Experiences
with CBL and the TI-92 in Austrian High School classes integrating Math,
Physics and Chemistry |
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by
Brigitta Aspetsberger Bundesrealgymnasium Landwiedstrasse Landwiedstrasse 82, A-4020 Linz, Austria, Europe |
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by Klaus
Aspetsberger Paedagogische Akademie des Bundes in Oberoesterreich Kaplanhofstrasse 40, A-4020 Linz, Austria, Europe |
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We
report about first experience of CBL/TI-92 within the final exam at an
Austrian grammar school. Basic skills for making experiments, documenting
results and using and transferring basical knowledge are discussed in
this presentation. In
this presentation we will report about the experiences made with students
at the age of 17 to 18 carrying out experiments in chemistry and physics
in science courses. We concentrate on how the students can apply their
knowledge from mathematics and sciences in these practical situations
and how they document their results. |
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Introduction | |
CBL is a
Calculator Based Laboratory which allows to collect data during physical
and chemical experiments. Data are stored directly to a calculator e.g.
the TI-92 for graphical visualization and further manipulations. Due
to these features experimenting is getting easier. However, this does
not mean, that the students can work less exactly. A careful experimenting
is absolutely necessary for obtaining good quantitative results. CBL
and TI-92 are supporting collecting and manipulating data only. We report
about a project being carried out at the Bundesrealgymnasium Landwiedstrasse,
which is an Austrian Grammar school in Linz, in the year 1999/2000. The
students are interested in natural sciences. Six different groups of
students have been involved in this project consisting of 61 students
at the age of 16 to 18 years. About 50% of the students were girls and
there was one group consisting of girls only. All of them did not have
much basic knowledge in chemistry and no experiences with the TI-92 or
the CBL system. Experimenting and working in groups was a new experience
for the students. |
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Experiments | |
As an example
we treat the experiment about "discovering" Boyle“s law in more
detail. It is quite easy to understand and the practical execution is
unproblematic. However the concept of combing experimental activities
and mathematical reasoning using different representation forms (tables,
graphs, algebraic expressions) is easy to recognize and can be transferred
to all other experiments. The objective of this experiment is to determine the relationship between pressure and volume of a confined gas. For this experiment we use a syringe which is connected to a pressure sensor (see figure 1). Decreasing the volume in the syring by moving the piston of the syringe, the pressure of the confined gas will increase. The pressure of the gas is collected by the CBL system and stored to a data matrix of the connected TI-92. Using the TI-92 the students can immedeatly visualize the relationship between volume and pressure of the gas and analyze data by fitting suited functions for describing the relationship. We assume that the temperature is constant throughout the experiment. |
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Figure
1: pressure sensor and syringe for investigating Boyle“s Law |
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After
preparing the pressure sensor, the CBL system and the TI-92 the students
start collecting data by varying the volume of the gas and simultaneously
meassuring the pressure. Both volume and pressure are stored to a data
matrix of the TI-92. By
inspecting data stored to data matrix cbldata of the TI-92 the students
can find out that the pressure stored in column c2 decrease for increasing
volumes stored in column c1. For verifying the assumption that there
is an inverse proportionality between volume V and pressure p of the gas,
the students compute the product p*V in column c3 by entering the product
c1*c2 to the head of c3. The students learn, that they do not obtain
exact the same values for all data pairs. It is an important experience
for them to learn that experimental data are always affected by an error.
This is a good motivation for introducing statistical methods like mean
and standard deviation and discussing the meaning of these concepts (see
fig. 2). |
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Fig. 2: Collecting data in a data matrix and calculating mean and standard
deviation.
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The students can define a scatter plot and visualize data in a graph window of the TI-92. The shape of the imaginary line of scatter points is typical for reciprocal functions. The students can try to find experimentally functions that are fitting data best. Maybe they start with the function y1(x) = 1/x learning that the graph of the function is running below the data points. They have to mulitply the function expression by a constant. A good choice is the mean of column c3. The function y2(x) = 9.5/x fits data much better than y1(x). However, even for this function all data points do not lay on the graph of y2. Especially, data points for small volumina deviate from the graph (see fig. 3). |
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Fig
3: Visualizing data points and fitting them by reciprocal functions
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Using
the function PowerReg of the TI-92 we can compute a regression curve of
the type a*xb for the given data points obtaining the function
6.9*x-0.86. We can use a situation like this for intrducing
the concept of regression. However, the students at least should be able
to interpret the results. For reciprocal functions the exponent b should
be -1. A
possible error could caused by neglecting the volume of the tube connecting
the syringe with the pressure sensor inside the sensor box. We assume
this volume to be 1 ml. We can add this volume to the volumes measured
in the experiment before by computing c4 = c1 + 1. We can see that the
products p*V with the new values for V do not vary so strong around the
mean value 10.6 (see fig. 4) and the function y2(x) = 10.6/x fits the
data points quite well. |
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Fig.
4: Investigating new values for the volumes by adding the volume of the
tubing
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Computing the regression curve with PowerReg of the TI-92 we obtain 6.9*x-0.96 with an exponent near to -1. Now the regression curve corresponds well to invere relationship and reciprocal functions. |
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Basic Skills | |
Experimenting
with the CBL and the TI-92 in science courses requires basic skills in
different areas, e.g. mathematical skills, verbal skills, practical skills
and social skills. As the main
basic skill in mathematics the students should be able to recognize functional
interdependences from data. For this reason knowledge about different
types of functions is required, e.g. linear, reciprocal, potential or
exponential functions. The students should know the typical shapes of
the graphs and how the graphs alter if occuring parameters are varied. As a special
case of functions the students should know about direct and inverse relationships.
