Establishing a new paradigm for teaching mathematics at engineering schools

This paper analyzes an ideal model of teaching, thinking after 5-10 years in Universities in the world. We propose the collaborative work for a fruitful learning. According with that, we expose some of our previous projects in this area and some ideas for the ?global education?, focused on the teaching and learning of mathematics to engineering students. Furthermore we explain some of our initiatives for implementing the "Bologna process?. Aspects related to the learning and assessments will be analyzed. The establishment of the new teaching paradigm has to change the learning process and we will suggest some possible initiatives for adapting the learning to the new model. The paper ends by collecting some conclusions.

Physics and Mathematics in the Engineering Curriculum: Correlation with Applied Subjects

This paper presents a study in which the relationship between basic subjects (Mathematics and Physics) and applied engineering subjects (related to Machinery, Electrical Engineering, Topography and Buildings) in higher engineering education curricula is evaluated. The analysis has been conducted using the academic records of 206 students for five years. Furthermore, 34 surveys and personal interviews were conducted to analyze the connections between the contents taught in each subject and to identify student perceptions of the correlation with other subjects or disciplines. At the same time, the content of the different subjects have been analyzed to verify the relationship among the disciplines.Aproper coordination among subjects will allow students to relate and interconnect topics of different subjects, even with the ones learnt in previous courses, while also helping to reduce dropout rates and student failures in successfully accomplishing the different courses.

Preliminary description of the cranium of Proteopithecus sylviae, an Egyptian late Eocene anthropoidean primate

Recent discovery of crania, dentitions, and postcrania of a primitive anthropoidean primate, Proteopithecus sylviae, at the late Eocene L-4l quarry in the Fayum, Egypt, provides evidence of a new taxonomic family of early African higher primates, the Proteopithecidae. This family could be part of the basal radiation that produced the New World platyrrhine primates, or it could be unrelated to any subsequent lineages. Although no larger than a small callitrichid or a dwarf lemur, this tiny primate already possessed many of the derived features of later anthropoids and was a diurnal and probably dimorphic species. In dental formula and other dental proportions, as well as in known postcranial features, Proteopithecus more nearly resembles platyrrhines than does any other Old World higher primate. The small size of the Proteopithecus cranium demonstrates that the defining cranial characteristics of Anthropoidea did not arise as a consequence of an increase in size during derivation from earlier prosimians.

Canine sexual dimorphism in Egyptian Eocene anthropoid primates: Catopithecus and Proteopithecus

Two very small late Eocene anthropoid primates, Catopithecus browni and Proteopithecus sylviae, from Fayum, Egypt show evidence of substantial sexual dimorphism in canine teeth. The degree of dimorphism suggests that these early anthropoids lived in social groups with a polygynous mating system and intense male–male competition. Catopithecus and Proteopithecus are smaller in estimated body size than any living primates showing canine dimorphism. The origin of canine dimorphism and polygyny in anthropoids was not associated with the evolution of large body size.

A brief survey of symmetry in mathematics

This paper presents a brief survey of the idea of symmetry in mathematics, as exemplified by some particular developments in algebra, differential equations, topology, and number theory.

The cranium of Parapithecus grangeri, an Egyptian Oligocene anthropoidean primate

A nearly complete skull of Parapithecus grangeri from the early Oligocene of Egypt is described. The specimen is relatively undistorted and is undoubtedly the most complete higher primate skull yet found in the African Oligocene, which also makes it the most complete Oligocene primate cranium worldwide. Belonging in superfamily Parapithecoidea, a group regarded by some as the sister group to all other Anthropoidea, this skull reveals important information about the radiation of stem anthropoideans. This cranium is about 15% larger than size estimates based on a fragmentary cranium of its contemporary and close relative Apidium phiomense. It is about the same size as that of the gray gentle lemur, Hapalemur griseus, or of platyrrhines such as the owl monkey, Aotus trivirgatus, or the titi monkey, Callicebus torquatus. Comparatively small orbits and size differences in jaws and teeth show it was both diurnal and dimorphic. This is the only specimen of the species that shows (from sockets) that there were four small upper incisors. Several mandibular specimens of the species establish that there were no permanent lower incisors and that the symphysis was fused. Like other early anthropoideans this species possessed a lower encephalization quotient and less-developed orbital frontality than later anthropoideans. There is full postorbital closure and fusion of the metopic suture, and the ectotympanic forms a rim to the auditory aperture. A probable frontal/alisphenoid contact is a potentially derived resemblance to Catarrhini. A proposed separate genus for the species P. grangeri is not sustained.

"Our Father Isaac": Reading the Sahidic Testament of Isaac in an Egyptian Monastic Context

This dissertation argues that the textual community of fourth or fifth century monastic Egypt read Testament of Isaac as an ascetical regimen in order to transform themselves into children of Isaac. T. Isaac highlights three particular dimensions of Isaac's character from the remembered tradition of Isaac that would have resonated in the Egyptian monastic context of the textual community - Isaac as priestly authority, Isaac as sacrifice, and Isaac as blind ascetic - to create a model for the new self that the textual community aimed to achieve. Two important ascetic practices in T. Isaac that the textual community was to perform were copying and reading T. Isaac. These two practices functioned as technologies of the self that helped the members of the textual community to transform their present subjectivity into a new self modeled on Isaac in T. Isaac.

