Defining Connections
 The Connections Standard | The Interconnectedness of Mathematics | Applying Mathematics to Other Subjects | Asking Questions | Relating Connections to the Other Process Standards | Your Journal
 In the previous sessions, we studied, practiced, and reflected on the five process standards, and we can easily see that the process standards are very closely connected. For example, we use problem solving to set the stage for mathematical learning, to get students involved in interesting mathematics, and to connect mathematical concepts to the real world. Representations, such as drawings and models, help students see the relationships between mathematical ideas. In the middle grades, students should build new knowledge by extending their previous experiences. All of this happens through having students communicate about their thinking both orally and in writing. Watch the video segment (duration 0:33) in the viewer box on the upper left to hear a reflection from Ruth Ann Duncan, a middle school mathematics teacher. Since the process standards are closely related, an effective mathematics lesson should incorporate all of them. In other words, we should not teach problem solving on Monday, communication on Tuesday, reasoning and proof on Wednesday, representation on Thursday, and connections on Friday! Rather, every lesson should include some aspect of each of the process standards. In this section, we have looked at mathematical connections in a wide variety of contexts: Connections within mathematics Connections to the real world Connections to other subject areas Connections outside of school Connections between the process standards We have also looked at how teachers incorporate connections as part of the mathematics their students study by asking questions that help students recognize connections, by planning lessons and activities that integrate mathematics with other subject areas and with life situations, and by reflecting on the connectedness of the process standards.
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