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."
The kindergarten students in this lesson have previously counted and worked with manipulatives. Now matched with sixth-grade coaches, the kindergartners experience the numbers 1 through 50 at various stations. Twenty stations are set up inside and outside the school building. Some stations involve grouping objects; other stations have students count out various numbers of objects or perform a certain number of actions, such as bouncing a ball fifty times or taking fifty swings on a swing. All the stations encourage children to construct number meanings through real-world experiences and the use of physical materials. Some children group objects into tens, fifteens, or twenties. Other children just count out a specific number of objects or actions, such as fifty, by ones. In some stations, children also work with place-value concepts, the concept of addition, and the writing and recognition of numerals. Throughout all the stations, children engage in counting and in developing a better sense of the relative magnitudes of numbers. To conclude the lesson, the kindergarten students discuss their favorite activities of the day. 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.
Designing Number Experiences
- Why do you think Mr. Walker had so many centers set up? What was the value of having so many different number stations? What are the advantages and disadvantages to having this many centers?
- List as many learning centers as you can remember from the video and describe the mathematical content of each task. What concepts, skills, and knowledge were being developed in each center?
- One aspect of number sense is understanding the relative magnitudes of numbers. How did this lesson help children develop this aspect of number sense? What else did students learn through this lesson?
- In what ways did any of the work or thinking by the children surprise you? Why?
- What was the purpose of bringing students together as a whole group at the end of the lesson?
Using a Buddy System
- Once a week, sixth-grade students work with the kindergarten students in Mr. Walker's classroom. Describe the setup of this buddy system and the role of the big buddy.
- How did Mr. Walker interact with the buddy teams? Describe a teacher's role in a classroom with mathematics buddies like Mr. Walker's.
- Describe the advantages and disadvantages of using cross-grade buddy systems.
- Identify areas of mathematics learning in which buddy systems would benefit students.
- List ways to establish a buddy system in your classroom.
Inexpensive Learning Materials
Compile a list of inexpensive materials that could be used for learning mathematics. What everyday materials that are often thrown away could be used for learning mathematics? The list could include such items as plastic forks, empty boxes, old keys, plastic bread tags, film canisters, containers of various sizes, food wrappers, and buttons. Develop ways in which you can acquire these types of materials, such as asking parents or businesses to collect and donate such items or going to rummage sales.