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November 15, 2020 - March 7, 2021
there are students who cannot get past the fact that you have not answered their question.
What is important, is that you do not answer proximity or stop-thinking questions and that you read the situation so as to be able to give the best response when such questions are asked.
Are there any strategies that can be used before the question is asked to prevent it being asked at all?
three strategies that we have played with—the first of which involves strategically reducing proximity. The first three to four minutes after the first task is given is, by far, the period of time in a thinking classroom when the greatest number of questions is asked. During these three to four minutes, stay in the very center of the room, as far away from the students as possible.
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.
The third method is to lead with your own questions when you approach a group.
the more subtle practices of when, where, and how the tasks are given is as important as the quality of the task itself.
NRICH (nrich.maths.org), NCTM Illuminations (illuminations.nctm.org), or simply type problem of the day into your favorite search engine, you will find endless lists of potentially good thinking tasks.
how are you going to give it to them?
teachers tend to give tasks in one of three ways—they project it or write it on a vertical surface, they give it as a handout, or they assign it from a textbook or workbook. Of these, which is the worst?
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 their notes.
How we give the tasks matters, and it turns out to matter a great deal. The same is true of when we give the task, and even where in the room we give the task. And like the textbook/workbook example, how we naturally do it, how we have been taught to do it, often produced the lowest levels of thinking in our research.
students prefer to occupy lower energy states.
So, if a lesson begins with the low-energy state of passively receiving knowledge in the form of a lecture or taking notes, it is
much harder to then raise their energy level and get them...
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A class given these same tasks at the beginning of the lesson came to it with energy, enthusiasm, determination, and a greater sense of self-reliance.
It was the timing of the task that made a difference.
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.
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.
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
The further into the lesson the teacher waited before giving the task, the le...
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the teacher has three to five minutes from the beginning of the lesson to give the task befor...
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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.
having students stand, loosely clustered around the teacher, creates a higher-energy and active environment for the students.
what turned out to be best—giving the task verbally.
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.
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.
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.
What is on the board is meaningless without the accompanying verbal dialogue and instructions. This turned out to be the definition of what separated verbally given tasks from textually given tasks—t...
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discern what the ...
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This particular task also highlights a fourth characteristic that is present in some tasks—the constraints of the task emerge out of, and after, actions have been taken.
On the other hand, when we
observed students who received the task verbally, they began by talking about the mathematics.
Somehow, the posing of the task verbally cut through all of the words and positioned the task in the minds of the students in such a way that they could immed...
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When the task is given textually, students ask lots of questions, primarily during the phases where they are reading, discussing words, and discussing constraints.
The degree to which these questions were answered, and how quickly they were answered, had a lot to do with whether or not the students persisted, or not, through the aforementioned three phases.
That is, when the textual format was not working, several teachers were driven to shift to verbal means to help the students get to the mathematics.
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.
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.
The important thing is to have them standing and to have them clustered in one area. It also helps if you vary where this cluster will be from day-to-day.
that giving a task verbally and textually at the same time produces the same results as giving the task textually only.
All students are verbal learners long before they are textual learners.
What those students you are thinking about may not be good at is taking verbal instruction in large-group settings.
research showed that when the boundaries are very porous (Chapter 2) and there is a lot of autonomy in the room (Chapter 8), then only about 20% of the students need to understand the task. Knowledge mobility takes care of the rest.
think hard about what the minimum knowledge that is necessary for them to start the first task and what can they learn in the first task that will help them with the second task, et cetera.
say words, and write numbers, symbols, and images.
