Recreational Mathematics - Only For Fun?

In this paper, I explore recreational mathematics from two perspectives. I first study how the concept appears in educational policy documents such as standards, syllabi, and curricula from a selection of countries to see if and in what way recreational mathematics can play a part in school mathematics. I find that recreational mathematics can be a central part, as in the case of India, but also completely invisible, as in the standards from USA. In the second part of the report, I take an educational historical approach. I observe that throughout history, recreational mathematics has been an important tool for learning mathematics. Recreational mathematics is then both a way of bringing pleasure and a tool for learning mathematics. Can it also be a tool for social empowerment?

Patterns, mathematics and culture : the search for symmetry in Azorean sidewalks and traditional crafts

In the hustle and bustle of daily life, how often do we stop to pay attention to the tiny details around us, some of them right beneath our feet? Such is the case of interesting decorative patterns that can be found in squares and sidewalks beautified by the traditional Portuguese pavement. Its most common colors are the black and the white of the basalt and the limestone used; the result is a large variety and richness in patterns. No doubt, it is worth devoting some of our time enjoying the lovely Portuguese pavement, a true worldwide attraction. The interesting patterns found on the Azorean handicrafts are as fascinating and substantial from the cultural point of view. Patterns existing in the sidewalks and crafts can be studied from the mathematical point of view, thus allowing a thorough and rigorous cataloguing of such heritage. The mathematical classification is based on the concept of symmetry, a unifying principle of geometry. Symmetry is a unique tool for helping us relate things that at first glance may appear to have no common ground at all. By interlacing different fields of endeavor, the mathematical approach to sidewalks and crafts is particularly interesting, and an excellent source of inspiration for the development of highly motivated recreational activities. This text is an invitation to visit the nine islands of the Azores and to identify a wide range of patterns, namely rosettes and friezes, by getting to know different arts and crafts and sidewalks.

Mathematical education and interdisciplinarity : promoting public awareness of mathematics in the Azores

Mathematical literacy in Portugal is very unsatisfactory in what concerns international standards. Even more disturbingly, the Azores archipelago ranks as one of the worst regions of Portugal in this respect. We reason that the popularisation of Mathematics through interactive exhibitions and activities can contribute actively to disseminate mathematical knowledge, increase awareness of the importance of Mathematics in today’s world and change its negative perception by the majority of the citizens. Although a significant investment has been undertaken by the local regional government in creating several science centres for the popularisation of Science, there is no centre for the popularisation of Mathematics. We present our first steps towards bringing Mathematics to unconventional settings by means of hands-on activities. We describe in some detail three activities. One activity has to do with applying trigonometry to measure distances in Astronomy, which can also be applied to Earth objects. Another activity concerns the presence of numerical patterns in the Azorean flora. The third activity explores geometrical patterns in the Azorean cultural heritage. It is our understanding that the implementation of these and other easy-to-follow and challenging activities will contribute to the awareness of the importance and beauty of Mathematics.

Mathematics and fiber arts

Mathematics can be found all over the world, even in what could be considered an unrelated area, like fiber arts. In knitting, crochet, and counted-thread embroidery, we can find concepts of algebra, graph theory, number theory, geometry of transformations, and symmetry, as well as computer science. For example, many fiber art pieces embody notions related with groups of symmetry. In this work, we focus on two areas of Mathematics associated with knitting, crochet, and cross-stitch works – number theory and geometry of transformations.

Public and student awareness science: recreational science as a catalyst

When discussing the traditional and new missions of higher education (1996 Report to UNESCO of the International Commission on Education for the 21st Century) Jacques Delors stated that "Excessive attraction to social sciences has broken equilibrium of available graduates for workforce, thus causing doubts of graduates and employers on the quality of knowledge provided by higher education". Likewise, when discussing the progress of science and technology, the 1998 UNESCO World Conference on Higher Education concluded that "Another challenge concerts the latest advancements of Science, the sine qua non of sustainable development"; and that “with Information Technology, the unavoidable invasion of virtual reality has increased the distance between industrial and developing countries". Recreational Science has a long tradition all over the Educational World; it aims to show the basic aspects of Science, aims to entertain, and aims to induce thinking. Until a few years ago, this field of knowledge consisted of a few books, a few kits and other classical (yet innovative) ways to popularize the knowledge of Nature and the laws governing it. In Spain, the interest for recreational science has increased in the last years. First, new recreational books are being published and found in bookstores. Second the number of Science-related museums and exhibits is increasing. And third, new television shows are produced and new short science-based, superficial sketches are found in variety programs. However, actual programs in Spanish television dealing seriously with Science are scarce. Recreational Science, especially that related to physical phenomena like light or motion, is generally found at Science Museums because special equipment is required. On the contrary, Science related mathematics, quizzes and puzzles use to gather into books, e.g. the extensive collections by Martin Gardner. However, lately Science podcasts have entered the field of science communication. Not only traditional science journals and television channels are providing audio and video podcasts, but new websites deal exclusively with science podcasts, in particular on Recreational Science. In this communication we discuss the above mentioned trends and show our experience in the last two years in participating at Science Fairs and university-sponsored events to attract students to science and technology careers. We show a combination of real examples (e.g., mathemagic), imagination, use of information technology, and use of social networks. We present as well an experience on designing a computational, interactive tool to promote chemistry among high school, prospective students using computers ("Dancing with Bionanomolecules"). Like the concepts related to Web 2.0, it has been already proposed that a new framework for communication of science is emerging, i.e., Science Communication 2.0, where people and institutions develop new innovative ways to explain science topics to diverse publics – and where Recreational Science is likely to play a leading role

