1. ABE 2015 THINKING, LEARNING, OR STUDENTING: THE VIEW FROM THE BACK OF THE CLASSROOM - Peter Liljedahl

2. ABE 2015 MS. AHN’S CLASSROOM If 6 cats can kill 6 rats in 6 minutes, how many cats are required to kill 100 rats in 50 minutes? - Lewis Carroll

3. ABE 2015 MS. AHN’S CLASSROOM If 6 cats can kill 6 rats in 6 minutes, how many cats are required to kill 100 rats in 50 minutes? - Lewis Carroll

4. ABE 2015 MS. AHN’S CLASSROOM UNDERSTANDING NON-THINKING CLASSROOMS BUILDING THINKING CLASSROOMS 12 YEARS OF RESEARCH

5. ABE 2015 UNDERSTANDING NON-THINKING CLASSROOMS

6. ABE 2015 CONTEXT OF RESEARCH LOTS OF CLASSROOMS

7. ABE 2015 CONTEXT OF RESEARCH NOW YOU TRY ONEHOMEWORKTAKING NOTES

8. ABE 2015 TYPOLOGY BUILDING Observation PhaseTypology BuildingTypology Testing

9. ABE 2015 NOW YOU TRY ONE catching up on notes (n=0) n=32 STUDENTING

10. ABE 2015 NOW YOU TRY ONE n=32 Liljedahl, P. & Allan, D. (2013). Studenting: The case of "now you try one". Proceedings of the 37 th Conference of the PME, Vol. 3, pp. 257-264. Kiel, Germany: PME.

11. ABE 2015 HOMEWORK Marked (n=60) Not Marked (n=40) Marked (n=60) Not Marked (n=40) Didn't Do It1516 Got Help1812 I forgot53 Felt they would fail quiz61 I was busy42 Felt they would pass quiz33 I tried, but I couldn't do it33 Felt they would excel98 I took a chance30 Did it On Their Own1311 It wasn't worth marks08 Mimicked from notes45 Cheated141 Did not mimic from notes66 Copied71 Mimicked but completed30 Faked50 Half homework risk20

12. ABE 2015 HOMEWORK Marked (n=60) Not Marked (n=40) Marked (n=60) Not Marked (n=40) Didn't Do It1516 Got Help1812 I forgot53 Felt they would fail quiz61 I was busy42 Felt they would pass quiz33 I tried, but I couldn't do it33 Felt they would excel98 I took a chance30 Did it On Their Own1311 It wasn't worth marks08 Mimicked from notes45 Cheated141 Did not mimic from notes66 Copied71 Mimicked but completed30 Faked50 Half homework risk20

13. ABE 2015 HOMEWORK Liljedahl, P. & Allan, D. (2013). Studenting: The Case of Homework. Proceedings of the 35 th Conference for PME-NA. Chicago, USA.

14. ABE 2015 TAKING NOTES (n=30) don’t n=3 don’t use notes n=27 yes n=3 don’t keep up n=16 USE NOTES TO STUDY

15. ABE 2015 TAKING NOTES (n=30) gaming 90% gaming 63% USE NOTES TO STUDY

16. ABE 2015 FRAMEWORK OF GAMING GAMING WITH FAÇADE (intentional) ALTERNATE IDEAS preferred learning style teacher is wrong institutional norms BEATING THE SYSTEM avoidance economy of action doing being practical rationality … NO FAÇADE (unintentional) wrong objective wrong rules

17. ABE 2015 BUILDING THINKING CLASSROOMS

18. ABE 2015 EARLY EFFORTS just do it teaching with problem solving TASKS teaching problem solving

19. ABE 2015 EARLY EFFORTS just do it teaching with problem solving TASKS some were able to do it they needed a lot of help they loved it they don’t know how to work together they got it quickly and didn't want to do any more they gave up early FILTERED THROUGH EXISTING NORMS! assessing problem solving

20. ABE 2015 REALIZATION

21. ABE 2015 CASTING ABOUT INSERVICE TEACHERS  learning teams  workshops  master's students MY OWN TEACHING  undergraduate courses  graduate courses  guest teaching

22. ABE 2015 THINGS I (WE) TRIED tasks hints and extensions how we give the problem how we answer questions how we level room organization how groups are formed student work space how we give notes assessment …

