This paper presents results of a two year study, at Master’s level, which was undertaken to investigate how two Grade 9 Arts and Culture teachers incorporated mathematics in their Arts and Culture lessons in their classrooms in South Africa. Data from concept mapping activities and subsequent interviews with both teachers were collected and analysed using typological methods of analysis. Data collected from the study revealed that teachers still continue to grapple with the notion of integration. Lack of proper training and insufficient teacher knowledge seem to be the challenging factors for teachers to navigate successfully through the notion of integrated teaching and learning. Drawing from the theory of situated learning, this paper argues that although integration between mathematics and Arts and Culture is desirable in teaching and learning, it is problematic in practice. The analysis from this study raises important pedagogical issues about the link between ‘integrated teaching’ and ‘teacher training-and-content knowledge’.

Modern Internet technologies open new possibilities in a wide spectrum of traditional methods, used in mathematical education. One of the areas, where these technologies can be efficiently used, is an organization of mathematical competitions. Contestants can stay in their schools or universities in different cities and even different countries and try to solve as many mathematical problems as possible and then submit their solutions to organizers through the Internet. Simple Internet technologies supply audio and video connection between participants and organizers in a time of the competitions.

In this workshop, we present a model of problem that we call Research Situation for the Classroom (RSC). The aim of a RSC is to put students in a role close to a mathematical researcher in order to make them work on mathematical thinking/skills. A RSC has some characteristics : the problem is close to a research one, the statement is an easy understandable question, school knowledge are elementary, there is no end, a solved question postponed to new questions... The most important characteristic of a RSC is that students can manage their research by fixing themselves some variable of the problem. So, a RSC is completely different from a problem that students usually do in France. For short : there is no final answer, students can try to resolve their own questions : a RSC is a large open field where many sub-problems exist; the goal for the students is not to apply a technique: the goal is, as for a researcher, to search. These type of situations are particularly interesting to develop problem solving skills and mathematical thinking. They can also let students discover that mathematics are “alive” and “realistic”. This workshop will be split into two parts. First, we propose to put people in the situation of solving a RSC to make them discover practically what is it. After, we present the model of a RSC and some results of our experimentations.

Several years of my experiences in the use of real-time experiments are now upgraded in order to enhance also the teaching of mathematics. The motion sensor device enables us to get real time x(t) and v(t) graphs of a moving object or person. We can productively use these graphs to introduce differentiation on visual level as well as to show the integration procedure. The students are fully involved in the teaching as they are invited to walk in front of the sensor. This approach motivates them by the realistic aspects of mathematical structures. The method could help to fulfill the credo of teaching: comprehension before computation. The steps of such an approach are explained and discussed in further detail below.

The transition from school to tertiary study of mathematics is rightly coming under increasing scrutiny in research. This paper employs Tall’s model of the three worlds of mathematical thinking to examine key variables in teaching and learning as they relate to this transition. One key variable in the transition is clearly the teacher/lecturer and we consider the perspectives of both teachers and lecturers on teaching related matters relevant to upper secondary and first year tertiary calculus students. While this paper deals with a small part of the data from the project, which aims to model the transition, the results provide evidence of similarities and differences in the thinking of teachers and lecturers about the transition process. They also show that each group lacks a clear understanding of the issues involved in the transition from the other’s perspective, and there is a great need for improved communication between the two sectors.

In this paper the project for 15-year-old students with the title Ancient Greece and Rome and the sub-title Is the Legacy of Ancient Greece and Rome really the Cradle of European Civilization? is introduced. It shows how to connect mathematics with art, history, physics, geography and philosophy by studying ancient Greek scientists and their achievements. Collaborative teaching is introduced. The major aim of the project was to show mathematics as a part of human civilization and to follow its development through history. Some topics from theory of numbers and geometry were studied. One part of the project was also a theatre performance, which should make the students aware of the difficulties of many dedicated mathematicians to find the answers to some problems from the ancient times.

The main aim of this contribution is to introduce the potential that modern information technologies open to authors converting a teaching material from a printed to an electronic version. The authors come out of their own experience and propose options that are suitable especially for creation of study materials in mathematics education. Among others the contribution presents the use of flash animations, java scripts and Computer Algebra Systems.

In mathematics the parameter is used as a special kind of a variable. The classification of the terms \"variable\" and \"parameter\" is often done by intuition and changes due to different situations and needs. The history of mathematics shows that these two terms represent the same abstract object in mathematics. In today´s mathematics, compared to variables, the parameter is declared as an unknown constant measure. This interpretation of parameters can be used in set theory for describing sets with an infinite number of elements. Due to this perspective the structure of vector spaces can be developed as a special structured set theory. Further, the concept of parameters can be seen as a model for developing mathematics education in linear algebra.

In recent years, the Internet has increasingly been used to provide significant resources for student to learn mathematics and to learn about mathematics, as well as significant resources for teachers to support these. Effective access to and use of these has been hampered in practice by limited facilities in schools and the limited experience of many mathematics teachers with the Internet for mathematical purposes. This paper offers models for understanding the effective use of Internet resources, based on typologies of resources for learning and teaching mathematics. Six categories of Internet resources for mathematics student use are identified: (i) Interactive resources; (ii) Reading interesting materials; (iii) Reference information; (iv) Communication; (v) Problem solving; and (vi) Webquests. Similarly, five categories of Internet resources for mathematics teacher use are identified: (i) Lesson preparation; (ii) Official advice and support; (iii) Professional engagement; (iv) Commercial activity and support; and (v) Local school web sites. The paper recognises that web resources can be used in a range of ways, including supporting both teaching and learning. The prospects for sound use of the Internet are briefly described in terms of these models of use.

For the past two decades, both pros and cons of calculus reform have been discussed. A question often asked is, “Has the calculus reform project improved students’ understanding of mathematics?” The advocates of the reform movement claim that reform-based calculus may help students gain an intuitive understanding of mathematical propositions and have a better grasp of the real-world applications. Nonetheless, many still question its effect and argue that calculus reform purges calculus of its mathematical rigor and poorly prepares students for advanced mathematical training. East Asian students often rank in the top 10 of TIMSS and PISA. However, out-performing others in an international comparison may not guarantee their success in the learning of calculus. Taiwanese college students usually have a high failure rate in calculus. The National Science Council of Taiwan therefore initiated several projects in 2008 for improving students’ learning in calculus. This paper provides a preliminary report on one of the projects, PLEASE, and discusses how it was planned to respond to the tenets of calculus reform movement.