The Fiftieth Anniversary of the Institute of Mathematics and Informatics

In October 1997 we celebrate the fiftieth anniversary of the founding of the Institute for Mathematics and Informatics (IMI) of the Bulgarian Academy of Sciences (BAS).

Faculty of Mathematics and Informatics, Sofia University

The Faculty of Mathematics and Informatics (FMI) of Sofia University “St. Kliment Ohridski” is briefly presented as an educational and research institution. The possible contribution of FMI to KT-DigiCULT-BG project is analyzed.

Digitization of Old Mathematical Periodicals Published by the Institute of Mathematics and Informatics, Bulgarian Academy of Sciences

The digitization practice for retro-converting of the mathematical periodicals, published by the Institute of Mathematics and Informatics, Bulgarian Academy of Sciences (IMI-BAS) and the followed benefits for long-term preserving and assuring open access to these materials is discussed in the article.

An investigation of mathematics and science instruction in English and Spanish for English language learners

The contextual demands of language in content area are difficult for ELLS. Content in the native language furthers students' academic development and native language skills, while they are learning English. Content in English integrates pedagogical strategies for English acquisition with subject area instruction. The following models of curriculum content are provided in most Miami Dade County Public Schools: (a) mathematics instruction in the native language with science instruction in English or (b) science instruction in the native language with mathematics instruction in English. The purpose of this study was to investigate which model of instruction is more contextually supportive for mathematics and science achievement. ^ A pretest and posttest, nonequivalent group design was used with 94 fifth grade ELLs who received instruction in curriculum model (a) or (b). This allowed for statistical analysis that detected a difference in the means of .5 standard deviations with a power of .80 at the .05 level of significance. Pretreatment and post-treatment assessments of mathematics, reading, and science achievement were obtained through the administration of Aprenda-Segunda Edición and the Florida Comprehensive Achievement Test. ^ The results indicated that students receiving mathematics in English and Science in Spanish scored higher on achievement tests in both Mathematics and Science than the students who received Mathematics in Spanish and Science in English. In addition, the mean score of students on the FCAT mathematics examination was higher than their mean score on the FCAT science examination regardless of the language of instruction. ^

The development of a semantic model for the interpretation of mathematics including the use of technology

The semantic model developed in this research was in response to the difficulty a group of mathematics learners had with conventional mathematical language and their interpretation of mathematical constructs. In order to develop the model ideas from linguistics, psycholinguistics, cognitive psychology, formal languages and natural language processing were investigated. This investigation led to the identification of four main processes: the parsing process, syntactic processing, semantic processing and conceptual processing. The model showed the complex interdependency between these four processes and provided a theoretical framework in which the behaviour of the mathematics learner could be analysed. The model was then extended to include the use of technological artefacts into the learning process. To facilitate this aspect of the research, the theory of instrumentation was incorporated into the semantic model. The conclusion of this research was that although the cognitive processes were interdependent, they could develop at different rates until mastery of a topic was achieved. It also found that the introduction of a technological artefact into the learning environment introduced another layer of complexity, both in terms of the learning process and the underlying relationship between the four cognitive processes.

Perspectives of Teachers Regarding the Integration of Mathematics and Science at the Secondary School Level

The integration of mathematics and science in secondary schools in the 21st century continues to be an important topic of practice and research. The purpose of my research study, which builds on studies by Frykholm and Glasson (2005) and Berlin and White (2010), is to explore the potential constraints and benefits of integrating mathematics and science in Ontario secondary schools based on the perspectives of in-service and pre-service teachers with various math and/or science backgrounds. A qualitative and quantitative research design with an exploratory approach was used. The qualitative data was collected from a sample of 12 in-service teachers with various math and/or science backgrounds recruited from two school boards in Eastern Ontario. The quantitative and some qualitative data was collected from a sample of 81 pre-service teachers from the Queen’s University Bachelor of Education (B.Ed) program. Semi-structured interviews were conducted with the in-service teachers while a survey and a focus group was conducted with the pre-service teachers. Once the data was collected, the qualitative data were abductively analyzed. For the quantitative data, descriptive and inferential statistics (one-way ANOVAs and Pearson Chi Square analyses) were calculated to examine perspectives of teachers regardless of teaching background and to compare groups of teachers based on teaching background. The findings of this study suggest that in-service and pre-service teachers have a positive attitude towards the integration of math and science and view it as valuable to student learning and success. The pre-service teachers viewed the integration as easy and did not express concerns to this integration. On the other hand, the in-service teachers highlighted concerns and challenges such as resources, scheduling, and time constraints. My results illustrate when teachers perceive it is valuable to integrate math and science and which aspects of the classroom benefit best from the integration. Furthermore, the results highlight barriers and possible solutions to better the integration of math and science. In addition to the benefits and constraints of integration, my results illustrate why some teachers may opt out of integrating math and science and the different strategies teachers have incorporated to integrate math and science in their classroom.

