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.

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 effects of sequence context on DNA curvature.

Recent experiments have exposed significant discrepancies between experimental data and predictive models for DNA structure. These results strongly suggest that DNA structural parameters incorporated in the models are not always sufficient to account for the influence of sequence context and of specific ion effects. In an attempt to evaluate these two effects, we have investigated repetitive DNA sequences with the sequence motif GAGAG.CTCTC located in different helical phasing arrangements with respect to poly(A) tracts and GGGCCC.GGGCCC sequence motifs. Methods used are ligase-mediated cyclization and gel mobility experiments along with DNase I cutting and chemical probe studies. The results provide new evidence for curvature in poly(A) tracts. They also show that the sequence context in which bending and flexible sequence elements are found is an important aspect of sequence-dependent DNA conformation. Although dinucleotide models generally have good predictive power, this work demonstrates that in some instances sequence elements larger than the dinucleotide must be taken into account, and hence it provides a starting point for the appropriate modification and refinement of existing structural models for DNA.

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.

La identidad como producto del aprendizaje en la práctica de enseñar matemáticas en profesores de primaria

Esta investigación estudia la identidad como producto del aprendizaje en la práctica situada de enseñar matemáticas de cuatro profesores de primaria en México. Las características de la identidad de “ser profesor de matemáticas” se infieren desde la trayectoria de formación y la práctica de los profesores. Los resultados indican que los profesores construyen y reconstruyen su identidad a partir de su práctica cotidiana lo que supone la negociación de maneras de realizar una práctica en un contexto a partir de tres aspectos: (i) El significado y sentido que los profesores atribuyen a las experiencias que acumulan en su trayectoria de formación, (ii) a la acción mediada con las tareas y los instrumentos que utilizan, y (iii) a la interacción entre el significado y sentido y la acción mediada al gestionar la clase de matemáticas.

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.

Do first-year university students understand the language of mathematics?

The aim of the project is to determine if the understanding of the language of Mathematics of students starting university is propitious to the development of an appropriate cognitive structure. The objective of this current work was to analyse the ability of first-year university students to translate the registers of verbal or written expressions and their representations to the registers of algebraic language. Results indicate that students do not understand the basic elements of the language of Mathematics and this causes them to make numerous errors of construction and interpretation. The students were not able to associate concepts with definitions and were unable to offer examples.

Earth’s Rotation: A Challenging Problem in Mathematics and Physics

A suitable knowledge of the orientation and motion of the Earth in space is a common need in various fields. That knowledge has been ever necessary to carry out astronomical observations, but with the advent of the space age, it became essential for making observations of satellites and predicting and determining their orbits, and for observing the Earth from space as well. Given the relevant role it plays in Space Geodesy, Earth rotation is considered as one of the three pillars of Geodesy, the other two being geometry and gravity. Besides, research on Earth rotation has fostered advances in many fields, such as Mathematics, Astronomy and Geophysics, for centuries. One remarkable feature of the problem is in the extreme requirements of accuracy that must be fulfilled in the near future, about a millimetre on the tangent plane to the planet surface, roughly speaking. That challenges all of the theories that have been devised and used to-date; the paper makes a short review of some of the most relevant methods, which can be envisaged as milestones in Earth rotation research, emphasizing the Hamiltonian approach developed by the authors. Some contemporary problems are presented, as well as the main lines of future research prospected by the International Astronomical Union/International Association of Geodesy Joint Working Group on Theory of Earth Rotation, created in 2013.

Mathematics notebook, ca. 1714-1718

This heavily illustrated notebook contains extensive notes on spheric triangles and spheric angles. These include rules and examples with their solutions.

Mathematics notebook, ca. 1714-1718, with chronology of the reign of Augustus

The first two pages of this notebook contain a comparative chronology of the reign of Augustus, outlined in two columns. One column outlines the chronology according to ecclesiastical scholar Laurence Echard, and the other column outlines the chronology according to William Cave. The rest of the notebook contains extensive entries on the following subjects, with related rules, problems, and illustrations: fractions, decimals, arithmetical progression, geometrical progression, "disjunct proportion, or ye Golden Rule," signs and symbols, integers, geometrical definitions, and Euclidian geometry.

Mathematics notebook : manuscript, 1782

With sections on numeration, surveying, trigonometry and other topics, accompanied by diagrams and hand-colored illustrations.