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The subject matter of computer vision and pattern recognition can play a useful role in the education of mathematics for students in middle school. New standards in education call for new content relevant to students' lives, and new pedagogical methods involving construction, group work, discovery, and the use of new technology. The project "Mathematics Experiences Through Image Processing" at the University of Washington has developed software and learning activities that enable middle school and high school students to use mathematical tools and concepts to explore some exciting ideas of image processing. This paper describes these materials and discusses how the ideas of computer vision and pattern recognition can be integrated into the curriculum. Not only do we use 2D topics such as digital geometry and edge detection, but also 3D topics such as surface construction and stereogram generation.

Learning takes place over long periods of time that are hard to study directly. Even the learning experience involved in solving a challenging math problem in a collaborative online setting can be spread across hundreds of brief postings during an hour or more. Such long-term interactions are constructed out of posting-level interactions, such as the strategic proposition of a next step. This paper identifies a pattern of exchange of postings that it terms math proposal adjacency pair, and describes its characteristics. Drawing on the methodology of conversation analysis, the paper adapts this approach to investigating mathematical problem-solving communication and to the computer-mediated circumstances of online chat. Math proposals and other interaction methods constitute the collaborative group as a working group, give direction to its problem solving and help to sustain its shared meaning making or group cognition. Groups sustain their online social and intellectual work by building up longer sequences of math proposals, other adjacency pairs and a variety of interaction methods. Experiences of collaboration and products of group cognition emerge over time.

The Plenary Panel 3 at ICME-14 was especially devoted to the COVID-19 pandemic. Its goal was to review and reflect on the challenges raised by the pandemic, the responsibilities and roles for mathematicians and mathematics educators in this context, and to draw some lessons for the future. This text begins with the presentation of the panel and the four invited panelists. Then each panelist synthesizes her/his contribution to the panel, and we end by some lessons drawn from these contributions and the exchanges between the panelists and with the audience.

TSG-48 examined historical, current, and emerging trends as well as issues and experiences in research with/in/on multicultural environments, across four themes: theoretical perspectives, methodological perspectives, emergent perspectives, and knowledge mobilization perspectives.

Performance-Based Learning is an advanced teaching approach that emphasizes what students can do as a result of instruction. In other words, teachers cultivate and assess students’ competencies by requiring them to solve a problem or create something in real-life or simulated scenarios using their mathematical knowledge. Hangzhou Yungu School’s math teachers have designed three types of performance tasks: 1) daily-class performance tasks, which are small assignments used in one class, 2) unit performance tasks, which are used during a whole unit of instruction, and 3) multiple-unit performance tasks, which are long-term tasks that last among several related units. Performance tasks focus on competencies acquired in the learning process, assess how well students learn, and guide students to what they can do. Completing performance tasks in mathematics is an excellent deep learning process that meets the expectations of mathematical education. This article presents some cases of the above three performance tasks and provides several suggestions for future research directions.

The present lecture engages a speculative reading of “The Masters”, a science-fiction novel written by Ursula K. Le Guin to narrate a state where citizens are governed by the law of negating mathematics education. In this oppressive context, Le Guin crafts a collective whose desire to practice mathematics subverts the fear for death used as punishment for mathematical heresy. This allows to ponder into thinking as “negation” and “affirmation” and, consequently, to speculate two interweaved assemblages of mathematics education; first, the assemblage where negating mathematics enforces masculine knowledge enclosures and second, the assemblage of affirming the practice of mathematics as knowledge commons. The chapter contributes by rethinking of mathematics education as/for/with the commons and by discussing about speculation as an act of thinking.

We will explore the role of history as a resource through which students can gain experience with authentic mathematical modeling in scientific contexts i.e., when mathematical modeling is used as a research tool, a practice, to gain knowledge in other areas. Three modeling episodes from the 20^th century will be presented and analyzed with respect to modeling strategies, practices, items used in the modeling construction and cross-disciplinary epistemic issues — and an analytical framework for analyzing modeling episodes in scientific context will be presented. The framework will be discussed with respect to the modeling cycle in mathematics education, highlighting issues in the framework which are not featured explicitly in the modeling cycle. It will be illustrated how and in what sense history makes it possible to invite students into the work place of scientists that used and experimented with mathematical modeling as a research practice, i.e. its significance in creating such teaching and learning environments. Finally, the value of developing students’ historical awareness for preparing them for tertiary studies where mathematical modeling might play a role will be discussed.

I focus here on several aspects of cultures related to digital technologies and mathematics education. One first aspect is that any integration of digital technologies for mathematical (or other) teaching and learning creates and transforms the classroom culture. On the other hand, in order for learning to be meaningful through the use of digital technologies, these may need to be embedded in a certain “culture” that empowers students to engage pro-actively with those technologies. I present different types of teaching and classroom “cultures” that have been found when using digital technologies, how these impact mathematical learning, as well as different conditions and teacher-training opportunities for the use of digital technologies found in different countries, illustrating all of these with examples from my own experience and from literature. I discuss how the different conditions and access opportunities in different regions and cultures create digital gaps. Finally, I discuss what could be done to support teachers to create meaningful contexts and classroom cultures when integrating digital technologies within established school systems (but at the same time transforming these), so that these can empower learners (e.g., to “do mathematics”) and promote the construction of knowledge.

