1. Politecnico di Milano 2015 BUILDING THINKING CLASSROOMS - Peter Liljedahl

2. Politecnico di Milano 2015 SOME BACKGROUND CREATIVITY INVENTION DISCOVERY AHA! 2000

3. Politecnico di Milano 2015 SOME BACKGROUND CREATIVITY INVENTION DISCOVERY AHA! CREATIVITY INVENTION DISCOVERY AHA! 2000 PROBLEM SOLVING

4. Politecnico di Milano 2015 DESCRIPTIVE RESULT 2003 AHA! POSITIVE AFFECT

5. Politecnico di Milano 2015 2003 PROBLEM SOLVING POSITIVE AFFECT PRESCRIPTIVE INTERVENTION

6. Politecnico di Milano 2015 PRESCRIPTIVE INTERVENTION If 6 cats can kill 6 rats in 6 minutes, how many cats are required to kill 100 rats in 50 minutes? - Lewis Carroll 2004

7. Politecnico di Milano 2015 PRESCRIPTIVE INTERVENTION If 6 cats can kill 6 rats in 6 minutes, how many cats are required to kill 100 rats in 50 minutes? - Lewis Carroll 2004

8. Politecnico di Milano 2015 conducive to problem solving occasion problem solving thinking classrooms QUEST 2003 2014

9. Politecnico di Milano 2015 BOTH A MEANS AND AN END problem solving

10. Politecnico di Milano 2015 EARLY EFFORTS just do it teaching problem solving teaching with problem solving TASKS 2005 2006

11. Politecnico di Milano 2015 EARLY EFFORTS just do it teaching with problem solving TASKS 2005 2006 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

12. Politecnico di Milano 2015 REALIZATION

13. Politecnico di Milano 2015 CASTING ABOUT INSERVICE TEACHERS  learning teams  workshops  master's students  teachers' questions and comments  observation  proxies for engagement MY OWN TEACHING  undergraduate courses  graduate courses  guest teaching  proxies for engagement 2006 2014

14. Politecnico di Milano 2015 THINGS I (WE) TRIED VARIABLE 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 …

15. Politecnico di Milano 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 (CMEF 2009) …

16. Politecnico di Milano 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 (CMEF 2009) …

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

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

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

20. Politecnico di Milano 2015 VERTICAL NON-PERMANENT SURFACES

21. Politecnico di Milano 2015 DATA SOURCES TYPE I: qualitative written reports interviews field notes TYPE II: quantitative(ish) comparators - five different treatments per class 5 classes time measurements criterion measurements (0, 1, 2, 3)

22. Politecnico di Milano 2015 QUALITATIVE MEASURES 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.

23. Politecnico di Milano 2015 QUALITATIVE MEASURES

24. Politecnico di Milano 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 QUANTITATIVE MEASURES

25. Politecnico di Milano 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 QUANTITATIVE MEASURES

26. Politecnico di Milano 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 QUANTITATIVE MEASURES

27. Politecnico di Milano 2015 VISIBLY RANDOM GROUPS

28. Politecnico di Milano 2015 EMPIRICAL 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.

29. Politecnico di Milano 2015 QUALITATIVE MEASURES

30. Politecnico di Milano 2015 TOGETHER - THREE PILARS good tasksvertical surfaces random groups

31. Politecnico di Milano 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?

32. Politecnico di Milano 2015 QUALITATIVE MEASURE

33. Politecnico di Milano 2015 SO, WHY IS IT WORKING?

34. Politecnico di Milano 2015 1st PERSON EXPERIENCE FOR STUDENTS …

35. Politecnico di Milano 2015 1st PERSON VICARIOUS EXPERIENCE FOR TEACHERS …

36. Politecnico di Milano 2015 THANK YOU! liljedahl@sfu.ca www.peterliljedahl.com/presentations

37. Politecnico di Milano 2015

38. … FOR TEACHERS?

39. Politecnico di Milano 2015 REALIZATION

40. Politecnico di Milano 2015 METHODOLOGY 3 lessons prior to implementation 3 weeks after implementation once every 2 weeks for 2 months participant observer (Eisenhart, 1988) field notes from observations, interactions, and conversations interviews with 12 students and teacher analytic induction (Patton, 2002)