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Teaching Math: A Video Library, K-4

Mathematical Connections

The goals of the NCTM's connections process standard are that "in grades K-4, the study of mathematics should include opportunities to make connections so that students can:

link conceptual and procedural knowledge;
relate various representations of concepts or procedures to one another;
recognize relationships among different topics in mathematics;
use mathematics in other curriculum areas;
use mathematics in their daily lives." (NCTM, Curriculum and Evaluation Standards for School Mathematics, p. 32)
Video Overview
This video profiles more than a dozen classroom episodes that illustrate mathematical connections. Connections are made among different topics in mathematics, to other curriculum areas, and to students' daily lives. For example, students are observed in the following contexts:

comparing results from a survey of cyclists on a bike path
investigating the number of Valentine exchanges in their class
creating quilt squares from triangles to celebrate Thanksgiving
computing the cost of furnishing a milk-carton house
combining physical activities with counting
dividing paper cookies evenly among members of a group
analyzing graphs found in newspapers
estimating animal populations in Yellowstone National Park
exploring ladybugs to collect and analyze data
engaging in various activities that connect to mathematics in a story
exploring numbers through drama and music
discovering diameter and circumference in ordinary objects
using place-value mats to record measurements
finding fractions within geometric shapes made with pattern blocks
converting results from a bubble-gum contest into fractions
writing how they determined the number of marshmallows needed for the class camping trip
An Exploration
For Teacher Workshops
Noting the News
This investigation focuses on mathematical connections. Each pair will need these items:

a page from a newspaper
scissors
highlighters

Divide teachers into pairs and give each pair a page from the newspaper. Be sure to vary the type of pages that each pair receives. For example, give some pairs a page from the local, state, or national news, some a page from the business section, and some a page from the sports section. The pairs should examine the page for mathematical connections, highlight all the mathematics—such as numbers and references to numbers—and cut out each article or advertisement that contains a mathematical connection.

Have the pairs hold up what remains of their newspaper pages. Analyze what sections of the paper contain many or few mathematical connections.
How many pairs have very little of their page remaining? What sections of the newspaper did their pages come from?
How many have most of their page remaining?
How many have about one-half of the page remaining?

Examine the connections that were identified. Have the pairs take turns presenting the mathematical connections that they highlighted on their pages.
Topics for Discussion
The following areas provide a focus for discussion after you view the video. You may want to customize these areas or focus on your own discussion ideas.
Making Mathematical Connections

The NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) states, "Students need to see when and how mathematics can be used, rather than be promised that someday they will use it" (p. 35). Identify examples in the video that showed students connecting mathematics to their daily lives.

What classroom episodes showed students using and learning mathematics related to other curriculum areas? How was mathematics being used? What mathematical ideas were students learning? How could you assess the students' understanding in both areas simultaneously?

It is important for students to recognize relationships among different topics in mathematics and to see that mathematical ideas are related. Cite examples in the video of students making connections among topics in mathematics.

What instructional interventions are necessary if teachers are to better help students make connections between and among various mathematical ideas?

In what ways should students experience school mathematics if they are to make connections between mathematics and their out-of-school experiences?

What are effective ways to assess the degree to which students are making connections between and among different topics in mathematics?
Planning for Connections

Select your favorite task from all those profiled in the video. Why did you select this particular task?

Brainstorm a list of task characteristics that emphasize making mathematical connections.

Discuss ways to find and develop learning tasks that are rich in mathematical connections, such as the use of the newspaper, telecommunications, or field trips.

What are some ways to develop an integrated set of activities that allow students to explore mathematics within the context of other disciplines?

Discuss the implications of modifying the sequence of the mathematics presented in instructional materials, such as textbooks, to better accomplish the goal of helping students make connections between and among mathematical ideas.
Extensions
Who Uses Mathematics?
Generate a list of occupations. In a matrix, put the occupations down one side and the curriculum and evaluation standards across the top. For each standard, identify some mathematical concepts and skills that are important for each occupation. Devise a lesson that will help students learn about these occupations.
Examining Mathematical Connections
Each classroom excerpt profiled in this video is from a featured lesson in TEACHING MATH: A Video Library, K-4. You may want to watch the full version of these lessons to examine and further explore the role of connections in learning mathematics. The following list provides information about each video and the page number on which its print unit is found. Videos are listed in the order in which their excerpts appear in the Connections video.