BUILDING THINKING CLASSROOMS Peter Liljedahl Liljedahl P 2014
BUILDING THINKING CLASSROOMS - Peter Liljedahl
• 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. 127 -144). 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. 361 -386). New York, NY: Springer. • Liljedahl, P. (2016). Flow: A Framework for Discussing Teaching. Proceedings of the 40 th 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 1 st 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 10 th 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. • Beth Baldwin, MSc (2018). The Relationship Between Mathematics Students’ Self and Group Efficacies in a Thinking Classroom • Maria Kerkoff, MSc (2018). Experiencing Mathematics through Problem Solving Tasks. • Chris Mc. Gregor, MSc, (2018). Reduction of Mathematics Anxiety through use of Non. Permanent Vertical Surfaces and Group Discussion. • Oana Chiru, MSc (2017). Occasioning Flow in the Mathematics Classroom: Optimal Experiences in Common Places. • Mike Pruner, MSc (2016). Observations in a Thinking Classroom.
There was a time when Sara used to like math, when it came easy to her marks were good. All through her elementary education (K-7) she was confident in her ability, “I would answer questions in class and take charge when we were working in groups. ”
Then she moved onto high school and into Math 8. The year started out with review. “I found this easy. However, for the first time in my life I had mathematics homework. ” But the homework was on content from the year before so it went quickly and without difficulty. At the end of all the review there was a test. “I aced it – I had an almost perfect score. ”
The next unit was on fractions. She had been good at fractions in elementary school so she was feeling very confident about this unit as well. “But my mark on the unit test was a shock. ” For the first time in her life on a math test. She didn't even get she didn't get an A or a B. She got 70% (C+). “I was devastated. ”
“Then came algebra!” This was new content so she didn't start off feeling overly confident. Sara worked extra hard, doing extra homework questions, rewriting all her notes, and paying extra careful attention in class. She was nervous going to the test. She got 80% (B). “I was working twice as hard as in grade 7 and doing worse. ”
This set the pattern for Sara for the next three years. She worked harder and harder, but didn’t do better. In grade 9 she almost failed the rational expressions unit, and she thought, “I'm not going to pass the year”. Her dreams of becoming a doctor were starting to look impossible – “I may not get into university”. Sara finished the year with a C+.
In grade 10 she doubled her efforts again and her parents hired a tutor. “I finished the year with a B but remember feeling completely wrung out. ” She had lost all her self-confidence in mathematics, it had been two years since she volunteered an answer in class, and during group work she just listened.
But none of that compared to the devastation when her school councillor offered her the possibility of moving to the Apprenticeship and Workplace (A&W) math course for grade 11 so she could finish math and ensure she would graduate. Sara had always known that A&W was for “dummies and burn-outs. He thought I was one of them. There was no way I was going into that class. ” So, Sara enrolled into Pre-Calculus 11 and landed in Ms. Marina's class.
The first week was very challenging for Sara. She shied away from group work and here every class, all class, was group work. Sara didn't like this at all. “The only good thing was that the problems were fun. They didn't feel like math. And I actually found myself contributing a little bit here and there. ”
In the second week the problems shifted to curriculum and suddenly they were factoring polynomials. This was one of Sara's least favourite topics so she became very anxious. “I felt like they were going to figure out that I don't know anything, that I'm a fraud, and that I shouldn't be in this class. I wanted to transfer to a different class – to a normal class. But I was afraid to go to my councillor because he would just say 'I told you so'. ” So Sara endured.
Then something interesting happened. “I saw that my group had done something wrong. I just sort of said, 'I don't think that's right'. My group mates looked at me and waited for me to explain, but I didn't know how. So, I took the pen and started writing on the board. ” And she was right. That was a turning point for Sara. After that she was more willing to offer ideas and even occasionally hold the pen. Before long Sara found herself in a group where she wanted to hold the pen at the start of the problem. This is now the norm for Sara. “It doesn't matter who grabs the pen first. We need to start. It will work out in the end if we just start. ”
At the end of the polynomial unit Sara scored a low B on her test. “I was super happy with that. I mean, I knew I could do it in a group with others, but I wasn't sure how that was rubbing off on me. But it seems to have worked just fine. " Sara wasn't anxious about homework or marks anymore. “The learning is happening in class now. I don't feel like I have to go home and learn it on my own after class, or re-write note, like last year. ”
As the term rolled on Sara started to enjoy herself in the class more and more. “This is now my favourite class. ” She especially liked when the problems got tough. “Every once in a while we get a really tough one. We usually don't know that it is a tough one when we start, but we get to this point when you just realize 'this is tough'. And you look at each other and you grin and you just kind of dig in. And usually it works out. There is no feeling like it and everyone is high fiving each other. ”
Sara received a B (75%) on her first report card. “That's awesome. I mean I would have liked an A, but there were some really tough units in there. ” Sara is even rethinking her future. “If I can get Ms. Marina again next year, I think I'll take Math 12. Maybe even if I can't get Ms. Marina I'll take Math 12. I can do this. ” Her dream to become a doctor is back on the table.
