Fold & Cut

This paper describes a method of constructing 3d fractal objects by stretching/folding about simple geometric objects. The history of fold/cut construction as related to Mathematics is explored. The major new contribution of this paper is to generalize the concept of folding and cutting paper to folding and cutting space

Using Lamina Emergent Mechanisms to Address Needs for a Space Environment

Technology that will be used in a space environment must meet certain design contraints. These include the ability to endure the harsh environment as well as be efficiently transported. The use of compliance in the design of space technologies addresses some of these issues. Compliant mechanisms are mechanisms which use the deflection of flexible members to achieve a particular motion or transmit energy. The use of deflection allows for the elimination of parts and thus reduces weight. A subset of compliant mechanisms is lamina emergent mechanisms (LEMs). They have a flat initial state with motion emerging from the fabrication plane. The purpose of this research was to identify design strategies for LEMs. We propose the use of origami and kirigami for the identification of design strategies since they are essentially LEMs

Paper folding for an active learning of mathematics: an experience with preservice teachers

Students are active individuals that build, modify and integrate ideas, interacting with the physical world, materials and other students. Furthermore, not all students learn in the same way, some learn better by seeing, others by listening, others by moving. So, we developed an exploratory study of qualitative nature, with elementary preservice teachers, where the emphasis was on a teaching approach based on problem solving, mathematical communication and collaborative work that involved the manipulation of a sheet of paper. We intended to identify the relevance of this approach with preservice teachers and what were the main difficulties revealed, related to the proposed tasks. Preliminary results allowed to identify several difficulties in terms of mathematical communication and the manipulation of the sheet of paper to solve a problem. However, they reacted positively to the tasks, expressing interest, motivation and recognition of its importance in mathematical learning at any level.Les étudiants sont des individus actifs, qui construisent, modifient et intègrent des idées, en interaction avec le monde physique, des matériaux et d’autres étudiants. En outre, tous n'apprennent pas de la même manière: certains apprennent mieux en regardant, d'autres en écoutant, d'autres en bougeant. Nous avons donc développé une étude exploratoire de nature qualitative, avec des futures instituteurs, promouvant une approche pédagogique basée sur la résolution de problèmes, la communication mathématique et le travail collaboratif impliquant la manipulation d’une feuille de papier. Nous voulions déterminer la pertinence de cette approche pour les futures enseignants et identifier les les principales difficultés révélées face aux tâches proposées. Les résultats préliminaires ont permis d'identifier plusieurs difficultés relevant de la communication mathématique et de la manipulation de la feuille de papier pour résoudre un problème. Cependant, les participants ont réagi positivement aux tâches, exprimant leur intérêt et motivation et reconnaissant leur importance pour l’apprentissage des mathématiques à tous les niveaux.publishe

A Study on the Boundary Conditions of 90° Paper Pop-up Structures

The design of a pop-up book or card has hitherto been labour intensive with tasks of trials and errors. The constructions of collapsible pop-up structures can be demanding and inefficient without adequate knowledge of their geometric properties. This paper examines the properties of creases in 90° pop-up structures. A 90° pop-up structure is one that erects fully when two adjacent base pages, on which it sits, are opened to a right angle. In particular, we define a boundary region for creating 90° pop-ups. Similarly, paper folds are able to achieve pop-up effects and can be integrated with 90° pop-up constructions. The development of these pop-up structures can be represented graphically. Through this study, a fundamental foundation for pop-up topology and geometry is built. This foundation would be vital for understanding the applications of pop-up making techniques. The mathematical relationships devised would be useful for developing computer-enhanced pop-up design.Singapore-MIT Alliance (SMA

Development of a low-profile planar sensor for the detection of normal and shear forces

Individuals with balance and mobility problems might benefit by the use of devices that detect small changes in ground reaction forces and potentially be used to assist movement. For maximum effectiveness, such sensors must measure pressure in all three dimensions. Impact and shear plantar force are essential variables in inverse dynamics reconstructions of the human joint force. Various force sensors have been proposed to monitor plantar forces of the human foot. Most of them have a single-axis measurement, and few are intended for monitoring normal and shear stress. This article proposes a low-cost, biocompatible triaxial piezoresistive sensor developed using simple fabrication techniques and inexpensive machinery. The sensor can detect pressures from 0-800kPa with high response and recovery with minimum hysteresis and repeatable results of over than 100 cycles

Investigating Preservice Mathematics Teachers’ Pedagogical Content Knowledge through Microteaching

The purpose of this study was to investigate how pre-service mathematics teachers’ pedagogical content knowledge was reflected in their microteaching. Twenty preservice secondary mathematics teachers participated in the study. The participants formed groups of two, three or four people of their choice, resulting in six groups in total. Each group designed and conducted a microteaching on a topic of their choice. The videotapes of the groups’ microteaching and their lesson plans constituted the data set for the study. We analyzed the data per the components of the pedagogical content knowledge framework outlined by various researchers. We found that the preservice mathematics teachers in general were knowledgeable about different instructional strategies and the curriculum about the topic of their microteaching, but their knowledge of learners was relatively poor. Implications for teacher education are discussed