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.

Evaluation of online tools as didactic resource in the university education

Recently, many efforts have been made in the academic world to adapt the new degrees to the new European Higher Education Area (EHEA). New technologies have been the most important factor to carry out this adaptation. In particular, the tools 2.0 have been spreading quickly, not just the Web 2.0, but even in all the educational levels. Nevertheless, it is now necessary to evaluate whether all these efforts and all the changes, carried out in order to obtain improved academic performance among students, have provided good results. Therefore, the aim of this paper is focused on studying the impact of the implementation of information and communication technologies (ICTs) in a subject belonging to a Master from the University of Alicante in the academic year (2010-2011). In special, it is an elective course called "Advanced Visual Ergonomics" from the Master of Clinical Optometry and Vision. The methodology used to teach this course differs from the traditional one in many respects. For example, one of the resources used for the development of this course is a blog developed specifically to coordinate a series of virtual works, whose purpose is that the student goes into specific aspects of the current topic. Next, the student participates in an active role by writing a personal assessment on the blog. However, in the course planning, there is an attendance to lessons, where the teacher presents certain issues in a more traditional way, that is, with a lecture supported with audiovisual materials, such as materials generated in powerpoint. To evaluate the quality of the results achieved with this methodology, in this work the personal assessment of the students, who have completed this course during this academic year, are collected. In particular, we want to know their opinion about the used resources, as well as the followed methodology. The tool used to collect this information was a questionnaire. This questionnaire evaluates different aspects of the course: a general opinion, quality of the received information, satisfaction about the followed methodology and the student´s critical awareness. The design of this questionnaire is very important to get conclusive information about the methodology followed in the course. The questionnaire has to have an adequate number of questions; whether it has many questions, it might be boring for the student who would pay no enough attention. The questions should be well-written, with a clear structure and message, to avoid confusion and an ambiguity. The questions should be objectives, without any suggestion for a desired answer. In addition, the questionnaire should be interesting to encourage the student´ s interest. In conclusion, this questionnaire developed for this subject provided good information to evaluate whether the methodology was a useful tool to teach "Advanced Visual Ergonomics". Furthermore, the student´s opinion collected by this questionnaire might be very helpful to improve this didactic resource.

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.