Book SummaryBuilding Thinking Classrooms in Mathematics, by Peter Liljedahl

1-Page Summary1-Page Book Summary of Building Thinking Classrooms in Mathematics

Fostering an educational environment that bolsters the intellectual activities of students by facilitating substantive interactions with teachers.

Peter Liljedahl recommends shifting away from traditional teaching approaches that impede the cultivation of learners' critical thinking abilities towards a carefully designed set of norms, routines, and structures that promote an environment where analytical thinking can thrive. This involves not only changing the physical layout of the classroom but also deliberately shifting teaching practices and how teachers interact with students.

Fostering a setting that stimulates active mental participation and collaborative effort.

The author fervently supports creating a learning space that encourages active participation and cooperative work. A significant shift away from the traditional arrangement that restricts both collaboration and mobility is necessary. He recommends arranging the learning environment in a way that fosters cooperative interaction and facilitates the uninhibited sharing of ideas.

Introducing the practice of utilizing temporary vertical workspaces instead of the traditional arrangement of seated desks.

Liljedahl advocates for a shift from traditional seating configurations to the adoption of upright, transient working areas. Peter Liljedahl's research conclusively demonstrates that learners show a marked improvement in engagement, thought processes, and collaborative abilities when they work together on vertical surfaces that allow for easy erasure while standing. This setup serves several purposes:

• The method encourages active participation both mentally and physically by having students remain standing rather than seated.

• Walls that can be repositioned and aren't rigidly set in an upright position foster a dynamic exchange of thoughts among individuals and across different teams, promoting an environment conducive to the collective sharing of ideas and the joint solving of problems.

• Employing vertical, erasable surfaces creates an environment in the classroom that encourages students to confidently explore and adjust their work as needed.

Various materials such as whiteboards, blackboards, windows, portable writing surfaces, vinyl tablecloths, or layers of transparent cellophane exemplify workspaces designed for temporary application. The crucial element is to guarantee that the surface can be easily erased and arranged in an upright position for visibility by everyone.

Practical Tips

• Introduce a mobile whiteboard in your living space or home office to jot down ideas and tasks while standing. This can serve as a visual and physical prompt to keep you on your feet and engaged with your work. You could use the whiteboard to plan your day in the morning and then roll it to a different room to track progress or brainstorm in the afternoon.
• Encourage dynamic interaction in your workplace by initiating a 'space swap' day where teams exchange work areas. This can lead to fresh perspectives and spontaneous brainstorming sessions as people interact with new colleagues and different surroundings.
• Use transparent, adhesive dry-erase sheets on windows or glass partitions to create additional vertical writing spaces. These can be particularly useful for visualizing tasks, organizing schedules, or brainstorming sessions, and they can be easily moved or replaced as your needs change.
• Transform your shower space into a brainstorming hub by using waterproof notepads and pencils. While showering, the relaxed state of mind and privacy can spark creativity. Waterproof notepads stick to your shower walls, allowing you to jot down ideas as they come without worrying about water damage.
• Use glass instead of traditional walls for office partitions to foster an open and transparent work environment. This can encourage the sharing of ideas and keep everyone informed about ongoing work. For instance, if you're working on a design project, sketches and diagrams can be displayed on glass surfaces for easy viewing by passersby, inviting feedback and discussion.

Forming student groups in a manner that is both random and adaptable, as opposed to allowing learners to choose their own fixed groups.

The findings of Peter Liljedahl suggest that the cognitive functions and teamwork skills of students significantly enhance when they work together in groups that are deliberately shuffled in a random manner. When students form their own groups or are strategically placed into them, they tend to assume particular roles such as leader or follower, which may restrict their level of participation.

Forming student groups spontaneously, particularly by distributing playing cards, disrupts established social cliques, fosters the sharing of thoughts, and promotes shared responsibility among team members. Collaboration among students becomes smoother, as barriers to social interaction decrease and the sharing of ideas between groups improves. The author recommends creating groups of three to harmonize the sharing of group comprehension with personal revelations.

