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BUILDING THINKING CLASSROOMS THE NARRATIVE BEHIND THE NARRATIVE (part I)
- Peter Liljedahl
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@pgliljedahl
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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 ). 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 ). New York, NY: Springer. Liljedahl, P. (2016). Flow: A Framework for Discussing Teaching. Proceedings of the 40th 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 1st 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 10th 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.
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Liljedahl, P. (2014). What Teachers Want from their Professional Learning Opportunities. The Mathematics Enthusiast, 11(1), Liljedahl, P. & Allan, D. (2013). Studenting: The case of "now you try one". In Lindmeier, A. M. & Heinze, A. (Eds.). Proceedings of the 37th Conference of the International Group for the Psychology of Mathematics Education, Vol. 3, pp Kiel, Germany: PME. Liljedahl, P. & Allan, D. (2013). Studenting: The Case of Homework. Proceedings of the 35th Conference for Psychology of Mathematics Education – North American Chapter, pp Chicago, USA. Liljedahl, P. (2011). The Theory of Conceptual Change as a Theory for Changing Conceptions. Nordisk Matematikkdidaktikk, 16(1-2), Liljedahl, P. (2015). Numeracy Task Design: A Case of Changing Mathematics Teaching Practice. ZDM: The International Journal on Mathematics Education, 47(4), Liljedahl, P. (2010). Noticing Rapid and Profound Mathematics Teacher Change. Journal of Mathematics Teacher Education, 13(5), Liljedahl, P. (2018). Relationship between Proxies for Learning and Mathematics Teachers’ Views. In Palmér H., Skott J. (eds) Students' and Teachers' Values, Attitudes, Feelings and Beliefs in Mathematics Classrooms, pp New York, NY: Springer. Liljedahl, P. (2017). Card Tricks, Discovery Learning, and Flow in Mathematics Teacher Education. In J. Cummings & M. Blatherwick (eds.), Creative Dimensions of Teaching and Learning in the 21st Century. (pp ). Rotterdam, NL: Sense Publishers. Liljedahl, P. (2008). Teachers' insights into the relationship between beliefs and practice. In J. Maaß & W. Schlöglmann (eds.), Beliefs and Attitudes in Mathematics Education: New Research Results. (pp ). Rotterdam, NL: Sense Publishers. Liljedahl, P. (2013). Approaching Professional Learning: Teachers' Goals. Proceedings of the 8th Congress of the European Society for Research in Mathematics Education. Antalya, Turkey.
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Chris McGregor, MSc, (2018). Reduction of Mathematics Anxiety through use of Non- Permanent Vertical Surfaces and Group Discussion. Darien Allan, PhD (2017). Student Actions as a Window into Goals and Motives in the Secondary Mathematics Classroom. Neena Bauch, MSc (2017). The Transition from High School Mathematics to First Year Calculus. Oana Chiru, MSc (2017). Occasioning Flow in the Mathematics Classroom: Optimal Experiences in Common Places. Robert Lovell, MSc (2016). Real-World Applications in Math Class. Mike Pruner, MSc (2016). Observations in a Thinking Classroom.
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PROBLEM 12 cm x 20 cm 10 cm x 18 cm
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PROBLEM HEIGHT TIME
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DISCUSS YOUR EXPERIENCES DOING THIS TASK.
LIST THE QUALITIES STUDENTS NEED TO BE SUCCESSFUL DOING A TASK LIKE THIS. NOW STEAL IDEAS FROM OTHERS. NOW CIRCLE THE THREE QUALITIES THAT ARE THE MOST VALUABLE TO YOUR GROUP.
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QUALITIES Perseverance Risk taking Collaboration Communication
Tolerance for ambiguity Resourcefulness Valuing the process Confidence Visualization Some math skills Flexible Critical questioning Mutual respect Connect representations Listening skills
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THINKING CLASSROOM QUALITIES Perseverance Risk taking Collaboration
Communication Tolerance for ambiguity Resourcefulness Valuing the process Confidence Visualization Some math skills Flexible Critical questioning Mutual respect Connect representations Listening skills THINKING CLASSROOM
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THINKING CLASSROOM DEFINE A QUALITIES Perseverance Risk taking
Collaboration Communication Tolerance for ambiguity Resourcefulness Valuing the process Confidence Visualization Some math skills Flexible Critical questioning Mutual respect Connect representations Listening skills THINKING CLASSROOM DEFINE A
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A thinking classroom is "a classroom that is not only conducive to thinking but also occasions thinking, a space that is inhabited by thinking individuals as well as individuals thinking collectively, learning together, and constructing knowledge and understanding through activity and discussion" (Liljedahl, 2016a, p.364)
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HOW DO WE BUILD A THINKING CLASSROOM? QUALITIES Perseverance
Risk taking Collaboration Communication Tolerance for ambiguity Resourcefulness Valuing the process Confidence Visualization Some math skills Flexible Critical questioning Mutual respect Connect representations Listening skills HOW DO WE BUILD A THINKING CLASSROOM?
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JANE’S CLASS – 15 YEARS AGO
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If 6 cats can kill 6 rats in 6 minutes, how many cats are required to kill 100 rats in 50 minutes? - Lewis Carroll
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DISASTER! If 6 cats can kill 6 rats in 6 minutes, how many cats are required to kill 100 rats in 50 minutes? - Lewis Carroll
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Students were not thinking.
