A recurring question in science and engineering education is why the students do not link knowledge from theoretical classes to the real world met in laboratory courses.

Mathematical models and visualisations are widely used in engineering and engineering education. Very often it is assumed that the students are familiar with the mathematical concepts used. These may be concepts taught in high school or at university level. One problem, though, is that many students have never or seldom applied their mathematical skills in other subjects, and it may be difficult for them to use their skills in a new context. Some concepts also seem to be "too difficult" to understand.

One of these mathematical tools is to use Laplace Transforms to solve differential equations, and to use the derived functions to visualise transient responses in electric circuits, or control engineering. In many engineering programs at college level the application of the Laplace Transform is considered too difficult for the students to understand, but is it really, or does it depend on the teaching methods used?

When applying mathematical concepts during lab work, and not teaching the mathematics and practical work in different sessions, and also using examples varied in a very systematic way, our research shows that the students approach the problem in a very different way. It shows that by developing tasks consequently according to the Theory of Variation, it is not impossible to apply the Laplace Transform already in the first year of an engineering program.

The original aim of this thesis was to show:

- how students work with lab-tasks, especially concerning the goal to link theory to the real world
- how it is possible to change the ways students approach the task and thus their learning, by systematic changes in the lab-instructions

During the spring 2002 students were video-recorded while working with labs in Electric Circuits. Their activity was analysed. Special focus was on what questions the students raised, and in what ways these questions were answered, and in what ways the answers were used in the further activities.

This work informed the model ”learning of a complex concept”, which was used as well to analyse what students do during lab-work, and what teachers intend their students to learn. The model made it possible to see what changes in the lab-instructions that would facilitate students learning of the whole, to link theoretical models to the real world, through the labactivities.

The aim of the thesis has thus become to

- develop a model: The learning of a complex concept
- show how this model can be used as well for analysis of the intended object of learning as students activities during lab-work, and thus the lived object of learning
- use the model in analysis of what changes in instruction that are critical for student learning.

The model was used to change the instructions. The teacher interventions were included into the instructions in a systematic way, according to as well what questions that were raised by the students, as what questions that were not noticed, but expected by the teachers, as a means to form relations between theoretical aspects and measurement results. Also, problem solving sessions have been integrated into the lab sessions.

Video recordings were also conducted during the spring 2003, when the new instructions were used. The students' activities were again analysed. A special focus of the thesis concerns the differences between the results from 2002 and 2003.

The results are presented in four sections:

- Analysis of the students' questions and the teachers' answers during the lab-course 2002
- Analysis of the links students need to make, the critical links for learning
- Analysis of the task structure before and after changes
- Analysis of the students' activities during the new course

The thesis ends with a discussion of the conclusions which may be drawn about the possibilities to model and develop teaching sequences through research, especially concerning the aim to link theoretical models to the real world.