1. FLOW AND THE THINKING CLASSROOM
Peter Liljedahl

2.
@pgliljedahl

3. Liljedahl, P. (in press). On the edges of flow: Student problem solving behavior. In S. Carreira, N. Amado, & K. Jones (eds.), Broadening the scope of research on mathematical problem solving: A focus on technology, creativity and affect. New York, NY: Springer.

4. FLOW AND THE THINKING CLASSROOM
Peter Liljedahl

5. FLOW AND THE THINKING CLASSROOM
Peter Liljedahl

6. THE THINKING CLASSROOM

7. JANE’S CLASS – 13 YEARS AGO

8. If 6 cats can kill 6 rats in 6 minutes, how many cats are required to kill 100 rats in 50 minutes? - Lewis Carroll

9. If 6 cats can kill 6 rats in 6 minutes, how many cats are required to kill 100 rats in 50 minutes? - Lewis Carroll
DISASTER!

10. REALIZATIONS Students are not thinking.
Teachers are planning their teaching on the assumption that students either cannot or will not think.
REALIZATIONS

11. NON-NEGOTIATED NORMS

12. RENEGOTIATING THE NON-NEGOTIATED NORMS
ACTION RESEARCH (n = 400+)

13. BUILDING THINKING CLASSROOMS

14. THINKING CLASSROOM

15. BUILDING THINKING CLASSROOM
Liljedahl, P. (in press). Building Thinking Classrooms. In A. Kajander, J. Holm, & E. Chernoff (eds.) Teaching and learning secondary school mathematics: Canadian perspectives in an international context. New York, NY: Springer.
Liljedahl, P. (2016). Building thinking classrooms: Conditions for problem solving. In P. Felmer, J. Kilpatrick, & E. Pekhonen (eds.), Posing and Solving Mathematical Problems: Advances and New Perspectives. (pp ). New York, NY: Springer.
Liljedahl, P. (2014). The affordances of using visibly random groups in a mathematics classroom. In Y. Li, E. Silver, & S. Li (eds.), Transforming Mathematics Instruction: Multiple Approaches and Practices. (pp ). New York, NY: Springer.
BUILDING THINKING CLASSROOM

16. THINKING CLASSROOM

17. THINKING CLASSROOM

18. PHENOMENA OF INTEREST student activity in the thinking classroom
student engagement in the thinking classroom
PHENOMENA OF INTEREST

19. PHENOMENA OF INTEREST student activity in the thinking classroom
student engagement in the thinking classroom
PHENOMENA OF INTEREST

20. MIHALY CSÍKSZENTMIHÁLYI
THE OPTIMAL EXPERIENCE
MIHALY CSÍKSZENTMIHÁLYI

21. OPTIMAL EXPERIENCE There are clear goals every step of the way.
There is immediate feedback on one’s actions.
There is a balance between challenges and skills.
Attention is focused on one’s actions.
Distractions are excluded from consciousness.
There is no worry of failure.
Self-consciousness disappears.
The sense of time becomes distorted.
The activity becomes satisfying in its own right.
- Csíkszentmihályi (1990)
OPTIMAL EXPERIENCE

22. OPTIMAL EXPERIENCE - internal
There are clear goals every step of the way.
There is immediate feedback on one’s actions.
There is a balance between challenges and skills.
Attention is focused on one’s actions.
Distractions are excluded from consciousness.
There is no worry of failure.
Self-consciousness disappears.
The sense of time becomes distorted.
The activity becomes satisfying in its own right.
- Csíkszentmihályi (1990)
OPTIMAL EXPERIENCE - internal

23. OPTIMAL EXPERIENCE - external
There are clear goals every step of the way.
There is immediate feedback on one’s actions.
There is a balance between challenges and skills.
Attention is focused on one’s actions.
Distractions are excluded from consciousness.
There is no worry of failure.
Self-consciousness disappears.
The sense of time becomes distorted.
The activity becomes satisfying in its own right.
- Csíkszentmihályi (1990)
OPTIMAL EXPERIENCE - external

24. OPTIMAL EXPERIENCE FLOW There are clear goals every step of the way.
There is immediate feedback on one’s actions.
There is a balance between challenges and skills.
ANXIETY
FLOW
BOREDOM
OPTIMAL EXPERIENCE

25. FLOW EXPERIENCE FLOW There are clear goals every step of the way.
There is immediate feedback on one’s actions.
There is a balance between challenges and skills.
ANXIETY
FLOW
BOREDOM
FLOW EXPERIENCE

26. FLOW
ANXIETY
BOREDOM
FLOW EXPERIENCE

27. FLOW
ANXIETY
BOREDOM
FLOW EXPERIENCE

28. FLOW
ANXIETY
BOREDOM
FLOW EXPERIENCE

29. FLOW
ANXIETY
BOREDOM
MOMENTS OF IMBALANCE

30. STUDY ONE What do teachers do in a moment of imbalance
STUDY ONE What do teachers do in a moment of imbalance? STUDY TWO What do student do in a moment of imbalance?
TWO STUDIES

31. STUDY 1 What do teachers do in a moment of imbalance
STUDY 1 What do teachers do in a moment of imbalance? STUDY TWO What do student do in a moment of imbalance?

