Mathematical modeling activity in Pre-service Teacher Education: A case of mathematical activity to discovery

In Colombia, the mathematical training of students in primary and secondary school has, among other purposes, to recognize the cultural diversity, the need for greater equity levels and individuals able to be have a critic position facing the different social and democratic requirements; hence the mathematical modeling has gained ground as a way to meet these education purposes and, therefore, it is suggested as one of the processes the mathematics curriculum must articulate. Such realities require the school mathematics to be developed in places consistent with the environment needs; in turn, this situation imposes the teachers and researchers challenges to reveal the nuances and characteristics the mathematical knowledge has in such environments. As a result of this situation, the view on school mathematics should not be focused only on knowledge as a result that must be acquired, but on the ways in which this knowledge can emerge. In that sense, we focused on the mathematical activity and we put our minds to develop a study that would allow us to understand some aspects of this activity when it is developed in mathematical modeling environments focused on the interests of modelers

Book Review: Love and Math: The Heart of Hidden Reality by Edward Frenkel

This review traces Edward Frenkel’s attempt to convey the excitement of mathematical research to a popular audience. In his expositions and explanations of his own research program, he shows how processes of mathematical discovery depend on the juxtaposition of various iconic and symbolic modes of representation as disparate fields of research are brought together in the service of problem solving. And he shows how crucial the encouragement of various older mathematicians was to his own development, as they guided his choice of problems, and served as inspiration

Mathematics is Art: The Impact of a Non-traditional Metaphor on Teacher Mindset and Instructional Practices in Mathematics

Many teachers hold the belief that one is either a “math person” or not, which impacts their mathematical mindset and instructional practices, and in turn impacts their students’ mindsets and learning experiences. Fostering the development of a mathematical mindset in teachers is critical to dispelling the “math person” myth. As we are metaphorical in nature (Lakoff & Johnson, 1980), the metaphors that we use to conceptualize mathematics are born out of and impact our experiences in its study and provide a means for eliminating this myth. In this mixed-methods study I sought to understand the metaphors that in-service elementary teachers use to conceptualize mathematics; how those metaphors impact their mindset and instructional practices; and the impact of professional development guided by the metaphor mathematics is art on their mindset and instructional practices in mathematics. I studied four in-service elementary teachers in a small rural district and collected data on teacher mathematical mindset, instructional practices, and metaphorical frameworks both before and after engaging the participants in professional development guided by the metaphor mathematics is art. The results suggest that elementary in-service teachers predominantly conceptualize mathematics through eight metaphors - mathematics is a destination, a product, a process, a discovery, human, lens, work, and art. The results also indicate that there may be a relationship between teachers’ metaphorical frameworks for mathematics and their mindset and instructional practices and that the combination of mathematics is a process, a discovery, human, and art as dominant metaphors may positively impact their mathematical mindset instructional practices

The Resolved and Unresolved Conjectures of R.D. Carmichael

Even before heading to Princeton University to work on his doctoral degree, Robert Daniel Carmichael started influencing the path of number theory in the 20th century. From his study of Euler\u27s totient function to his discovery of the first absolute pseudoprime, he set the stage for years of productive research. This talk will present a brief overview of Carmichael\u27s life, including his breadth of mathematical interests and his service on behalf of the Mathematical Association of America. It will focus mainly on his two most famous conjectures- which one has been settled, and which one remains open to this day

Mathematical investigations: A primary teacher educator's narrative journey of professional awareness

As a teacher educator, I used narrative inquiry to investigate my professional practice in working alongside pre-service primary teachers in mathematics education. One theme that emerged from this research was the exploration of narrative as a powerful means with which to pursue professional development. In this process I encountered, and subsequently changed, previously unknown personal beliefs about learning mathematics. A second theme focused on the value of mathematical investigations, for myself as a mathematical learner and for supporting pre-service teachers to develop their understandings of what it means to learn and teach mathematics

Forum Session at the First International Conference on Service Oriented Computing (ICSOC03)

The First International Conference on Service Oriented Computing (ICSOC) was held in Trento, December 15-18, 2003. The focus of the conference ---Service Oriented Computing (SOC)--- is the new emerging paradigm for distributed computing and e-business processing that has evolved from object-oriented and component computing to enable building agile networks of collaborating business applications distributed within and across organizational boundaries. Of the 181 papers submitted to the ICSOC conference, 10 were selected for the forum session which took place on December the 16th, 2003. The papers were chosen based on their technical quality, originality, relevance to SOC and for their nature of being best suited for a poster presentation or a demonstration. This technical report contains the 10 papers presented during the forum session at the ICSOC conference. In particular, the last two papers in the report ere submitted as industrial papers

Issues about the Adoption of Formal Methods for Dependable Composition of Web Services

Web Services provide interoperable mechanisms for describing, locating and invoking services over the Internet; composition further enables to build complex services out of simpler ones for complex B2B applications. While current studies on these topics are mostly focused - from the technical viewpoint - on standards and protocols, this paper investigates the adoption of formal methods, especially for composition. We logically classify and analyze three different (but interconnected) kinds of important issues towards this goal, namely foundations, verification and extensions. The aim of this work is to individuate the proper questions on the adoption of formal methods for dependable composition of Web Services, not necessarily to find the optimal answers. Nevertheless, we still try to propose some tentative answers based on our proposal for a composition calculus, which we hope can animate a proper discussion

Making Upper Division Mathematics Courses Relevant for Pre-Service Teachers

This article addresses the disconnect that in-service and pre-service secondary school teachers feel between the material presented in upper division mathematics courses and high school classroom practice. Two examples are given from an abstract algebra course in which this problem is addressed

Balancing classroom management with mathematical learning: Using practice-based task design in mathematics teacher education

In this paper we present the results from a study conducted in a UK institution in which 21mathematics pre-service teachers engage with two practice-based tasks featuring incidents where classroom management interferes with mathematical learning. We investigate their considerations when they make decisions in classroom situations and how these tasks can trigger their reflections on the teaching and learning of mathematics. In our analysis we used the constructs of social and sociomathematical norms (Cobb & Yackel, 1996) and Teaching Triad (Jaworski, 1994). Results indicate commendable norms pre-service teachers aspire to establish in their classroom, such as peer respect, value of discussion and investigative mathematical learning. However, they often miss the opportunity to engage students with metacognitive discussions and mathematical challenge as they focus on behavioural issues or endorse dichotomous and simplistic views of mathematical learning. We credit these tasks with allowing insight into pre-service teachers’ considerations and we propose their further implementation in teacher education programs