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

by Peter Liljedahl

are details about the task that you do not want to burden the students’ cognitive loads with.

teachers who do this well do not begin with this until the last third of the year, and then they do it only intermittently.

The question is really what it means to be successful. For a long time, education in general has taken that to mean that they can mimic well. Out of this has emerged a discourse of being deliberate and intentional about the examples and instructions we give

students.

So, if we want our measure of success to be that our students are thinking, then we have to be deliberate and intentional about how we create and maintain an environment that promotes and sustains

thinking—and this cannot include mimicking.

where and when we give the task is still relevant. We found that, even in primary classrooms, there was a decrease in the number of questions asked when students were given the task early in a lesson versus later in the lesson.

The same was true of having students

stand vers...

However, this does not invalidate practices like carpet time at the beginning of the day, which ...

The research showed that it was important to give the tasks within three to five minutes of when the teacher declares that the lesson has started. In primary grades, th...

We are now going to do a new activity. So, I want everyone to stand up and meet in that corner over there, and ...

In every

case in which we were able to create a story, students’ uptake of the task was better—they had fewer questions, they were able to more quickly begin the task, and they were less likely to misunderstand what they were meant to do.

What is inherent in storytelling that can transfer to all tasks, however, is a narrative structure—a sense of chronology.

four basic studenting behaviors—didn’t do it, cheated, got help, and tried it on their own—within each of which there were nuances and variation

a lot of students are legitimately very

busy.

A second major reason students don’t do homework is that they forget. This forgetfulness is usually symptomatic of two issues—homework is not important to them, and/or they have poor record keeping.

A more common reason students do not do their homework, however, is that they don’t know how to do it. This is often masked by excuses of being busy or forgetting. At its core, not knowing how to do the homework is the most legitimate reason for not doing it.

Finally, students do not do their homework because they don’t want to do it.

The least common, but most interesting, answer was that some students cheated because it was fun—they

More common was that they didn’t know how to do the homework. Cheating, for these students, was a way to mask their lack of ability.

The most common reason for cheating, however, was that the homework was for marks—and cheating assured t...

When asked why they sought help, almost all students claimed it was because they didn’t know how to do the assigned work. There

So, what did they get help with? They got help with getting the homework done—not with learning.

Of these students, the vast majority completed the homework by mimicking from either their notes or the textbook.

it is clear that when marks start to matter to the students and their parents, their homework behavior changes markedly for the worse.

Homework, in its current formulation, needs to be upgraded. It needs to be rebranded. It needs to become a thinking activity.

what teachers really want it to achieve—for homework to be a safe place for students to make mistakes as they check their understanding. In here lies the rebranding needed. So, we stopped calling it homework and started calling it check-your-understanding questions.

Calling it check-your-understanding questions specified who it was for—the student (you)—and what it was for—to check understanding.

First, the questions could not be marked. They couldn’t even be checked. In fact, there can be no overt actions on the part of the teacher to enforce that the questions are being done—either positively or punitively.

This is not to say that you cannot talk to your students about them doing their check-their-understanding questions. This turned out to be very important—but also very risky. The discourse around this, as it turns out, needs to be focused on check-your-understanding questions as an opportunity to learn from their mistakes (without risk), to check their understanding, and, above else, is for them and only them. We need to drop any references to words like practice—which invokes mimicking behavior—and assignments—which invokes a sense that it is for a mark.

Another change in practice was that answers needed to be provided at the same time as the questions were given. If check-your-understanding questions were truly to be seen as a way for students to check their understanding, they needed something to check against—they needed answers to see if their understanding was correct.

Fully worked out solutions can also be provided, bu...

So, the questions may be the same as what we previously gave as “homework.” But to make doing them a thinking activity, everything around them changes—what we call it, how we talk about it, the autonomy students have to do it, and our openness to the fact that students may not do some or all of the questions.

Of all the things we researched, check-your-understanding questions is one of the most sensitive to disruption.

The use of words such as opportunity are helpful—and the use of words like practice and assignment are not.

This is about messaging around why and for whom these questions are done.

The research showed that giving worked solutions became more and more important the more complex the questions were.

The research also showed that worked solutions should not be given out until the students have had a chance to work on the questions, checked the answer they arrived at against the answers provided, and, if needed, retried the questions—sometimes multiple times.

if the worked solutions are provided the next day, or a few days after, the students now have a chance to compare their thinking to that of the worked solution as well as to get help with any questions they were unable to resolve on their own.

All of these changes require a greater independence on the part of the students.

that in a thinking classroom you, as the teacher, have a lot less control over what is happening in the room.

the teacher has a lot of control around what is happening for all the students in each moment—in

or at least seemingly so.

There is much happening outside of your control, and in order for it all to work well, students need to take on much more responsibility for their learning. This cannot happen unless they have the autonomy to do so. The question is, exactly what should they have autonomy over, and how are you going to foster this?

these practices are meant to be thought of as a framework much more than an overly prescriptive set of pedagogical moves that must be adhered to.

When I began to pay closer attention to the classes where students rarely, if at all, put up their hands, I began to notice that there was much more interaction between groups and that this interaction was both passive (looking at other groups’ work) and active (talking to other groups).

What was clear from all these interactions, both passive and active, was that, in these classrooms, knowledge moved easily from group to group. This made the work of the teacher much easier.