Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

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

Reflect on each of the following questions about the communication you observed in Ms. Pearson's class, then select "Show Answer" to reveal our commentary.

 Question: What previous knowledge do students need to bring to this activity? Show Answer
 Our Answer: Students need to have a sense of the meaning of the number 20. They need to know how it is related to other numbers. Students should have previous experience with the symbols for the numbers, the operations, and the equal sign as well as with the operations of addition and subtraction.
 Question: How does writing story problems help students deepen their understanding of the meaning of addition and subtraction? Show Answer
 Our Answer: Students need to know the action related to each of these operations. Addition indicates putting together. Subtraction indicates either taking away or comparing. When they write their stories, such actions need to be included to demonstrate the operation. This is not a simple concept for young students.
 Question: What forms of communication do students experience during the parts of the lesson you viewed? Show Answer
 Our Answer: Students are listening to one another as the lesson is introduced. The teacher writes the equations, which reinforces the written symbols for the mathematical concepts. Students work in groups to share ideas and develop real-life situations for their equations. They must come to consensus on their problem. Students use manipulative materials to model their problems, draw pictures, and translate their ideas into words and, for those students who are ready, mathematical symbols. Note the progression from concrete representation (manipulative materials) to semi-concrete (pictures) to semi-abstract (tallies) to abstract (symbols).
 Question: Ms. Pearson presented the task as follows: "The answer is 20. What is the question?" How does this type of question encourage communication in mathematics? Show Answer
 Our Answer: This question is open-ended. There are many correct and appropriate responses. This enables children to work with the mathematics at their own level of understanding. They can use a variety of strategies to approach the problem and then translate their strategies into communication by using models, pictures, words, and numbers. An open-ended question addresses students at their individual developmental level so they can deal with the mathematics in a way that makes sense to them. When the mathematics makes sense, students are able to communicate their understanding.
 Question: At the end of the lesson, students shared their stories and number sentences with the class. Describe the value of these types of presentations for students who are presenting, students who are listening, and the teacher. Show Answer
 Our Answer: Students who are presenting need to think clearly about their ideas and how they will communicate those ideas to help others understand what they did. The listeners learn listening skills and must work to make sense of the mathematics, whether it is communicated through models, pictures, words, or numbers. Listeners also learn to develop questioning skills to ask questions that will help the speaker clarify his or her ideas and help the listener better understand. The teacher orchestrates the lesson and the mathematics learned by selecting which students will share their thinking. The teacher has the opportunity to ask questions that will help all of the students deepen their understanding of the mathematics. The teacher can also use this as an opportunity to assess students' understanding: What strategies did different students use? What level of understanding are students demonstrating? This sharing also helps teachers make informed decisions about planning future activities. Do students need more experience with this concept? Which students need more practice, and which are ready to move on? What will the next lesson need to include?

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