### Presentation

#### Abstract

For over a decade, under the leadership of Maria Salett Biembengut, a research group on Mathematical Modelling in Education has been active at FURB/Fundação Universidade Regional de Blumenau. This gave origin to the *CREMM/Reference Center for Mathematical Modelling in Teaching*. The *Journal of Mathematical Modelling and Application* is the result of the international visibility of *CREMM* in this growing research area.

This new issue offers a variety of articles spanning several strands of mathematical modelling, coming from many parts of the world: Germany, Greece, Italy, Singapore and the USA. This broad coverage is evidence of the international reach of *CREMM* and of its journal.

Burkhard Alpers, of Aalen University of Applied Sciences, describes the results of a four-year project with engineering students, focusing on identifying the mathematical expertise and mathematical expectations of these students. The focus on the practice-oriented needs of mechanical engineers in their daily work allowed to recognize the ways mathematical concepts were used when the students worked on the tasks.

The article from Cinzia Bonotto, of the University of Padua, focuses on the relationship between mathematics in the workplace and scholastic Mathematics. She observes that in the workplace mathematics makes sophisticated use of elementary mathematics, while in the classroom we see elementary use of sophisticated mathematics. She discusses proposals to change the type of activity aimed at creating interplay between real world and mathematics with more realistic and less stereotyped problem situations; to change students’ conceptions, beliefs and attitudes as a result of changing teachers’ conceptions, beliefs and attitudes; to change classroom culture by establishing also new classroom socio-mathematical norms. She wants to show how these changes can be brought about at primary school level through classroom activities that are more easily related to the experiential world of the student and consistent with a sense-making disposition. The discussion draws on results of several teaching experiments. Then she proposes classroom activities favorable for these changes. She gives emphasis to the relations between modeling, problem posing and problem solving.

In a very original paper, Michael Gr. Voskoglou, of the Graduate Technological Educational Institute of Patras, presents the theory CBR/Case-Based Reasoning for problem-solving and learning in computers and people. Considering problem-solving in a wide sense, not restricted to finding a concrete solution to an application problem, he discusses the process of solving new problems as based on the solutions of similar past problems.

Chan Chun Ming Eric, of the National Institute of Education and Nanyang Technological University, in Singapore, uses a mixed-method design where both quantitative and qualitative data were collected and analyzed to investigate the interaction of students, task, and teacher. The interaction implies the generation of a discourse rich in mathematical and metacognitive thinking that sees students developing models through making conceptual and mathematical representations.

Daniel Clark Orey, from California State University, and Milton Rosa, from Encina Preparatory High School, both in Sacramento CA, raise the fundamental issue of respect for social diversity of distinct cultural groups through understanding different ways of doing mathematics. They propose ethnomodeling as a pedagogical approach that connects the diversity of cultural forms of mathematics, which serves as a strategy that allows educators to rethink how and what is taught, encouraging students to recognize that there is mathematics in their daily lives, not just the required formal curriculum.

For over a decade, under the leadership of Maria Salett Biembengut, a research group on Mathematical Modelling in Education has been active at FURB/Fundação Universidade Regional de Blumenau. This gave origin to the *CREMM/Reference Center for Mathematical Modelling in Teaching*. The *Journal of Mathematical Modelling and Application* is the result of the international visibility of *CREMM* in this growing research area.

This new issue offers a variety of articles spanning several strands of mathematical modelling, coming from many parts of the world: Germany, Greece, Italy, Singapore and the USA. This broad coverage is evidence of the international reach of *CREMM* and of its journal.

Burkhard Alpers, of Aalen University of Applied Sciences, describes the results of a four-year project with engineering students, focusing on identifying the mathematical expertise and mathematical expectations of these students. The focus on the practice-oriented needs of mechanical engineers in their daily work allowed to recognize the ways mathematical concepts were used when the students worked on the tasks.

The article from Cinzia Bonotto, of the University of Padua, focuses on the relationship between mathematics in the workplace and scholastic Mathematics. She observes that in the workplace mathematics makes sophisticated use of elementary mathematics, while in the classroom we see elementary use of sophisticated mathematics. She discusses proposals to change the type of activity aimed at creating interplay between real world and mathematics with more realistic and less stereotyped problem situations; to change students' conceptions, beliefs and attitudes as a result of changing teachers' conceptions, beliefs and attitudes; to change classroom culture by establishing also new classroom socio-mathematical norms. She wants to show how these changes can be brought about at primary school level through classroom activities that are more easily related to the experiential world of the student and consistent with a sense-making disposition. The discussion draws on results of several teaching experiments. Then she proposes classroom activities favorable for these changes. She gives emphasis to the relations between modeling, problem posing and problem solving.

In a very original paper, Michael Gr. Voskoglou, of the Graduate Technological Educational Institute of Patras, presents the theory CBR/Case-Based Reasoning for problem-solving and learning in computers and people. Considering problem-solving in a wide sense, not restricted to finding a concrete solution to an application problem, he discusses the process of solving new problems as based on the solutions of similar past problems.

Chan Chun Ming Eric, of the National Institute of Education and Nanyang Technological University, in Singapore, uses a mixed-method design where both quantitative and qualitative data were collected and analyzed to investigate the interaction of students, task, and teacher. The interaction implies the generation of a discourse rich in mathematical and metacognitive thinking that sees students developing models through making conceptual and mathematical representations.

Daniel Clark Orey, from California State University, and Milton Rosa, from Encina Preparatory High School, both in Sacramento CA, raise the fundamental issue of respect for social diversity of distinct cultural groups through understanding different ways of doing mathematics. They propose ethnomodeling as a pedagogical approach that connects the diversity of cultural forms of mathematics, which serves as a strategy that allows educators to rethink how and what is taught, encouraging students to recognize that there is mathematics in their daily lives, not just the required formal curriculum.

All together, the five articles points to the broad range of different styles of reasoning in different cultural settings.