Building Thinking Classrooms in Mathematics, Grades K-12: 14 Teaching Practices for Enhancing Learning (Corwin Mathematics Series)

by Peter Liljedahl

The autonomy the students were afforded was specific to knowledge mobility. If you need help, get it. If you need another question to work on, find it. This was clearly important and, therefore, became one of the practices identified as being needed for building thinking classrooms.

rather than being the source of knowledge in the room, teachers were working to mobilize the knowledge already in the room.

they were being deliberately less helpful.

Getting these groups to talk to each other without specifying which was correct or incorrect (sometimes both) proved to be a very effective way to deepen students’ thinking.

A thinking classroom is a classroom where students think individually and collectively. The collective goes well beyond the

limits of the group boundaries and encompasses the whole class.

We need to also help them to break down the barriers around their groups by mobilizing the knowledge in the room for them.

Not only does this build the independence that is needed for a thinking classroom to function well, it also engenders the type of 21st century skills that people need to work and collaborate in the real world.

When you find such a moment, the key is to not say or show something another group can.

But, in the collaborative setting of a thinking classroom, groups tend to self-correct.

What this work is telling us is that students need teaching built on the idea of asynchronous activity—activities that meet the learner where they are and are customized for their particular pace of learning.

Regardless, if differentiation is something that you have or have not been able to achieve in your teaching, the question remains, how does it look in a thinking classroom where students spend much of their time thinking in groups?

If we are thinking, we will be engaged. And if we are engaged, we are thinking.

he noticed that whenever someone had an optimal experience, they lost track of time, and much more time passed than the person realized. He noticed that when someone was having an optimal experience, they were undistractible and unaware of things in their environment that would otherwise interfere with their focus.

He noticed that their actions became a seamless and efficient extension of their will. And he noticed that they became less self-conscious, stopped worrying about failure, and were doing the activity for the sake of doing it and not for the sake of getting done—it became an end unto itself.

that whenever there was an optimal experience, there were three qualities also present in the environment in which the optimal experience

was taking place—clear goals every step of the way, immediate feedback on one’s actions, and a balance between the ability of the doer and the challenge of the task.

balance between challenge and ability—is central to Csíkszentmihályi’s analysis of the optimal experience

When there is a balance in this system, a state of what Csíkszentmihályi refers to as flow is created

In essence, flow is where engagement and, as a consequence, thinking happens. Therefore, to build a thinking classroom we need to be able to get students into, and keep them in, flow. And to do this, we need to first understand how students move about inside of flow.

In essence, when students are in flow, their ability will always be increasing, and in order to keep them in flow we, as teachers, have to keep increasing the challenge by giving them extensions—harder and harder tasks to solve.

is—timing matters.

If we increase the challenge of a task before a student has had the chance to fully grow their ability, then, rather than keeping them

in flow, we have pushed them into...

Likewise, if we wait too long to increase the challenge, we pu...

two main principles of variation theory

The first principle is that we can only see variation against a backdrop of non-variation. That is, that before something changes, it has to stay the same.

The second principle is that only one thing is varied at a time.

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The short answer is that when students are not thinking, everything we teach them is difficult. When students are thinking, however, almost anything is possible. When students are thinking, they are learning and understanding—and this transfers to success.

This is where you start to earn back the time you spent doing non-curricular thinking tasks.

the increase in challenge from one task to the next is incrementally small.

Thin slicing sequences stand in contrast to the thick slicing sequence we see in thinking tasks such as tax collector

unless you have mobilized the knowledge in the room (Chapter 8). Once that happens, students begin to use the autonomy afforded them to keep themselves in flow by stealing the next

tasks from groups around them—essentially increasing the challenge of the tasks on their own.

The rest of the groups got their next task by stealing it from others—when they were ready for it and to keep themselves in flow. This frees the teacher up to spend more time attending to the groups for whom, despite your best efforts, there is an imbalance between their ability and the challenge of

the task, and they start to head for frustration

hints that decrease challenge and hints that increase ability

hints that decrease challenge are only useful in that moment, whereas a hint that increases ability continues to be useful even as students move on to the next task.

Obviously, hints that increase ability are better in the long run. But frustration is not about the long run. Frustration is an intensely negative emotion that needs a rapid intervention, and sometimes the best way to intervene quickly is to reduce the challenge.

shift their mode of engagement with the same task

doing the task. This is the easiest way to engage with a task.

shifted their mode of engagement from doing to justifying. Justifying is more challenging and involves students convincing themselves that they are correct.

Explaining is harder than justifying, as it requires the

articulation of thought for an audience outside of those who did the original thinking.

teaching them something. If we subscribe to the notion that teaching is different than telling or explaining, then this is another increase in challenge.

create a new task for that group. Creating is the most difficult mode of engagement,

The goal of thinking classrooms is to build engaged students that are willing to think about any task.

Because curriculum tasks are not innately engaging for students, we need to manufacture engagement through giving clear goals, ensuring there is an ability to get immediate feedback on actions, and asynchronously maintaining the balance between the group’s ability and the challenge of the task at