MASSIVE AFFECTIVE CHANGE
MASSIVE AFFECTIVE CHANGE • • self-efficacy enjoyment emotions confidence goals attitudes beliefs
MASSIVE AFFECTIVE CHANGE • • self-efficacy enjoyment emotions confidence goals attitudes beliefs
MASSIVE AFFECTIVE CHANGE • • self-efficacy enjoyment emotions confidence goals attitudes beliefs HOW TO EXPLAIN THIS?
WHAT IS THIS?
15 YEARS AGO …
S IN U T TI A N O I T N L S M OR
N D R O E T IA N N O N T O EG S M
M E T S S A L C R S M O O S A Y S A
M E T S S A L C R S M O O S A Y S A
In a system, all the features reinforce each other. (Stiegler & Hiebert, 1999) If one feature is changed, the system will rush to repair the damage. (Stiegler & Hiebert, 1999)
E T S E G N A H Y S A ? M C O T W O H In a system, all the features reinforce each other. (Stiegler & Hiebert, 1999) If one feature is changed, the system will rush to repair the damage. (Stiegler & Hiebert, 1999)
400+ TEACHERS | 13 YEARS | 2 WEEK CYCLES
E T A I T S O M G R E O N N E L R A O ION T G T N U I T I Y T TR INS E H T 400+ TEACHERS | 13 YEARS | 2 WEEK CYCLES
G N T A H C M O T E T G S N Y I S Y R E H T E 400+ TEACHERS | 13 YEARS | 2 WEEK CYCLES
G N T A H C M O T E T G S N Y I S Y R E H T E
OPPORTUNITIES 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 consolidate 12 formative assessment 13 summative assessment 14 reporting out
OPPORTUNITIES 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 consolidate 12 formative assessment 13 summative assessment 14 reporting out OPTIMAL PRACTICES FOR THINKING
OPPORTUNITIES FOR THINKING OPTIMAL 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 consolidate from 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)
OPPORTUNITIES FOR THINKING OPTIMAL 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 consolidate from 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)
OPPORTUNITIES FOR THINKING OPTIMAL 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 consolidate from 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)
OPPORTUNITIES FOR THINKING OPTIMAL 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 consolidate from 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)
OPPORTUNITIES FOR THINKING OPTIMAL 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 consolidate from 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)
OPPORTUNITIES FOR THINKING OPTIMAL 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 consolidate from 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)
THANK YOU! liljedahl@sfu. ca www. peterliljedahl. com/presentations @pgliljedahl | #vnps | #thinkingclassroom Global Math Department
• begin lessons with good problems • form visibly random groups • use vertical nonpermanent surfaces
• use verbal instructions • defront the classroom • answer only keep thinking questions • use meaningful notes • foster autonomous actions
• use hints and extensions to manage flow • consolidate from the bottom • assign check your understanding questions
• communicate where students are and where they are going • evaluate what you value • report out based on data (not points)
BUILDING THINKING CLASSROOMS (year 1)
BUILDING THINKING CLASSROOMS (year 2+) • • • begin with good problems use vertical non-permanent surfaces form visibly random groups use verbal instructions defront the classroom answer only keep thinking questions build autonomy consolidate from the bottom use hints and extensions to manage flow • give check your understanding questions • use mindful notes • communicate where a student is and where they are going • evaluate what you value • report out based on data (not points)
THANK YOU! liljedahl@sfu. ca www. peterliljedahl. com/presentations @pgliljedahl | #vnps | #thinkingclassroom Global Math Department
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