# Investigations

By Lamphere, Patricia | Teaching Children Mathematics, September 1994 | Go to article overview

# Investigations

Lamphere, Patricia, Teaching Children Mathematics

The "Investigations" department is designed for teachers who wish to give students new insights into familiar topics in grades pre-K-6. It includes both directed and open-ended activities. A basic assumption is that the teacher will facilitate the investigation so as to let students be actively involved in shaping their learning.

In the activities that follow, the student page is presented in reproducible format and the teacher commentary appears on the back of the page. Teachers are encouraged to use these materials in a flexible manner to stimulate similar activities designed by the students themselves.

This month's investigation uses the theme of collecting and interpreting data from the students' own classroom. Students in the primary grades make graphs from physical objects, including themselves, and move into simple representational graphs. In the middle elementary grades, students collect and interpret data to make a personal profile of the students in their class. In the upper elementary grades, students compare the personal characteristics of different groups of students. The activities stress communication among students and between students and the teacher.

Teachers may duplicate and use this material in their own classes without requesting permission from the National Council of Teachers of Mathematics.

Student Activity Goals

* Students will gather and organize data.

* Students will represent collected data in object graphs and will construct representational bar graphs.

Planning for Instruction and Assessment

Display the graph from figure 1 and ask your students whether their class is like the one pictured in terms of the types of shoes they wear.

Collect class data and help students organize the data into an object graph similar to those in figures 1 and 2. Articles of clothing and other personal items can be used to make the graphs. Students can "line up" on the graph themselves to show certain characteristics.

1. What is the most popular type of shoe in your class?

2. What is the most popular type of shoe in the graph in figure 1?

3. What is the least popular type of shoe in your class?

4. What is the least popular type of shoe in the graph in figure 1?

5. In what season do you think the data in figure 2 were collected?

6. If a new student came to your class, what type of shoe is the person most likely to be wearing?

7. If a new student came to the class that developed the data in figure 1, what type of shoe is he or she most likely to be wearing?

On the basis of the data collected, have the students write about the two classes and their preferences. Have the students dictate or write questions that they think other students could answer on the basis of the displays of data.

Discuss with the class the difference between a graph made from real objects (shoes, students, and so on) and a representational graph. Have students make a representational graph from one of the graphs made with real objects. Discuss the advantages of the representational graph.

Display several representational graphs and questions in your classroom or in common areas in the school. Photograph both the representational and the object graphs and class picture graphs in which students lined up according to some preference, such as favorite day of the week. Be sure the photograph clearly shows the categories.

Other topics about which students may want to collect data include the following: pets, favorite color, favorite food, favorite type of book, favorite sport, favorite video game, favorite television program, and least-favorite chore. As students' data-collecting and graphing skills become more sophisticated, the types of information they gather may become more complicated. Teachers may want to have students assemble all data and graphs in a Class Almanac. …

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