Integrated Learning Environment for Developing "Function Sense"
From Velocity to First Steps in Calculus Using Spreadsheets
Infomatics & Media Studies
Tsukuba Gakuin University
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.
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
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.
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