Teacher resources and professional development across the curriculum
Teacher professional development and classroom resources across the curriculum
Students in this lesson use linear measurement as the context for learning about decimals. Students work in groups to divide a meter-long piece of string into ten equal parts and to mark the tenths with colored tape. Students measure different items in the room, and record their results on a bar graph and on a chart on the computer. The class is introduced to decimals and shown how to record with symbols a length that is one meter plus two parts, or two tenths, long. These units help students develop the concepts of a meter and of decimals as they learn to write their measurements using decimal notation. Group members are assigned specific roles and the students begin measuring objects, such as the door, window, chairs, and tables. Students record their measurements by creating bar graphs and discuss notions of accuracy and precision. Students use computers to store and compare data and to create graphs. As they work, students are questioned on their understanding and guided without being given the answers. To conclude the lesson, the class discusses the student-made and computer-generated graphs. 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.
Using Measurement to Introduce Decimals
- Describe how measurement was a context for introducing the need to learn about decimals.
- What do you think of the approach used in the video for introducing students to decimals? What other approaches could be used?
- What are the advantages and disadvantages of reading decimals as "inone and two tenths" versus "inone point two"? How would you ensure that students understand this connection?
- One group measured the width of the table as twelve parts, but they were not sure how to record with decimals the result of their measurement. Students finally decided to ask Ms. Wise for assistance. What were they confused about and how did Ms. Wise respond? In what other ways could the students have been helped?
- To what extent did students demonstrate an understanding of decimals? What is your evidence?
Facilitating Students' Reasoning
- What did Ms. Wise say and do to facilitate the students' reasoning throughout the lesson?
- What kinds of questions facilitated the students' thinking and reasoning in this lesson? What is the role of open-ended questions in promoting reasoning?
- Describe and evaluate the ways in which the data were displayed in this lesson. How did the graphs facilitate the students' reasoning and their discussions? What other visual representations of data could further facilitate the students' learning?
- How did the computer contribute to the students' reasoning? How else could the computer have been used in this lesson?
- What was the purpose of bringing students back together after they had finished their measurements and the graphs?
- One boy in the video was unsure of the meaning of quarters. Discuss the advantages and disadvantages of using the term quarters versus fourths. How did Ms. Wise handle this situation during the lesson and assist the boy in his thinking? In what other ways could you help a student make the connection between quarters and fourths?
- Students were asked to point out the perimeter of a table during the lesson. How did Ms. Wise help students understand the meaning of perimeter? Was the meaning of perimeter clear to students? What are some other ways to help students understand the concept of perimeter?
Investigate the use of computers for organizing and displaying data. Consider the advantages and disadvantages of different pieces of software. Discuss how to choose software to supplement mathematics lessons. For example, you can work with a spreadsheet program and specific graphing packages to investigate displaying data as was done in the video. Once you become comfortable using some of the programs, think of and list ways to integrate them into mathematics teaching.