32. METHODOLOGY – TEACHING STYLE
BUILDING THINKING CLASSROOMS
start with a good problem
visibly random groups
vertical non-permanent surfaces
oral instructions
defront the classroom
answer only keep thinking questions
build autonomy
levelling to the bottom
use hints and extensions to guide flow
do mindful notes
use 4 purposes of assessment
METHODOLOGY – TEACHING STYLE

33. LESSON PROGRESSION Task #3 Task #2 VRG, VNPS, (short lesson), Task #1
Levelling to the bottom
Thoughtful notes
3 – 6 tasks to check understanding
Task #3
Task #2
LESSON PROGRESSION

34. LESSON PROGRESSION Task #3 Task #2 VRG, VNPS, (short lesson), Task #1
Levelling to the bottom
Thoughtful notes
3 – 6 tasks to check understanding
Task #3
Task #2
LESSON PROGRESSION

35. METHODOLOGY - THE DATA two classrooms (grade 11 &12 pre-calculus)
each class visited 5 times over a 7 week period
watching for moments of imbalance
video didn’t work (too narrow a field of vision)
field notes
photographs
interviews
NOTEABILITYTM
METHODOLOGY - THE DATA

36. FLOW
ANXIETY
BOREDOM
MOMENTS OF IMBALANCE

37. FLOW
ANXIETY
BOREDOM
CHALLENGE TOO LOW

38. CHALLENGE TOO LOW: CASE 1 (n=4)
Researcher I notice you are not working on the assigned questions. What's up? Mikaela We did some of them. Researcher I saw that. I noticed that you did two very quickly. Took a little break from the math and then went back and did another one. I was sort of waiting to see if you would get back to it. Allison This stuff is easy. I'll finish it at home on my own. Mikaela Its actually too easy. I don't even think I will bother finishing it at home. Allison … Yeah. I probably won't either. Researcher It's easy? Is that why you stopped working on it? Mikaela Yeah.
QUITTING
CHALLENGE TOO LOW: CASE 1 (n=4)

39. CHALLENGE TOO LOW: CASE 2 (n=3)
Researcher I have been watching you while I have been here. I notice that you always do a lot of questions. Can you tell me about that? Jennifer Yeah. I like to do a lot of questions. It's good practice. It's how I learn. Researcher So, are you looking for harder and harder questions to challenge yourself. Jennifer Not really. I just do all of them. So, if the teacher asks us to do 4a, I will also do 4bc and d and so on. Researcher Do you find them easy. Jennifer Yeah.. Researcher How many do you do? Jennifer I just work the whole time at the end of class and then for maybe an hour at home.
TOLERANCE FOR THE MUNDANE
CHALLENGE TOO LOW: CASE 2 (n=3)

40. CHALLENGE TOO LOW: CASE 3 (n>20)
Researcher So, I notice that you guys are now on question 5 and your teacher has not visited you once. How are you getting your questions? Ameer We just look around and see what the next question is and do that one. Researcher What would your teacher say about that? Carl Um … he'd probably want to check to see that we got the previous one before giving us the next one … Ameer … but we are doing that. Researcher Why don't you just wait for your teacher to get here and give you the next question? Carl We're on a roll. And sometimes we have to wait a long time. Researcher Do you realize that you are doing the problems out of sequence from the order your teacher is giving them? Colton Oh really? That’s probably why some were so hard.
AUTONOMOUSLY SEEKING INCREASED CHALLENGE
CHALLENGE TOO LOW: CASE 3 (n>20)

