Abstract Submitted to the 10th Asian Technology Conference in Mathematics
December 12-19, 2005, South Korea

## An Integrated Learning Environment for Developing "Function Sense" (2) From Velocity to First Steps in Calculus Using Spreadsheets

Chieko FUKUDA
PXM03664@nifty.ne.jp
Hakuoh University

Kakihana Kyoko
kakihana@tsukuba-g.ac.jp
Infomatics & Media Studies
Tsukuba Gakuin University
Japan

### Abstract

In this study, we present a case study for exploring how to develop a "function sense" at an integrated learning environment (Kakihana et. al, 2000) with spreadsheets and experiments with a graphing calculator. In this case study, high school students and junior college students were examined, how to use their "function sense" to understand the relation between a velocity and the concept of differential. We reported on this study by the poster of last year. We report on them in detail because we added some experiments afterwards.

Methods:

1. At first students tried to understand the velocity and the shape of a function with a graphing calculator by actually walking.

2. Based on the previous activity, they simulated many situations of walking at an integrated environment of spreadsheets. That is, they input the walking data (velocity or distance) or the expression of the velocity of this duration on the spreadsheet. Graphs of the distance and velocity were drawn automatically.

3. They thought the relation of graph between the distance and the velocity without technology.

Results and Conclusion:

1. This environment helped students to understand the relation between the distance and the velocity on a graph through inputting numeric data.

2. On the spreadsheet students can experience the situation which they are not able to activate actually in a real world

3. Students were able to connect the velocity graph with the distance graph without technology.

4. Some students confused the increase and decrease of the speed with the increase and decrease of the distance. Guidance that clearly distinguishes them is necessary.

5. These activities were able to motivate students to learn calculus.

References:

Fukuda;C. Kakihana;K., and Shimizu,K. (2001); gThe Effect of the Use of Technology to Explore Functions (3) ~ The Development of Function Sense with Technology ~h, ACTM2001 pp.130-139.

Thomas W. Judson and Toshiyuki Nishimori (2005), Concepts and Skills in High School Calculus: An Examination of a Special Case in Japan and the United States, Journal for Research in Mathematics Education,Vol.36,No.1 pp.24-43

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