Applying Communication
 Introduction | Equivalent Expressions | Problem Reflection | Classroom Practice | Communication in Action | Classroom Checklist | Your Journal

When we have students work in small groups or as a class and share their thinking using gestures or other motions, materials, pictures, numbers, and words, they are communicating with and learning from one another. Communication, however, can also take place at the individual level as a result of reflecting on our own thinking. You did some very real communicating with yourself as you looked at each of these expressions and determined whether or not they were equivalent to 20. You even had to do some communicating to help yourself understand the error in your thinking if you selected any that were incorrect. So, while you did not formally communicate with another person, communication was happening as you completed this task.

The questions below will help you reflect on your thinking about the task you just completed. You might also think about each question in the context of planning for effective communication with and among your students. After you've formulated your responses, select "Show Answer" to see our sample responses.

 Question: How do the real-life situations posed in the activity help bring meaning to the operations in the expressions? Show Answer
 Our Answer: From the information in the word problem, one can draw a picture or make a model with concrete materials to represent the objects and actions in the problem. From that, you can connect the action in the problem to the operation and its symbolic representation. This is a much more powerful strategy than having students look for "key words" to solve a problem, as key words can often relate to more than one operation ("In all," for example, can actually refer to any operation). Focusing on the action when applying the concept reinforces the meaning of the operation.
 Question: Take one of the expressions from the problem and write your own real-world story problem that it could represent. What do you need to understand about the meaning of the operation in order to write the problem? Show Answer
 Our Answer: You need to know what action the operation represents. In the case of the two-step (addition and multiplication) example, you need to know that the multiplication must take place before the addition.
 Question: What methods of communication can be used to explain your thinking about the meaning of a problem situation, or the meaning of an expression? What are the advantages of using more than one method? Show Answer
 Our Answer: You can use pictures, models, words, and numbers to communicate the strategies and mathematical concepts. Using more than one method of communication not only stretches and clarifies one's thinking, it can also help others gain a clearer understanding of your thought process.

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