Developing multiple - choice questions in mathematics

In this paper we wish to illustrate different perspectives used to create Multiple-Choice questions and we will show how we can improve these in the construction of math tests. As it is known, web technologies have a great influence on student’s behaviour. Based on an on-line project beginning at 2007 which has been contributing to help students on their individual work, we would like to share our experience and thoughts with colleagues who have a common concern when they have the task of constructing Multiple-Choice tests. We feel that Multiple-Choice tests play an important and a very useful supporting role in selfevaluation or self-examination of our students. Nonetheless, good Multiple–Choice Test Items are generally more complex and time-consuming to create than other types of tests. It requires a certain amount of skill. However, this skill maybe increases through study, practice and experience. This paper discusses a number of issues related to the use of Multiple-Choice questions, lists the advantages and disadvantages of this question format contrasting it with open questions. Some examples are given in this context.

How to teach mathematics with MOODLE

The aim of this article is to present a Project in the Oporto’s Institute of Accounting and Administration, which pretends to contribute for a change in the way of teaching and learning Mathematics. One of the main objectives of this project is to innovate the teaching and learning processes, exploring technologies as a pedagogical resource and to induce higher motivation to students, improve the rate of success and make available to students a set of materials adapted to their needs. This concern is justified due to the fact that students have a weak preparation, without consolidated basis. Since the year 2007/2008 the courses were adjusted to the Bologna process, which requires several changes in teacher’s and student’s roles, methodologies and assessment. The number of weekly classes has been reduced, so it was necessary to develop new strategies and methodologies to support the student. With the implementation of the Bologna Process in the Accounting degree, we felt a great need to provide other types of activities to students. To complement our theoretical and practical classes we have developed a project called MatActiva based on the Moodle platform offered by PAOL - Projecto de Apoio On-Line (Online Support Project). Moodle allows us to use the language TEX to create materials that use mathematical symbols. Using this functionality, we created a set of easy to use interactive resources. In MatActiva project, the students have access to a variety of different materials. We have followed a strategy that makes the project compatible with the theoretical and practical subjects/classes, complementing them. To do so, we created some resources, for instance multiple-choice tests, which are the most accessed by the students. These tests can be realized and corrected on-line and for each wrong answer there is a feedback with the resolution. We can find other types of resources: diagnostic tests, theoretical notes. There are not only the pre-requirements for subjects mathematics, but also materials to help students follow up the programs. We also developed several lessons. This activity consists of a number of pages, where each page has contents and leads to other pages, based on the student's progress. The teacher creates the choices and determines the next page that the student will see, based upon their knowledge. There is also an area of doubts, where the students can place all the mathematical doubts they have, and a teacher gives the answers or clues to help them in their work. MatActiva also offers an area where we can find some humour, curiosities, contests and games including mathematical contents to test the math skills, as well as links to pages about mathematical contents that could be useful for the study. Since ISCAP receives ERASMUS students and some of them attend mathematics, we developed some materials in English, so they can also use MatActiva. The main objectives of our project are not only to bring success in the subjects of mathematics, but also to motivate the students, encourage them to overcome theirs difficulties through an auto-study giving them more confidence and improve their relationship with the mathematics as well as the communication between students and teachers and among students.

Using neural networks and support vector regression to relate marchetti dilatometer test parameters and maximum shear modulus

In the last two decades, small strain shear modulus became one of the most important geotechnical parameters to characterize soil stiffness. Finite element analysis have shown that in-situ stiffness of soils and rocks is much higher than what was previously thought and that stress-strain behaviour of these materials is non-linear in most cases with small strain levels, especially in the ground around retaining walls, foundations and tunnels, typically in the order of 10−2 to 10−4 of strain. Although the best approach to estimate shear modulus seems to be based in measuring seismic wave velocities, deriving the parameter through correlations with in-situ tests is usually considered very useful for design practice.The use of Neural Networks for modeling systems has been widespread, in particular within areas where the great amount of available data and the complexity of the systems keeps the problem very unfriendly to treat following traditional data analysis methodologies. In this work, the use of Neural Networks and Support Vector Regression is proposed to estimate small strain shear modulus for sedimentary soils from the basic or intermediate parameters derived from Marchetti Dilatometer Test. The results are discussed and compared with some of the most common available methodologies for this evaluation.

