1. Oliver 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 …

2. Oliver 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 …

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

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

5. Oliver 2015 VERTICAL NON-PERMANENT SURFACES

6. Oliver 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 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

7. Oliver 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 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 Liljedahl, P. (in press). Building thinking classrooms: Conditions for problem solving. In P. Felmer, J. Kilpatrick, & E. Pekhonen (eds.) Posing and Solving Mathematical Problems: Advances and New Perspectives. New York, NY: Springer.

8. Oliver 2015 VISIBLY RANDOM GROUPS

9. Oliver 2015 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 co-constructed intra- and inter-group answers increases reliance on the teacher for answers decreases engagement in classroom tasks increase students become more enthusiastic about mathematics class Liljedahl, P. (2013). 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. EFFECT ON STUDENTS

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

11. Oliver 2015 liljedahl@sfu.ca www.peterliljedahl.com/presentations