Building Thinking Classrooms in Mathematics, Grades K-12: 14 Teaching Practices for Enhancing Learning (Corwin Mathematics Series)
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What we found was that answering a question with a question (and only a question) was only effective when it was immediately followed by the teacher walking away from the students, with no other statements or suggestions being made.
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During these three to four minutes, stay in the very center of the room, as far away from the students as possible. By distancing yourself from the students, you reduce proximity questions.
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The second method is to not answer any questions asked by an individual student. Individual students ask their group members questions; groups ask the teacher questions.
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Students, especially students above Grade 7, have been socialized to believe that questions are assigned from the textbook or workbook after they have first been shown how to do them. This is not an unreasonable assumption on their part, as questions are typically assigned from books near the end of the lesson—after a lesson full of worked examples. This assumption, however, interferes with the way they engage with the task. Rather than approaching questions in the book as something to think about, they approach them as something to be answered by mimicking the examples from the lesson and ...more
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One of the earliest results from the research was that the same task given either in the middle of the lesson or near the end of the lesson produced much worse results than if it was given right at the beginning of the lesson.
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Even when we ran tasks on the same students at different points of the lesson, we saw a huge difference between a task given early versus late in a lesson. It wasn’t about the task, and it wasn’t about the students. It was the timing of the task that made a difference.
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From our data it became clear that the longer the lesson progressed before a thinking task was given, the more likely the teacher would begin to preteach the task in some way.
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The idea of preparing our students for what is to come is so engrained in the fabric of teaching that, even when we know it is counterproductive to thinking, it is difficult to stop.
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This preteaching, coupled with the initial passive positioning of the students, undermines the effectiveness of a task to generate thinking in an almost linear fashion
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the longer you talk, and the longer they listen, the less likely you are going to be able to get them to think.
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having students stand, loosely clustered around the teacher, creates a higher-energy and active environment for the students.
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when the students stood and gathered around the teacher, they were quicker to get going on the task and were less likely to ask questions.
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Nothing came close to being as effective as giving the task verbally.
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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.
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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.
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mimicking is not the same as learning, and mimicking is antithetical to thinking. 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.
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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.
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Homework, in its current institutionalized normative form as daily iterative practice to be done at home, doesn’t work. Almost every teacher I have interviewed says the same thing—the students who need to do their homework don’t, and the ones who do their homework are the ones who don’t really need to do it. It is a broken construct that long ago lost the good intention under which it was conceived.
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What emerged from this research was a set of four basic studenting behaviors—didn’t do it, cheated, got help, and tried it on their own—within
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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.
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Not doing their homework was not something that was unique to middle and high school students. This behavior was seen with almost equal distribution in all classes where homework was assigned—irrespective of grade.
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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.
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the vast majority completed the homework by mimicking from either their notes or the textbook.
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this mimicking behavior was such a dominant strategy that when the examples ran out, so did their ability to answer homework questions.
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Of all of the students we interviewed who used mimicking as a strategy to complete the homework on their own, less than 20% were even willing to move beyond this strategy when the examples ran out, and less than half of those were able to answer questions for which an analog did not exist in their notes or the textbook.
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When homework was not marked, cheating disappeared almost completely (Figure 7.2), and, whereas the number of students who did not do their homework increased, so too did the number of students who did it on their own. That is, in situations where homework was marked, approximately 50% didn’t do it or cheated. When homework was not marked, this percentage drops to approximately 40%—not marking homework had a positive effect on how many students did their homework.
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it is clear that when marks start to matter to the students and their parents, their homework behavior changes markedly for the worse.
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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.
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we stopped calling it homework and started calling it check-your-understanding questions.
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Calling it check-your-understanding questions specified who it was for—the student (you)—and what it was for—to check understanding. This had an immediate effect on students. We saw more students doing check-your-understanding questions on their own than had we seen with “homework”—and they were doing it for the right reason. Even when students were seeking help, they were now seeking to understand rather than seeking to be done. And, students were, for the most part, no longer talking about marks, practice, mimicking, or doing it for the teacher or their parents.
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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.
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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.
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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.
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The use of words such as opportunity are helpful—and the use of words like practice and assignment are not.
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Check-your-understanding questions are for the students, and they have autonomy over all aspects of them. If they choose to do them in groups, we cannot and should not prevent them from doing so—and we should not control who is in the groups. In fact, if you give class time to do check-your-understanding questions, 40–70% of your students will choose to do them in self-selected groups of two or three.
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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. As mentioned above, if we give the worked solution at the same time as the question, some students will read the solution and think that, because they understand what is happening, they understand how to do it on their own. However, if the worked solutions are provided the next day, or a few days after, the students now have a chance ...more
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Rebrand what you would previously refer to as homework or practice into a set of check-your-understanding questions. Give it to your students with the answers, and emphasize how this is an opportunity for them to see whether they have understood what happened in their groups. Do not collect it, or mark it, and the next day provide the worked solutions for them to use to check whether they truly did understand it.
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All of these changes require a greater independence on the part of the students.
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the stronger the structure, the lesser the need for the students to be independent—and the lesser the need for students to have autonomy.
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The amount of thinking students were required to do, and did, was sharply reduced in situations where their actions were managed—even micromanaged.
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I went back to the teachers whose students were not only given autonomy but who also used that autonomy to keep themselves moving forward through passive and active interactions. Even closer inspection of what the teachers did in these classrooms revealed that they, themselves, frequently made use of the knowledge in the room to move groups forward. That is, rather than directly answer questions, help, or give the next question, they would sometimes direct a group’s attention to what another group was doing.
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Rather than being the source of knowledge in the room, teachers were working to mobilize the knowledge already in the room.
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students’ abilities are more different than they are alike, and the idea that they can all receive, and process, the same information at the same time is outlandish.
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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.
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If we are thinking, we will be engaged. And if we are engaged, we are thinking.
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Csíkszentmihályi also noticed 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.
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if the challenge of the activity far exceeds a person’s ability, they are likely to experience a feeling of frustration. Conversely, if their ability far exceeds the challenge, they are likely to experience boredom. When there is a balance in this system, a state of what Csíkszentmihályi refers to as flow is created
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So, if we manage to get our students into flow, giving them extensions synchronously will not work. We have to work asynchronously—we have to get the timing right for each student. If students are working individually in their seats, this is almost impossible.
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When we have used this sequence, or one similar to it, with Grade 10 students, we get through the entire sequence in 40–60 minutes. That is, depending on the curriculum, we are able to cover the entire factoring quadratics unit in one lesson. How is this possible? 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.
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The groups that get there sooner are given increasingly harder and harder questions beyond this to keep them in flow while the rest of the groups catch up.