S_SESSIONS_BROWSE_OVERVIEW
S_ADMIN_PAPERS_RESULTS_SESSION
Edu. Resources: Open Educational Resources in Mathematics (working group)
S_SESSIONS_BROWSE_TIME:
S_DATE_DOW_0, 28/Sep/2014:
11:00am - 1:00pm

S_SESSIONS_BROWSE_CHAIR: Paul Libbrecht
S_SESSIONS_BROWSE_ROOM: VSP 1.04
Von-Seckendorff-Platz 1 Room 1.04

S_SESSIONS_BROWSE_PRESENTATIONS

Adaptations to a DGS learning resource

Paul Libbrecht

University of Education Weingarten, Germany

Learning resources have been created to represent digital units of exchangeable materials that teachers and learners can "pull from" in order to support the learning processes. Leveraging the web, one can often find learning these resources; but what characteristics does it need in order to be easily exchangeable? Although several investigations have explored the ways to publish and, in particular, the ideal best practice to do so, few have considered realistic use cases, where the technical competency of the teacher is counterb

In this paper we consider a simple language-crossing situation which was stimulated by the i2geo.net platform. A learning resource has been re-purposed from a French context to a German context, from one school and its software reality to another (Cabri to DynaGeo, Windows French to Windows German, Google Earth to Google Maps), from one set of learners' competency to another.

In neighbouring fields, practices such as that of the PhET repository of physics simulations, which collects simulations as "center-points" of the learning resources' exchange process, while "scenarios" are satelite resources, are described as candidate sharing mechansims.

This need for adaptations is not uncommon. Until a large diversity in the available resources can be achieved and searched through, it will remain the mainstream practice of teachers that attempt to employ learning resources. However, quite an amount of learning resources' publishers do not make it fully possible. This research highlights a few learning resources' characteristics that support this, from the legal and technical point of views, from the ease of perception to the ease of adaptation.

Libbrecht-CADGME2014-149_a.pdf
Libbrecht-CADGME2014-149_b.pdf

The Use of Computers for Calculus Teaching

Sonia Barbosa Camargo Igliori, Marcio Vieira Almeida, Celina Abar

Pontifícia Universidade Católica, Brazil

This paper aims at analyzing the use of computers when teaching differentiability and continuity in real functions and real variable. The relation is approached in the case of a non-differentiable continuous function in the interval of straight lines. This example is found in an article written by David Tall and is used to evidence a way in which a computer helps the learning and teaching of concepts of Differential and Integral Calculus when didactic and meaningful materials are produced. Elements of Tall’s theory on the advantages of the use of computers in Education, as well as the historical importance of the development of an example of a continuous non-differentiable function are presented in this paper. Also, a case of a function defined as limit to a series of functions is explored. In addition, commands and tools which are available in the software named GeoGegra are presented. As a result, we present tools which will hopefully contribute to the practice as well as advancements in Mathematics Education at Higher Education level.
Igliori-CADGME2014-162_a.pdf
Igliori-CADGME2014-162_b.pdf

Using dynamic geometry in problem-based engineering courses

Světlana Tomiczková, Miroslav Lávička

University of West Bohemia, Czech Republic

It is a modern trend today when formulating the curriculum of a geometric course at the technical universities to start from a real problem originated in technical praxis and subsequently to define which geometric theories and which skills are necessary for its solving. Nowadays, interactive and dynamic geometry software plays a more and more important role in this scenario as it helps to think algorithmically, enables to discuss the solvability of the whole class of geometric problems from different point of views and mainly serves as a first step to variational geometry needed later in geometric modelling. This makes the teaching and learning process more efficient and also more interesting for students. In our contribution we will present this approach on several particular examples taken mainly from the courses for mechanical engineering, of course with emphasis on the application of dynamic geometry. All examples are characterized by a unique structure. First, we present a real engineering problem, then we subdivide it to a number of elementary sub-problems and finally we show how the curriculum and the corresponding teaching procedures are chosen to satisfy the goal to teach the students to solve the real-life problems. We will present our experience with the problem-based teaching of geometry using dynamic geometry software and discuss some aspects of this approach.
Tomiczková-CADGME2014-160_a.pdf
Tomiczková-CADGME2014-160_b.zip

Isogonal and isotomial transformations of a triangle

Péter Körtesi

University of Miskolc, Hungary

The median and symmedian lines, the centroid and the symmedian point of a given triangle present interesting properties. Part of these properties can be formulated in a more general context for isogonals and isotomials, based on the trigonometric and algebraic forms of the Ceva’s theorem.

In a triangle the isogonal of a line passing through one of the vertices of the triangle is a line symmetric to the bisector of the given angle. Similarly a line passing through one of the vertices of a triangle and its isotomial intersect the opposite side of the triangle in two points which are symmetric to the midpoint of the given side. It can be proven that the three isogonals, respectively isotomials of three concurrent lines which pass through the three vertices of the triangle, are concurrent as well. This property serves as definition for the isogonal respectively isotomial transformation, the image of a given point in this transformation will be the intersection point of the three isogonals, respectively isotomials of the three lines which pass through the given point and the vertices of the triangle. The lecture is aimed to present some of the properties of the isogonal and isotomial transformations, and to visualize them using GeoGebra.

Körtesi-CADGME2014-164_b.zip