1. PDS – April 2015 PROBLEM BASED LEARNING: BUILDING THINKING CLASSROOMS - Peter Liljedahl

2. PDS – April 2015 CONTEXT OF RESEARCH NOW YOU TRY ONEHOMEWORKTAKING NOTES

3. PDS – April 2015 TYPOLOGY BUILDING Observation PhaseTypology BuildingTypology Testing

4. PDS – April 2015 NOW YOU TRY ONE catching up on notes (n=0) n=32 STUDENTING

5. PDS – April 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.

6. PDS – April 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

7. PDS – April 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

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

9. PDS – April 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

10. PDS – April 2015 TAKING NOTES (n=30) gaming 90% gaming 63% USE NOTES TO STUDY

11. PDS – April 2015 BUILDING THINKING CLASSROOMS

12. PDS – April 2015 EARLY EFFORTS just do it teaching with problem solving TASKS teaching problem solving

13. PDS – April 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

14. PDS – April 2015 REALIZATION

15. PDS – April 2015 CASTING ABOUT INSERVICE TEACHERS  learning teams  workshops  master's students MY OWN TEACHING  undergraduate courses  graduate courses  guest teaching

16. PDS – April 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 …

17. PDS – April 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 …

18. PDS – April 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 …

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

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

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

22. PDS – April 2015 VERTICAL NON-PERMANENT SURFACES

23. PDS – April 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

24. PDS – April 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

25. PDS – April 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

26. PDS – April 2015 VISIBLY RANDOM GROUPS

27. PDS – April 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.

28. PDS – April 2015 TOGETHER - THREE PILARS good tasksvertical surfaces random groups

29. PDS – April 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?

30. PDS – April 2015 TOGETHER

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

32. PDS – April 2015 THANK YOU! liljedahl@sfu.ca www.peterliljedahl.com/presentations