Viktor Freiman

Research On and Activities For Mathematically Gifted Students

The aim of this Topical Survey is to give a brief overview of the current state of research on and activities for mathematically gifted students around the world, being of interest to educational researchers, research mathematicians, mathematics teachers, teacher educators, curriculum designers, doctoral students, and other stakeholders. The focal topics include empirical, theoretical and methodological issues related to the following themes: Nature of Mathematical Giftedness; Mathematical Promise in Students of Various Ages; Pedagogy and Programs that contribute to the development of mathematical talent, gifts and passion; and Teacher Education. Current and historical research and suggestions for new research paths are included in each category.

Visual Mathematics and Cyberlearning

This first book in the series will describe the Net Generation as visual learners who thrive when surrounded with new technologies and whose needs can be met with the technological innovations. These new learners seek novel ways of studying, such as collaborating with peers, multitasking, as well as use of multimedia, the Internet, and other Information and Communication Technologies. Here we present mathematics as a contemporary subject that is engaging, exciting and enlightening in new ways. For example, in the distributed environment of cyber space, mathematics learners play games, watch presentations on YouTube, create Java applets of mathematics simulations and exchange thoughts over the Instant Messaging tool. How should mathematics education resonate with these learners and technological novelties that excite them?

Visual Mathematics and Cyberlearning in View of Affordance and Activity Theories

How do new digital tools and environments affect mathematics learning of students who belong to the Net Generation? In order to explore the complexity of the use of multimedia and Internet to make mathematics teaching and learning more visual and cyber-oriented, our chapter reflects on an add-on value of the new developments in research and practice as discussed by contributing authors of the book. This meta-conceptual analysis of the variety of perspectives on visual mathematics and cyberlearning presented in different chapters of the volume is conducted through the lenses of the Activity Theory and Affordance Theory thus allowing for comprehensive connections of affordances of computational tools to the new structures of activity system in the digital era that make mathematics learning collaborative and self-directed, and increase opportunities of democratization, emergence of mathematical discourse, and multimodalities of embodied interactions.

The competencies demonstrated by farmers while adapting to climate change

World population growth, overconsumption of resources, competition among countries and climate change are putting significant pressure on agriculture. In Canada, changes in precipitation, the appearance of new pests and poor soil quality are threatening the prosperity of small farmers. What human competencies could facilitate citizens’ adaptation to climate change? The competencies displayed by six Canadian farmers were observed as they tried to improve the quality of their soil in order to increase its climate resilience. The farmers in the case study demonstrated a wide array of skills while adapting to climate change. Used to adjusting their farming practices to bad weather, the participants predicted that their already declining soil was very vulnerable to extreme events. They implemented some adaptations: planting forage radish and practicing more crop rotations. During the adaptation process, the farmers showed in-depth local and agricultural knowledge, critical thinking (which they used to assess the solutions), futures thinking and hindsight, identification and control of the variables affecting the crops, openness to novelty, collaboration, optimism and self-efficacy. The research, which results in the identification of competencies conducive to adaptation, leads to the recommendation of a few educational strategies to strengthen adaptive competencies when supporting citizens in a climate change adaptation process.

Technological Environments beyond the Classroom

This chapter discusses several options that technology can bring tomathematics teaching and learning, in providing access to many challenging virtual resources that become easily available to all learners. Recent studies point to new challenging learning opportunities that may be enhanced by technology by means of dynamic and interactive tools of modeling and experimenting. Finally, recent developments of flexible and sophisticated communication tools create numerous virtual spaces where people can meet, ask questions, discuss, and work collaboratively on challengingmathematical learning tasks.We present a broad view of existing worldwide practices and analyze concrete examples that deepen our understanding of the advantages and disadvantages related to integrating technology into challenging mathematical activities in and beyond the classroom. We conclude with several research paths that are opening in this relatively new field of study in mathematics education.

Human competences that facilitate adaptation to climate change: a research in progress

Purpose – For communities threatened by current or impending climate change, adaptation is becoming a necessity. Although little research has been done on human competences so far, this research shows that some appear to facilitate the adaptation process. The purpose of this multiple‐case study is to identify adaptive competences demonstrated by two groups of Canadian citizens: municipal employees in a coastal community and farmers.Design/methodology/approach – As part of workshops based on a problem solving process, the two groups analyzed the impacts of climate change in their field of work and geographical area, chose a problem related to these impacts, suggested and then implemented adaptation measures. The municipal employees worked on sea level rise, whereas the farmers focused on poor soil quality, which makes it vulnerable to bad weather.Findings – By thematically analyzing the verbatim transcripts of the workshops and by building narratives, the authors were able to identify similar adaptive comp...

