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Fostering Indonesian Prospective Mathematics Teachers' Geometry Proof Competence
Full text linkIt is widely accepted that comprehending and constructing mathematical proof is an essential topic at any level of mathematics education, including higher education. Prospective mathematics teachers (PMTs) learn mathematical proof in university because proof competence could help them understand and explain mathematical concepts to their students when they are a high school teacher. From a small-scale observational study at a university in Malang, Indonesia, I learned that most students faced difficulties understanding and constructing mathematical proof. This situation motivated me to investigate and improve PMTs’ proof competence.For that purpose, I designed a course and investigated how this course supported PMTs in developing proof competence in geometry. My findings indicated that the course supported PMTs in developing their proof competence, particularly in conjecturing, which is a precursor activity of proving, and their understanding and construction of proof. A quasi-experimental study showed that students achieved better results than in the regular course. The designed learning trajectory can inform curriculum designers about effective teaching strategies for geometrical proof, particularly in an early stage at Indonesian universities. I recommend that in the future, PMTs at all Indonesian universities should acquire not only the content knowledge of mathematical proofs (on which this study focused) but also the pedagogical content knowledge. Following this study, proof should be promoted in Indonesian secondary schools, along with guidance for teachers about implementation in their classrooms
Understanding geometric proofs: scaffolding pre-service mathematics teacher students through dynamic geometry system (dgs) and flow-chart proof
Full text linkInternational audienceThe objective of this paper is to discuss the pedagogic potential that is offered by the use of a flow-chart proof with open problems and a Dynamic Geometry System in understanding geometric proofs by pre-service mathematics student teachers at an Indonesian university. Based on a literature review, we discuss aspects and levels of understanding of geometric proof and how to assess students’ understanding of the structure of deductive proofs, and how the use of a Digital Geometry System may support students’ understanding of geometric terms and statements, including definitions, postulates, and theorems. The pedagogic focus consists of exploiting the semiotic potential of a DGS, especially the use of GeoGebra tools that may function as tools of semiotic mediation to understand the geometry statements and the scaffolding potential of flow-chart proof with open problems in identifying the structure of deductive geometry proofs
ELICITING MATHEMATICAL THINKING OF STUDENTS IN ADDITION OF FRACTIONS THROUGH REALISTIC MATHEMATICS EDUCATION
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Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
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