Other Perspectives

• The approach could ignore the value of sustained collaboration with the same peers, which can lead to deeper understanding and more cohesive team development over time.
• Role assumption is not inherently negative; it can reflect natural group dynamics and can be an opportunity for students to explore and develop different aspects of their personalities and skill sets.
• This method assumes that all students are willing to work with anyone, which might not be the case due to personal conflicts or past negative experiences.
• Such an approach may inadvertently isolate students who are introverted or less socially adept, as they might struggle more to integrate into new groups frequently.
• Randomly formed groups might lack the necessary diversity of skills or knowledge to...

Building Thinking Classrooms in Mathematics Summary Developing a course of study designed to engage students cognitively and ensure their consistent active progress.

It's essential to integrate the curriculum content into the classroom environment in a manner that captivates students and guarantees an uninterrupted progression of their educational journey.

Advancing to activities that prioritize mental involvement in the academic curriculum.

The author emphasizes the importance of transitioning from activities unrelated to the curriculum to ones that are connected, which paves the way for intellectual engagement and ensures that students remain attentive.

Initiating tasks that gently stimulate the intellectual functions within learners.

The author underscores the importance of starting with engaging tasks that diverge from the usual curriculum to create a classroom atmosphere that nurtures critical thinking. The accomplishment of these tasks is crucial for creating a classroom atmosphere that encourages students to approach challenging material with assurance, persist through obstacles, and be comfortable with the idea of venturing into uncertain outcomes.

Tasks can be exemplified by:

• Mathematical card tricks: They present engaging exercises that spark students' interest and fuel their curiosity in mathematical...

Building Thinking Classrooms in Mathematics Summary Fostering an educational environment that motivates students to actively engage in and assume responsibility for their learning journey.

Creating a learning space and employing teaching techniques that nurture self-reliance and responsibility in learners is crucial, especially in the context of a classroom aimed at encouraging analytical thought. Students not only participate actively in their learning process but also take charge of their educational path.

Learners steering their educational journey and making use of accessible tools.

The author highlights the importance of fostering independence among students and their ability to utilize available resources.

Encouraging the exchange of ideas and cooperative work among student teams.

Liljedahl proposes methods to foster self-directed learning in students throughout their educational journey. This entails fostering a dynamic interchange of thoughts among groups instead of depending exclusively on the instructor for direction. Educators cultivate a cooperative atmosphere where students are motivated to solicit feedback, investigate different methods, and compare their answers with those of their classmates, thus leveraging the collective intellect of the classroom. This approach promotes independence, diminishes the sense of defeat, and reinforces...

Building Thinking Classrooms in Mathematics Summary Assessment strategies ought to be crafted to nurture the development of individual understanding.

In an educational environment that emphasizes the mental activities of learners, the methods used for assessment and evaluation must be transformed to align with the goals and principles of such a setting.

Utilizing assessment methods that emphasize outcomes and the evaluation of data.

The author advocates for a transition from traditional point-based grading systems to alternative assessment strategies that emphasize learning outcomes, student growth, and mastery through a thorough examination of educational data.

Creating assessment standards collaboratively with students to gauge attributes like perseverance and collaborative effort.

Liljedahl advocates for the creation of uniform standards to evaluate student attributes like persistence, readiness to embrace risks, and collaborative skills. The evaluation framework, developed in partnership with students, emphasizes the significance of these skills and provides a basis for teacher evaluations and for students to gauge their own progress. Incorporating student voices and emphasizing clear, observable indicators transforms these tools into potent elements that foster a learning environment that encourages the...

Building Thinking Classrooms in Mathematics Summary The foundational components and necessary aspects to create and implement a "Thinking Classroom"

To successfully apply these methods, Liljedahl recommends a structured strategy aimed at creating a learning atmosphere that supports and encourages critical thinking.

A systematic approach to implement the framework designed for the cultivation of Thinking Classrooms.

The structure underpinning "Building Thinking Classrooms" is carefully designed to foster a setting that is favorable to reflection and learning. This framework is not merely an assortment of practices; it is a carefully developed sequence aimed at enhancing student engagement, mental processes, and academic achievements, all of which are supported by thorough research and empirical evidence.

The foundational set of tools includes the development of key elements like assignments, collaborative group structures, and designated workspaces.

The core strategies necessitate a thorough transformation of the educational environment's framework and the creation of new routine practices. The modifications aimed to transform the educational environment and change how students view their role in the learning process.

Other Perspectives

• Focusing solely on these elements might overlook the importance of...