Online Mathematical Competition: Using Virtual Marathon to Challenge Promising Students and to Develop Their Persistence

In our study, we looked for an insight into students’ persistence and success in coping with challenging mathematics beyond the school walls and curriculum. The data received from the competition Web site were analysed from two perspectives. First, we analyzed the relationship between success in solving the problems and their persistence in participation in the competition. We found that though many students were trying some of the problems at least once, a small group of students were engaged in the competition over a long period of time. These students, who we identify as persistent, were also more successful problem solvers and seemed to be less influenced by intermediate results when deciding to continue the marathon. Second, we focused on the solutions of the most persistent participants and analyzed which of the problems were the most difficult for them. Our findings enlighten directions in which virtual competitions can be improved in both content and design perspectives.RésuméDans notre étude, nous avons cherché à mieux comprendre la persévérance et le succès des étudiants lorsqu’il s’agit de résoudre des problèmes mathématiques hors du contexte scolaire et du curriculum. Nous avons analysé les données du site du concours à partir de deux points de vue différents. d’abord, nous nous sommes penchés sur les relations qui existent entre la capacité de résoudre les problèmes et la persévérance en termes de participation au concours. Nous avons ainsi constaté que, bien que de nombreux étudiants tentent de résoudre les problèmes au moins une fois, un petit groupe d’élèves participent au concours sur une période assez longue. Ces étudiants, que nous qualifions de persévérants, ont également un taux de réussite plus élevé pour ce qui est de la résolution de problèmes, et semblent moins affectés par un résultat moyen lorsqu’ils décident de poursuivre le marathon. Ensuite, nous avons centré notre attention sur les solutions proposées par les participants les plus persévérants et nous nous sommes concentrés en particulier sur les problèmes qui s’étaient avérés les plus difficiles. Nos résultats mettent en évidence certaines améliorations qu’on pourrait apporter à ce type de concours virtuel, aussi bien sur le plan des contenus que sur celui de leur conception.

Competencies Demonstrated by Municipal Employees During Adaptation to Climate Change: A Pilot Study

Since coastal communities are already subjected to the impacts of climate change, adaptation has become a necessity. This article presents competencies demonstrated by Canadian municipal employees during an adaptation process to sea level rise. To adapt, the participants demonstrated the following competencies: problem solving (highlighting components of the problem and identifying constraints), futures thinking, risk prediction, vulnerability analysis, local knowledge, planning, and communication. However, some competencies that could be potentially useful in adaptation were used less frequently by participants: developing solutions, knowledge of adaptation, math skills, hope, and self-efficacy.

Mathematically Gifted Students in Inclusive Settings

In many countries including Canada, an inclusive view of mathematics education aims to reach all students in mathematics classroom allowing everybody to make progress at her own pace. When we say ‘all students’, this also includes the gifted ones. Or, research shows that an appropriate mathematical provision for the most able students is still an unsolved task. For example Diezmann and Watters (2002) argue that in mathematics education, the focus is now put on numeracy with the emphasis on ‘minimums’ of mathematical capability and lacking of attention to the ‘maximums’.

Complex and Open-Ended Tasks to Enrich Mathematical Experiences of Kindergarten Students

At a very young age, some children already manifest unusually strong mathematical abilities that need to be fully developed and nurtured in school. The chapter investigates in what way a kindergarten curriculum can offer all students a richer mathematical experience by means of open-ended and complex tasks. Hence, I developed and implemented challenging activities for kindergarten students. The data collected during the experiment helped us examine learning opportunities within challenging situations in terms of the mathematics structures the kindergarten students create during such activities and the strategies they use. The chapter analyses how kindergarten students approach three challenging situations, showing a great variety in students’ authentic strategies and mathematical approaches. While some students struggle with increasing complexity of tasks but still remain engaged and try to overcome obstacles, others seem to exhibit more structured (in terms of mathematical relationships), systematic (in terms of problem-solving strategies), and abstract (in terms of mathematical symbolism) approaches. In addition, all students, even at a very young age, can benefit from a classroom culture of questioning, investigating, communicating, and reflecting on more advanced and meaningful mathematics that can help develop their mathematical mind.