our Reflections “This was easy when we did everyone one at a time, we could really think about where everyone was standing” - Daffy “I didn’t look at where our faces and our legs where when I first did my picture. That really helped me when I did” – Kelsie “We are all different when we stand in different spots, we just need to look” – Matt “Drawing people upside down is not right, as we are never playing with our feet in the air” - Greta

25. “Language shapes the way we think, and determines what we can think about.” Benjamin Lee Whorf American linguist noted for his hypotheses regarding the relation of language to thinking and cognition 1897-1941.

26. Daffy’s Projection “I would like to be able to draw ring around the rosie by myself”.

27. Final Drawing – (produced with guidance and advice from her friends)

28. More Than Just Play….. Learning process through problem solving: Development of vocabulary Development of verbal language through communication of ideas Development of spatial concepts Deductive thinking as a process of refining thinking Fine tuning of visual representation Construction of hypotheses Formulation of theories Strategies of action Team work and cooperative thinking

29. Children become smart by being treated as if they already are intelligent. Resnick & Hall, 1998 Pressed to raise questions Accept challenges Risk take Make predictions Justify reasons Seek information