Audit of mathematics learning support in Ireland in 2015 – the key findings

In 2015 the Irish Mathematics Learning Support Network (IMLSN) commissioned a comprehensive audit of the extent and nature of mathematics learning support (MLS) provision on the island of Ireland. An online survey was sent to 32 institutions, including universities, institutes of technology, further education and teacher training colleges, and a 97% response rate was achieved. While the headline figure – 84% of institutions that responded to the survey provide MLS – sounds good, deeper analysis reveals that the true state of MLS is not so solid. For example, in 25% of institutions offering MLS, only five hours per week (at most) of physical MLS are available, while in 20% of institutions the service is provided by only one or two staff members. Furthermore, training of tutors is minimal or non-existent in at least half of the institutions offering MLS. The results provide an illuminating picture, however, identifying the true state of MLS in Ireland is beneficial only if it informs developments in the years ahead. This talk will present some of the findings of the survey in more depth along with conclusions and recommendations. Key among these is the need for institutions to recognise MLS as a vital element of mathematics teaching and learning strategy at third level and devote the necessary resources to facilitate the provision of a service which can grow and adapt to meet student requirements.

Promotion and diffusion of tha career Bachelor and Licenciature of Mathematics Teaching in rural areas of Costa Rica project: effects and results

This article describes the purpose and activities of the project Promoting Mathematics Education in Rural Areas of Costa Rica. The activity has focused on two objectives. First, supporting and monitoring students who have expressed interest in studying a mathematics teacher. To achieve this, it has been working with students who have an ideal profile for the career, mainly from rural areas. The second objective is to conduct training workshops for high school in-service teachers, to strengthen and improve their knowledge in the area of mathematics. Among the results of the project, it can be highlighted a significant increase in the enrollment of students in the career of Mathematics Education in 2010 and 2011, and the training processes in the field of Real Functions of Real Variable and Geometry at different regional areas mostly rural as Aguirre, Sarapiquí, Coto, Buenos Aires, Limón, Cañas, Pérez Zeledón, Nicoya, Los Santos, Turrialba, Puriscal, Desamparados, San Carlos, Puntarenas, Limón, Liberia, Santa Cruz y Upala.

Closing Pandora's box: a defence of Alvin Plantinga's epistemology of religious belief

I argue (1) that Alvin Plantinga’s theory of warrant is plausible and (2) that, contrary to the Pandora’s Box objection, there are certain serious world religions that cannot successfully use Plantinga’s epistemology to demonstrate that their beliefs could be warranted in the same way that Christian belief can be warranted. In arguing for (1), I deploy Ernest Sosa’s Swampman case to show that Plantinga’s proper function condition is a necessary condition for warrant. I then engage three objections to Plantinga’s theory of warrant, each of which attempts to demonstrate that his conditions for warrant are neither necessary nor sufficient. Having defended the plausibility of Plantinga’s theory of warrant, I present and expand his key arguments to the effect that naturalism cannot make use of it. These arguments provide the conceptual tools that are needed to argue for (2): that there are certain world religions that cannot legitimately use Plantinga’s theory of warrant to demonstrate that their beliefs could be warranted in the same way that Christian belief can be warranted.

EXAMINING SECONDARY MATHEMATICS TEACHER CANDIDATES’ LEARNING AND ENACTMENT OF MATHEMATICS TEACHING PRACTICES: A MULTIPLE CASE STUDY

This qualitative case study explored three teacher candidates’ learning and enactment of discourse-focused mathematics teaching practices. Using audio and video recordings of their teaching practice this study aimed to identify the shifts in the way in which the teacher candidates enacted the following discourse practices: elicited and used evidence of student thinking, posed purposeful questions, and facilitated meaningful mathematical discourse. The teacher candidates’ written reflections from their practice-based coursework as well as interviews were examined to see how two mathematics methods courses influenced their learning and enactment of the three discourse focused mathematics teaching practices. These data sources were also used to identify tensions the teacher candidates encountered. All three candidates in the study were able to successfully enact and reflect on these discourse-focused mathematics teaching practices at various time points in their preparation programs. Consistency of use and areas of improvement differed, however, depending on various tensions experienced by each candidate. Access to quality curriculum materials as well as time to formulate and enact thoughtful lesson plans that supported classroom discourse were tensions for these teacher candidates. This study shows that teacher candidates are capable of enacting discourse-focused teaching practices early in their field placements and with the support of practice-based coursework they can analyze and reflect on their practice for improvement. This study also reveals the importance of assisting teacher candidates in accessing rich mathematical tasks and collaborating during lesson planning. More research needs to be explored to identify how specific aspects of the learning cycle impact individual teachers and how this can be used to improve practice-based teacher education courses.

e-Math Workshops : a forum for exchanging experiences of mathematics e-learning at university level

We report here about a series of international workshops on e-learning of mathematics at university level, which have been jointly organized by the three publicly funded open universities in the Iberian Peninsula and which have taken place annually since 2009. The history, achievements and prospects for the future of this initiative will be addressed.