Educational experiences about using different computer programs in calculus courses at the University of Kaposv

1
(No Transcript)
2
Educational experiences about using different
computer programs in calculus courses at the
University of Kaposvár

• Anna Takács Klingné
• University of Kaposvar, Faculty of Economic
  Sciences, Mathematics and Physics Department

Second Central- and Eastern European Conference
on Computer Algebra- and Dynamic GeometrySystems
in Mathematics Education 11-13 July, 2009 RISC,
Linz, Austria
3
(No Transcript)
4
(No Transcript)
5

• My students study
• Agribusiness and agricultural rural development
  programme
• Agricultural engineering programme
• Finance and accountancy programme

Subject and number of subject per week taught by
Mathematic Department
1. semester 2. semester 3. semester
Finance BA Calculus I. 22 (Analysis) Calculus II. 22 (Probability and Linear algebra) Optimization 22
Agricultural rural development BSc Calculus I. 22
Agricultural engineering BSc Calculus I. 22
6
We find that our students have little success in
mathematics. But why it is?
One of his reasons, that the higher education
became multitudinous
On the other hand the problem is that in the
teaching-learning process the foundations of is
left for higher education
7
Before starting studying the students are
assisted from mathematics. We ask the number and
function abstraction and about the model creation
in the test. We reveal their deficiencies based
on their solutions.
The pretest
8
We found out that our students have deficiencies
in the following

• The order of doing operations on numbers ( this
  is very important)
• The rules of the index laws
• Methods of fractions
• Etc

9

• The teaching-learning process in damaged on the
  different levels of the education.
• How can we make up for there differences in
  higher education?
• I think this topic important because analysis of
  mathematics is a basic subject for our students
  and they have to know functional operations in
  order to be able to describe economic processes
  with the help of functions.

10

• I have been dealing with the Bruners
  representational theory and I am trying to adapt
  it to my research. Bruner examined what the man
  is like with the help of codes stores the
  information arriving from the external world. All
  thought processes may happen on of three kinds of
  plane according to it
• Material level (actual objective acts,
  activities)
• Iconic level ( visual education, situation)
• Symbolic level

11

• The 3 representation methods take part in each
  phase of the teaching process.
• To my mind the visual education is very
  important, thats why I tried to provide
  everyday, lifelike illustrations to help the
  acquisition of the material.

12
I think the use of the computer is an opportunity
to help the interaction between the cognitive
levels listed above. We recommend an optional
subject to the students. It was called Teaching
of mathematics using computer. This course was
going in parallel with the Mathematics I-II
(calculus) subject.
13
The subject had a threefold aim

• The development and conditioning of the basis
• To link it closely with higher mathematics
• To link it with the use of computers.

14
In the last semesters we collected positive
feedback during teaching this subject. We used
Excel and GeoGebra, too. It was important to use
a programme which is available for every student
and they can use it during preparation. Within
the frames of this subject there is a possibility
for development. This is my opinion.
15
Teaching of mathematics using computer I. in
parallel with the Mathematics I. (calculus)
subject.
Themes
16
1. Revision of some parts of secundary education
curriculum Algebraic identity, absolute value,
solve of equations and inequality Raising to a
power, extraction of a root, definition of
logarithm, identity of logarithm Definition of
function, function attributes, draw and
elementary functions graphs Function
transformations, operations Definition of
sequnces, arithmetic, geometric sequnces 2.
Solving tasks which are closely connected to the
syllabus of basic mathematics. Compared to the
practice of Calculus it helps the student achieve
the necessary level by solving task rows built
on top of each other in a smaller and easier
steps. 3. Calculation and draw of elements of the
sequnces, draw functions graphs in Excl and
GeoGbra, geometrical illustration of Newton
quotient, derivative in Excel and GeoGebra
17
Representacion of the series in Excel
C1B1-2A1
18
(No Transcript)
19
The graph representation of the function in Excel
We put lot of effort to draw graph of function
with Excel because we experience that the
students can solve function analysis problems
well, except drawing the graph of function. They
determine the 1st and 2nd derivative, their root,
sign, but the drawing the graph of function is
still causes trouble. We have to select the
interval, on wich we draw the grapf of function,
so we give here to subset of the domain of
function. After this we choose step value, it is
important how large an the step value, because it
may happen on the case of a big step value, that
everywhere differentiable functions have
breakpoints on the graph. (We can correct this,
when we select smooth lines diagram) As an
example we selected a function, which has break
point, extremal value, inflection point also.
How do we choose the right interval? Which ones
are the important, exciting points, which have to
contain the selected subset of the domain of
function? These are the singularity points,
roots, extremal values, inflection points of
function.
20
(No Transcript)
21
(No Transcript)
22
GeoGebra in the education of analysis
23
Observe the shape of the first derivative algebra!
24
Teaching of mathematics using computer II. in
parallel with the Mathematics II. (calculus)
subject.
Themes
25
Linear approximation and approximation by Taylor
series of the functions with GeoGebra Riemann sum
of function (integral) with GeoGebra, with Excel
not, because that is too difficult Calculation of
faktorial and binomial coefficient. Permutations
with and without repetitions, combinations with
and without repetitions Modeling the random
effects, frequency, relativ frequency.
Probability distribution (discrete and
continuous) Mátrix operations multiplication,
inverse. Determinant, solution to a system of
linear equtions with computation inverse matrix
and with Cramer's rule wih Excel and LINV
pogramm I think the LINV program is used by our
university.
26
Taylor-polynomial with GeoGebra
The more members are pictured, the Taylor
polynomial approximates the function better.
27
Approximate amount of the lower with GeoGebra
28
Distributions exercise
29
Mátrix operations multiplication, inverse.
Determinant, solution to a system of linear
equtions with LINV programm
LINV Open LINV.ZIP
30
Here you can choose the number of rows and
columns.
The produkt
The program controls that we can make the
product.
31
Teaching of mathematics using computer III. in
parallel with the Research of operation subject
Themes
System of linear equtions, linear and nonlinear
programming (LP, NLP) problems, transport
optimization, sensibility analysis in Excel
Solver and LINV program (home (self) made
program)
32
Solving the LP exercise
with LINV We can solve with simplex method by
LINV The revised standard and the general LP
task can be solved with the program.
with Excel
33
(No Transcript)
34
Three variables LP exercise with Euler3D
35
Thank you for your attention!