41. FLOW
BOREDOM
CHALLENGE TOO LOW

42. CHALLENGE TOO LOW: CASE 1 (n=4)
FLOW
BOREDOM
CHALLENGE TOO LOW: CASE 1 (n=4)

43. CHALLENGE TOO LOW: CASE 2 (n=3)
FLOW
TOLERANCE
BOREDOM
CHALLENGE TOO LOW: CASE 2 (n=3)

44. CHALLENGE TOO LOW: CASE 3 (n>20)
FLOW
TOLERANCE
BOREDOM
CHALLENGE TOO LOW: CASE 3 (n>20)

45. FLOW
ANXIETY
BOREDOM
CHALLENGE TOO HIGH

46. CHALLENGE TOO HIGH: CASE 1 (n=6)
Researcher I have been watching your group for a bit and I notice that you aren’t working? Robert We gave up. This question is stupid. Katrina We tried, but we weren't getting anywhere. So we gave up. Researcher What do you think the problem is? Shannon This question is too hard. Robert … too hard. We don't get it. Katrina And the teacher hasn’t come over to help us. Researcher What kind of help are you looking for? Shannon You know, a hint or something. Researcher What would a hint do for you. Shannon Help us understand the question. Katrina … or remind us a little bit about how to do it.
QUITTING
CHALLENGE TOO HIGH: CASE 1 (n=6)

47. CHALLENGE TOO HIGH: CASE 2 (n=2)
PERSEVERANCE
IN THE FACE OF CHALLENGE
Researcher Question #5 was a tough one, huh? Oliver Yeah, that one took us a while. Connor In the end it wasn't that hard though. We were just missing something. Researcher Oh really. How did you figure it out? Connor We just kept at it and then we saw it. Researcher I noticed that your teacher came over to help. Did she help you? Oliver No, we wouldn't let her. We knew we knew how to do it and we wanted to figure it out ourselves.
CHALLENGE TOO HIGH: CASE 2 (n=2)

48. CHALLENGE TOO HIGH: CASE 3 (n>20)
Researcher I notice that you have been moving about the room a bit. Why? Michael Oh. We were just stuck so we went over there to get some ideas. Researcher Did it help? Michael Oh yeah. We got it now. Mikaela Michael got it. It took me a little longer, but I'm good now. Researcher You were also moving around a little bit earlier in the class? Mikaela Oh, you mean when we were checking answers? Yeah, we thought we were doing something wrong, but we were good. Researcher Lena, you like to look around a lot. Lena I do? What do you mean? Researcher You know, when Michael was working on the board you look around a lot at the other groups. Lena Right. I am just making sure we are on the right track.
AUTONOMOUSLY SEEKING HELP
CHALLENGE TOO HIGH: CASE 3 (n>20)

49. FRUSTRATION
FLOW
TOLERANCE
BOREDOM
CHALLENGE TOO HIGH

50. CHALLENGE TOO HIGH: CASE 1 (n=6)
FRUSTRATION
FLOW
TOLERANCE
BOREDOM
CHALLENGE TOO HIGH: CASE 1 (n=6)

51. CHALLENGE TOO HIGH: CASE 2 (n=2)
FRUSTRATION
FLOW
PERSEVERANCE
TOLERANCE
BOREDOM
CHALLENGE TOO HIGH: CASE 2 (n=2)

52. CHALLENGE TOO HIGH: CASE 3 (n>20)
FRUSTRATION
FLOW
PERSEVERANCE
TOLERANCE
BOREDOM
CHALLENGE TOO HIGH: CASE 3 (n>20)

53. DISCUSSION & CONCLUSIONS
FRUSTRATION
FLOW
BOREDOM
DISCUSSION & CONCLUSIONS

54. DISCUSSION & CONCLUSIONS
FRUSTRATION
FLOW
PERSEVERANCE
TOLERANCE
BOREDOM
DISCUSSION & CONCLUSIONS

55. DISCUSSION & CONCLUSIONS
FRUSTRATION
FLOW
PERSEVERANCE
TOLERANCE
BOREDOM
DISCUSSION & CONCLUSIONS

56. DISCUSSION & CONCLUSIONS
students autonomously sought to increase their ability or decrease the challenge
FRUSTRATION
FLOW
PERSEVERANCE
TOLERANCE
BOREDOM
DISCUSSION & CONCLUSIONS

57. DISCUSSION & CONCLUSIONS
students autonomously sought to maintain flow
FRUSTRATION
FLOW
PERSEVERANCE
TOLERANCE
BOREDOM
DISCUSSION & CONCLUSIONS

58. DISCUSSION & CONCLUSIONS
perseverance and tolerance serve as a buffer to allow this autonomy to function
FRUSTRATION
FLOW
PERSEVERANCE
TOLERANCE
BOREDOM
DISCUSSION & CONCLUSIONS

59. DISCUSSION & CONCLUSIONS
the Thinking Classroom facilitates this autonomy to function
FRUSTRATION
FLOW
PERSEVERANCE
TOLERANCE
BOREDOM
DISCUSSION & CONCLUSIONS

60. THANK YOU! liljedahl@sfu.ca www.peterliljedahl.com/presentations
@pgliljedahl