Using neural networks and support vector regression to relate marchetti dilatometer test parameters and maximum shear modulus

In the last two decades, small strain shear modulus became one of the most important geotechnical parameters to characterize soil stiffness. Finite element analysis have shown that in-situ stiffness of soils and rocks is much higher than what was previously thought and that stress-strain behaviour of these materials is non-linear in most cases with small strain levels, especially in the ground around retaining walls, foundations and tunnels, typically in the order of 10−2 to 10−4 of strain. Although the best approach to estimate shear modulus seems to be based in measuring seismic wave velocities, deriving the parameter through correlations with in-situ tests is usually considered very useful for design practice.The use of Neural Networks for modeling systems has been widespread, in particular within areas where the great amount of available data and the complexity of the systems keeps the problem very unfriendly to treat following traditional data analysis methodologies. In this work, the use of Neural Networks and Support Vector Regression is proposed to estimate small strain shear modulus for sedimentary soils from the basic or intermediate parameters derived from Marchetti Dilatometer Test. The results are discussed and compared with some of the most common available methodologies for this evaluation.

A Spanish version of the short Mathematics Anxiety Rating Scale (sMARS)

The aim of this studywas to adapt and assess the psychometric properties of the Spanish version of the sMARS in terms of evidence of validity and reliability of scores. The sMARS was administered to 342 students and, in order to assess convergent and discriminant validity, several subsamples completed a series of related tests. The factorial structure of the sMARSwas analyzed by means of a confirmatory factor analysis and results showed that the three-factor structure reported in the original test fits well with the data. Thus, three dimensions were established in the test: math test, numerical task and math course anxiety. The results of this study provide sound evidence that demonstrates the good psychometric properties of the scores of the Spanish version of the sMARS: strong internal consistency, high 7-week testretest reliability and good convergent/discriminant validity were evident. Overall, this study provides an instrument that allows us to obtain valid and reliable math anxiety measurements. This instrument may be a useful tool for educators and psychologists interested in identifying individuals that may have a low level of math mastery because of their anxiety.

Utilising student profiles in mathematics course arrangements

This thesis develops a method for identifying students struggling in their mathematical studies at an early stage. It helps in directing support to students needing and benefiting from it the most. Thus, frustration felt by weaker students may decrease and therefore, hopefully, also drop outs of potential engineering students. The research concentrates on a combination of personality and intelligence aspects. Personality aspects gave information on conation and motivation for learning. This part was studied from the perspective of motivation and self-regulation. Intelligence aspects gave information on declarative and procedural knowledge: what had been taught and what was actually mastered. Students answered surveys on motivation and self-regulation in 2010 and 2011. Based on their answers, background information, results in the proficiency test, and grades in the first mathematics course, profiles describing the students were formed. In the following years, the profiles were updated with new information obtained each year. The profiles used to identify struggling students combine personality (motivation, selfregulation, and self-efficacy) and intelligence (declarative and procedural knowledge) aspects at the beginning of their studies. Identifying students in need of extra support is a good start, but methods for providing support must be found. This thesis also studies how this support could be taken into account in course arrangements. The methods used include, for example, languaging and scaffolding, and continuous feedback. The analysis revealed that allocating resources based on the predicted progress does not increase costs or lower the results of better students. Instead, it will help weaker students obtain passing grades.

