Curriculum Interventions for Area Measurement Instruction to Enhance Children’s Conceptual Understanding

This study examined the effectiveness of 3 curriculum interventions focused on strengthening children’s ability to solve area measurement problems and explored the instructional perspectives of the instructor who implemented the interventions. The interventions involved various degrees of emphasis on area measurement and knowledge of 2-dimensional geometry. Participants were 131 fourth graders, recruited from a city in northern Taiwan, and 1 instructor. The results confirmed the effectiveness of an enriched curriculum integrating knowledge of 2-dimensional geometry in enhancing children’s conceptual understanding of area measurement. The group that received the enriched curriculum outperformed the other groups that received the curricula stressing only 2-dimensional geometry or numerical calculations for area measurement in solving the area problems requiring mathematical judgments and explanations. The curriculum also facilitated children’s reasoning in distinguishing between the perimeter and area of a rectangle, which required higher-order mathematical thinking. Interview data revealed that approximately all children from the 3 intervention groups could identify the mathematical subject-matter components highlighted in the curricula. Interviewees tended to consider the use of formulae to solve area measurement problems to be important, despite some differences in learning gains among the 3 groups. In interviews, the participating instructor revealed a change of perspective regarding the importance of offering students opportunities for manipulation and geometric operations when teaching area measurement, prompted by curriculum enactment.     

Gödel’s proof

In 1931, the great Austrian mathematician Kurt Gödel proved “all consistent axiomatic formulations of number theory include undecidable propositions”. This discovery of Gödel and its proof had enormous repercussions in mathematics and computer science. The proof hinged upon the writing of a self-referential mathematical statement, in the same way as the liar’s paradox — I am lying — is a self-referential statement. In this three-part article, we describe Gödel’s discovery and his famous proof.     

Transmission line realization of subwavelength resonator formed by a pair of conventional and LHM slabs

INTRODUCTION Left-handed materials (LHMs), first investigated theoretically by Veselago (1968), have received sub- stantial attention in the scientific and engineering communities. The unique properties of these meta- materials are promising for a diversity of microwave applications, such as new types of beam steerers, modulators, filters, superlens (Pendry, 2000), cou- plers and antenna radoms (Smith et al., 2004). Re- cently, a transmission line (TL) approach has been successfully in…     

He Asked Me What!?—Using Shared Online Accounts as Training Tools for Distance Learning Librarians

ABSTRACT

This study explores the idea of creating a knowledge base from shared online accounts to use in training librarians who perform distance reference services. Through a survey, follow-up interviews and a case study, the investigators explored current and potential use of shared online accounts as training tools. This study revealed that the participants viewed the concept positively, but many encountered barriers to effectively employing a local knowledge base as a training tool.     

I am sailing—towards a transactional analysis of ‘body techniques’

In recent years there has been a growing interest in questions related to embodiment and learning. Within the field of ‘body pedagogics’ great efforts have been made to develop theory and methodology that can deal with the corporeal aspects of experience and knowledge without adopting any form of dualistic conceptions of body/mind and organism/environment. This article connects to this body of research. The purpose is to first present a synthesis of James' radical empiricism, Dewey's transactional understanding of experience and learning and Marcel Mauss' concept of ‘body techniques’ and the notion of education embedded in it. Against the background of this theoretical development, and with a Transactional Model of Analyzing Bodying (TMAB), we then show how we can analytically come to terms with different dualistic problems that research into ‘body pedagogics’ has to deal with. We use an empirical example of dinghy sailing to create knowledge about what we learn when learning embodied knowledge, and how this learning takes place. We argue that experience is an important concept for understanding the acting knowing human being, describing how experience is organized and developed and outlining how this organization can be understood as learning. We hold that situations where someone learns to embody certain knowledge are cases of overt actions, in which we can see what kinds of relations are created and how these relations become meaningful for further action.     

The effect of acceleration signal processing for head impact numeric simulations

Brain injury research in sport employs a variety of physical models equipped with accelerometers. These acceleration signals are commonly processed using filters. The purpose of this research was to determine the effect of applying filters with different cutoff frequencies to the acceleration signals used as input for finite element modeling of the brain. Signals were generated from reconstructions of concussion events from American football and ice hockey in the laboratory using a Hybrid III headform. The resulting acceleration signals were used as input for the University College Dublin Brain Trauma Model after being processed with filters. The results indicated that using a filter with a cutoff of 300 Hz or higher had little effect on the resulting strain measures. In some cases there was some effect of the filters on the peak linear (8–30g) and rotational measures (1000–4000 rad/s²), but little effect on the finite element strain result (approximately 2–6 %). The short duration and high magnitude accelerations, such as the puck impact, were most affected by the cutoff frequency of different filters.