Building Thinking Classrooms Through Reflective Practices

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Reflecting on Practice: Using Inquiry to Build Thinking Classrooms Unit 2, Session 2 2017 Reflecting on Practice Park City Mathematics Institute 2

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Thinking classrooms Last night you read about characteristics of a thinking classroom. On Desmos, follow the instructions to submit which element from a Thinking Classroom resonated with you the most. At your tables, share out what resonated with you from the Liljedahl reading. Reflecting on Practice Park City Mathematics Institute 4

Connections to RoP What of Liljedahl s recommendations have you seen implemented at times in RoP? 5

Vertical non-permanent surfaces What advantages does this method of doing work have for the teacher? for students? Are there any disadvantages? How could you adapt these ideas to your own classroom? Reflecting on Practice Park City Mathematics Institute 6

#VNPS http://tinyurl.com/BuyVNPS 7

Please go to your #VNPS 8

Full Group Discussion Think about how your group engaged in the problem. What external factors, if any, affected your group s progress? Reflecting on Practice Park City Mathematics Institute 9

Problem Solving Pathways Go back to desmos and follow the instructions there to graph your individual experience while working on this task. Reflecting on Practice Park City Mathematics Institute 10

Region of engagement Reflecting on Practice Park City Mathematics Institute 11

Too great an increase in challenge Too fast an increase in skill Reflecting on Practice Park City Mathematics Institute 12

Classroom Vignettes What does flow look like in the classroom? Take some time to read two classroom scenarios. As you read think about how students are engaged in each class. Reflecting on Practice Park City Mathematics Institute 13

Whole Group Debrief What structures and strategies allowed the student to stay in flow or return to flow? Think from the perspective of both students who are underwhelmed and those that might be bored. Reflecting on Practice Park City Mathematics Institute 14

Flow Clear mathematical goals (essential to any lesson) Feedback (including hints and extensions) Managing challenge for all students Reflecting on Practice Park City Mathematics Institute 15

Related to flow... How did your ideas that came up at your table relate to Liljedahl s recommendations for the nine elements of classroom practice? 16

Elements of Classroom Practice 1. type of tasks, when and how they are used; 2. the way tasks are given to students; 3. how groups are formed; 4. student work space while they work on tasks; 5. room organization, in general and for tasks; 6. how student questions are answered; 7. hints and extensions while students work; 8. when and how a teacher levels the classroom during or after tasks; 9. assessment, in general and during work on tasks. 17

Elements of Classroom Practice 1. type of tasks, when and how they are used; 2. the way tasks are given to students; 3. how groups are formed; 4. student work space while they work on tasks; 5. room organization, in general and for tasks; 6. how student questions are answered; 7. hints and extensions while students work; 8. when and how a teacher levels the classroom during or after tasks; 9. assessment, in general and during work on tasks. 18

7. Hints and Extensions The ways in which hints and extensions are used while students work on tasks. Once a thinking classroom is established, it needs to be nurtured. This is done primarily through how hints and extensions are given to groups as they work on tasks. Hints and extensions need to be given so as to keep students in a perfect balance between the challenge of the current task and their abilities in working on it. If their ability is too high the risk is they get bored. If the challenge is too great the risk is they become frustrated. Reflecting on Practice Park City Mathematics Institute 19

References 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. Liljedahl, P. (2016). Flow: A framework for discussing teaching. Presentation at PME. Reflecting on Practice Park City Mathematics Institute 20

Claires Class It would be very unlikely that a student in Claire's class would be in flow. Few of the necessary conditions are present for this to happen... Feedback in her class was primarily provided during her recitations on the solutions of each of the tasks. These were both infrequent and impersonal providing feedback at times often inappropriate for the diverse stages of solving each of her students were in. Finally, her management of the level of challenge was synchronized with her teaching schedule and not the dynamic abilities of her students. Reflecting on Practice Park City Mathematics Institute 21

Connors Class Connor, on the other hand, created an environment rich in the necessary conditions for occasioning flow Feedback was timely and individualized to the groups' varying progress eventually becoming instantaneous when they learned how to check their own answers. Finally, the challenge of the activity increased in step with each group s evolving ability, first under the individualized attention of Connor and then through each group s own self-regulation. Reflecting on Practice Park City Mathematics Institute 22