Visualization and Simulation at UiA, Orientation

Per Henrik Hogstad, UiA, Norway

Is it possible to find some special approaches that increase interest of mathematics?

Is it possible that digital tools with interactive visualizations and simulations can be of any help in teaching, learning and understanding mathematics?

A brief account of visualizations/simulations at UiA.


Demonstration of random variation in statistics courses.

Hans Petter Hornæs, HiG, Norway.

Most students have a fairly good understanding of the frequency interpretation of probability and of uniform probability. However, when neither of those apply, students find that the concept of probability is hard to understand.

For example, when quantifying uncertainty in statistical methods, the students struggle with more abstract concepts like level of significance and test power.

By using a random generator in a suitable computer program, one can artificially produce large amounts of data according to a model defined by the lecturer. In this way repetition of experiments can be mimicked, and the relevant probabilities will be reflected in the frequencies. In this presentation I will demonstrate examples of ways of doing this appropriate for demonstration in lectures or videos. Many students have responded that this clarifies the concepts, and that a few minutes spent on this is well worth the time it takes away from discussing theory and examples.

The choice of programming environment is not important, but I do this in the computer algebra system Maple, which our students have some familiarity with.


Mathematics and programming for technology students at NTNU

Marius Thaule , NTNU, Norway

Mathematics is one of the most important basic subjects in the technology education offered at NTNU. All technology students take several mathematics courses during their studies at NTNU. These courses are subject to change and development and have in recent years seen the inclusion of programming. The overall objective for the inclusion of programming in the mathematics courses (where this is natural) is threefold: (1) To raise the students' general competency of ICT tools in general. (2) To increase their understanding of mathematics through visualization and simulation. (3) To raise their interest in the mathematics. In my talk I will report on the status of a pilot project aimed at connecting mathematics and programming. The pilot project focuses on three mathematics courses consisting of Laplace transformation, Fourier series and transformation, partial differential equations and numerical mathematics. In particular, I will discuss what has so far been implemented, what we believe works and what does not work as well as our future plans for the continuation of the pilot project.


Some reflections on the impact of computers in science education

Knut Mørken, UiO, Norway

The word 'digital' has become a buzzword in education as in many other areas of society. Often it simply means that computers have a role as a 'wrapping' of the classical mathematics and science curriculum in the form of a learning management system (LMS), tool for producing illustrations, an advanced calculator etc. In this talk I will try to reflect more broadly on what digital competency in mathematics and the sciences may involve and discuss some of the implications for curriculum design.

SimReal Workshop

Per Henrik Hogstad, UiA, Norway

Experiences at UiA combining video lessons, streaming, video simulations, interactive simulations.

A new version of the visualization/simulation package (SimReal) at UiA is available for other universities and university colleges. New ideas include programming visualizations/simulations by the help of only a browser.

How can we build a resource package together?

A short workshop where the participants can try the ideas of SimReal at different levels.


How to connect sound, music, physics, mathematics and programming together

Erlend Thune and Trond Helge Richardsen, The Norwegian Centre for ICT in Education, Norway

In this workshop we show how we can use the web standard Javascript and the working draft WebAudio to generate sound. We show how a music teacher and a computer scientist/science teacher at the Norwegian Centre for ICT (Information and Communication Technology) in Education put their heads together to create a workshop connecting sound, music, physics, mathematics and programming together. We believe the project can be adapted into a connecting thread from the primary school to the university.

The project partly started out ask the following question: “What is the easiest way to make a computer make a sound?". Except from throwing the computer on the ground, this turned out to be a difficult question, especially if you wanted a platform independent answer. We found WebAudio to be the best answer.

Inspired by the SimReal project from the University of Agder, we look into how that project can be converted from Adobe Flash to HTML5. Could the SimReal platform be something pupils and students could contribute to through crowd sourcing?


MATHEMATICS AS LANGUAGE AND MEANING

Hans Herlof Grelland, UiA, Norway.

By using mathematics we can understand things in the world outside us that cannot be understood by other means. Thus, mathematics is about more than doing calculations, it can function as a language which expresses something, a meaning content, that cannot be expressed in other ways, for instance by ordinary language. This is most clearly demonstrated in modern physics, for instance in the theories of relativity and quantum mechanics. Here the mathematical language cannot be translated into ordinary language, and describes the world as something which cannot be imagined. I will show this by some examples, beginning with discussing how an ordinary sentence has meaning, and then considering how mathematics acquires meaning by being applied to the real world, taking examples from statics and modern physics. I will argue that using mathematics is a means for understanding, not just a tool for doing calculations.

A jump forward with mathematics and physics

André Heck, University of Amsterdam, The Netherlands

In this presentation I will discuss data acquisition, analysis, modelling and simulation of

(1) the falling of a chained object in the context of bungee jumping and

(2) the reverted spring pendulum in the context of bouncing gait. Both are examples of research done by upper secondary school students.

With the help of ICT, the level and methods of the work of the students turns out to be quite close to the type of work of researchers in the field of biomechanics.