Validation of the Item-Attribute Matrix in TIMSS-Mathematics Using Multiple Regression and the LSDM

The purposes of this study were (1) to validate of the item-attribute matrix using two levels of attributes (Level 1 attributes and Level 2 sub-attributes), and (2) through retrofitting the diagnostic models to the mathematics test of the Trends in International Mathematics and Science Study (TIMSS), to evaluate the construct validity of TIMSS mathematics assessment by comparing the results of two assessment booklets. Item data were extracted from Booklets 2 and 3 for the 8th grade in TIMSS 2007, which included a total of 49 mathematics items and every student's response to every item. The study developed three categories of attributes at two levels: content, cognitive process (TIMSS or new), and comprehensive cognitive process (or IT) based on the TIMSS assessment framework, cognitive procedures, and item type. At level one, there were 4 content attributes (number, algebra, geometry, and data and chance), 3 TIMSS process attributes (knowing, applying, and reasoning), and 4 new process attributes (identifying, computing, judging, and reasoning). At level two, the level 1 attributes were further divided into 32 sub-attributes. There was only one level of IT attributes (multiple steps/responses, complexity, and constructed-response). Twelve Q-matrices (4 originally specified, 4 random, and 4 revised) were investigated with eleven Q-matrix models (QM1 ~ QM11) using multiple regression and the least squares distance method (LSDM). Comprehensive analyses indicated that the proposed Q-matrices explained most of the variance in item difficulty (i.e., 64% to 81%). The cognitive process attributes contributed to the item difficulties more than the content attributes, and the IT attributes contributed much more than both the content and process attributes. The new retrofitted process attributes explained the items better than the TIMSS process attributes. Results generated from the level 1 attributes and the level 2 attributes were consistent. Most attributes could be used to recover students' performance, but some attributes' probabilities showed unreasonable patterns. The analysis approaches could not demonstrate if the same construct validity was supported across booklets. The proposed attributes and Q-matrices explained the items of Booklet 2 better than the items of Booklet 3. The specified Q-matrices explained the items better than the random Q-matrices.

Sex, sin and salvation : a case study of the narrative pictorial cycle of Saint Mary the Egyptian at Bourges Cathedral

This paper studies the narrative stained glass cycle of the Life of Saint Mary the Egyptian at Bourges Cathedral within the context of prevailing—and often conflicting--civil and ecclesiastical attitudes toward sex, sexual sin, and prostitution in early thirteenth century France. Although the Church maintained that sexual sin was mortal sin, civil records suggest the public was skeptical. Through the example of a penitent harlot, this window, both structurally and in thematic content, attempts to map a doctrinally appropriate path from sexual sin to purity of spirit—and salvation—through complete submission to the Church and its clergy.

Development of prospective mathematics teachers’ professional noticing in a specific domain: proportional reasoning

The aim of this research is to identify aspects that support the development of prospective mathematics teachers’ professional noticing in a b-learning context. The study presented here investigates the extent to which prospective secondary mathematics teachers attend and interpret secondary school students’ proportional reasoning and decide how to respond. Results show that interactions in an on-line discussion improve prospective mathematics teachers’ ability to identify and interpret important aspects of secondary school students’ mathematical thinking.

A structural model of cognitive-motivational variables as explanatory factors of academic achievement in Spanish Language and Mathematics

In recent years, several explanatory models have been developed which attempt to analyse the predictive worth of various factors in relation to academic achievement, as well as the direct and indirect effects that they produce. The aim of this study was to examine a structural model incorporating various cognitive and motivational variables which influence student achievement in the two basic core skills in the Spanish curriculum: Spanish Language and Mathematics. These variables included differential aptitudes, specific self-concept, goal orientations, effort and learning strategies. The sample comprised 341 Spanish students in their first year of Compulsory Secondary Education. Various tests and questionnaires were used to assess each student, and Structural Equation Modelling (SEM) was employed to study the relationships in the initial model. The proposed model obtained a satisfactory fit for the two subjects studied, and all the relationships hypothesised were significant. The variable with the most explanatory power regarding academic achievement was mathematical and verbal aptitude. Also notable was the direct influence of specific self-concept on achievement, goal-orientation and effort, as was the mediatory effect that effort and learning strategies had between academic goals and final achievement.

Mathematics Game e-Library for Elementary School, study case: Mexico

One of the most relevant subjects for the intellectual formation of elementary school students is Mathematics where its importance goes back to ancient civilizations and which its importance is underestimated nowadays. This phenomenon occurs in Mexico, where 63.1% of the total population of elementary school students between the third and sixth grade have insufficient/elemental level of mathematics knowledge. This has resulted in the need to use a new mechanism to complement student’s classroom learning. With the rapid growth of wireless and mobile technologies, the mobile learning has been gradually considered as a novel and effective form of learning due to it inherits all the advantages of e-learning as well as breaks the limitations of learning time and space occurring in the traditional classroom teaching. This project proposes the use of a Mathematics Game e-Library integrated by a set of games for mobile devices and a distribution/management tool. The games are developed for running on mobile devices and for cover the six competencies related with the mathematics learning approach established in Mexico. The distribution/management tool allows students to reach contents according to their needs; this is achieved through a core engine that infers, from an initial profile, the games that cover the user’s knowledge gaps.

The curricular value of mathematics in non-mathematics degree

Higher education should provide the acquisition of skills and abilities that allow the student to play a full and active role in society. The educational experience should offer a series of conceptual, procedural and attitudinal contents that encourage “learning to know, learning to do, learning to be and learning to live together”. It is important to consider the curricular value of mathematics in the education of university undergraduates who do not intend to study mathematics but for whom the discipline will serve as an instrumental. This work discusses factors that form part of the debate on the curricular value of mathematics in non-mathematics degrees.