The effect of calculators on the numerical problem-solving skills and attitudes of primary students towards mathematics /

The purpose of this study was to determine the effect that calculators have on the attitudes and numerical problem-solving skills of primary students. The sample used for this research was one of convenience. The sample consisted of two grade 3 classes within the York Region District School Board. The students in the experimental group used calculators for this problem-solving unit. The students in the control group completed the same numerical problem-solving unit without the use of calculators. The pretest-posttest control group design was used for this study. All students involved in this study completed a computational pretest and an attitude pretest. At the end of the study, the students completed a computational posttest. Five students from the experimental group and five students from the control group received their posttests in the form of a taped interview. At the end of the unit, all students completed the attitude scale that they had received before the numerical problem-solving unit once again. Data for qualitative analysis included anecdotal observations, journal entries, and transcribed interviews. The constant comparative method was used to analyze the qualitative data. A t test was also performed on the data to determine whether there were changes in test and attitude scores between the control and experimental group. Overall, the findings of this study support the hypothesis that calculators improve the attitudes of primary students toward mathematics. Also, there is some evidence to suggest that calculators improve the computational skills of grade 3 students.

Mathematics education in Europe : common challenges and national policies

Resumen basado en el de la publicaci??n

Adecuación curricular del diagnóstico y la evaluación en matemáticas = Curricular validity of assessment and evaluation instruments in mathematics.

Resumen basado en el del autor

TIMSS, PISA, IGLU y dem??s : raz??n y sinraz??n de los estudios internacionales de rendimiento escolar

Monogr??fico con el t??tulo: 'La experiencia del PISA en Alemania'. Resumen basado en el de la publicaci??n

Mathematics, computers in Mathematics, and gender : public perceptions in context. 'Matemáticas, ordenadores en Matemáticas y género : percepciones públicas en contexto'.

Resumen basado en el de la publicación

TIMSS 2003 : Evaluación Internacional de Matemáticas y Ciencias : Euskadi : Primer informe de resultados

Existe versión de esta obra en euskera, con el título “TIMSS 2003. Matematikaren eta Zientzien Nazioarteko Ebaluazioa. Euskadi. Emaitzen lehenengo txostena"

On the convergence of the no response test

The no response test is a new scheme in inverse problems for partial differential equations which was recently proposed in [D. R. Luke and R. Potthast, SIAM J. Appl. Math., 63 (2003), pp. 1292–1312] in the framework of inverse acoustic scattering problems. The main idea of the scheme is to construct special probing waves which are small on some test domain. Then the response for these waves is constructed. If the response is small, the unknown object is assumed to be a subset of the test domain. The response is constructed from one, several, or many particular solutions of the problem under consideration. In this paper, we investigate the convergence of the no response test for the reconstruction information about inclusions D from the Cauchy values of solutions to the Helmholtz equation on an outer surface $\partial\Omega$ with $\overline{D} \subset \Omega$. We show that the one‐wave no response test provides a criterion to test the analytic extensibility of a field. In particular, we investigate the construction of approximations for the set of singular points $N(u)$ of the total fields u from one given pair of Cauchy data. Thus, the no response test solves a particular version of the classical Cauchy problem. Also, if an infinite number of fields is given, we prove that a multifield version of the no response test reconstructs the unknown inclusion D. This is the first convergence analysis which could be achieved for the no response test.

A multiwave range test for obstacle reconstructions with unknown physical properties

We develop a new multiwave version of the range test for shape reconstruction in inverse scattering theory. The range test [R. Potthast, et al., A ‘range test’ for determining scatterers with unknown physical properties, Inverse Problems 19(3) (2003) 533–547] has originally been proposed to obtain knowledge about an unknown scatterer when the far field pattern for only one plane wave is given. Here, we extend the method to the case of multiple waves and show that the full shape of the unknown scatterer can be reconstructed. We further will clarify the relation between the range test methods, the potential method [A. Kirsch, R. Kress, On an integral equation of the first kind in inverse acoustic scattering, in: Inverse Problems (Oberwolfach, 1986), Internationale Schriftenreihe zur Numerischen Mathematik, vol. 77, Birkhäuser, Basel, 1986, pp. 93–102] and the singular sources method [R. Potthast, Point sources and multipoles in inverse scattering theory, Habilitation Thesis, Göttingen, 1999]. In particular, we propose a new version of the Kirsch–Kress method using the range test and a new approach to the singular sources method based on the range test and potential method. Numerical examples of reconstructions for all four methods are provided.