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Building Thinking Classrooms in Mathematics, Grades K-12 Audiobook: 14 Teaching Practices for Enhancing Learning

First Edition

by Peter Liljedahl

Student Resources

Front Matter
Figures
Videos & Links
Back Matter

Figures

Figure i.1: Students in a traditional classroom work on a task
Figure i.2: Students not thinking
Figure i.3: Distribution of studenting behaviors on now-you-try-one tasks
Ski Trip Fundraiser Chart
Figure 1.1: Students in an elementary classroom engage in a thinking task
Figure 1.2: Three types of lessons
Figure 1.3: Pythagoras sheet
Chapter 1 Summary
Figure 2.1: A group of three students working collaboratively
Chapter 2 Summary
Figure 3.1: Students engage with wall-mounted whiteboards
Figure 3.2: Average times and scores on the nine measures
Figure 3.3: Student groups utilize non-permanent surfaces
Chapter 3 Summary
Chapter 3 Tasks
Figure 4.1: Classrooms with different furniture placement
Figure 4.2: Orderly classroom
Figure 4.3: Defronted classroom
Figure 4.4: A teacher fields questions from a group in a defronted classroom
Chapter 4 Summary
Figure 5.1: A student asks a proximity question as the teacher moves through the classroom
Figure 5.2: Elementary students ask questions as teachers approach their work stations
Chapter 5 Summary
Figure 6.1: Thinking achieved as a function of when the task is given
Figure 6.2: A teacher gives his students the task among standing students
Chapter 6 Summary
Chapter 6 Tasks
Figure 7.1: Studenting behaviors when homework is marked
Figure 7.2: Studenting behaviors when homework is not marked
Figure 7.3: Students doing check-your-understanding questions at lunch
Chapter 7 Summary
Figure 8.1: Students working independently in random groups on VNPSs
Figure 8.2: Students actively and passively interact between groups to further their learning
Chapter 8 Summary
Chapter 8 Tasks
Figure 9.1: Graphical representation of the balance between challenge and skill
Figure 9.2: Graphical representation of the balance between challenge and skill as a dynamic process
Figure 9.3: Too great an increase in challenge
Figure 9.4: Too long a wait without an increase in challenge
Chapter 9 Sequence of Extensions
Figure 9.5: The unusual baker’s cakes
Chapter 9 Primary Sequence Task
Figure 9.6: Thin slicing sequence of tasks
Figure 9.7: Two types of hints
Figure 9.8: Increase the challenge
Figure 9.9: Modes of engagement that increase challenge
Figure 9.10: Students in flow on curricular tasks
Figure 9.11: Perseverance and patience
Figure 9.12: Sequence of curricular concepts that can be used to build a flow sequence of tasks in calculus
Chapter 9 Summary
Figure 10.1: The unusual baker’s cakes
Figure 10.2: Time spent consolidating as challenge increases
Chapter 10 Summary
Figure 11.1: Teacher-generated notes
Figure 11.2: Type I: Graphic organizer with cells as restrictions
Figure 11.3: Type II: Graphic organizer with cells as demarcations
Figure 11.4: Type III: Graphic organizer with prelabeled cells to demarcate different subtopics
Figure 11.5: Student fills in a Type III graphic organizer with prelabeled cells to demarcate different subtopics
Figure 11.6: Type IV: Graphic organizer with prelabeled cells to demarcate different aspects of a topic.
Figure 11.7: Example student notes
Chapter 11 Summary
Chapter 11 Tasks
Figure 12.1: An existing four-column rubric
Figure 12.2: Collaboration rubric
Figure 12.3: K–1 collaboration rubric
Figure 12.4: Highlighted collaboration rubric with language in all three columns
Figure 12.5: Highlighted collaboration rubric with language in two end columns
Figure 12.6: Coconstructed T-chart for developing perseverance rubric
Chapter 12 Summary
Figure 13.1: Instrument for navigating where you are and where you are going for repeating patterns
Figure 13.2: Instrument for navigating where you are and where you are going for additive number patterns
Figure 13.3: Instrument for navigating where you are and where you are going for fractions
Figure 13.4: Navigation instrument without the outcomes (repeating patterns)
Figure 13.5: Navigation instrument without the outcomes (additive number patterns)
Figure 13.6: Student’s record of how they did on the fractions practice test
Chapter 13 Summary
Figure 14.1: Parachute packers
Figure 14.2: Instrument for recording student data on a repeating patterns unit
Figure 14.3: Instrument for recording student data on a fractions unit
Figure 14.4: Benjamin’s performance on the repeating patterns unit
Figure 14.5: Benjamin’s performance on the repeating patterns unit
Figure 14.6: Alicia’s performance on the fractions unit
Figure 14.7: Jennifer’s performance on the fractions unit
Figure 14.8: Instrument for recording student data on a fractions unit with scaling
Figure 14.9: The COP framework as triangulation of data
Figure 15.1: The Building Thinking Classrooms Framework
Figure 15.2: Transforming collective synergy into individual understanding
Figure 15.3: Typical lesson sequence
Figure 15.4: Typical lesson sequence spread over two days
Figure 15.5: The Rebuilding Thinking Classrooms Framework

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