23. ABE 2015 FINDINGS VARIABLEPOSITIVE EFFECT tasksgood tasks hints and extensionsmanaging flow how we give the problemoral vs. written how we answer questions3 types of questions how we levellevel to the bottom room organizationdefronting the room how groups are formedvisibly random groups student work spacevertical non-permanent surfaces how we give notesdon't assessment4 purposes …

24. ABE 2015 FINDINGS VARIABLEPOSITIVE EFFECT tasksgood tasks hints and extensionsmanaging flow how we give the problemoral vs. written how we answer questions3 types of questions how we levellevel to the bottom room organizationdefronting the room how groups are formedvisibly random groups student work spacevertical non-permanent surfaces how we give notesdon't assessment4 purposes …

25. ABE 2015 FINDINGS – BEST BYPASS good tasks vertical non- permanent surfaces visibly random groups answering questions oral instructions defronting the room levelling assessment flow

26. ABE 2015 FINDINGS – BIGGEST IMPACT good tasks vertical non- permanent surfaces visibly random groups answering questions oral instructions defronting the room levelling assessment flow

27. ABE 2015 FINDINGS – BIGGEST IMPACT good tasks vertical non- permanent surfaces visibly random groups answering questions oral instructions defronting the room levelling assessment flow

28. ABE 2015 VERTICAL NON-PERMANENT SURFACES

29. ABE 2015 ANECDOTES This was so great [..] it was so good I felt like I shouldn't be doing it. I will never go back to just having students work in their desks. How do I get more whiteboards? The principal came into my class … now I'm doing a session for the whole staff on Monday. My grade-partner is even starting to do it. The kids love it. Especially the windows. I had one girl come up and ask when it will be her turn on the windows.

30. ABE 2015 UPTAKE

31. ABE 2015 PROXIES FOR ENGAGEMENT time to task time on task time to first mathematical notation amount of discussion eagerness to start participation persistence knowledge mobility non-linearity of work EFFECT ON STUDENTS

32. ABE 2015 vertical non-perm horizontal non-perm vertical permanent horizontal permanent notebook N (groups)10 998 time to task12.8 sec13.2 sec12.1 sec14.1 sec13.0 sec time on task7.1 min4.6 min3.0 min3.1 min3.4 min first notation20.3 sec23.5 sec2.4 min2.1 min18.2 sec discussion2.82.21.51.10.6 eagerness3.02.31.21.00.9 participation2.82.31.81.60.9 persistence2.6 1.81.9 mobility2.51.22.01.31.2 non-linearity2.72.91.01.10.8 EFFECT ON STUDENTS

33. ABE 2015 vertical non-perm horizontal non-perm vertical permanent horizontal permanent notebook N (groups)10 998 time to task12.8 sec13.2 sec12.1 sec14.1 sec13.0 sec time on task7.1 min4.6 min3.0 min3.1 min3.4 min first notation20.3 sec23.5 sec2.4 min2.1 min18.2 sec discussion2.82.21.51.10.6 eagerness3.02.31.21.00.9 participation2.82.31.81.60.9 persistence2.6 1.81.9 mobility2.51.22.01.31.2 non-linearity2.72.91.01.10.8 EFFECT ON STUDENTS

34. ABE 2015 VISIBLY RANDOM GROUPS

35. ABE 2015 RESULTS students become agreeable to work in any group they are placed in there is an elimination of social barriers within the classroom mobility of knowledge between students increases reliance on the teacher for answers decreases reliance on co-constructed intra- and inter- group answers increases engagement in classroom tasks increase students become more enthusiastic about mathematics class Liljedahl, P. (in press). The affordances of using visually random groups in a mathematics classroom. In Y. Li, E. Silver, & S. Li (eds.) Transforming Mathematics Instruction: Multiple Approaches and Practices. New York, NY: Springer.

36. ABE 2015 UPTAKE

37. ABE 2015 TOGETHER - THREE PILARS good tasksvertical surfaces random groups

38. ABE 2015 TOGETHER I've never seen my students work like that they worked the whole class they want more how do I keep this up AND work on the curriculum? how do I assess this? where do I get more problems? I don't know how to give hints?

39. ABE 2015 TOGETHER

40. ABE 2015 UPTAKE

41. ABE 2015 WHAT NEXT? good tasks vertical non- permanent surfaces visibly random groups answering questions oral instructions defronting the room levelling assessment flow

42. ABE 2015 THANK YOU! liljedahl@sfu.ca www.peterliljedahl.com/presentations