The use of new tools for mathematics at school wins increasingly Importance. It follows from this that they are consquences as well as on aims and contents of mathematics at school us like on methods in the lessons. It is not unusual, that students and parents and also university professors are to be feared, that the calculation competence is decreasing with the use of CAS. In the lesson should be showed a possible way to developing such competences in the beginning phase of the learning process in Algebra. The examples refer to a level of school mathematics for students in the middle school age. The methods tell apart phases with and without CAS and shows a didactic principles of mathematics lessons in the case of use of CAS handheld technology.

In this workshop, participants engaged with and reflected on authentic artifacts from data modeling projects related to the solar system and to deforestation that were completed by elementary students in grade 5 (average age 11). These authentic examples were used to ground a discussion of using a data modeling approach to help elementary students make sense of and meaningful integrated use of mathematics and science concepts and tools. School-based ways of helping teachers understand this approach in order to be able to use it in their classrooms were also discussed.

This paper addresses the idea that the successful of mathematics reform demands the support of the full educational community including school principals, parents, and students. One of the most important group that affect mathematics reform is school principals. A project related to modifying UAE principals’ perceptions of mathematics is presented. This project consists three steps. In the first step, principals’ perceptions of the nature of Mathematics and its learning and teaching were examined. Results showed that those principals possess many improper perceptions related to Mathematics. In the second step, a professional training program for promoting school principals\' understanding of the new vision of teaching and learning mathematics has developed. This training program comprises two integrated phases: Clarification and conviction, and implementations for principal’s role. It includes a package of paper documents, videotapes, discussion sessions, and group and individual activities. In the third step, the training program is applied on eight principals in UAE. An initial analysis of the qualitative data showed many positive improvements in principals’ perceptions of mathematics education.

Lesson study is known as an effective Japanese professional development approach for teachers, since 1999.After that, this approach used dramatically as a way for improving teaching and learning in classroom through many countries and by many researchers. Review the literature of lesson study show that there is one common effort between the researchers to apply this approach. That is to make local model for using this Japanese approach as a localized one to release the unavoidable challenges of applying the method of another educational culture. This paper first reviews the literature on lesson study as a way of teachers\' professional development, which has been conducted since Meiji Period in Japan and is conducting for today\'s teaching in classroom. Then it clarifies how Iranian mathematics teachers encountered with this method. Finally, the finding of this research addresses a general translated model of lesson study that is preferred to apply lesson study for Iranian culture of education.

Students today need to be taught not only the real life context of their mathematics lessons but also the historical context of the theory behind their mathematics lessons. Using history to teach mathematics, makes your lessons not only interesting but more meaningful to a large percentage of your students as they are interested in knowing the who, how and why about certain rules, theorems, formulas that they use everyday in class. Students are captivated by learning the history behind mathematicians, rules, etc. and therefore can link the lesson to something in history and a concept. Even learning the mathematics behind historical events motivates and interests them. They cannot get enough!

Spatial sense is an important ability in mathematics. Formula application is very different from spatial concept acquisition. But it is often observed that in schools students learn spatial concepts by memorizing instead of understanding. In the past academic year we had tried out and developed a series of learning activities based on van Hiele’s model for guiding learners to explore the cube and its cut sections. The ideas in origami, and mathematical modelling by manipulative as well as mathematical software are integrated into our study. This paper gives a brief account on our works. We start by presenting a sequence of math-rich learning tasks, followed by some related folding ideas and mathematical background analysis. Finally we round up our paper with a concise discussion on some major elements of our design based on the van Hiele learning phases.

This study engaged fourth and fifth graders in solving a set of proportional tasks with focused discussion and concept development by the teacher. In order to understand the students’ ability to generalize the concept, they were asked to write problems that reflected the underlying concepts in the tasks and lessons. A qualitative analysis of the student generated problems show that the majority of the students were able to generalize the concepts. The analysis allowed for a discussion of problems solving approaches and a rich description of how students applied multiplicative reasoning in composing mathematics problems. These results are couched in a discussion of how the students solved the proportional reasoning tasks.

There is a wide consensus that including mathematical modeling into the curricula is an important aim. A lot of attention has been spent on the realistic problems whereas their embedding in a classroom situation is less investigated so far, although the methodical arrangements are of major importance for initiating students’ activities. In this paper, the implementation of the modeling task “swimming pool” in mathematics education in two lessons is compared concerning learning arrangement and teaching methods in depth with respect to the students’ activities. Two videos about this implementation will be shown and discussed in this workshop. They are supposed to demonstrate in which different ways teachers engage in modeling. The aim is to show teachers, especially those without experience in teaching modeling, how modeling tasks can be implemented.

The need for developing mathematics curricula was clarified. Models of mathematics curriculum development in Egypt were identified as: \"Temporary Committees\" (TC), center of developing curriculum and educational materials (CDCEM), \"National conferences\" (NC) and \"Educational standards\" (ES). The advantages and disadvantages of each one of these models were evaluated. Then a new model was suggested covering the whole advantages of these models and avoiding their disadvantages.

This paper presents a qualitative study in which an attempt was made to extend the debate surrounding the use of real life contexts to make mathematics more meaningful and real. The study investigated Grade 8 learners’ knowledge of number, understanding of number concepts and the kinds of connections they make between number and the context in which number is used. An important aspect of the study’s methodological approach involved an examination of the comments that learners made about what they said they know about number. A response to the question: “Why is the number in the picture?” provided a framework for establishing how learners saw relationships between number and the context in which numbers are used. A face scenario with four questions was given to learners to elicit these relationships. Results pointed to the usefulness of real life contexts as tools that have a central role in uncovering what learners know about number and how they use that knowledge to understand situations that call for proficiency in mathematics.