They should know techniques of how to prove which relationship is applicable.
E.g. the product p*V is constant if there is an inverse relationship between
the pressure p and the volume V of a confined gas. Furthermore the students
should be able to recognize e.g. direct relationships form plots of data
points in a graph window. There is a strong argument for a direct relationships
if the data points lie on a straight line running through the origin. Concerning
the use of the TI-92 during experimenting the main basic skill is a secure
handling of the windows for the different representations of data, i.e.
the Data/Matrix Editor, the Y= Editor for entering functions and plots,
the Graph window and the Window Editor for changing the settings in the
Graph window. There is a tight connection of these technical skills to
the mathematical skills of interpreting and manipulating data in different
representation forms. A verbal
basic skill is the ability of the students of doing experiments by using
detailed written instructions. It is surprising how difficult it is for
students to read and carry out instructions stepwise without additional
explanations of the teacher. A further problem was documenting the results.
The students have to learn how to write a technical report. Especially,
summarizing the chemical/physical background and interpreting the results
is quite difficult. Finally,
the students have to learn some practical and social skills when experimenting
in groups. We can not describe these skills in detail, but we have observed
that the students had problems in teamwork and experperimenting at the
beginning of the project and they mastered these problems at the end. Experimenting
in science courses is a good training for the multiple intelligences [Gardner
93] of the students. |
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Final exam | |
In Austria
it is usual to use computers not only in normal lessons but also in our
final exam called "Matura". In the verbal part of the final
exam students can choose a special topic for one question. In the final
exam this year one student choose the use of the CBL and the TI-92 in
chemistry courses as a special topic. It was one
task of the student to determine the unknown concentration of a green
coloured solution following Lambert Beer“s Law (Light absorption is direct
proportional to the concentration). The student had to make a serie of
different solutions from a stock solution of known concentration and to
measure their light absorbance using a colorimeter. Due to Beer“s Law
the concentration/absorption data points lie on a straight line. Measuring
the light absorbance of the unknown solution the student was able to determine
the unknown concentration of the solution. Furthermore the student gave
background information about how a colorimeter works and how to interpret
Beer“s law. Once more
a real time problem occured. 20 minutes for preparing the experiment
and 8 minutes for presentation were a very short time. It should be mentioned
that the show effect helped to attract the attention of the examinators.
It was amazing that the experimental data of the student were very accurate.
This showed the souvereignity of the student“s work. Nervousity could
cause problems in accuracy. Experiments
and the use of computers in final exams can lead to unpredictable situations,
especially if there is a break down of the computer. It is recomended
to keep an additional TI-92 with some basic data in reserve. |
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Experiences | |
The students
were really motivated. They spent more time as obligatory in the laboratory
and they would like to continue the CBL-TI-92 project. Students being
not very good in chemistry and mathematics got a real chance to do it
better. Some girls who did not be very interested in these two subjects
enjoyed the project. They were proud about their "beautiful curves"
and their good results. According
to a questionnaire, which the students answered at the end of the project,
they enjoyed practical work. They felt free of the "pressure of
learning" and appreciated being independent during experimenting.
Chemical and physical laws became more illustrative for the students.
Some students also mentioned that it was important to learn using technical
instruments and computers for their future life. Only 2 of 61 students
would not like to continue this project. We forced
the students to write reports for documenting their work and their results.
Most of them were not happy about that, but they accepted the need for
doing that. It turned out during discussions that the students understood
the background of the experiments after having written the reports and
they wished to repeat some of the experiments to obtain better results.
Background information before and an intensive discussion and interpretation
of the results after experimenting would have been neccessary. The major
problem was the lack of time. We had only 50 minutes per lesson for explaning
and doing the experiments. Therefore the discussion and interpretation
of the results often had to be deligated to the next lesson. That turned
out to be a loose of actuality. A further problem could be the large
number of students (~ 30 pupils) in regular science classes. In our project
we had only small groups of 10 to 16 students. However, also in this
"ideal" situation an additional person was helpful, e.g. when
problems with the calculators occured or explanations of mathematical
relations were neccessary. Working in chemical and physical laboratories
using new technology forced interdisciplinary thinking by the students.
The role
of a teacher is going to be changing. Instead of presenting well prepared
knowledge he has to assist students during their work. Using new technology
it is impossible for teachers to master all occuring situations. Sometimes
students know more than their teachers. It was quite
easy for the students to get familiar with the CBL and to apply the CHEMBIO
program on the TI-92. However, for further mathematical manipulation
of experimental data the students had to learn more about the handling
of data-matrices, plotting graphs, defining functions, determining regressions
curves etc. This required a detailed introduction of handling the TI-92.
This could have been skipped in our project, if the students would have
used the TI-92 in regular math lessons. A second obstacle was the simplicity
of the CHEMBIO program. It was easy to handle the program for the students,
if they did not make any mistakes. However, the program was not "fault
tolerant". If the students had entered a wrong value or selected
an inappropriate submenue it was very difficult to leave the program or
to correct the wrong inputs. It was new
for the students to work in groups. They had to learn to dedicate work
to different group members according to their abilities. The second problem
was the acceptance of a unique grade for the whole group. Finally, it
was quite difficult to find a fair grading for the students according
to their individual achievements. |
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References | |
[Gardner
1993] [Holmquist,
Randall, Volz 1998] |