CADGME2009, Linz Austria

On the visualization of function concept by using CAS

Djurdjica Takači,Department of mathematics and

informatics, Novi Sad, Serbia

On the visualization of function concept by using CAS

The function concept is the basic for calculus concept--mathematics

CAS—functions—calculus Numerical, Symbolic, Graphical

Representations of Calculus Concepts

GeoGebra, Scientific WorkPlace

On the visualization of function concept by using CAS

Questionnaire is given to first year university students

at the Faculty of Science, University of Novi Sad, Serbia,

whose major is chemistry. There were 20 students

Each student had his computer

On the use of computer in the class The questionnaire

1) Determine, without computer the function such that the function is its derivative and the function is given by:

a) , b) ,

c) , d) , and explain the answers. 2) Determine, by using programme package Scientific Workplace,

or GeoGebra, the function such that the function is its derivative and the function is given in the previous example, and explain the answers.

1( )g x

x 2

1( )

( 15)g x

x

xxg

1)( ax

xg1

)( Ra

3) Determine, with and without the computer, the functions,

where the function is given in example 1., and explain the answers.

4) Determine, with and without the computer

where the function is given in example 1., and explain the

answers.

dxxg )(

,)(,)(1

0

2

1 dxxgdxxg

On the visualization of function concept by using CAS

All students used both programme package

GeoGebra Scientific WorkPlace

The exercises are very simple The results, obtained without

computer, had to be compared with results obtained without computer.

The graph obtained by GeoGebra

2

1( )

( 15)f x

x

The results The students work:FIST: 12 students answer correctly, 3 students did not put absolute value and the constant C 6 students did not put the constant C

On the visualization of function concept by using CAS

Second: 5 students answer correctly, All 5 answer the first part correctly The student which forgot the constant

C in the first part, remark that the computer did not put it.

Remark: Lot of mistakes were caused by the symbolic representation.

On the visualization of function concept by using CAS

Third: All students recognized the first

two and the third tasks are almost the same.

14 students symbolic and numeric representation of integral, but 6 just determine the graph of integral function

The results of Ivana K.

1)

2)

4)

a) b) c) d)

a) b) c) d)

a) b) c) d)

60% 70% 70% 70%

70%60%25%45%

60% 50%75%90%

On the visualization of function concept by using CAS

Conclusion The students were very interested in work, hardworking, but enjouing satisfy with the results and marks “It was usefull test”