This article discusses some ways to combine software for interactive geometry and computer algebra, with an emphasis on using this software in teaching. Some arising mathematical problems and necessary software specific paradigms that have to be adjusted are considered, and solutions to these problems are presented. The article also highlights some of the aspects that drove the development of the mathematics software Cinderella.2, which integrates an interactive geometry software package, a physics simulation engine, and an all-purpose functional programming language.

Partisans of the constructivist approach to mathematics education, such as Brousseau or Chevallard, developed an accurate theoretical framework in which didactical systems are viewed in a systemic perspective. What they somewhat fail to draw, however, is a sharp distinction between role variables – concerning the roles played in the didactical interaction by the individual elements of the system (Student-Teacher-Knowledge) – and contextual variables – concerning the action on the learning process of the system as a whole.

Our research in progress on 2nd graders' word problem solving strategies applies the previous dichotomy to class management strategies adopted by teachers. Partial evidence collected so far points to the tentative conclusion according to which, contextual variables being equal, differences in teaching styles and methods may deeply reshape the role component of didactical systems. If we take into careful account this distinction, we can shed additional light into some hitherto unexplained phenomena observed in the literature.

There are several ways in which mathematics in school classrooms misses elements that are vital to mathematicians' practice. Here, we wish to emphasize processes such as selecting between or devising new representations, looking for invariances, observing extreme cases and typical ones to come up with conjectures, looking actively for counterexamples, estimating quantities, approximating terms, simplifying or generalizing problems to make them easier to address, building on answers to generate new questions for exploration, and so on. In terms of content area and the methodology of content creation, it may be hard to mirror the discipline of mathematics in the school classroom, but we suggest that bringing these processes into school classrooms is both feasible and desirable. This not only enriches school mathematics but can also help solve problems that are currently endemic to mathematics education: perceptions of fear and failure, and low participation. By way of illustration, we offer examples of classroom interactions that show such processes making for lively mathematical exploration.

We propose a review of the teaching of mathematics in Argentina based on the presence and evolution of problem-solving in textbooks for the secondary school. We also take into account the changes introduced by educational policies in curricular documents. The period selected (1950–2000) has significant influence on the current situation of teaching.

This chapter begins with a brief history of mathematics education in Brazil, contextualized within the socio-political and educational events in the country. Research in ethnomathematics and mathematical modeling provide the foundation for curriculum reform and teacher preparation initiatives that strive to achieve greater social justice and equity for Brazilian children.

Chile was one of the first countries in Latin America to develop formal institutions for teacher preparation and to establish graduate programs in mathematics and mathematics education. It is now going through a difficult stage of reevaluating the neoliberal economic policies that have led to a significant experiment in the privatization of education. Currently groups of mathematicians, mathematics educators, and other stakeholders are involved in far-reaching discussions and collaborations that hold the promise of leading to more equitable high-quality educational outcomes for the Chilean people.

This abbreviated history of Colombia's development as a modern nation highlights the role played by mathematics. From the Botanical Expedition in colonial times, to the present with its flourishing universities contrasting against an inefficient basic education system, it narrates the country's realizations while struggling against religious fanaticism and political violence.

A description of mathematics and its teaching in Costa Rica beginning in the nineteenth century is presented. It includes curricula, researchers, and practitioners (with special mention of foreign influences and individuals), educational institutions, reforms, and research in mathematics education. Perspectives on a recent ambitious school mathematics reform are elaborated.

This article presents an overview of the teaching of mathematics in Honduras throughout history. It tries to capture the events, personalities and institutions that have set standards in the conceptualization of mathematics and its teaching, recognizing turning points, demands and challenges of mathematics education in Honduras.

Mathematics and mathematics education in México has developed significantly since the twentieth century. Prior to that, only the academic practices of Spain or France were reproduced. Currently, there is a robust development of both disciplines. To illustrate this process, we give a historical background, from the Aztec and Mayan times to the Spanish subjugation, going through the struggle for independence until the present.

This article describes the history of mathematics and its teaching in Paraguay, from the founding of its first universities until the present. It tells how, in spite of isolated individual efforts, the country could not adjust to the rhythm of mathematical development in the region, with the result of falling behind. It also highlights the recent but promising creation of graduate programs, as well as an incipient but cohesive mathematical research activity.

In this chapter we present fundamental aspects of the history of mathematics in Perú — as an academic activity — begun at the National University of San Marcos. We highlight the importance of providing an adequate mathematical training for primary school teachers, and describe several initiatives that have been developed to address that, and to improve mathematics education in general, parallel to the development of mathematics in our country.