Teacher resources and professional development across the curriculum
Teacher professional development and classroom resources across the curriculum
The goals of the NCTM's reasoning process standard are that "in grades K-4, the study of mathematics should emphasize reasoning so that students can-
(NCTM, Curriculum and Evaluation Standards for School Mathematics, p. 29) Video Overview
- draw logical conclusions about mathematics;
- use models, known facts, properties, and relationships to explain their thinking;
- justify their answers and solution processes;
- use patterns and relationships to analyze mathematical situations;
- believe that mathematics makes sense."
Before this lesson, this class collected data on wildlife in different environments. Students now develop number sense and construct meaning for large numbers by estimating how many bison, elk, and pronghorn they saw on a recent field trip to Yellowstone National Park. Original estimates are recorded and students are divided into groups, given an animal designation, and supplied with maps of the park and information about the animals. Students then work to revise their estimates. After each group reaches consensus on its estimate, the class reconvenes to discuss its estimates and place them on a number line. Students debate the reasonableness of their placements, justify their estimates, and explain their reasoning in discussion and in writing. To conclude the lesson, Ms. Raymundo tells students Yellowstone Park's actual population numbers for the bison, elk, and pronghorn. Topics for Discussion
For Teacher workshops
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.
Developing Number Sense
- What was the role of number sense in this lesson?
- What is your assessment of the number sense of students in this class? What evidence can you offer to support your assessment?
- Identify instances in the lesson that focused on the use and development of number sense.
- How was the number line used as a vehicle to promote number sense?
- Describe any moments in which students displayed a clear sense of, or lacked sense of, the magnitude of number. How were the situations handled? What are other ways to handle these kinds of situations?
- Why do you think Ms. Raymundo let students decide how to proceed in finding the solution to the task? How does this approach contribute to making sense of numbers?
Making Interdisciplinary Connections
- Identify the various subject areas addressed in this lesson and the role of each.
- What mathematical ideas were embedded in the lesson?
- Interdisciplinary connections often make good tasks for engaging students in mathematics from several of the following strands: problem solving, reasoning, communication, and connections. Cite examples of each process strand in the lesson.
- What learning benefits exist for students engaged in interdisciplinary experiences? What are the drawbacks? What should you take into consideration as you plan for interdisciplinary experiences?
- List other ways to incorporate number-sense development into interdisciplinary instruction.
Brainstorm ideas for using field trips to facilitate mathematics learning. How can mathematics be explored at the zoo? In a park? At a history museum? At an art museum? At a business or industrial site? Think of ways to make connections to several subject areas in these field trips.
The study of animal populations can provide interdisciplinary links. For example, in this lesson, the populations of bison, elk, and pronghorn in Yellowstone National Park were reported. Consider ways to extend this lesson. How did the National Park Service arrive at these numbers? How often are populations counted? How does a species get on or off the endangered-species list? Use these questions as a basis for having students research how federal agencies, such as the National Park Service, arrive at the official census of wildlife populations.