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The learning environment (aka, the classroom) can play a significant role in students' success in mathematics. Shortly before filming the video above, the teacher made two important decisions concerning the learning environment. These decisions were instrumental in the creation of the scene depicted in the video.
Before we discuss these decisions, we must consider the video itself. As you watch (or re-watch) it, consider the following:
So, we have students who are still getting to know their teacher, working on a very demanding problem, with partners that they might not have chosen for themselves, on surfaces that are foreign to them. And, they only have a single marker. On the surface, these are not optimal learning conditions. Yet, what do we see ten minutes into the problem? We see students who are fully engaged. We see students communicating about the math on a deep level. We see students actively pursuing the solution to the problem. We see students who are very comfortable and confident in their ability to conquer the current mathematical challenge.
How did this happen?
The anecdote described above is the result of one teacher's wondering about a body of research conducted by Peter Liljedahl. In his seminal article, Building Thinking Classrooms: Conditions for Problem Solving, he wonders about the classroom conditions that are most conducive to deep student thought during mathematical problem solving. His conclusions include the following:
One could argue, given some of the points above, that there were many reasons why the students could or should fail in the face of the given problem. What the video does not show, however, is that all groups succeeded to a high degree in this setting. Did all groups find solutions for all numbers from 1 to 20. No, but all groups came really close, and the teacher was able to move all students forward in their mathematical understanding by facilitating an effective discussion at the end of the period. This discussion could only be successful if all groups had experienced a high degree of success solving the problem. And, as Liljedahl would say, the implementation NPVSs and random groupings had a significant impact on each group's success.
For a more detailed explanation of Peter Liljedahl's research, please read the article attached below.
Before we discuss these decisions, we must consider the video itself. As you watch (or re-watch) it, consider the following:
- This video was shot on the fourth day of school.
- The teacher of this class was new to the school. He/She was a virtual stranger to the students.
- The students are organized in random groupings. The teacher used a Microsoft Excel spreadsheet to generate nine completely arbitrary groups.
- The students did not have a history of doing mathematics at vertical non-permanent surfaces (VNPS) like a whiteboard.
- Only one whiteboard marker was provided to each group.
- The students were working on a very challenging problem: Using only 4 fours and any known operation/concept, create expressions to equal each whole number from 1 to 20.
- The students had already been working on the problem for ten minutes at the time of filming.
So, we have students who are still getting to know their teacher, working on a very demanding problem, with partners that they might not have chosen for themselves, on surfaces that are foreign to them. And, they only have a single marker. On the surface, these are not optimal learning conditions. Yet, what do we see ten minutes into the problem? We see students who are fully engaged. We see students communicating about the math on a deep level. We see students actively pursuing the solution to the problem. We see students who are very comfortable and confident in their ability to conquer the current mathematical challenge.
How did this happen?
The anecdote described above is the result of one teacher's wondering about a body of research conducted by Peter Liljedahl. In his seminal article, Building Thinking Classrooms: Conditions for Problem Solving, he wonders about the classroom conditions that are most conducive to deep student thought during mathematical problem solving. His conclusions include the following:
- Students make their first notations sooner and persist with problems longer while working at vertical non-permanent surfaces (VNPS) than at other types of surfaces (vertical permanent, horizontal non-permeant, horizontal permanent).
- Randomized groupings are best for student learning as they promote greater focus on the mathematical problem at hand.
One could argue, given some of the points above, that there were many reasons why the students could or should fail in the face of the given problem. What the video does not show, however, is that all groups succeeded to a high degree in this setting. Did all groups find solutions for all numbers from 1 to 20. No, but all groups came really close, and the teacher was able to move all students forward in their mathematical understanding by facilitating an effective discussion at the end of the period. This discussion could only be successful if all groups had experienced a high degree of success solving the problem. And, as Liljedahl would say, the implementation NPVSs and random groupings had a significant impact on each group's success.
For a more detailed explanation of Peter Liljedahl's research, please read the article attached below.
building_thinking_classrooms.pdf | |
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