Recreational fishing and fishing policies in the Netherlands and Australia: A comparative review

This article compares fisheries management, environmental problems and policies of the Netherlands and Australia. From this comparison lessons can be learned for countries that experience economic growth and on increase of leisure activity. In both countries, conflicts between the user groups, e.g. commercial and recreational fishers, are identified and the ways in which policymakers deal with these problems are outlined. Often suggested tools to address these problems are decision-making procedures based on a holistic framework in which economic, sociocultural, political/institutional, ecological aspects are included in the decision framework. Recreational fishing is today often the dominant factor in the resolution of these matters because of the relative economic, social and political power of recreational fishers as a group.

Participation in recreational physical activity: Why do socioeconomic groups differ?

This qualitative study explored how influences on recreational physical activity (RPA) were patterned by socioeconomic position. Face-to-face interviews were conducted with 10 males and 10 females in three socioeconomic groups (N = 60). Influences salient across all groups included previous opportunities, physical health, social assistance, safety, environmental aesthetics and urban design, physical and health benefits, and barriers of self-consciousness, low skill, and weather/time of year. Influences more salient to the high socioeconomic group included social benefits, achieving a balanced lifestyle, and the barrier of an unpredictable lifestyle. Influences more salient to the high and mid socioeconomic groups included efficacy, perceived need, activity demands, affiliation, emotional benefits, and the barrier of competing demands. Influences more salient to the low socioeconomic group included poor health and barriers of inconvenient access and low personal functioning. Data suggest that efforts to increase RPA in the population should include both general and socioeconomically targeted strategies.

The effects of plantar fasciitis and pain on plantar pressure distribution of recreational runners

Background: Plantar fasciitis is the third most frequent injury in runners. Despite its high prevalence, its pathogenesis remains inconclusive. The literature reports overload as the basic mechanism for its development. However, the way that these plantar loads are distributed on the foot surface of runners with plantar fasciitis and the effects of pain on this mechanical factor has not yet been investigated. Therefore, the aim of this study was to evaluate and compare the plantar pressure distributions during running in runners with symptom or history of plantar fasciitis and runners without the disease. Methods: Forty-five recreational runners with plantar fasciitis (30 symptomatic and 15 with previous history of the disease) and 60 runners without plantar fasciitis (control group) were evaluated. Pain was assessed by a visual analogue scale. All runners were evaluated by means of the Pedar system insoles during running forty meters at a speed of 12(5%) km/h, using standard sport footwear. Two-way ANOVAS were employed to investigate the main and interaction effects between groups and plantar areas. Findings: No interaction effects were found for any of the investigated variables: peak pressure (P=0.61), contact area (P=0.38), contact time (P=0.91), and the pressure-time integral (P=0.50). Interpretation: These findings indicated that the patterns of plantar pressure distribution were not affected in recreational runners with plantar fasciitis when compared to control runners. Pain also did not interfere with the dynamic patterns of the plantar pressure distributions. (C) 2010 Elsevier Ltd. All rights reserved.

In-shoe plantar pressure distribution during running on natural grass and asphalt in recreational runners

The type of surface used for running can influence the load that the locomotor apparatus will absorb and the load distribution could be related to the incidence of chronic injuries. As there is no consensus on how the locomotor apparatus adapts to loads originating from running Surfaces with different compliance, the objective of this study was to investigate how loads are distributed over the plantar surface while running on natural grass and on a rigid surface-asphalt. Forty-four adult runners with 4 3 years of running experience were evaluated while running at 12 km/h for 40 m wearing standardised running shoes and Pedar insoles (Novel). Peak pressure, contact time and contact area were measured in six regions: lateral, central and medial rearfoot, midfoot, lateral and media] forefoot. The Surfaces and regions were compared by three ANOVAS (2 x 6). Asphalt and natural grass were statistically different in all variables. Higher peak pressures were observed on asphalt at the central (p < 0.001) [grass: 303.8(66.7) kPa; asphalt: 342.3(76.3) kPa] and lateral rearfoot (p < 0.001) [grass: 312.7(75.8) kPa: asphalt: 350.9(98.3) kPa] and lateral forefoot (p < 0.001) [grass: 221.5(42.9) kPa asphalt: 245.3(55.5) kPa]. For natural grass, contact time and contact area were significantly greater at the central rearfoot (p < 0.001). These results suggest that natural grass may be a Surface that provokes lighter loads on the rearfoot and forefoot in recreational runners. (C) 2008 Sports Medicine Australia. Published by Elsevier Ltd. All rights reserved.