Defining Connections
 Introduction | Connections to Other Contexts | Connections Between Representations | Additional Connections | Your Journal

"School mathematics experiences at all levels should include opportunities to learn about mathematics by working on problems arising in contexts outside of mathematics. These connections can be to other subject areas and disciplines as well as to students' daily lives." (NCTM, 2000, pp. 65, 66)

Building Connections Outside of School

A situation in a literature story, or a student's enthusiastic report of an experience over the weekend, can become the introduction to a new mathematical topic or an opportunity to practice and extend previous skills. Such connections provide more than motivation for students -- they make it easier for students to build and retain new knowledge and skills by making links to familiar ideas. A teacher who has a clear understanding of mathematical goals for his or her students can best recognize and develop opportunities to build connections to mathematics outside of school.

Building Connections to Other Subjects

It truly is possible to "mathematize" lessons in all subjects at various points of the school year. Social science lessons can be enhanced by the discussion of numeric data, by the analysis and creation of graphs, and by the use of timelines. For example, graphs of data can be analyzed to compare population growth (predictions of the United States' population growth in the next few decades range from 280 to 515 millions of people!), or tables showing production of major products in various states or countries can be compared.

Considerable connections can be made between mathematics and science. "In grades 3-5, students should be developing the important processes needed for scientific inquiry and for mathematical problem solving -- inferring, measuring, communicating, classifying, and predicting. The kinds of investigations that enable students to build these processes often include significant mathematics as well as science" (NCTM, 2000, p. 201).

Language arts can be connected to mathematics through specific ideas that act as catalysts for mathematical inquiry. Problem solving and data collecting that stem from a literature experience provide connections between mathematics and its application in various settings. Writing to communicate one's ideas is similar in language arts and mathematics. In both cases, it is important for student writers to have a clear understanding of the topic, to consider their audience, to state their ideas clearly, and to use examples to illustrate their points.

Physical education, art, and music classes can be infused with the discussion of both geometric and numeric patterns. They can also have basic mathematics practice intertwined through the incorporation of such activities as skip-counting during exercises, and dividing to create equal groups.

When teachers are aware of the mathematics standards, goals, projects, and familiar contexts of the prior grades, they can intertwine references and experiences that help students make connections and build new knowledge on a familiar foundation. Students' success in subsequent grades can then be supported by providing foundational experiences that prepare a base for later learning of key concepts and skills.

For example, students who have explored the dartboard exercise illustrated earlier will be able to make good use of this experience when they study probability in later grades. The concept that probabilities must always add up to 1 is an inherent connection that can be drawn from the activity.

In a similar way, students who, from the earliest grades, are asked to make conjectures and justify their answers will have a stronger foundation when they explore concepts of formal proof in later grades. They will be able to connect their early habits to this new task.

"Viewing mathematics as a whole highlights the need for studying and thinking about the connections within the discipline, as reflected both within the curriculum of a particular grade and between grade levels." (NCTM, 2000, p. 64)

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