Advocating blended learning for university undergraduate level mathematical instruction beyond Covid-19

Institutional mathematics education has long been traditional in its ways of being teacher-centric, a tradition which perhaps dates back to the Ancient Greece. Much like the society in those days, where there was a wary public feeling about the rigidness of the mathematical instruction in Pythagoras’ school, mathematics educators find themselves in a similar position in the common era of 2020. Unlike the Ancient Greece however, the battle is for the sustained delivery of a comprehensive mathematics education in the midst of the Covid-19 pandemic. It would be fair to say that mathematics departments across all levels of the education sector have been affected drastically; more so on instructors who favour the traditional “chalk and talk” method of instruction. In this article, we share several lessons learned in the delivery of mathematical instruction at undergraduate university level during the Covid-19 pandemic, drawing on our experience at Universiti Brunei Darussalam. These include specific methods for implementing online learning effectively, the pros and cons of such methods, and how we can use computer based tools to make learning more conducive. We highly think that these implementations are beneficial to be adapted by mathematics departments anywhere as a means of adapting to the new realities post Covid-19.

Textbook: an Analysis in the Light of the Ontosemiotic Focus on Rational Numbers

Background: Many teachers consider the textbook the primary guide for the curriculum materialisation. This work analyses the content of the rational numbers in a textbook used in the 7th-grade of elementary school. For this analysis, the theoretical and methodological tools of the Ontosemiotic Approach to Knowledge and Mathematical Instruction (OSA) are used. Objective: Our goal was to understand the level of didactic suitability of the instruction process in the textbook. Design and setting: Thus, we analysed a section of the textbook about rational numbers using the categories described by OSA. Concepts, procedures, problem situations, definitions and arguments used by the authors were also analysed. Results: From the results obtained, we could infer that there are examples of the concepts worked in class, but without the proper definitions and arguments, hindering generalisation. The analysis also allowed us to highlight didactic-mathematical knowledge that can guide the teacher concerning the textbooks' possibilities and limitations, to achieve more didactic suitability in the process of teaching and learning rational numbers. Conclusions: the book under study should not be considered as planning for an instructional process to meet the current curriculum guidelines.

An online course to teach ATD research praxeologies: The ICMI Awardees Multimedia Online ResourcesUn cours en ligne pour enseigner les praxéologies de recherche ATD: les ressources multimédias en ligne des lauréats de l'ICMI

RésuméNous présentons quelques éléments d'un projet de ressource en ligne multimédia adressée à des chercheurs internationaux qui veulent s’initier à la TAD. Le projet a été lancé par le comité exécutif de la International Commission on Mathematical Instruction (ICMI) pour produire un projet pour chaque médailliste Felix Klein et Hans Freudenthal.Mots-clés: Théorie anthropologique du didactique, ICMI, Transposition didactique, Praxéologie, Parcours d'étude et de recherche, Enseignement par l'investigation.AbstractWe present some of the main elements of a project of Multimedia Online Resource addressed to international researchers willing to be initiated in the ATD. The project was launched by the executive committee of the International Commission on Mathematical Instruction (ICMI) to produce some material related to each Felix Klein and Hans Freudenthal medals awardees.Keywords: Anthropological theory of the didactic, ICMI, didactic transposition, Praxeology, Study and research paths, Enquiry-based teaching.

Actors in the changes of ICMI: Heinrich Behnke and Hans Freudenthal

The years after WWII up to the late 1960s were crucial in the evolution of ICMI (International Commission on Mathematical Instruction) for both the settlement of some institutional aspects (mainly concerning the relationship with mathematicians) and the establishment of new trends of the activities. By referring to unpublished documents, this paper focuses on the role of two key figures in those years: Heinrich Behnke and Hans Freudenthal. As ICMI Secretary and later as President, Behnke tried to reshape the newborn ICMI after WWII and clarify the relationship with mathematicians. His action was completed by Freudenthal, who, as ICMI President, broke with the past and promoted initiatives that fostered the development of mathematics education as an academic field and the independence of ICMI from the community of mathematicians. Keywords: history, ICMI, mathematicians, mathematics education

Mathematische, historische und didaktische Betrachtungen über die Einlagerungseigenschaft der Zerlegungsgleichheit

The present study aims to analyse some special errors in mathematical reasoning concerning a property of the relation “equivalence by dissection” in synthetic geometry (pure geometry). Although this property is of great importance it is regarded as obviousness and its problematic nature is usually concealed in mathematics teaching. This is deeply rooted in the heritage of greek mathematics and proves to be an obstacle to mathematical education. This subject belongs to a particularity of the mathematical background of teaching mathematics; nevertheless, this study includes some ideas both on other (similar) particularities and from different points of view. Classification: A30, B50, B60, CD30, D20, D30, E40. Keywords: Synthetic geometry, measure geometry, equivalence by dissection, mathematical background of mathematical instruction.