Building Thinking Classrooms in Mathematics, Grades K-12 Quotes

“rather than being the source of knowledge in the room, teachers were working to mobilize the knowledge already in the room. That is, they were being deliberately less helpful.”
― Peter Liljedahl, Building Thinking Classrooms in Mathematics, Grades K-12: 14 Teaching Practices for Enhancing Learning

“The use of words such as opportunity are helpful—and the use of words like practice and assignment are not.”
― Peter Liljedahl, Building Thinking Classrooms in Mathematics, Grades K-12: 14 Teaching Practices for Enhancing Learning

“Another change in practice was that answers needed to be provided at the same time as the questions were given.”
― Peter Liljedahl, Building Thinking Classrooms in Mathematics, Grades K-12: 14 Teaching Practices for Enhancing Learning

“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.”
― Peter Liljedahl, Building Thinking Classrooms in Mathematics, Grades K-12: 14 Teaching Practices for Enhancing Learning

“We stopped calling it homework and started calling it check-your-understanding questions. This had an immediate effect on students.”
― Peter Liljedahl, Building Thinking Classrooms in Mathematics, Grades K-12: 14 Teaching Practices for Enhancing Learning

“we stopped calling it homework and started calling it check-your-understanding questions.”
― Peter Liljedahl, Building Thinking Classrooms in Mathematics, Grades K-12: 14 Teaching Practices for Enhancing Learning

“when the terminology of practice was used, it increased the perception that mimicking was what students were meant to be doing and, as a result, increased mimicking behavior. And, as discussed, mimicking has limitations and is antithetical to the kind of thinking behaviors that thinking classrooms are trying to foster.”
― Peter Liljedahl, Building Thinking Classrooms in Mathematics, Grades K-12: 14 Teaching Practices for Enhancing Learning

“Homework is not working. Students are doing it, if at all, for the wrong reason (marks) and the wrong person (their teacher or their parents). And those who are doing it for the right reasons (to check their understanding) and for the right person (for themselves) are mimicking.”
― Peter Liljedahl, Building Thinking Classrooms in Mathematics, Grades K-12: 14 Teaching Practices for Enhancing Learning

“When students who got help from a tutor or parent were asked how they would do if a pop quiz based on the homework were given, 90% of the students said they would fail. So, what did they get help with? They got help with getting the homework done—not with learning.”
― Peter Liljedahl, Building Thinking Classrooms in Mathematics, Grades K-12: 14 Teaching Practices for Enhancing Learning

“In summary, the results showed that giving tasks verbally produced more thinking—sooner and deeper—and generated fewer questions at every grade level, in every context, and even in classes with high populations of English language learners. That is, there was no context in which giving a task verbally led students to perform worse than giving it textually—whether on a board, on a worksheet, or in a textbook/workbook.”
― Peter Liljedahl, Building Thinking Classrooms in Mathematics, Grades K-12: 14 Teaching Practices for Enhancing Learning

“There are three things to notice in this dialogue. The task is not given until the groundwork has been presented. The groundwork in no way reduces the thinking that the students will have to do. If a student walks into class late and looks at the board, they will have no clue what the task is.”
― Peter Liljedahl, Building Thinking Classrooms in Mathematics, Grades K-12: 14 Teaching Practices for Enhancing Learning

“Whereas the essence of the task is given verbally, the details of the task—quantities, measurements, geometric shapes, data, long algebraic expressions, et cetera—are written on the board as the teacher speaks. Verbal instructions are not meant to be about the students having to remember details, it is about having them hear the nature of the question. Likewise, verbal instructions are not about reading out a task verbatim. Rather, they are about unwinding the task through narrative, discussion, dialogue, and potentially working through a model of what is being asked with the students.”
― Peter Liljedahl, Building Thinking Classrooms in Mathematics, Grades K-12: 14 Teaching Practices for Enhancing Learning

“Nothing came close to being as effective as giving the task verbally.”
― Peter Liljedahl, Building Thinking Classrooms in Mathematics, Grades K-12: 14 Teaching Practices for Enhancing Learning

“I’m not going to answer that question”. Then tell them why— “Me telling you that it is right is worth almost nothing. If you can tell me that it is right, however, that is worth everything.” And, then tell them that you have confidence in them—“And I believe that you will be able to tell me if this is the right answer. So, keep going.” In some instances, you may wish to couple this with a hint (see Chapter 9).”
― Peter Liljedahl, Building Thinking Classrooms in Mathematics, Grades K-12: 14 Teaching Practices for Enhancing Learning

“Instead of walking away when a proximity or stop-thinking question is being asked, we would instead look at the student and smile as they asked their question. Then we would walk away.”
― Peter Liljedahl, Building Thinking Classrooms in Mathematics, Grades K-12: 14 Teaching Practices for Enhancing Learning