Jane was planning her teaching on the assumption that students either cannot or will not think.
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INSTITUTIONAL NORMS Students were not thinking.
Jane was planning her teaching on the assumption that students either cannot or will not think.
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NON-NEGOTIATED NORMS Students were not thinking.
Jane was planning her teaching on the assumption that students either cannot or will not think.
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ACTION RESEARCH ON STEROIDS (n = 400+)
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RENEGOTIATING THE NON-NEGOTIATED NORMS
ACTION RESEARCH ON STEROIDS (n = 400+)
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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 level 12 formative assessment 13 summative assessment 14 reporting out
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OPPORTUNITIES FOR THINKING
OPTIMAL PRACTICES 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 level 12 formative assessment 13 summative assessment 14 reporting out
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OPPORTUNITIES FOR THINKING
OPTIMAL PRACTICES 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 level 12 formative assessment 13 summative assessment 14 reporting out
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OPPORTUNITIES FOR THINKING
OPTIMAL PRACTICES FOR THINKING 1 problems begin lesson with good 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 level 12 formative assessment 13 summative assessment 14 reporting out
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OPPORTUNITIES FOR THINKING
OPTIMAL PRACTICES FOR THINKING 1 problems begin lessons with good 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 level 12 formative assessment 13 summative assessment 14 reporting out
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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 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 level 12 formative assessment 13 summative assessment 14 reporting out
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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 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 level 12 formative assessment 13 summative assessment 14 reporting out
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STOP THINKING QUESTIONS KEEP THINKING QUESTIONS
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 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 level 12 formative assessment 13 summative assessment 14 reporting out PROXIMITY QUESTIONS STOP THINKING QUESTIONS KEEP THINKING QUESTIONS
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STOP THINKING QUESTIONS KEEP THINKING QUESTIONS
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 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 level 12 formative assessment 13 summative assessment 14 reporting out PROXIMITY QUESTIONS STOP THINKING QUESTIONS KEEP THINKING QUESTIONS
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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 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 level 12 formative assessment 13 summative assessment 14 reporting out
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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 6 student work space 7 autonomy 8 how we give notes 9 what homework looks like 10 hints and extensions 11 how we level 12 formative assessment 13 summative assessment 14 reporting out
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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 6 student work space 7 autonomy 8 how we give notes 9 what homework looks like 10 hints and extensions 11 how we level 12 formative assessment 13 summative assessment 14 reporting out
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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 7 autonomy 8 how we give notes 9 what homework looks like 10 hints and extensions 11 how we level 12 formative assessment 13 summative assessment 14 reporting out
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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 7 autonomy 8 how we give notes 9 what homework looks like 10 hints and extensions 11 how we level 12 formative assessment 13 summative assessment 14 reporting out
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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 8 how we give notes 9 what homework looks like 10 hints and extensions 11 how we level 12 formative assessment 13 summative assessment 14 reporting out
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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 8 how we give notes 9 what homework looks like 10 hints and extensions 11 how we level 12 formative assessment 13 summative assessment 14 reporting out
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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 9 what homework looks like 10 hints and extensions 11 how we level 12 formative assessment 13 summative assessment 14 reporting out
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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 9 what homework looks like 10 hints and extensions 11 how we level 12 formative assessment 13 summative assessment 14 reporting out
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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 10 hints and extensions 11 how we level 12 formative assessment 13 summative assessment 14 reporting out
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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 10 hints and extensions 11 how we level 12 formative assessment 13 summative assessment 14 reporting out
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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 11 how we level 12 formative assessment 13 summative assessment 14 reporting out
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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 11 how we level 12 formative assessment 13 summative assessment 14 reporting out
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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 level 12 formative assessment 13 summative assessment 14 reporting out
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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 level 12 formative assessment 13 summative assessment 14 reporting out
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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 level level to the bottom 12 formative assessment 13 summative assessment 14 reporting out
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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 level level to the bottom 12 formative assessment 13 summative assessment 14 reporting out
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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 level level to the bottom 12 formative assessment show where they are and where they are going 13 summative assessment 14 reporting out
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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 level level to the bottom 12 formative assessment show where they are and where they are going 13 summative assessment 14 reporting out
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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 level level to the bottom 12 formative assessment show where they are and where they are going 13 summative assessment evaluate what you value 14 reporting out
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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 level level to the bottom 12 formative assessment show where they are and where they are going 13 summative assessment evaluate what you value 14 reporting out
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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 level level to 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)
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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 level level to 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)
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HIERARCHY OF IMPLEMENTATION
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begin lessons with good problems
form visibly random groups use vertical non-permanent surfaces
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use verbal instructions
defront the classroom answer only keep thinking questions use meaningful notes foster autonomous actions
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use hints and extensions to manage flow
level to the bottom assign check your understanding questions
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communicate where students are and where they are going
evaluate what you value report out based on data (not points)
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BUILDING THINKING CLASSROOMS
(year 1)
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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 level to the bottom use hints and extensions to manage flow BUILDING THINKING CLASSROOMS (year 2+) 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)
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Q+A: QUESTIONS AND ABUSE
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PROBLEM
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PROBLEM
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AND THE ANSWERS ARE:
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