The concept of function is crucial to a great extent in modern mathematics and is considered a major barrier to many mathematics students. Students have difficulty interpreting information related to functions in general, and quadratic functions in particular. Quadratic Function is one of the topics which are covered in a course which is compulsory for a large number of students in the General Education Program of Zayed University. This program leads to different majors, including Mathematics Education, Business, Information Technology, and other majors. The challenge in teaching Quadratic Function in a course like this is mostly based on the fact that many students think that Quadratic Function is a difficult topic to understand and learn, and some teachers would agree with them that it is difficult to teach. In this paper, I demonstrate real world problems aimed to improve the students understanding of Quadratic Functions; life problems on this topic support developing student’s knowledge, critical thinking, quantitative reasoning, and analytical skills. This paper also includes examples of the techniques used with graphing of quadratic function, the algebra, and inverses of the same function. International move to improve mathematics curriculum have supported new goals for student’s learning which highlights problem solving skills, reasoning, ability to work in groups and individually, and use of technology. Knowing that information technology plays considerable role in achieving the above goals, teaching students the concept of Quadratic Functions can be smoothly achieved by using Information Technology in solving real world problems.

Curricula in concentrated educational systems are prepared from an upper-stream reference and hand over teachers’ disposal. Curricula in Iran are compiled in the so-called math curriculum development office and then put at the disposal of teachers. The researches in this regard show that such plans provide some resistance against executing it which are named teacher - proof programs, even it changed to some extent for accept ion, its execution is suspeciable. This research first explains how math books of middle grade were changed as a result of investigations on TIMSS result in year 1995. These investigation show Iranian Books are weakness in problem solving methods as Polya had said. And so curricula developers in Iran tried to integrate Polya\\\'s method in math books and changed curricula based these frame work. Then, it shows how teachers treated these changes. The finding of analyzing the data has been collected in this research through observations and interviews. It is intended that teachers resist against these changes. Finally according to this research, we suggest a model which we refer if it is used through concentrated educational system, we could expect teachers tolerance against the changes would be decreased and so compiled curricula further matched to executed curricula.

The discourse presented here is aimed at examining the justification of applications of current analysis to real world problems.

Cryptography fascinates people of all generations and is increasingly presented as an example for the relevance and application of the mathematical sciences. Indeed, many principles of modern cryptography can be described at a secondary school level. In this context, the mathematical background is often only sparingly shown. In the worst case, giving mathematics this character of a tool reduces the application of mathematical insights to the message ”cryptography contains math”. This paper examines the question as to what else cryptography can offer to mathematics education. Using the RSA cryptosystem and related content, specific mathematical competencies are highlighted that complement standard teaching, can be taught with cryptography as an example, and extend and deepen key mathematical concepts.

The network "Developing Quality in Mathematics Education II" is a continuation of the associated project "Developing Quality in Mathematics Education" (http://www.dqime.unidortmund. de). In this project participate universities, teacher education institutions and schools from 11 European countries. Cross-cultural cooperation and exchange of ideas, materials, teachers and pupils support developing quality in mathematics education, especially in the area of mathematical modelling. The quality and application of the developed learning materials is also guaranteed by using, comparing and modifying them in eleven different countries. This comparison leads to an agreement about contents of mathematical learning and teaching in eleven European countries. Thus we want to establish a "European Curriculum for the teaching and learning of mathematics" in the 21st century. A special feature of this project is the strong connection between theory and practice and between the research and development of mathematics education. In this project our Faculty of Mathematics, Physics and Informatics of Comenius University Bratislava manage testing of translated teaching materials at the high school „Gymnazium Sturovo“. We know that using ICT and didactical software in schools is almost present and wide spread. So we try to focus on several possibilities in solving real-life tasks using this technologies, regard to the fact technologies are hard upon the young generation of students.

Developing professional expertise of prospective teachers not only in terms of theoretical knowledge but also in terms of competencies of designing challenging and cognitively activating learning opportunities in the mathematics classroom is certainly one of the key aims of internship phases in pre-service mathematics teacher training. As mathematics-related theoretical contents of teacher training and practice-related learning opportunities of school internships are not always linked in an optimal way, this paper aims at discussing a model of an intensive internship phase combined with a triple coaching approach partly integrated in a course accompanying the internship phase.

The purpose of this paper is to compare curriculum documents for K-12 education from the state of North Carolina from two time periods, 1920s and 2003. The historical development of the mathematics curriculum in North Carolina provides a snapshot of the shifts in mathematics teaching and learning. North Carolina, a state in the southeast of the United States, has had a statewide standard course over a period spanning more than eighty years. A document analysis of printed curriculum standards from allows a description of the mathematics concepts and tasks that were expected of students in those years. The analysis revealed stark contrasts in the focus of mathematics from a very computational emphasis to one of problem solving. The analysis also highlighted the understanding of algebraic concepts and ideas as an essential outcome of current mathematics programs.

This contribution describes an experiment carried out by a team within the ReMath (Representing Mathematics with Digital Media) European Project (http://remath.cti.gr). Within this project six digital dynamic artefacts (DDAs) have been developed, thirteen experiments have been planned (Artigue & al., 2007) and carried out, analysis of the collected data are still in progress. In this contribution, we focus on the case of the Aplusix DDA (http://aplusix.imag.fr), from the point in which the designers deliver their product to the team in charge of planning the experiment, up to the point in which the artefact is experimented within the ReMath project.

For many students, mathematics, traditionally thought to be difficult and dull, is often considered inaccessible, generating a negative attitude towards it. In order to encourage a positive attitude towards mathematics, we propose class practices that, through research activities, will lead the students to experiment a similar path to the one that has given, as a final product, a structured theory, so as to enhance their self-efficacy, give a correct vision of the discipline and stimulate positive emotions. This can be realized, for example, as a “laboratory activity” in which the students compare ideas, intuitions, arguments, and work together to obtain results, using their critical capabilities in a collaborative learning activity. A team of university professors and high school teachers has developed a laboratory activity that focuses on some properties of quadrilaterals. The activity has at any rate been experimented in different first biennium classes of some high schools and has obtained very good results.

The Comenius Network Project “Developing Quality in Mathematics Education II” funded by the European Commission consists of partners from schools, universities and teacher training centres from eleven European countries. One advantage of the project is the mutual exchange between teachers, teacher trainers and researchers in developing learning material. To support the teachers most effectively the researchers asked the teachers what they wanted the researchers to do. The answer was also a question: How can we identify (good) modelling tasks? A discussion ensued in the research group of this project which resulted in a list of descriptors characterising modelling tasks. This paper focuses on the theoretical background of mathematical modelling and will thereby substantiate the list of descriptors for modelling tasks.