1. Student Problem Solving Behaviour in a Thinking Classroom
Peter Liljedahl

2.
@pgliljedahl

3. 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.
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. (2016). Flow: A Framework for Discussing Teaching. Proceedings of the 40th Conference of the International Group for the Psychology of Mathematics Education, Szeged, Hungary.
Liljedahl, P. (2017). Building Thinking Classrooms: A Story of Teacher Professional Development. The 1st International Forum on Professional Development for Teachers. Seoul, Korea.
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.
Liljedahl, P. (in press). On the edges of flow: Student engagement in problem solving. Proceedings of the 10th Congress of the European Society for Research in Mathematics Education. Dublin, Ireland.
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. & Allan, D. (2013). Studenting: The case of "now you try one". In Lindmeier, A. M. & Heinze, A. (Eds.). Proceedings of the 37th Conference of the International Group for the Psychology of Mathematics Education, Vol. 3, pp Kiel, Germany: PME.
Liljedahl, P. & Allan, D. (2013). Studenting: The Case of Homework. Proceedings of the 35th Conference for Psychology of Mathematics Education – North American Chapter, pp  Chicago, USA.

4. Student Problem Solving Behaviour in a Thinking Classroom

5. Student Problem Solving Behaviour in a Thinking Classroom

6. Student Problem Solving Behaviour in a 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. Students were not thinking.
Jane was planning her teaching on the assumption that students either could not or would not think.

11. THREE REALIZATIONS! INSTITUTIONAL NORMS Students are not thinking!
Teachers are planning their teaching on the assumption that students either cannot or will not think.
Patricio – institutional reasons, institutional goals

12. THREE REALIZATIONS! NON-NEGOTIATED NORMS Students are not thinking!
Teachers are planning their teaching on the assumption that students either cannot or will not think.

13. 400+ TEACHERS OVER THE LAST 14 YEARS

14. ACTION RESEARCH ON STEROIDS
RENEGOTIATING THE
NON-NEGOTIATED NORMS
ACTION RESEARCH ON STEROIDS

15. ELEMENTS OF PRACTICE 1
problems 2
how we give the problem 3
how we answer questions 4
room organization 5
how groups are formed 6
student work space 7
how we give notes 8
hints and extensions 9
how we level

16. ELEMENTS OF PRACTICE 1
problems 2
how we give the problem 3
how we answer questions 4
room organization 5
how groups are formed 6
student work space 7
autonomy 8
how we give notes 9
what homework looks like 10
hints and extensions 11
how we level 12
formative assessment 13
summative assessment 14
reporting out

17. ELEMENTS OF PRACTICE
PRACTICES FOR THINKING 1
problems 2
how we give the problem 3
how we answer questions 4
room organization 5
how groups are formed 6
student work space 7
autonomy 8
how we give notes 9
what homework looks like 10
hints and extensions 11
how we level 12
formative assessment 13
summative assessment 14
reporting out

18. ELEMENTS OF PRACTICE
PRACTICES FOR THINKING 1
problems
begin lesson with good problems 2
how we give the problem 3
how we answer questions 4
room organization 5
how groups are formed 6
student work space 7
autonomy 8
how we give notes 9
what homework looks like 10
hints and extensions 11
how we level 12
formative assessment 13
summative assessment 14
reporting out

19. ELEMENTS OF PRACTICE
PRACTICES FOR THINKING 1
problems
begin lessons with good problems 2
how we give the problem 3
how we answer questions 4
room organization 5
how groups are formed
form visibly random groups 6
student work space 7
autonomy 8
how we give notes 9
what homework looks like 10
hints and extensions 11
how we level 12
formative assessment 13
summative assessment 14
reporting out

20. ELEMENTS OF PRACTICE
PRACTICES FOR THINKING 1
problems
begin lessons with good problems 2
how we give the problem 3
how we answer questions 4
room organization 5
how groups are formed
form visibly random groups 6
student work space
use vertical non-permanent surfaces 7
autonomy 8
how we give notes 9
what homework looks like 10
hints and extensions 11
how we level 12
formative assessment 13
summative assessment 14
reporting out

21. PRACTICES FOR THINKING
ELEMENTS OF PRACTICE
PRACTICES FOR THINKING 1
problems
begin lessons with good problems 2
how we give the problem
use verbal instructions 3
how we answer questions
answer only keep thinking questions 4
room organization
defront the classroom 5
how groups are formed
form visibly random groups 6
student work space
use vertical non-permanent surfaces 7
autonomy
foster autonomous actions 8
how we give notes
have students do meaningful notes 9
what homework looks like
use check your understanding questions 10
hints and extensions
manage flow 11
how we level
level to the bottom 12
formative assessment
show where they are and where they are going 13
summative assessment
evaluate what you value 14
reporting out
report out based on data (not points)

