Mathematically Able but Yet Underachieving in School Mathematics

Teacher observation has shown that some pupils achieve very high on the Kangaroo Competition test (KC) but very low on the Swedish National test in Mathematics (SNM). This study will investigate the number of pupils who have high achievement scores on the KC (top 10%) but low achievement scores on the SNM (bottom 50%). Individual results on the SNM given in grade 6 (age 12) will be compared to results on the KC given in grade 7; concerning approximately 700 individuals. Results will give an example of the quantity of mathematically able pupils who underachieve in School Mathematics in Sweden. Data interpretation will connect this study to international research concerning mathematical abilities and mathematical achievement among mathematically able pupils.

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.

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.

Pavimentações do plano : uma exploração com materiais manipulativos no 4º ano de escolaridade

Relatório de Estágio apresentado à Escola Superior de Educação do Instituto Politécnico de Castelo Branco para cumprimento dos requisitos necessários à obtenção do grau de Mestre em Educação Pré- Escolar e 1º Ciclo do Ensino Básico.

Knowledge and writing in school mathematics : a communicational approach

This thesis is about young students’ writing in school mathematics and the ways in which this writing is designed, interpreted and understood. Students’ communication can act as a source from which teachers can make inferences regarding students’ mathematical knowledge and understanding. In mathematics education previous research indicates that teachers assume that the process of interpreting and judging students’ writing is unproblematic. The relationship between what students’ write, and what they know or understand, is theoretical as well as empirical. In an era of increased focus on assessment and measurement in education it is necessary for teachers to know more about the relationship between communication and achievement. To add to this knowledge, the thesis has adopted a broad approach, and the thesis consists of four studies. The aim of these studies is to reach a deep understanding of writing in school mathematics. Such an understanding is dependent on examining different aspects of writing. The four studies together examine how the concept of communication is described in authoritative texts, how students’ writing is viewed by teachers and how students make use of different communicational resources in their writing. The results of the four studies indicate that students’ writing is more complex than is acknowledged by teachers and authoritative texts in mathematics education. Results point to a sophistication in students’ approach to the merging of the two functions of writing, writing for oneself and writing for others. Results also suggest that students attend, to various extents, to questions regarding how, what and for whom they are writing in school mathematics. The relationship between writing and achievement is dependent on students’ ability to have their writing reflect their knowledge and on teachers’ thorough knowledge of the different features of writing and their awareness of its complexity. From a communicational perspective the ability to communicate [in writing] in mathematics can and should be distinguished from other mathematical abilities. By acknowledging that mathematical communication integrates mathematical language and natural language, teachers have an opportunity to turn writing in mathematics into an object of learning. This offers teachers the potential to add to their assessment literacy and offers students the potential to develop their communicational ability in order to write in a way that better reflects their mathematical knowledge.

Avaliação do Processo de Ensino e Aprendizagem em Matemática: contribuições da teoria histórico-cultural

This article presents the results of a study that investigated the meaning of evaluation in mathematics from the historical cultural perspective, focusing on activity theory. In order to develop the investigation, a collaborative group was formed from the Oficina Pedagogica de Matematica de Ribeirao Preto - Sao Paulo (Math Pedagogic Workshop of Ribeirao Preto - OPM/RP), constituted of pre-school teachers and early elementary school teachers, who were participants in this research. The main role of the collaborative group was to offer guided development to the teachers about the teaching of mathematics from the historical-cultural perspective, aiming at collecting data on the process of appropriation of mathematical knowledge by the teachers. The syntheses about the teachers' learning process have contributed to systematize the guiding elements of evaluation in mathematics from the historical-cultural perspective.

Disciplinas de Fundamentos de Matemática: uma discussão à luz dos significados da palavra “fundamentos”

Based on a survey of summaries of courses on the Foundations of Mathematics, from Mathematics Teacher Education programs in the southern part of Brazil, and some remarks on the legislation related to the course syllabuses, we discuss the meaning of the word ""Foundations"" in order to reflect on the proposals of these issues in the courses, which will be undergoing reformulation. The opinions of students in one of these courses regarding the meaning of the term ""foundations"", as well as the data obtained from the survey and the remarks regarding legislation, may lead to considerations about the possibilities for a better qualification of the initial education of Mathematics teachers.

Do labor aos mitos: uma nova linha no mapa das pesquisas em Etnomatemática

In this paper we highlight the existence of a new line of research within the Ethnomathematics Program. In its origin, research in this area has sought to contribute to understanding regarding the diversity of mathematical thought through a careful look at work activities. In recent years, however, we have paid increasing attention to the affirmations of anthropologists that myths can be used to understand the most basic questions of human thought as well as specific questions regarding the society that produced them. Based on this idea, the myths of different peoples are perceived as informative with respect to their Ethnomathematics. Thus, together with work activities, myths constitute a source of support on which we draw to develop this line of research.

A formação de professores e suas relações com cultura e sociedade: a educação escolar indígena no centro das atenções

This paper reflects the current situation surrounding indigenous teacher education by means of the construction of a dialogue among three educators, two of them non-indigenous educators involved with indigenous school education and one indigenous educator committed to the education of his people. Teacher education, situated in a socio-cultural way, is the center of attention in this paper. ""Listening"" as a way of talking with the ""other"" is one of the theoretical focuses of this exercise between teacher educators and teachers, which uses dialogue as a means to increase awareness. In the dialogic process mentione, it was possible to realize how rich a dynamic between educators from different cultural contexts can be. The desire of the indigenous educator and his/her people to contribute their ideas to the construction of the indigenous school became evident. This shows the great challenge for non-indigenous educators seeking to contribute to the organization of the school education of distinct indigenous nations.

A Análise Matemática no Ensino Universitário Brasileiro: a contribuição de Omar Catunda

The goal of this paper is to show the diffusion, reception, and utilization of Omar Catunda's book Course of Mathematical Analysis for mathematics and engineering teaching in Brazilian universities, e. g., University of Sao Paulo and the University of Bahia from 1950 to 1976. We used interviews of some ex-alumni or users of his book. We also present some signs of the influence of his book and of Catunda himself at University of Rio Grande do Sul. We argue that Catunda and his book were important agents of process of modernizing the teaching of calculus and analysis, through his classes as well as his book.

O Intuitivo e o Lógico no Conhecimento Matemático: análise de uma proposta pedagógica em relação a abordagens filosóficas atuais e ao contexto educacional da matemática

In this paper, we consider Meneghetti & Bicudo's proposal (2003) regarding the constitution of mathematical knowledge and analyze it with respect to the following two focuses: in relation to conceptions of mathematical knowledge following the fundamentalist crisis in mathematics; and in the educational context of mathematics. The investigation of the first focus is done analyzing new claims in mathematical philosophy. The investigation of the second focus is done firstly via a theoretical reflection followed by an examination of the implementation of the proposal in the process of development of didactic materials for teaching and learning Mathematics. Finally, we present the main results of the application of one of those materials.