I read an article from Teaching Children Mathematics titled Three Strategies for Promoting Math Disagreements by Angela T. Barlow and Michael R. McCrory. It appears in the May 2011 edition which is part of the National Council of Teachers of Mathematics. This edition had many timely articles relating to math that I enjoyed reading. However, this article focuses on the importance of promoting math disagreements or debates with students. It caught my attention as our math series seems to place much importance on daily discussions and being able to communicate ideas to others. It is important for students to communicate, listen, add insight, and challenge their classmates' ideas. This in turn provides students with experiences that allow them to think more deeply in order to make sense of things.
One of the strategies is to force students to choose a side. With the use of writing prompts, students need to think about their response, choose a side, and explain their reasoning for their response. Then provide opportunities for students to share and support their reasoning with other classmates. An example of this idea is seen using the following writing prompt. I think 4 X 8 and 8 X 4 are or are not the same because . . .
Another strategy to promote disagreements or debates is to reveal students' misconceptions. The teacher should use tasks that address misconceptions as they create opportunities for disagreements to arise. An example of this is to have students measure with a broken ruler. Many students are beginning to learn how to measure with the ruler and this will often lead to a discussion of where to line up the broken ruler with an object. As we are working with measurement now, I am curious to how my students will respond to this idea. They have mentioned to line up the rule with the edge of an object, I wonder how it will change when students are given a broken ruler - will they know what to do in order to measure accurately?
The third strategy is to recall last year's disagreements. If a teacher has had previous disagreements that have arose, they seem to be natural to bring them up in future years. Purposefully ask and design questions that have led to strong discussions from years past. An example of this is with 10 flats (place value) being equivalent to ten hundred or one thousand. From my experience these questions always generate disagreements. A question similar to this always leads to a good debate with my students and one that I need to bring up every year. Is this equation true or false? 20 = 20. We also work with problems like 8 + 5 = __ + 10. These problems also allow for debate and discussions for students to reason and thus be able to explain what they think is the missing number.
In order to have purposeful mathematical debates, the author points out three things in order to accomplish this. 1. Must center on a mathematical concept 2. Are accessible to all 3. Can be debated. Through all of this, the teacher plays an important role in creating a safe environment with respect, risk taking, and placing values on other's ideas. The teacher is responsible in facilitating the discussion while fighting the urge to participate. Valuable opportunities are lost when teachers give their viewpoint or simply give the answer to early, let the students discuss their understanding and reasoning before stepping in. However, after disagreements the teacher needs to know how to follow up. Are there any misconceptions that we need to clear up? How well do the students understand it? What if they all agree on the idea and they are wrong? The teacher should follow up by creating a task that allows students to share their new learning or reasoning about an idea.
As a result, creating these opportunities for disagreements offers students opportunities to reason and make sense on their own. We do spend a lot of time engaged in discussions but it is difficult for me to fight the urge to share the answer or reasoning as time is usually a factor. There seems to be much to accomplish during a math period and not enough time to engage in the deep discussions that should be taking place.
I know investigations devotes numerous opportunities for students to engage in discussions which in turn leads to disagreements. I am hoping to work harder in fighting the urge to step in and share my thoughts with my students. Do other math programs allow for these disagreements and discussions to be taking place?
One of the strategies is to force students to choose a side. With the use of writing prompts, students need to think about their response, choose a side, and explain their reasoning for their response. Then provide opportunities for students to share and support their reasoning with other classmates. An example of this idea is seen using the following writing prompt. I think 4 X 8 and 8 X 4 are or are not the same because . . .
Another strategy to promote disagreements or debates is to reveal students' misconceptions. The teacher should use tasks that address misconceptions as they create opportunities for disagreements to arise. An example of this is to have students measure with a broken ruler. Many students are beginning to learn how to measure with the ruler and this will often lead to a discussion of where to line up the broken ruler with an object. As we are working with measurement now, I am curious to how my students will respond to this idea. They have mentioned to line up the rule with the edge of an object, I wonder how it will change when students are given a broken ruler - will they know what to do in order to measure accurately?
The third strategy is to recall last year's disagreements. If a teacher has had previous disagreements that have arose, they seem to be natural to bring them up in future years. Purposefully ask and design questions that have led to strong discussions from years past. An example of this is with 10 flats (place value) being equivalent to ten hundred or one thousand. From my experience these questions always generate disagreements. A question similar to this always leads to a good debate with my students and one that I need to bring up every year. Is this equation true or false? 20 = 20. We also work with problems like 8 + 5 = __ + 10. These problems also allow for debate and discussions for students to reason and thus be able to explain what they think is the missing number.
In order to have purposeful mathematical debates, the author points out three things in order to accomplish this. 1. Must center on a mathematical concept 2. Are accessible to all 3. Can be debated. Through all of this, the teacher plays an important role in creating a safe environment with respect, risk taking, and placing values on other's ideas. The teacher is responsible in facilitating the discussion while fighting the urge to participate. Valuable opportunities are lost when teachers give their viewpoint or simply give the answer to early, let the students discuss their understanding and reasoning before stepping in. However, after disagreements the teacher needs to know how to follow up. Are there any misconceptions that we need to clear up? How well do the students understand it? What if they all agree on the idea and they are wrong? The teacher should follow up by creating a task that allows students to share their new learning or reasoning about an idea.
As a result, creating these opportunities for disagreements offers students opportunities to reason and make sense on their own. We do spend a lot of time engaged in discussions but it is difficult for me to fight the urge to share the answer or reasoning as time is usually a factor. There seems to be much to accomplish during a math period and not enough time to engage in the deep discussions that should be taking place.
I know investigations devotes numerous opportunities for students to engage in discussions which in turn leads to disagreements. I am hoping to work harder in fighting the urge to step in and share my thoughts with my students. Do other math programs allow for these disagreements and discussions to be taking place?
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