22. SEQUENCE OF IMPLEMENTATION

23. BUILDING THINKING CLASSROOMS
… a classroom that is not only conducive to thinking but also occasions thinking, a space that is inhabited by thinking individuals as well as individuals thinking collectively, learning together and constructing knowledge and understanding through activity and discussion. It is a space wherein the teacher not only fosters thinking but also expects it, both implicitly and explicitly. (Liljedahl, 2016b, p.364)

24. Student Problem Solving Behaviour in a Thinking Classroom

25. MIHALY CSÍKSZENTMIHÁLYI
THE OPTIMAL EXPERIENCE

26. 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)

27. 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)

28. 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)

29. 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.
FRUSTRATION
FLOW
BOREDOM

30. 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.
FRUSTRATION
FLOW
= ENGAGEMENT
BOREDOM

31. FLOW EXPERIENCE
FLOW EXPERIENCE
FLOW
FRUSTRATION
BOREDOM

32. FLOW EXPERIENCE
FLOW EXPERIENCE
FLOW
FRUSTRATION
BOREDOM

33. FLOW EXPERIENCE
FLOW EXPERIENCE
FLOW
FRUSTRATION
BOREDOM

34. MOMENTS OF IMBALANCE
FLOW EXPERIENCE
FLOW
FRUSTRATION
BOREDOM

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

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

37. METHODOLOGY: THE TEACHING

38. METHODOLOGY: THE DATA two classrooms (grade 11 & 12 pre-calculus)
curricular problems
non-curricular problems
watching for moments of imbalance
video didn't work (too narrow a field of vision)
field notes
photographs
interviews
NOTEABILITYTM

39. METHODOLOGY: THE ANALYSIS
flow (Mihaly Csíkszentmihályi, 1998, 1996, 1990)
there is a balance between challenges and skills
restoring of balance

40. MOMENTS OF IMBALANCE
FLOW EXPERIENCE
FLOW
FRUSTRATION
BOREDOM

41. CHALLENGE TOO LOW
FLOW EXPERIENCE
FLOW
FRUSTRATION
BOREDOM

42. 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.
Researcher I saw you two work together before at the end of class. I don't recall seeing you two giving up before.
Allison We aren't giving up. Sometimes we don't finish all the questions because they are hard and we run out of time. But these are easy.
Researcher What makes them easy.
Mikaela They just are. The first three are exactly the same and we could do them no problem.
QUITTING

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

44. 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

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

46. 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

47. CHALLENGE TOO HIGH: CASE 3 (n>20)
FLOW EXPERIENCE
FLOW
TOLERANCE
BOREDOM

48. MOMENTS OF IMBALANCE
FLOW EXPERIENCE
FLOW
ANXIETY
BOREDOM

49. 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

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

51. CHALLENGE TOO HIGH: CASE 2 (n=2)
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.
PERSEVERANCE

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

53. 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

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

55. DISCUSSION + CONCLUSIONS
FRUSTRATION
FLOW
BOREDOM

56. DISCUSSION + CONCLUSIONS
FLOW EXPERIENCE
FRUSTRATION
FLOW
There are states between flow and boredom and flow and frustration.
PERSEVERANCE
TOLERANCE
BOREDOM

57. DISCUSSION + CONCLUSIONS
FRUSTRATION
FLOW
Students autonomously sought to increase their ability or decrease the challenge.
PERSEVERANCE
TOLERANCE
BOREDOM

58. DISCUSSION + CONCLUSIONS
FLOW EXPERIENCE
FRUSTRATION
FLOW
Students autonomously sought to maintain flow.
PERSEVERANCE
TOLERANCE
BOREDOM

59. DISCUSSION + CONCLUSIONS
FLOW EXPERIENCE
FRUSTRATION
FLOW
Perseverance and tolerance serve as a buffer to allow this autonomy to function.
PERSEVERANCE
TOLERANCE
BOREDOM

60. DISCUSSION + CONCLUS
Good problems, vertical non-permanent surfaces, and random groups help facilitate this autonomy.

61. DISCUSSION + CONCLUSIONS
THEORY OF
THEORY FOR
TEACHING

62. DISCUSSION + CONCLUSION
foster autonomous actions

63. THANK YOU! liljedahl@sfu.ca www.peterliljedahl.com/presentations
@pgliljedahl | #vnps | #thinkingclassroom