Which Graph Is Which?
Sakshaug, Lynae, Teaching Children Mathematics
The goal of the "Problem Solvers" department is to foster improved communication among teachers by posing one problem each month for K-6 teachers to try with their students. Every teacher can become an author: pose the problem, reflect on your students' work, analyze the classroom dialogue, and submit the resulting insights to this department. Remember that even student misconceptions are interesting.
Please spend some time discussing this problem with your students. Although the students may need help understanding the problem and the constraints under which they are to work, please avoid giving too much guidance. Encourage your students to write about what factors helped them solve the problem. Collect actual students' work, and jot down notes about discussions that occurred and the variety of students' solution processes. View this task as more than an exercise for which students are seeking a correct answer.
As you reflect on your experience with the problem, keep in mind these questions:
* What strategies did the students use in determining which graph fit which situation?
* Did misconceptions surface, or did other ideas occur that hindered students' thinking?
* How well did students explain and support their choices?
* What surprised you?
* How could you assess students' work on such an exploration?
Please send us your thoughts and reflections. Include how you posed the problem and samples of students' work. Please send your results with your name, grade level, and school by 20 May 2000 to Lynae Sakshaug, Department of Education and Human Development, SUNY Brockport, Brockport, NY 14420.
Your analyses will help other teachers better understand children's thinking about mathematics. Selected submissions will be published in a subsequent issue of Teaching Children Mathematics and acknowledged by name, grade level, and school unless otherwise indicated. If you would like an acknowledgment and a set of solution strategies before that time, send a self-addressed, stamped envelope to Lynae Sakshaug at the address shown.
Lynae Sakshayg, Department of Education and Human Development, SUNY at Brockport, Brockport, NY 14420
Friel, Susan, George Bright, and Frances Curcio. "Graph Sense." Paper presented at the meeting of the Research Council for Diagnostic and Prescriptive Mathematics, College Park Maryland, 1998.
Graph A and graph B show information about two different situations. One graph shows how man pets each of the thirty students in the class has, and the other graph shows how many times in month each child in the class brings lunch to school instead of eating the food served in the cafe teria. Which graph do you think represents which data set? Why? After you decide, label both axes on each graph. Then write a letter to a friend who disagreed with your choice Explain why you think that your representation is correct.
Which of the following questions can be answered from the graphs?
1. How many students have cats for pets?
2. On which day do most students pack a lunch?
3. Which student has the most pets?
Chose one of the graphs, and describe another situation that the graph might represent. Write and answer a question about the new situation.
Where's the Math?
This exploration allows for a range of discussion concerning what is known about a data set from the information represented and what can and cannot be determined from the graph. This problem represents explorations currently being used to help children develop graph sense. Graph sense is described by Friel, Bright, and Curcio (1998) as the ability to--
* compose and decompose graphs,
* recognize elements and interrelationships among elements in a graph,
* speak the language of graphs when reasoning about information in graphs,
* describe the shape of the data from the graph,
* recognize when one graph is more useful than another on the basis of a knowledge of the data being represented,
* move flexibly among graphs and see interrelationships among them, and
* respond to different levels of questions associated with graph comprehension. …