“The only questions that should be answered in a thinking classroom are the small percentage (10%) that are keep-thinking questions.”
― Peter Liljedahl, Building Thinking Classrooms in Mathematics, Grades K-12: 14 Teaching Practices for Enhancing Learning

“In these perfectly organized classrooms, the physical spaces in which they are being asked to think is incommensurate with the messiness of thinking. This is a problem. On the other hand, thinking should not be completely unstructured. It needs elements of representation and organization for patterns to begin to emerge. Therefore, overly chaotic spaces are not the answer either.”
― Peter Liljedahl, Building Thinking Classrooms in Mathematics, Grades K-12: 14 Teaching Practices for Enhancing Learning

“using vertical whiteboards is enhanced by each group having only one marker.”
― Peter Liljedahl, Building Thinking Classrooms in Mathematics, Grades K-12: 14 Teaching Practices for Enhancing Learning

“Having students standing immediately takes away that sense of anonymity and, with it, the conscious and unconscious pull away from the tasks at hand.”
― Peter Liljedahl, Building Thinking Classrooms in Mathematics, Grades K-12: 14 Teaching Practices for Enhancing Learning

“When students are sitting, they feel anonymous. And when students feel anonymous, they are more likely to disengage.”
― Peter Liljedahl, Building Thinking Classrooms in Mathematics, Grades K-12: 14 Teaching Practices for Enhancing Learning

“produced better results across almost all variables than if the students worked on flipchart paper—irrespective of whether they were standing or sitting. The data also show that across almost all variables, any alternate workspace produced better results than having students work through thinking tasks in their notebooks while sitting at their desks.”
― Peter Liljedahl, Building Thinking Classrooms in Mathematics, Grades K-12: 14 Teaching Practices for Enhancing Learning

“Knowledge mobility takes one of three forms: (1) members of a group going out to other groups to borrow an idea to bring back to their group, (2) members of a group going out to compare their answer to other answers, or (3) two (or more) groups coming together to debate different solutions. Or, like it did for Idris’s group, it takes on a combination of these forms.”
― Peter Liljedahl, Building Thinking Classrooms in Mathematics, Grades K-12: 14 Teaching Practices for Enhancing Learning

“thinking tasks should be asked in the first five minutes from the time you begin the lesson.”
― Peter Liljedahl, Building Thinking Classrooms in Mathematics, Grades K-12: 14 Teaching Practices for Enhancing Learning

“mimicking tends to create short-term success without the long-term learning that allows students to make connections with other topics in the same and subsequent grades. So they do not develop the web of connections that helps them understand mathematics.”
― Peter Liljedahl, Building Thinking Classrooms in Mathematics, Grades K-12: 14 Teaching Practices for Enhancing Learning

“Mimicking is an addiction that is easily acquired at lower grades and difficult to give up at higher grades.”
― Peter Liljedahl, Building Thinking Classrooms in Mathematics, Grades K-12: 14 Teaching Practices for Enhancing Learning

“to get students thinking about curriculum tasks, they need to first be primed to do so using non-curricular tasks. Nothing in my research has shown a way to avoid this. You have to go slow to go fast.”
― Peter Liljedahl, Building Thinking Classrooms in Mathematics, Grades K-12: 14 Teaching Practices for Enhancing Learning

“begin by asking a question that is review of prior knowledge; then ask a question that is an extension of that prior knowledge.”
― Peter Liljedahl, Building Thinking Classrooms in Mathematics, Grades K-12: 14 Teaching Practices for Enhancing Learning

“Once a word problem is decoded, the mathematics is often trivial, procedural, and analogous to the mathematics that was taught that day. This is not true of rich problem-solving tasks. Whereas rich tasks get students to think at the expense of meeting curriculum goals, word problems more predictably and reliably push students to use specific bits of learned knowledge—but often at the expense of engagement and the thinking that we need to foster in our students.”
― Peter Liljedahl, Building Thinking Classrooms in Mathematics, Grades K-12: 14 Teaching Practices for Enhancing Learning

“what makes a task a good problem-solving task is not what it is, but what it does. And what they do is make students think.”
― Peter Liljedahl, Building Thinking Classrooms in Mathematics, Grades K-12: 14 Teaching Practices for Enhancing Learning

“Problem-solving tasks are often called non-routine tasks because they require students to invoke their knowledge in ways that have not been routinized. Once routinization happens, students are mimicking rather than thinking—or as Lithner (2008) calls it, being imitative rather than creative.”
― Peter Liljedahl, Building Thinking Classrooms in Mathematics, Grades K-12: 14 Teaching Practices for Enhancing Learning